Citation
Coordination dynamics of walking

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Title:
Coordination dynamics of walking
Creator:
Worster, Katy Lynn. ( author )
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
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1 electronic file (313 pages). : ;

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Subjects / Keywords:
Walking ( lcsh )
Gait in humans ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Although coordination has been identified as a fundamental element necessary for the successful achievement of walking, this aspect of gait has yet to be embraced into instrumented gait analysis, perhaps in part due to the lack of a normative reference and unfamiliarity of mathematical methods that are best suited to capture this essential behavior. Therefore, this work focused on expanding clinical gait analysis techniques by validating nonlinear methods that describe the influence of neurological control on the musculoskeletal system. This body of work investigated the coordination dynamics during gait in both prospective and retrospective subjects free of gait pathology, subjects with spastic cerebral palsy, and subjects with a lower limb amputation using motion capture and mathematical models to help elucidate the complexities of gait and enhance therapeutic interventions. This investigation quantified coordination strategies employed by an unimpaired subject when presented with various walking conditions and challenges mimicking various inhibitions associated with performing the task of swing limb advancement. Two novel indices of coordination dynamics were created to provide a concise metric and ease their inclusion into future research applications. The first normative reference dataset of these coordination measures was created from a large cohort of unimpaired subjects. While there is presently not a gold standard method for quantifying coordination during gait, the exciting correlations between the proposed measures and select clinical performance tasks indicate the coordination measures quantify essential inter-segmental coordination dynamics of walking. The theoretical pendular software model created shows swing limb advancement is not a purely passive motion, but instead an actively controlled motion. Comparisons between the various cohorts revealed the proposed measures of coordination are more suitable for characterizing motor control strategies contributing to a gait pattern, quantify organization of individual segments, identify mechanisms of change, and reveal the loci of impairment(s). The proposed measures of coordination dynamics are capable of distinguishing between different gait pathologies and patterns associated with altered limb advancement during the swing period of gait. Results from this multidisciplinary work have the strong potential to directly impact the clinical treatment of persons with aberrant coordination dynamics during gait.
Thesis:
Thesis (Ph.D.)--University of Colorado Denver. Bioengineering
Bibliography:
Includes bibliographic references.
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System requirements: Adobe Reader.
General Note:
Department of Bioengineering
Statement of Responsibility:
by Kathy Lynn Worcester.

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|University of Colorado Denver
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|Auraria Library
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All applicable rights reserved by the source institution and holding location.
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913577218 ( OCLC )
ocn913577218

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COORDINATIONDYNAMICSOFWALKING by KATYLYNNWORSTER B.S.,UniversityofColorado,2005 Athesissubmittedtothe FacultyoftheGraduateSchoolofthe UniversityofColoradoinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy Bioengineering 2015

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ThisthesisfortheDoctorofPhilosophydegreebyKatyLynnWorster hasbeenapprovedforthe DepartmentofBioengineering by JamesJ.Carollo,Advisor KendallHunter,Chair JoanneValvano ZhaoxingPan RichardWeir April20,2015 ii

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Worster,KatyLynn(Ph.D.,Bioengineering) CoordinationDynamicsofWalking ThesisdirectedbyAssociateProfessorJamesJ.Carollo ABSTRACT Althoughcoordinationhasbeenidentiedasafundamentalelementnecessaryforthesuccessful achievementofwalking,thisaspectofgaithasyettobeembracedintoinstrumentedgaitanalysis, perhapsinpartduetothelackofanormativereferenceandunfamiliarityofmathematical methodsthatarebestsuitedtocapturethisessentialbehavior.Therefore,thisworkfocusedon expandingclinicalgaitanalysistechniquesbyvalidatingnonlinearmethodsthatdescribethe inuenceofneurologicalcontrolonthemusculoskeletalsystem.Thisbodyofworkinvestigatedthe coordinationdynamicsduringgaitinbothprospectiveandretrospectivesubjectsfreeofgait pathology,subjectswithspasticcerebralpalsy,andsubjectswithalowerlimbamputationusing motioncaptureandmathematicalmodelstohelpelucidatethecomplexitiesofgaitandenhance therapeuticinterventions.Thisinvestigationquantiedcoordinationstrategiesemployedbyan unimpairedsubjectwhenpresentedwithvariouswalkingconditionsandchallengesmimicking variousinhibitionsassociatedwithperformingthetaskofswinglimbadvancement.Twonovel indicesofcoordinationdynamicswerecreatedtoprovideaconcisemetricandeasetheirinclusion intofutureresearchapplications.Therstnormativereferencedatasetofthesecoordination measureswascreatedfromalargecohortofunimpairedsubjects.Whilethereispresentlynota goldstandardmethodforquantifyingcoordinationduringgait,theexcitingcorrelationsbetween theproposedmeasuresandselectclinicalperformancetasksindicatethecoordinationmeasures quantifyessentialinter-segmentalcoordinationdynamicsofwalking.Thetheoreticalpendular softwaremodelcreatedshowsswinglimbadvancementisnotapurelypassivemotion,butinstead anactivelycontrolledmotion.Comparisonsbetweenthevariouscohortsrevealedtheproposed measuresofcoordinationaremoresuitableforcharacterizingmotorcontrolstrategiescontributing toagaitpattern,quantifyorganizationofindividualsegments,identifymechanismsofchange,and revealthelociofimpairment(s).Theproposedmeasuresofcoordinationdynamicsarecapableof distinguishingbetweendi erentgaitpathologiesandpatternsassociatedwithalteredlimb advancementduringtheswingperiodofgait.Resultsfromthismultidisciplinaryworkhavethe strongpotentialtodirectlyimpacttheclinicaltreatmentofpersonswithaberrantcoordination dynamicsduringgait. iii

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Theformandcontentofthisabstractareapproved.Irecommenditspublication. Approved:JamesJ.Carollo iv

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ACKNOWLEDGMENT IwouldliketoacknowledgetheJ.T.Tai&Co.FoundationanditsendowmentfortheCenter forGaitandMovementAnalysisLaboratoryattheChildren'sHospitalColorado.Iwillforeverby thankfulforthisnancialgenerosity,whichsupportedmystudiesandresearchduringmytimeasa graduatestudentandprovidedtheopportunityformetopursuemydreams. v

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DEDICATION Thisdissertationisdedicatedtomymomanddad,fortheirendlesslove,support,andencouragement. vi

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TABLEOFCONTENTS Chapter 1Introduction 1 1.1ProblemStatement....................................1 1.2Rationale..........................................2 1.3ResearchObjectives....................................3 1.4OrganizationofDissertationChapters..........................7 2BackgroundandPreviousWork8 2.1PhysiologyofLocomotion.................................8 2.1.1NeurologicControlofMusculoskeletalSystem..................9 2.2ModelingLocomotion...................................16 2.2.1TaskofSwingLimbAdvancement........................20 2.2.2ModelingSwingLimbAdvancementasaPendulum..............22 2.2.3GaitPatternswithImpairedSwingLimbAdvancement............25 2.2.3.1SpasticCerebralPalsy..........................25 2.2.3.2LowerLimbAmputation........................28 2.2.4ConventionalMeasuresofInstrumentedGaitAnalysis.............34 2.2.4.1Temporal-SpatialVariables.......................34 2.2.4.2Kinematics................................36 2.2.5ConventionalMeasuresofCoordination.....................37 2.2.5.1PerformanceMeasures..........................37 2.3InvestigationsPriortoPre-doctoralWork........................40 3AModelfortheCoordinationDynamicsofWalking43 3.1DynamicSystemsTheoryApproachtoCoordination..................43 3.1.1PhasePortrait...................................47 3.1.2ContinuousRelativePhaseDiagram.......................49 3.2ModelAssumptions&Limitations............................52 3.3AlternativePerspectivestoModelingCoordinationinGait..............54 3.3.1CentralPatternGenerators&MotorPlanTheories..............54 3.3.2UsingElectromyographytoQuantifyCoordination...............55 vii

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3.4RationaleforModel'sMethodology............................55 4ExperimentalMethodology59 4.1PurposeofExperiments..................................59 4.2Subjects...........................................59 4.2.1UnimpairedSubjects................................61 4.2.2SubjectswithCerebralPalsy...........................62 4.2.3SubjectswithaLowerLimbAmputation....................62 4.3Equipment.........................................63 4.3.1Over-groundMotionCaptureEnvironment...................64 4.3.2TreadmillMotionCaptureEnvironment.....................64 4.3.2.1BodyWeightSupportSystem.....................65 4.3.2.2SwingLimbAssistDevice........................65 4.3.2.3RestrictingRangeofMotion......................66 4.3.3Software.......................................67 4.4ExperimentalProtocols..................................68 4.4.1UnimpairedProspectiveSubjectExperimentalProtocol............70 4.4.1.1ProspectiveUnimpairedSubject:Over-groundWalkingTask....71 4.4.1.2ProspectiveUnimpairedSubject:Speed-AccuracyTask.......71 4.4.1.3ProspectiveUnimpairedSubject:ModiedICARS/SARATasks..74 4.4.1.4ProspectiveUnimpairedSubject:TreadmillWalkingTask......76 4.4.1.5ProspectiveUnimpairedSubject:ChangesinWalkingSpeedTask.76 4.4.1.6ProspectiveUnimpairedSubject:ChangesinAssistiveForcesTask76 4.4.1.7ProspectiveUnimpairedSubject:ChangesinResistiveForcesTask76 4.4.1.8ProspectiveUnimpairedSubject:ChangesinJointRangeofMotion Tasks...................................77 4.4.1.9ProspectiveUnimpairedSubject:SCALEExamandModiedICARS Task....................................77 4.4.2ExperimentalProtocolforProspectiveSubjectswithanAtypicalGaitPattern80 4.4.2.1ProspectiveAtypicalSubject:Over-GroundWalkingTask.....80 4.4.2.2ProspectiveAtypicalSubject:Speed-AccuracyTask.........80 4.4.2.3ProspectiveAtypicalSubject:ModiedICARS/SARATasks....81 4.4.2.4ProspectiveAtypicalSubject:TreadmillWalkingTask.......81 viii

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4.4.2.5ProspectiveAtypicalSubject:SCALEandModiedICARSTasks.82 4.4.3RetrospectiveSubjectMotionCaptureData...................82 4.4.4MathematicalSoftwareModelofaCompoundPendulum...........82 4.4.4.1CompoundPendulumSoftwareModel.................83 4.4.4.2AdditionalInvestigationsofthePendulumModel..........85 4.5HypothesisTestingandDataAnalysis..........................85 4.5.1Aim1DataAnalysisMethodsandMeasures..................86 4.5.2Aim2DataAnalysisMethodsandMeasures..................87 4.5.3Aim3DataAnalysisMethodsandMeasures..................91 4.5.4Aim4DataAnalysisMethodsandMeasures..................93 4.5.4.1CoordinationDeviationIndex(CDI)..................94 4.5.4.2CoordinationPerformanceScore(CPS)................97 4.5.4.3CurveFeatureTrendsbyGaitPattern.................104 4.6ExperimentalLimitationsAssociatedwithHumanSubjects..............105 5Results 108 5.1SubjectDemographics...................................108 5.2ProspectiveExperimentalResults.............................110 5.2.1ProspectiveSubjects:Over-GroundWalkingTask...............111 5.2.2ProspectiveSubjects:TreadmillWalkingTasks.................112 5.2.3UnimpairedProspectiveSubjects:ChangesinAssistive/ResistiveForcesTask114 5.2.4UnimpairedProspectiveSubjects:Over-groundvs.TreadmillWalking...115 5.2.5UnimpairedProspectiveSubjects:ChangesinAssistive/ResistiveForcesTask118 5.2.6UnimpairedProspectiveSubjects:ChangesinJointRangeofMotionTasks.118 5.3AimsandHypothesesTestResults............................121 5.3.1Aim1Results....................................121 5.3.2Aim2Results....................................122 5.3.2.1Hypothesis2AResults.........................123 5.3.2.2Hypothesis2BResults..........................125 5.3.2.3Hypothesis2CResults..........................127 5.3.3Aim3Results....................................130 5.3.4Aim4Results....................................132 5.3.4.1CoordinationDeviationIndexResults.................132 ix

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5.3.4.2CoordinationPerformanceScoreResults...............134 5.3.4.3ComparisonofTwoNewCoordinationIndices............137 5.3.4.4MissingCoordinationEventsbyGaitPattern.............139 5.3.4.5ExploratoryInvestigationtoIdentifyCriticalCoordinationEvents.143 5.3.5Hypothesis4AResults...............................144 5.4TranstibialAmputationCaseStudyResults......................145 6Discussion 146 6.1DiscussionofProspectiveExperiments.........................146 6.1.1Over-GroundWalkingTask............................146 6.1.2TreadmillWalkingTasks.............................147 6.1.3ProspectiveUnimpairedSubjects:Over-groundandTreadmillWalking...148 6.1.4ProspectiveSubjectswithCerebralPalsy:Over-groundvs.TreadmillWalking152 6.1.5ProspectiveUnimpairedSubjects:TreadmillWalkingatVariousSpeeds...153 6.1.6ChangesinAssistive/ResistiveForcesTask...................154 6.1.7ChangesinJointRangeofMotionTasks....................155 6.1.7.1FixedKneeExtension..........................155 6.1.7.2FixedKneeFlexion...........................156 6.1.7.3FixedAnkleDorsiexion........................157 6.2DiscussionofAimsandHypotheses...........................158 6.2.1Aim1........................................158 6.2.1.1PPandCRPDCurveFeatures.....................160 6.2.2Aim2........................................161 6.2.2.1Hypothesis2A..............................161 6.2.2.2Hypothesis2B..............................162 6.2.2.3Hypothesis2C..............................163 6.2.3Aim3........................................165 6.2.3.1Hypothesis3A..............................166 6.2.3.2Hypothesis3B..............................166 6.2.3.3Hypothesis3C..............................166 6.2.4Aim4........................................167 6.2.4.1TheCoordinationDeviationIndex...................168 6.2.4.2TheCoordinationPerformanceScore.................171 x

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B.1.4.3HipFlexionSynergyTest.......................217 B.1.5SCALEDesriptors.................................217 B.1.5.1HipAdductionContracture......................217 B.1.5.2HamstringTightness..........................218 B.1.5.3ThomasTest...............................218 B.1.5.4DuncanElyTest.............................219 B.2SelectICARSandSARATasks.............................219 B.2.1ForwardWalkingCapacities...........................219 B.2.290 ¡ TurningTask..................................220 B.2.3TandemWalkingTask...............................220 B.2.4Knee-TibiaSlideTask...............................221 B.2.5ActionTremorinHeel-to-Kneetest.......................221 CPendulumEquationsofMotion222 C.1EquationsofMotion....................................222 C.2MatlabCode........................................227 DPhaseAngleInvestigation228 EAdditionalMethods231 E.1RepresentativeTrialSelection..............................231 E.2CoordinationDeviationIndexCalculation........................231 E.3LegendofSwingPeriodCoordinationEvents..........233 E.4TranstibialAmputationCaseStudyMethods..........234 FNormalCoordinationDynamics236 F.1CoordinationMechanismsofUnimpairedSwingLimbAdvancement....236 F.1.1UncouplingofThigh-FootTrajectories..........237 F.1.2Knee-AnkleFunctionalParadox............238 F.1.3PassiveKneeExtension..............239 F.1.4AnticipationofHeelFirstInitialContact..........239 F.2SagittalThigh-ShankCoordinationDynamics..........240 F.2.1Pre-Swing50-60%................240 F.2.1.1ThighPhasePortrait............240 F.2.1.2ShankPhasePortrait............241 xii

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F.2.1.3ContinuousRelativePhaseDiagram........241 F.2.2InitialSwing60-75%...............242 F.2.2.1ThighPhasePortrait............242 F.2.2.2ShankPhasePortrait............242 F.2.2.3ContinuousRelativePhaseDiagram........243 F.2.3Mid-Swing75-87%................245 F.2.3.1ThighPhasePortrait............245 F.2.3.2ShankPhasePortrait............245 F.2.3.3ContinuousRelativePhaseDiagram........246 F.2.4TerminalSwing87-100%..............246 F.2.4.1ThighPhasePortrait............246 F.2.4.2ShankPhasePortrait............247 F.2.4.3ContinuousRelativePhaseDiagram........248 F.3SagittalShank-FootCoordinationDynamics...........248 F.3.1Pre-Swing50-60%................248 F.3.1.1ShankPhasePortrait............248 F.3.1.2FootPhasePortrait.............249 F.3.1.3ContinuousRelativePhaseDiagram........249 F.3.2InitialSwing60-75%...............249 F.3.2.1ShankPhasePortrait............249 F.3.2.2FootPhasePortrait.............250 F.3.2.3ContinuousRelativePhaseDiagram........250 F.3.3Mid-Swing75-87%................250 F.3.3.1ShankPhasePortrait............250 F.3.3.2FootPhasePortrait.............251 F.3.3.3ContinuousRelativePhaseDiagram........251 F.3.4TerminalSwing87-100%..............252 F.3.4.1ShankPhasePortrait............252 F.3.4.2FootPhasePortrait.............253 F.3.4.3ContinuousRelativePhaseDiagram........253 GAdditionalResults255 G.1AdditionalResultsforProspectiveExperiments..........255 xiii

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G.2AdditionalResultsforAim2...............261 G.3AdditionalResultsforAim3...............268 G.4AdditionalResultsforAim4...............270 G.4.1AdditionalResultsforCoordinationDeviationIndex(CDI)....270 G.4.2AdditionalResultsforCoordinationPerformanceScoreStatisticalAnalysis272 G.4.3AdditionalResultsforHypothesis4A...........278 G.5AdditionalResultsforTranstibialAmputationCaseStudy.......282 G.6AdditionalResultsforExploratoryInvestigationtoIdentifySignicantCoordination Events.....................283 xiv

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LISTOFTABLES Table 4.2.1Study'sprospectiveandretrospectivesubjectdesignations..............61 4.3.1ListofcustomMatlabprogramsusedfordataanalysis.................67 4.4.1Anthropometricsmeasuredfromeachsubject,where*indicatesprospectivesubject measurements.......................................68 4.4.2Overviewofthelocationandinstrumentationusedforexperimentsfortheunimpairedprospectivesubjects................................71 4.4.3Changesinwalkingspeedconditionsforunimpairedprospectivesubjects......76 4.4.4Jointrangeofmotionlimitationsforunimpairedprospectivesubjects........77 4.4.5Overviewofthelocationandinstrumentationusedforexperimentsfortheprospectivesubjectswithanatypicalgaitpattern........................80 4.4.6Pendulummodelparameters,model'sinitialconditions,andthesubjectinstrumentedgaitanalysisdatafromwhichtheyarederived.Thesubjectdatavariables aremeanvaluesforeachofthestudy'scohortsandFOindicatestheinstanceof footo duringthegaitcycle...............................83 4.4.7Descriptionofthefourdampingconditionsandcorrespondinglinkagedampingcoe cientvalues.......................................84 4.5.1Primarysagittalplaneoutcomemeasures,theircorrespondingaimsandhypotheses, andmotioncapture(MoCap)environment(OG=over-ground,TM=treadmill)that providesthesourcedataforthesemeasures.......................85 4.5.2Secondaryoutcomemeasures,theircorrespondingaimsandhypotheses,andsource ofthedataforthesemeasures(e.g.motioncaptureenvironment=MoCap).....86 4.5.3Subjectclassicationforcoordinationdeviationindexanalysis............94 4.5.4Variablesusedtocreatethebackwardstepwiseregressionmodels...........100 4.5.5Variablesusedtocreatethenominalregressionmodels................100 5.1.1Averagetimesforprospectivesubjectdatacaptureandanalysis...........108 5.1.2Prospectiveandretrospectivedemographicsforallsubjectsfreeofgaitpathology, withmean(standarddeviation)valuesreported....................109 xv

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5.1.3ProspectiveandRetrospectivedemographicsforallsubjectswithcerebralpalsy, withmean(standarddeviation)valuesreported....................110 5.1.4Retrospectivedemographicsforallsubjectswithalowerlimbamputation,with mean(standarddeviation)valuesreported.......................110 5.2.1MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSofthe unimpairedsubjects,subjectswithCP,andsubjectswithalowerlimbamputation forover-groundwalking..................................112 5.2.2Thecoe cientofvariation(CV)andvarianceration(VR)fortheangulardisplacement(AD),angularvelocity(AV)andcontinuousrelativephasediagramsfor allunimpairedretrospective(n=120)andprospective(n=20)subjectsduringovergroundwalking.......................................112 5.2.3MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSofthe unimpairedprospectivecohortforvariouswalkingconditions.............112 5.2.4MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSofthe prospectivesubjectswithCPforover-groundandtreadmillwalkingconditions...113 5.2.5MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSofthe unimpairedprospectivecohortfortwowalkingtreadmillconditions.........115 5.2.6ConventionalTemporal-Spatial,GaitEvents,andKinematicDescriptorsofGait Themean,standarddeviation,andp-valuesfortemporal-spatial,kinematic,and criticalgaiteventsfromthecohort'sover-ground(OG)andtreadmill(TM)walkingconditions.*Signicantlydi erentfromover-groundwalking,p 0.05.1 Calculatedasdistancewalkeddividedbytimetowalkcorrespondingdistance...116 5.2.7Swingperiodcoordinationeventswithsignicantchangesintimingandmagnitude. Themean,standarddeviation,andp-valueforthemagnitudeand/ortiming(percentgaitcycle=%GC)ofswingperiodcoordinationeventsthatweresignicantly di erent(adjustedp 0.0091)betweenthecohort'sover-groundandtreadmill walkingconditions.EachCEisalsoassociatedwithamechanismcategory.....117 5.2.8MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSofthe unimpairedprospectivecohortfortwowalkingtreadmillconditions.........118 5.2.9MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSofthe unimpairedprospectivecohortfortwowalkingtreadmillconditions.........118 xvi

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5.3.1Coe cientofvariation(CV)andvarianceratio(VR)forunimpairedretrospective cohort'smeanangulardisplacement(AD),meanangularvelocity(AV),andrelative phaseangles........................................122 5.3.2Mean,1standarddeviation,and95%condenceintervalsfortherelativephaseangles(degrees)atcommontemporalgaiteventsforunimpairedprospectivesubjects. Theprospectivecohort'smeanand1standarddeviationforthepercentgaitcycle foreachtemporalgaiteventisalsoreported......................122 5.3.3Meantiming(%GC)andmagnitudeofthemaximuminstantaneousslope(MiS), withitsstandarddeviation,forthetwoprospectivecohorts'thigh-shankcontinuous relativephasediagram...................................124 5.3.4Meantiming(%GC)andmagnitudeofthemaximuminstantaneousslope(MiS), minimum(Min),andinectionpoint(IP)withstandarddeviation,fortheprospectivecohorts'thigh-shankandthigh-footcontinuousrelativephasediagrams(CRPDs).126 5.3.5Rankingsofthethreegeneralsubjectcohortsfor4di erentpendulummodeldampingconditions.Thesubjectgroupwiththelowestrankingforeachdampingcaseis indicatedwitharectanglesurroundingthesummednormalizedrootmeansquare error( NRMSE).Threesubjectcohortswereconsidered:unimpaired(N),cerebral palsy(C),andalowerlimbamputation(LLA).....................131 5.3.6Gaitpatterncohortrankingsfor4di erentpendulummodeldampingconditions. Fivegaitpatternswereconsidered:unimpaired(N),sti kneegait(SKG),crouch (C),belowkneeamputation(BK),andabovekneeamputation(AK)........131 5.3.7Descriptionofthesixsignicantcoordinationeventslistedinorderofoccurrence duringswingperiodwiththenormativecohort'smean(standarddeviation)value foreachCE,and95%condenceinterval(CI)fromthenormativecohort.Thegait cyclewasindexedfrom1to101%............................134 5.3.8Descriptionofthetenswingperiodcoordinationeventsmissinginsubjectswith CP,whereasuperscriptLandNindicatethiscoordinationeventisalsomissingin subjectswithaLLAandunimpairedsubjects,respectively..............141 5.3.9Themeantiming(standarddeviation)andvarianceforthe120unimpairedretrospectivesubjects'fourcriticalcoordinationeventsareprovidedalongwithadescriptionofeachevent...................................143 B.1.1SCALEscoringforkneeextensionwithrestedlimbextensiontask..........216 xvii

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B.1.2SCALEscoringforplantarexioncontracturetask...................216 B.1.3SCALEscoringforhipexionsynergytask.......................217 B.1.4SCALEscoringforhipadductioncontracturetask...................217 B.1.5SCALEscoringforhamstringtightnesstask......................218 B.1.6SCALEscoringforThomastest.............................218 B.1.7SCALEscoringforDuncanElytest...........................219 D.0.1Propertiesofthetangentandarctangentfunctions..................229 E.3.1Legendofswingperiodcoordinationevents.......................234 F.1.1Themeanandstandarddeviationforthemagnitudeand/ortiming(percentgaitcycle=%GC)ofswingperiodcoordinationevents(CE)fortheunimpairedprospective cohort'sover-groundandtreadmillwalkingconditions.EachCEisalsoassociated withamechanismcategory................................237 G.1.1Meanvaluesforthetimingofcriticalandtemporalgaitevents............255 G.1.2Cohorts'commontemporal-spatialdescriptorsofgait.................255 G.1.3Relativephaseanglesforcommontemporalgaiteventsforunimpairedprospective subjects...........................................256 G.1.4Comparisonoftheunimpairedprospectiveandretrospectivesubjects'relativephase angles............................................256 G.1.5r 2 andPearson(P)valuesforfourcriticalcoordinationevents............259 G.1.6Timingoffourcriticalcoordinationeventsforallsubjects...............260 G.1.7Timingoffourcriticalcoordinationeventsidentiedwiththeindependentandinvariantmethodology....................................260 G.2.1Averageaccuracyoffoottapshittingthetargetforthethreetargetsizes(80%, 100%,120%)usedinHypothesis2Afortheprospective...............261 G.2.2T-testresultsbetweenthemeantiming(%GC)andmagnitudeforinitialswing thigh-shankcontinuousrelativephasediagram(CRPD)coordinationeventsforthe prospectiveunimpairedsubjectsandsubjectswithCP.Thecoordinationevents wereaminimum(min),maximuminstantaneousslope(MiS),inectionpoint(IP), andazerocrossing(0x)..................................261 xviii

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G.2.3T-testresultsbetweenthemeantiming(%GC)andmagnitudeforinitialswing thigh-footcontinuousrelativephasediagram(CRPD)coordinationeventsforthe prospectiveunimpairedsubjectsandsubjectswithCP.Thecoordinationevents wereaminimum(min),maximuminstantaneousslope(MiS),inectionpoint(IP), andazerocrossing(0x)..................................262 G.2.4SCALEandICARSvaluesforprospectivesubjectswithcerebralpalsy........262 G.2.5Correlationmatrixforforwardswinglimbvelocityandtargetaccuracy.......263 G.2.6Correlationmatrixforcoordinationeventsforsubjectswithcerebralpalsy.....264 G.2.7Correlationmatrixforcoordinationeventsforunimpairedsubjects.........265 G.2.8Correlationmatrixforprospectivesubjectswithcerebralpalsy............266 G.2.9Correlationmatrixforunimpairedprospectivesubjects................266 G.2.10Correlationmatrixforunimpairedprospectivesubjectsfor90 ¡ turningtask.....267 G.2.11Correlationmatrixforprospectivesubjectswithcerebralpalsyfor90 ¡ turningtask.267 G.2.12Baseofsupportvaluesforsubjects............................267 G.3.1Unimpairedcohort'srankingsfor4pendulummodeldampingconditions......268 G.3.2Rankingsofsubjectswithasti kneegaitpatternfor4pendulummodeldamping conditions..........................................268 G.3.3Rankingsofsubjectswithacrouchgaitpatternfor4pendulummodeldamping conditions..........................................269 G.3.4Rankingsofsubjectswithabelowkneeamputationfor4pendulummodeldamping conditions..........................................269 G.3.5Rankingsofsubjectswithanabovekneeamputationfor4pendulummodeldamping conditions..........................................269 G.4.1Demographiccharacteristicsandindicesvaluesforsubjects..............272 G.4.2Responseprolefortheatypicalvs.typicalgaitpatternregressionmodel,where probabilitymodeledisCP=1...............................272 G.4.3Modeltstatisticsfortheatypicalvs.typicalgaitpatternregressionmodel.....272 G.4.4Resultsofmaximumlikelihoodestimatesanalysisfortheatypicalvs.typicalgait patternregressionmodel.................................273 xix

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G.4.5Oddsratioestimatesfortheatypicalvs.typicalgaitpatternregressionmodelcoordinationevents,whereP1isthemagnitudeoftheminimumangulardisplacement ofthepelvisinswing,TF1isthemagnitudeofthethigh-footCRPDminimum nearfooto ,andpF2isthepercentgaitcycleofthefootPP'smaximumangular displacement........................................273 G.4.6Receiveroperatorcurveassociationstatisticsfortheatypicalvs.typicalgaitpattern regressionmodel......................................274 G.4.7Receiveroperatorcurvecontrasttestresultsfortheatypicalvs.typicalgaitpattern regressionmodel,withdegreesoffreedom(DF),Chi-squarevalue,andcorresponding probability(Pr)oftheChi-square............................274 G.4.8Analysisofvariancefortheatypicalvs.typicalgaitpatternregressionmodel,with degreesoffreedom(DF),sumofsquares,meansquare,andFteststatisticand probabilityfromtheFtest................................274 G.4.9Parameterestimatesforthecoordinationeventsoftheatypicalvs.typicalgaitpattern,withstandarderrorofeachestimate,tvalue,probabilityfromt-test,tolerance (TOL),andvarianceinationfactor(VIF).......................274 G.4.10Responseproleforthesti kneevs.crouchgaitpatternregressionmodel,where probabilitymodeledissti kneegait=1.........................274 G.4.11Modeltstatisticsforthesti kneevs.crouchgaitpatternregressionmodel....275 G.4.12Testingglobalnullhypothesis( =0)forthesti kneevs.crouchgaitpatternregressionmodel.......................................275 G.4.13Resultsofmaximumlikelihoodestimatesanalysisforthesti kneevs.crouchgait patternregressionmodel.................................275 G.4.14Receiveroperatorcurveassociationstatisticsforthesti kneevs.crouchgaitpatternregressionmodel...................................276 G.4.15Receiveroperatorcurvecontrasttestresultsforthesti kneevs.crouchgaitpattern regressionmodel,withdegreesoffreedom(DF),Chi-squarevalue,andcorresponding probability(Pr)oftheChi-square............................276 G.4.16Analysisofvarianceforthesti kneevs.crouchgaitpatternregressionmodel,with degreesoffreedom(DF),sumofsquares,meansquare,andFteststatisticand probabilityfromtheFtest................................277 xx

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G.4.17Parameterestimatesforthecoordinationeventsofthesti kneevs.crouchgaitpattern,withstandarderrorofeachestimate,tvalue,probabilityfromt-test,tolerance (TOL),andvarianceinationfactor(VIF).......................277 G.6.1Comparisonofunimpairedprospective(shoes)subjects'criticalcoordinationevents andunimpairedretrospective(barefoot)subjects'criticaleventsusingtheindependenceandinvariancecriteria...............................283 xxi

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LISTOFFIGURES Figure 2.2.1Periods,task,phases,andimportanttemporalandcriticaleventsoftheunimpaired gaitcycle[26,32]......................................17 2.2.2Motionofthelowerlimbsegmentsprogressingthroughthegaitcycleillustrating thesimilarityofaninvertedpendulum(left)andcompoundpendulum(right)...23 2.2.3Diagramoflongitudinallevelsofamputationforthelowerextremity.........29 2.2.4Divisionsofthegaitcycledepictedonaunitcircle,readclockwise,foractitious subject'sleft(red)andright(green)gaitcycleswithreferencetoanormativecontrol (grey)usingthevaluesdisplayedinFigure2.2.1....................35 2.2.5Isometricviewdepictingvariablesusedtodescribespatialrelationshipsbetweenthe feet(typicallyusingthecentroidlocationoftheheelmarker)andtheirplacement ontheground(greyrectangles).A=rightsteplength,B=rightstridelength,C =leftsteplength.....................................35 3.1.1Diagramofanideal,closedorbitlimitcycle(blue)withdi erenttrajectories(green) ofatheoreticaldynamicalsystem.Astablelimitcycleisanalogoustoanormalgait patternbecauseitreturnstoapreferredstateevenafterperturbationsorchanges ininitialconditions.Anunstablelimitcycleisanalogoustoanirregularpathologicalgaitpatternbecausethesubjectisunabletoreturntothesamestateafter perturbationorfromonegaitcycletothenext.....................48 3.1.2Phaseportraitconstructionfromtri-planarmarkerdata................49 3.1.3Diagramofhowasegment'sphaseangleiscalculatedwithrespecttothehorizontal ofthephaseportrait,foronecompletegaitcyclefromanormalreferencesubject's thigh(leftcolumn)andshank(rightcolumn).Vectorsfromtheorigin(0,0)tothe phaseportraitcoordinatesforeachpercentgaitcycle(A).Zoomed-inviewofthe vectorsandphaseportraittrajectory(B).Phaseangleforonepercentgaitcycleon thethighandshank(C)..................................50 4.3.1Legswingextensionassistivedeviceprovidingswinglimbassistance(A)andresistance(B)whenaprospectivesubjectwalksonthetreadmillwiththebodyweight supportsystem.......................................66 xxii

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4.4.1Anterior(left)andposterior(right)viewsoffullbodystaticmarkerset.......69 4.4.2Anterior(left)andposterior(right)viewsofthefullbodydynamicmarkerset...70 4.4.3Speed-Accuracytasktargetsetupandsizing.A)Targetsetupforarightleg,B) targetsetupforaleftleg.................................73 4.4.4Functionaldiagramofthelowerextremityspeed-accuracytask............74 4.4.5Functionaldiagramofover-groundtandemwalkingtask................75 4.4.6Diagramof90 ¡ walkingtasksetupwiththeT'tapetargetindicatingwhereto initiatetheturn(transverseview)............................75 4.4.7FlowchartoftheSCALEtasksperformedforeachprospectivesubject........78 4.5.1Denitionofthebaseofsupportwidthduringdoublelimbsupport..........90 4.5.2Comparisonofcoordinationsystemsfornonlinearmeasures(left)andpendulum model(right)........................................91 4.5.3Flowchartoftheoreticalpendulummodeltoagaitpatterncohort'sactualthighand shanksegmentmotionsduringtheswingperiodofgait................93 4.5.4Flowchartofprocessusingregressionmodelstoidentifysignicantswingperiod coordinationevents....................................101 5.2.1Unimpairedprospectivesubjects'(blue)meanphaseportraitsandensemblecontinuousrelativephasediagramswiththeretrospectiveunimpairedcohort'smean coordinationcurves(grey).................................111 5.2.2Phaseportraitsandcontinuousrelativephasediagramsfortreadmillwalkingconditionsoftheunimpairedprospectivesubjects(green=80%Vss,purple=90%Vss, blue=100%Vss,orange=110%Vss,red=120%Vss)....................113 5.2.3Phaseportraitsandcontinuousrelativephasediagramsforover-ground(OG)and treadmill(TM)walkingconditionsofprospectivesubjectswithCP(blue=OG, red=TM)..........................................114 5.2.4Sagittalplanekinematiccurvesforprospectiveunimpairedsubjectsduringoverground(OG,blue)andtreadmill(TM,red)walkingconditions,withcoe cientsof variation(CV).......................................115 5.2.5Meanphaseportraitsandcontinuousrelativephasediagramsforunimpairedprospectivesubjectsover-ground(OG,blue)andtreadmill(TM,red)walkingconditions andsignicantcoordinationevents............................117 xxiii

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5.2.6Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjectswalkingonthetreadmillwithxed180 ¡ kneeextension(lightred),overgroundwalkingofallsubjectswithasti kneegaitpattern(darkred),andovergroundwalkingforallretrospectiveunimpairedsubjects(grey)............119 5.2.7Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjectswalkingonthetreadmillwithxed60 ¡ kneeexion(orange),over-ground walkingofallsubjectswithacrouchgaitpattern(red),andover-groundwalking forallretrospectiveunimpairedsubjects(grey).....................120 5.2.8Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjectswalkingonthetreadmillwithxedankledorsiexion(lightgreen),overgroundwalkingofallsubjectswithatranstibialamputation(darkgreen),andovergroundwalkingforallretrospectiveunimpairedsubjects(grey)............121 5.3.1Meanpercentageofhits(accuracy)fortheprospectiveunimpairedsubjects(blue) andsubjectswithcerebralpalsy(red)forthethreefoottargetsizes(80%,100%, 120%).Alineartrendlineisprovidedand*indicatesasignicant(p<0.05)di erencebetweenthetwosubjectgroups...........................123 5.3.2Meanspeedoftheforwardswinginglegfortheprospectiveunimpairedsubjects (blue)andsubjectswithcerebralpalsy(red)forthethreetargetsizes(80%,100%, 120%).Alineartrendlineisprovidedand*indicatessignicant(p<0.05)di erences betweenthetwosubjectgroups..............................124 5.3.3Meanensemblethigh-shankCPRDfortheunimpairedretrospectivesubjects(grey), unimpaired(blue)prospectivesubjects,andprospectivesubjectswithCP(red)with thesignicantcoordinationevent.Verticallinesindicatethemeanoccurrenceoffoot o foreachgroup.....................................125 5.3.4Meanensemblethigh-shank(top)andthigh-foot(bottom)CPRDfortheunimpaired retrospectivesubjects(grey),unimpaired(blue)prospectivesubjects,prospective subjectswithCP(red),andthesignicantcoordinationevents.Verticallinesindicatethemeanoccurrenceoffooto foreachgroup...................127 5.3.5ICARS/SARAscoresforallunimpairedprospectivesubjects(bluecircle)andall prospectivesubjectswithcerebralpalsy(redsquare)..................128 5.3.6Meanmaximumcurvature(K)forleft(red)andright(green)turnsforallunimpairedprospectivesubjects(n=20)andprospectivesubjectswithCP(n=4).....129 xxiv

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5.3.7MeanCenterofMass(CoM)trajectoriesforleft(red)andright(green)turning tasksofprospectivesubjects...............................130 5.3.8A)ComparisonofGDI(greysquare)andCDI(bluesquare)meanscoresforeach subjectgroup:unimpaired(N),lowerlimbamputation(LLA),belowkneeamputation(BK),abovekneeamputation(AK),cerebralpalsy(CP),hemiplegia(H), diplegia(D),sti kneegaitpattern(SKG),andcrouchgaitpattern(C).B)Mean GDI(grey)andCDI(blue)valuesforNandCPsubjectswithcondenceintervals with95%condenceintervalsarepresentedbyGMFCSlevel.Signicantdi erences betweengroups(p 0.05)andbetweenGMFCSlevelsIandIII............133 5.3.9A)ScatterplotofallGDIscoresagainstallCDIscoreswiththelineofbestt(red). B)Cumulativedistributionfunctions(CDF)fortheGDI(black)andCDI(blue)in comparisontothetheoreticalnormalCDF(red)....................134 5.3.10ThesixsignicantCEsareindicatedoneachcohort'scorrespondingPPsandensembleCPRDs,wheregreycorrespondstotheunimpairedsubjects,redcorresponds tosubjectswithaSKGpattern,andorangecorrespondstosubjectswithacrouch gaitpattern........................................136 5.3.11Abox-plotofeachcohort'sCoordinationPerformanceScore(CPS)isprovided, whereoutliersareindicatedwithared+andablack*indicatesmeancohortCPSs thatweresignicantly(p<0.001)fromtheunimpairedcohort'smeanCPS......137 5.3.12A)ComparisonofGDI(greysquare),CDI(bluesquare),andscaledCPS(yellow square)meanscoresforeachsubjectgroup:unimpaired(TD),lowerlimbamputation(LLA),belowkneeamputation(BK),abovekneeamputation(AK),cerebral palsy(CP),hemiplegia(H),diplegia(D),sti kneegaitpattern(SKG),andcrouch gaitpattern(C).B)MeanGDI(grey),CDI(blue),andCPS(yellow)valuesfor TDandCPsubjectswithcondenceintervalswith95%condenceintervalsare presentedbyGMFCSlevel.Signicantdi erencesbetweengroups(p 0.05)and betweenGMFCSlevelsIandIII.............................138 5.3.13A)ScatterplotofallGDIscoresagainstallscaledCPSvalueswiththelineofbest t(red).B)Cumulativedistributionfunctions(CDF)fortheGDI(black),CDI (blue),andscaledCPS(green)incomparisontothetheoreticalnormalCDF(red).139 5.3.14Percentageofcoordinationevents(CE)missingfromallunimpaired(N)subjects..140 xxv

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5.3.15ThepercentageofsubjectswithCPmissingatleastonecoordinationevent(CE)are displayedforeachgaitcategory:allsubjectswithCP,hemiplegic(hemi),diplegic (dipl),sti kneegaitpattern(SKG),andcrouchgaitpattern.............140 5.3.16PercentagesofcoordinationeventsmissingfromsubjectswithCPwhoareorganized byvegaitcategories:allsubjectswithCP,hemiplegic(hemi),diplegic(dipl),sti kneegaitpattern(SKG),andcrouchgaitpattern...................141 5.3.17ThepercentageofsubjectswithaLLAmissingatleastonecoordinationevent (CE)aredisplayedforeachgaitcategory:allsubjectswithaLLA,belowknee amputation(BK),abovekneeamputation(AK),bilateralamputation(Bilat),and unilateralamputation(Unilat)..............................142 5.3.18PercentagesofcoordinationeventsmissingfromsubjectswithaLLAwhoareorganizedbyvegaitcategories:allsubjectswithaLLA,belowkneeamputation (BK),abovekneeamputation(AK),bilateralamputation(Bilat),andunilateral amputation(Unilat)....................................143 5.3.19Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingfor allsubjectswithCP(red),allsubjectswithaLLA(green),andallretrospective unimpairedsubjects(grey)................................145 A.4.1SCALEdatacaptureandscoringsheet.........................213 C.1.1Part1ofLagrangianapproachtosolvingtheequationsofmotionforadouble pendulumwithoutdampingorinertiaterms......................222 C.1.2Part2ofLagrangianapproachtosolvingtheequationsofmotionforadouble pendulumwithoutdampingorinertiaterms......................223 C.1.3Part1ofLagrangianapproachtosolvingtheequationsofmotionforadouble pendulumwithdampingandinertiaterms.Thissetofequationswereusedforthe softwaremodelandallanalyses..............................224 C.1.4Part2ofLagrangianapproachtosolvingtheequationsofmotionforadouble pendulumwithdampingandinertiaterms.Thissetofequationswereusedforthe softwaremodelandallanalyses..............................225 C.1.5Part3ofLagrangianapproachtosolvingtheequationsofmotionforadouble pendulumwithdampingandinertiaterms.Thissetofequationswereusedforthe softwaremodelandallanalyses..............................226 xxvi

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D.0.1Quadrantsforatan(left)andatan2(right)functions.................228 D.0.2Calculationofpelvis-thighrelativephaseanglesusingMatlab'satanfunction(blue) andatan2function(red).................................229 D.0.3Calculationofthigh-shankrelativephaseanglesusingMatlab'satanfunction(blue) andatan2function(red).................................229 D.0.4Calculationofshank-footrelativephaseanglesusingMatlab'satanfunction(blue) andatan2function(red).................................229 D.0.5Calculationofthigh-footrelativephaseanglesusingMatlab'satanfunction(blue) andatan2function(red).................................230 E.1.1AlgorithmusedbycustomMatlabfunctiontoselectasubject'srepresentativemotioncapturetrial......................................231 E.4.1Diagramofthethreeprostheticalignmentstested,whereblackindicatesstandard prosthesisalignment,blueindicateslateralalignment,andgreenindicatesmedial alignment.Transverseviewofprosthetic(A)andisometricviewofprosthetic(B).235 F.1.1CoordinationeventsassociatedwiththeproposedswinglimbadvancementmechanismareshowonthemeansagittalPPs(readclockwise)andensembleCRPDsfor therightthigh,shank,andfootfromtheunimpairedprospectivecohort'sOGand TMwalkingtrials.....................................236 F.1.2Diagramofknee-anklefunctionalparadoxandcorrespondingthigh,shank,andfoot phaseportraits.......................................238 F.2.1Thighandshankphaseportraits&continuousrelativephasediagramfrom50-60% ofgaitcycle.........................................240 F.2.2Thighandshankangulardisplacementchangesatthestartandendofpre-swing..241 F.2.3Thighandshankphaseportraits&continuousrelativephasediagramfrom60-75% ofgaitcycle.........................................242 F.2.4Dynamicconnectionbetweenkneeandanklemovementcriticalforfootclearance.243 F.2.5Momentofoptimalfootclearancedemonstratedonthethigh-shank&shank-foot continuousrelativephasediagrams............................244 F.2.6Thighandshankphaseportraits&continuousrelativephasediagramfrom75-87% ofgaitcycle.........................................245 F.2.7Compoundthigh-shankpendulumfreebodydiagram,withforceofhipexionon shank(greenarrow)andforceofgravityonshank(bluearrow)............245 xxvii

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F.2.8Thighandshankphaseportraits&continuousrelativephasediagramfrom87-100% ofgaitcycle.........................................246 F.2.9Angleofthethighwithrespecttoglobalhorizontalandglobalverticalatmaximum hipextensioninterminalstancephase..........................247 F.2.10Hamstringsactivationpreventingexcessivekneeextensiononthighphaseportrait.247 F.3.1Shankandfootphaseportraits&continuousrelativephasediagramfrom50-60% ofgaitcycle.........................................248 F.3.2Minimumsagittalankle(kinematic)plantarexioncorrespondingtolocalminimum onshank&footphaseportraits.............................248 F.3.3Shankandfootphaseportraits&continuousrelativephasediagramfrom60-75% ofgaitcycle.........................................249 F.3.4Shankandfootphaseportraits&continuousrelativephasediagramfrom75-87% ofgaitcycle.........................................250 F.3.5Initiationofincreasedinternaldorsiexionmomentandankleapproachesneutral position...........................................251 F.3.6Therstarrowindicatesnearlyhorizontalslopeandthesecondarrowdemarcates therapidchangetowardthelocalmaximumatankleneutral/tibiavertical.....252 F.3.7Shankandfootphaseportraits&continuousrelativephasediagramfrom87-100% ofgaitcycle.........................................252 F.3.8Ankleneutralandtibiavertical(circled).Dorsiexiontrendinpreparationforheel contact(arrow).......................................253 G.1.1Continuousrelativephasediagramsfortreadmillwalkingconditionsofunimpaired prospectivesubjects....................................257 G.1.2Kinematiccurvesforunimpairedprospectivesubjects.................258 G.1.3Diagramofthetimingofthefourcriticalcoordinationeventsidentiedbythe invariantandindependentcriteriawiththetimingoftemporalandcriticalgait eventsduringtheswingperiodofthegaitcycle.Themeanandstandarddeviation ofeventtimingswerecalculatedfromtheunimpairedretrospectivesubjects(n=120) andthegaitcyclewasindexfrom0to100%......................260 G.4.1NumberofcontrolfeaturesforCDI...........................270 G.4.2Reconstructionofcoordinationcurves..........................271 G.4.3Receiveroperatorcurve(ROC)comparisonbetweentheregressionmodelandROC1.273 xxviii

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G.4.4Receiveroperatorcurve(ROC)comparisonbetweentheregressionmodelandROC1.276 G.4.5Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingfor allsubjectswithacrouchgaitpattern(orange),allsubjectswithasti kneegait pattern(red),andallretrospectiveunimpairedsubjects(grey)............278 G.4.6Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingfor allsubjectswithCPclassiedashemiplegic(red),allsubjectswithCPclassiedas diplegic(orange),andallretrospectiveunimpairedsubjects(grey)..........279 G.4.7Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingfor allsubjectswithabelowkneeLLA(darkgreen),allsubjectswithanaboveknee LLA(lightgreen),andallretrospectiveunimpairedsubjects(grey)..........280 G.4.8Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjects(darkblue)forover-ground(OG)walkingataself-selectedspeed(Vss), unimpairedprospective(lightblue)fortreadmillwalking(TM)atthesameVss,and retrospectiveunimpairedcohort'smeancoordinationcurves(grey)forover-ground walkingatVss.......................................281 G.5.1Sagittalplanekinematicandkineticcurvesfortheleft(red)andright(green)legs forthethreeprostheticalignmentconditions......................282 G.5.2Sagittalandcoronalplanephaseportraitsandcontinuousrelativephasediagrams fortheleft(red)andright(green)legsforthethreeprostheticalignmentconditions.283 G.6.1Timingofcriticalcoordinationeventswithrespecttothecriticalandtemporal eventsofgaitduringswingperiod............................284 xxix

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1Introduction 1.1ProblemStatement Instrumentedgaitanalysis(IGA)isoftenemployedtoquantitativelydescribethepathological gaitpatternofanindividualwhosewalkingisnegativelya ectedbyneuromuscularimpairments. Overtheyears,IGAmeasureshaveservedavitalroleinbothclinicalandresearchapplicationsby providingameanstoquantitativelyandobjectivelyidentifyfactorscontributingtoapathological gaitpattern,providesupportingevidenceforclinicalinterventions,andassistinassessmentoftreatmentoutcomes.DuetothemethodsforconstructingconventionalIGAmeasuresandthenatureof theactionsorrelationshipstheyquantify(e.g.jointangles,jointkinetics,temporal-spatial),these measuresdescribethemotionoflimbsorjointsbutareunabletocharacterizetheunderlyingdynamicsofthemotion.Togethertheseunderlyingdynamicsformaconstitutiveelementofbipedalism, coordination.Forthisbodyofwork,coordinationisdenedastheorganizationofthetimingand positionofindividualsegmentsandsegmentpairsinthecyclicaltaskofgait.Thevitalroleof coordinationinmaintaininganormativegaitpatternbecomesapparentinthegaitpatternsofindividualswithneurologicalpathologies.Aberrantcoordinationisahallmarkbehaviorofneurological pathologiesandincasesofimpairedselectivemotorcontroloftencontributestotheinabilitytosuccessfullyachieveswinglimbadvancement.Swinglimbadvancementisacriticaltaskofbipedalism becauseitadvancestheleg,a ectsfootfallforthenextcycle,andrequirestheappropriatecoordinationandcontrolofbodysegments.Thecoordinatedbehavioroflegsegmentsingaitistheresult ofacomplexdynamicalsystemthatrequiresorganizedneurologicalcontrolofthemusculoskeletal system.Duetothecomplexityofthisresultantmotorbehavior,dynamicsystemstheorybased measuresprovidemoresuitablemethodsthanconventionalIGAmeasuresforcharacterizingselectivemotorcontrolstrategiescontributingtoagaitpatternbecausetheyquantifyorganizationof individualsegments,identifymechanismsofchange,andlociofimpairment.Sincethefundamental organizationofthelegsegmentsduringgaitislinkedtogaitpathologyandguidestherationale forinterventions,thisdissertationproposestheincorporationofmeasuresofcoordinationdynamics intoIGAwillopennewavenuesforunderstandingthecomplexityoffundamentalelementofgait andallowcliniciansthemeanstomoree ectivelyande cientlytreatpatientswithneuromuscular gaitimpairments.ThepurposeofthisdissertationistoexpandclinicalIGAtechniqueswithmeasuresofinter-segmentalcoordinationbyvalidatingnonlinearmethodsthatdescribetheresultant motorbehavior,coordinationdynamics,ofthelegsegmentsduringthecriticaltaskofswinglimb 1

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advancementingait. 1.2Rationale Coordinationisanessential,thoughoftenelusive,aspectofmovementthathaslongbeenrecognizedasanimportantfactorofmotion[1,2,4,5].However,theabilitytoemployamethodthat e ectivelycapturescoordinationandpresentsthebehaviorinaconcisemannerhasoftenbeenjust aselusiveastheconceptofcoordination.Theapplicationofangle-anglediagramswasastepinthe rightdirectionsincethesemeasuresdescribetherelationshipbetweentwojointsasalowdimensionaldescriptor[3].SimilartoconventionalIGAmeasures,angle-anglediagramsareconstructed fromaskeletalhierarchyandthereforethesejointbasedmeasuresproveunsuitabletoolsfordelving deeperintothebehaviorofindividualsegmentsorpairingofsegments.Thisneedforquantitative descriptorsofcoordinationwasidentiedinthedevelopmentofmotorcontroltheoryandthemathematicaleldofdynamicalsystemstheorywasproposedasasolution[4,5,6].Withconsiderable advancementsinmotioncaptureequipmentandcomputers,themarriagebetweenmovementanalysisanddynamicsystemstheorywaslaterrevisitedbyStergiouetal.(2004)whodemonstrated dynamicsystemstheorybasedmeasurescanbeeasilyderivedfromsegmentmarkertrajectoriesof motioncapturedata.Thesee ortssupportthetheoreticalconstructthatdynamicsystemstheory cane ectivelycharacterizecoordinationdynamicsandthepracticalityofapplyingdynamicsystems theorymeasurestothepositionaldataofIGAinordertogeneratesuchmeasures.IfthesemeasuresofcoordinationaretobeadoptedinclinicalorresearchIGAapplications,thenitmustbe demonstratedthatthesemeasuresprovidevaluableinsightsintoanaberrantgaitpatternthatis otherwiseunobtainablewithexisting,traditionalIGAmeasures.Therefore,thesenonlinearmethods wereappliedtothemotioncapturedataofsubjectswithanormalgaitpatternandtwosubject groupswithdi erentcausesforimpairedswinglimbadvancement(SLA):cerebralpalsyandlower limbamputation.Sincethefundamentalorganizationofthelegsegmentsduringgaitislinkedto gaitpathologyandguidestherationaleforinterventions,thisdissertationevaluatedcoordination dynamics,inthecontextofacompoundpendulum,forthreecohortsandprovidesanewframeworkforswingperiodcoordinationdynamics.Thecyclicalmotionofthelegsduringgaitisoften comparedtothemotionofvarioustypesofpendulums.Whilethispendularmotionofthelegs hasbeenmodeledasalimitcycleindynamicsystemstheory,thismotionanalogyhasalsobeena cornerstoneforassumptionsusedinsoftwareandhardwaremodelingofhumangait,especiallyin robotics,passivedynamicwalkers,andclinicalIGA.Althoughafewstudieshaveinvestigatedthe 2

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validityofthesependularanalogiesbetweennormalhumangaitandtheoreticalpendulummodels, themajorityfocusonthestanceperiodinvertedpendulummodelofanormalgaitpattern,used conventionaldescriptorsofgait,andtypicallyadjustedthesmallsampleofhumanbasedgaitdata totatheoreticalmodel.Therefore,thesenonlinearmethodswereappliedtodescribetheswing periodcoordinationdynamicsoftwolinkagesinamathematicalmodelofdoublecompoundpendulumandcomparedtothethigh-shankcoordinationdynamicsgeneratedfromtheIGAdataof humansubjects. 1.3ResearchObjectives Theresearchobjectivesofthisdissertationweredividedintofouraims.Therstaimofthis dissertationwastoconstructanormativereferenceforcoordinationmeasuresthatcharacterizes normalgait.Thisnormativereferencenotonlyprovidedacontrolforthetwopopulationswith impairedswinglimbadvancementstudiedinthisworkbutalsoo ersaframeworkforcoordination dynamicsofthelegsegmentsinthenormalgaitcycle.Sincethereisnotagoldstandardcoordinationmeasureduringthetaskofgait,thesecondaimofthisdissertationcomparestheproposed modelofcoordinationdynamicsforthethreedi erentsubjectpopulationstoperformancemeasures fromselecttasksthatcharacterizecertainaspectsofcoordination.Thisaimrelatestheproposed measuresofcoordinationtotheimpairedswinglimbadvancementconditionando ersameans tomapcoordinationndingsfromtheproposedmodeltothesegaitpathologies.Thethirdaim assessedthepassivependularofthelegduringswinglimbadvancementbyusingcoordinationdynamicsmeasurestocomparevarioustheoreticalpenduladynamicstothecoordinationdynamicsof subjectswithnormalandatypicalgaitpatterns.Finally,thefourthaimgeneratesthesecoordination measuresfortwosubjectgroupswithdi erentcausesforimpairedswinglimbadvancementinorder todemonstratetheclinicalvalueandutilityofthesemeasures.Coordinationofthelegsduringwalkingrequirestheelegantorganizationoftheneuromuscularsystem'smanyelementsandappropriate consolidationofthesystem'sredundantdegreesoffreedomwhileconsideringtaskandenvironmental constraints.Coordinationofthelegsegmentsduringgaitisadverselya ectedinindividualswith selectivemotorcontrolimpairmentsresultingfromneuromuscularpathology.Elucidatingthecoordinationofthiscomplexbiologicalsystemrequiresananalysismethodologyofmotioncapturedata capableofisolatinganindividualsegment'scontributiontothesystem'sbehaviorandidentifying thetimingandsequencingofadjacentandnon-adjacentsegmentpairs.Phaseportraits(PP)and continuousrelativephasediagrams(CRPD)aredynamicsystemstheoryderivednonlinearmethods 3

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thatquantifythependularlikemotionofthelegsandrespectivesegmentsduringthecontinuous, cyclicaltaskofgait.Itisproposedthelackofaunifying,renedmethodology,normativereference, andclinicallymeaningfuldemonstrationsofthepracticalbenetsandimportantmotorcontrolinsightso eredbythesenonlinearmeasureshavestalledtheirincorporationintoIGA.Therefore,the proposedmodelofcoordinationdynamicsduringwalkingdescribesastraightforwardmethodology forgeneratingdescriptorsofcoordinationdynamicsbasedondynamicalsystemstheory.Therst aimofthisworkwastogenerateareferencedatasetofcoordinationmeasuresinthesagittalplane coordinationforthepelvis,thigh,shank,andfootsegmentsandsegmentpairings(pelvis-thigh, thigh-shank,shank-foot,thigh-foot)fromalargegroupofindividualsfreeofgaitpathology. Aim1. Demonstratetheproposedmeasuresofcoordinationdynamicscharacterizeanormalgait patternandconstructanormativereferencefromalargecohortofindividualsfreeofgaitpathology. Thereiscurrentlynotastandardmethodforquantifyingcoordinationdynamicsduringthecyclicaltaskofgaitinclinicalpopulationsdemonstratinggaitpathology.Sincethereisnotanestablished referencetocomparetheproposedmeasuresofcoordinationdynamics,thesecoordinationdynamics measureswillbecomparedtothreeclinicalanalogues.Whilenoneoftheseanaloguesindividually encompasstheglobalbehaviorofinter-segmentalcoordination,eachanaloguedescribesaconstitutiveelementofcoordinationandthereforewillbeusedtocreatedescriptionofthepopulation.First, performancemeasuresfromtheSelectiveControlAssessmentoftheLowerExtremity(SCALE)will beemployedtoassesseachprospectivesubject'svoluntaryselectivemotorcontrolability.Although theSCALEexamhasbeenvalidatedforsubjectswithcerebralpalsy,itwillbeadministeredtoall prospectivesubjectsbecauseselectivemotorcontrolisessentialtosuccessfullyexecutelimbadvancementduringswingperiod.Secondly,allprospectivesubjectswillalsoperformlowerextremitytasks fromtheInternationalCooperativeAtaxiaRatingScale(ICARS)andScalefortheAssessmentand RatingofAtaxia(SARA)exams,whichhavebeenvalidatedforindividualswithcerebellarataxia. EachprospectivesubjectwillperformgaitrelatedICARS/SARAtasksbecausethischaracterizes anindividual'sexecutionofamotorplanandsimultaneousabilitytomakecorrections,bothof whichareessentialtotheexecutionofthefeed-forwardmotortaskofadvancingtheswinglimb. Lastly,eachprospectivesubjectwillperformalowerextremityversionofthespeed-accuracytest toprovideameasureofthesubject'sinformationprocessingabilitiesduringswing.Thisallowsfor characterizationofeachsubject'sabilitytoprocessandintegrateproprioceptiveandcognitiveinformationusedbythemovementcontrolsystemtosuccessfullyadvancethelimbduringswingperiod. 4

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Characterizinganindividualorpopulationwithselectconstitutiveelementsofcoordinationfrom theseclinicalexamsprovidesinsightintofeaturesofthemovementcontrolsystem.Whilethereis notagoldstandardmeasureofinter-segmentalcoordination,theconstructvalidityofcoordination describedbytheseindividualcomponentsofmotorcontrolshouldberelatedtotheglobalbehavior quantiedbytheproposedmeasuresofcoordinationdynamics. Aim2. Exploretherelationshipbetweentheproposedmeasuresofcoordinationdynamicsand selectclinicalperformancemeasuresthatcharacterizeaspectsofcoordination. Hypothesis 2A.Impairmentsinthespeedandaccuracyofvoluntaryreciprocalmovements,as testedinatimed,spatiallyconstrainedlowerextremitytappingtask,willbesignicantlycorrelated withtaskspeciccoordinationdecitscharacterizingselectivemotorcontrol. Hypothesis 2B.Thedegreeofselectivemotorcontrolimpairments,astestedbytheSelective ControlAssessmentoftheLowerExtremity(SCALE),willbesignicantlycorrelatedwithtask speciccoordinationdecits. Hypothesis 2C.Cerebellarbasedimpairmentsinspatialaccuracyofmovementanddynamic balance,testedbylowerextremitytasksfromtheInternationalCooperativeAtaxiaRatingScale (ICARS)andScalefortheAssessmentandRatingofAtaxia(SARA),aresignicantlycorrelated withtaskspeciccoordinationdecits. Modelinghumanmovementnotonlyeliminatesthecomplexandintrinsicvariablesassociated withhumanbaseddatabutalsothisallowsforexperimentationofconditions,suchasthoseoutlined bythehypothesesofthisaim,thatcannotbetestedonhumansubjectsduetothepracticalityof suchexperiments.Furthermoreanaccuratemodelofswinglimbadvancementprovidesameansfor determininganoptimalsolutiontothetaskofwalkingandamoreaccurateframeworkforclinicalinterventions.Themotionofthelegsduringthestanceandswingphasesofwalkinghasbeen likenedtothemotionofinvertedandcompoundpendula,respectively.Thisanalogyisgroundedin thefactthatwalkingappearstobehighlyoptimizedwithrespecttothemechanicsofthemotion andimportanceoftheconservationofenergydrivenbyevolutionaryadoptionandrenementof bipedalgait.Thevastmajorityofswingperiodgaitmodelsaltertheinitialconditionsofthemodel inordertoproduceamotionthatissimilarthatofthehumanlegs.Whilethesemodelsmayachieve theirgoalofreplicatingamotionthatissimilartothatofahuman'sswingleg,ahumanisnot abletoalterinertialpropertiesoftheirlegs.Sinceinertialpropertiesandinitialconditionsofmost existingswinglimbmodelsarealtered,itbecomesnearlyimpossibletodistinguishwhichaspects 5

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oftheresultingmotionareduetomotorcontrolstrategiesandthoseofthemodel'salterations. Althoughtheprovidedpendulummodelismoresimplisticthanotherswingperiodpendulummodels,thispendulummodelretainstheinitialconditionsandinertialproperties,derivedfromdataof humansubjects,andisthereforemoreaptlysuitedforcomparingtheswingperiodmotiontothat ofactualhumansubjects.Whilethevastmajorityofpatientswithneurologicalmovementdisorders primarilystrugglewithadvancingthelimbinswing,thiscriticalportionofthegaitcycleisrarely addressedinclinicalinterventions,inpartduetothelackofmathematicalmodelsandclinically usefultechniquesforidentifyingthelocusofdeviationfromtheoptimalmotion.Thehypotheses ofAim3determinetheoptimal,idealpendulumforeachsubjectpopulationduringswingperiod usingnonlinearmeasuresofcoordinationdynamics. Aim3. Assesstheconstructvaliditythatthesagittalplanemotionofthethighandshank duringswingperiodofgaitisanalogoustothemotionofacompoundpendulumusingmeasuresof coordinationdynamics. Hypothesis 3A. Asubjectwithalowerlimbamputationwillhavecoordinationdynamicsmeasureswiththesmallestresidualwhencomparedtoapassivedoublependulum. Hypothesis 3B.Asubjectwithcerebralpalsywillhavecoordinationdynamicsmeasureswiththe smallestresidualwhencomparedtoanover-dampeddoublependulum. Hypothesis 3C.Asubjectfreeofgaitpathologywillhavecoordinationdynamicsmeasureswith thesmallestresidualwhencomparedtoacriticallydampeddoublependulum. Thefourthaimofthisbodyofworkfocusesonidentifyingabnormalswingperiodcoordination dynamicsinpopulationswhostrugglewiththiscrucialtask.Althoughimpairedselectivemotor control,resultinginaberrantcoordinationdynamics,isthehallmarkofneurologicalpathologies, conventionalmeasuresofgaitfailtocapturethisessentialelement.Withouttheabilitytoquantify coordinationdynamics,currentrehabilitationtherapieswillremaininadequateandtheabilityto accuratelyassesstherelativee ectivenessbetweentherapeuticinterventionsremainselusive.Traditionally,datafrominstrumentedgaitanalysisisusedtoprovidelinearmeasuresofgaitcritical fortheproperselectionofclinicalinterventionstargetedatreducingaberrantmotions.Ourinitial investigationsusingnonlinearmeasuressupportthetheoreticalsignicanceofdetectingcoordination ingait,revealdistinctpatternsofmovementassociatedwithvariouspathologicalgaits,ando er aframeworkforinsightintofaultycoordinationdynamicsthatisnotavailableintraditionalgait measures.Thecoordinatedcouplinganduncouplingoflegsegmentscanbedescribedusingnonlin6

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earmeasuresderivedfromprinciplesofdynamicalsystemstheory.Usingtheconstructofrepetitive pendularmotion,thesedynamicsystemstheorybasednonlinearmeasuresteaseoutthee ectsof coordinationdynamicsbyquantifyingchangesintheunderlyingorganizationoflegsegments,unveil themechanismofchange,andlociofimpairmentinthegaitcycle;allofwhicharenotavailable withconventionalgaitmeasures.Sincethefundamentalorganizationofthelegsegmentsduring gaitislinkedtogaitpathologyandguidestherationaleforclinicalinterventions,itisessentialprior toclinicaladoptionofthesemeasurestodemonstratethattheproposednonlinearmeasuresofcoordinationdynamicsareabletodistinguishbetweenthegaitpatternsofpopulationswithdi erent physiologicalreasonsforimpairedswinglimbadvancement. Aim4. Demonstratetheproposedmeasuresofcoordinationdynamicscandistinguishbetween di erentgaitpathologiesandpatternsassociatedwithalteredlimbadvancementduringtheswing periodofgait. Hypothesis 4A.Thereisastatisticallysignicantdi erence(p 0.05)betweenselectmeasures fromthemeanphaseportraitsandrelativephasediagramsfornormal,sti knee,crouch,andmechanicallyalteredgaitpatterns. 1.4OrganizationofDissertationChapters Thischapterprovidesanintroductiontotheresearchprojectandanoverviewoftheobjectivesof thisinvestigation.Chapter2presentsbackgroundinformationrelevanttothethreemainsubjects encompassedbythisresearch:coordination,pendulardynamics,andinstrumentedgaitanalysis. Chapter3providesadescriptionoftheproposedmodelforcoordinationdynamicsoftheswing periodofgait.Chapter4describestheexperimentalandanalyticalmethodologyofthisbodyof work.Chapter5presentstheresultsfromtheexperimentsdetailedinthepreviouschapterandas aresultofimplementingthemodelanddataanalysisprocedures.Chapter6containsadiscussion andinterpretationoftheseresultswithrespecttotheaimsandhypothesesfromchapter1.Lastly, chapter7summarizestheprojectando erssuggestionsforfuturedirectionsandimprovementsto theproposedmodelofcoordinationdynamics. 7

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2BackgroundandPreviousWork Bipedallocomotionisalearnedmotorbehaviorthat,intheabsenceofpathology,appearstobea simplemotion,butisinfacttheemergentbehaviorofacomplex,dynamicalsystem.Characteristics ofanadultwalkingpatternaretheresultofyearsofexperimentingwithvariouscontrolstrategies ofthelocomotorsystemindiverseenvironmentsandconstraints,whichiswhythesepatternsare typicallynotachieveduntilages7to9years[8].Toestablishageneralrelationshipbetweenelements oftheneuromusculoskeletalsystem,thischapterbeginswithabriefoverviewofthephysiologyoflocomotioninregardstotheneurologicalcontrolofthemusculoskeletalsystemduringgait.Assisting inclinicalassessmentandtreatmentofindividualswithanabnormalgaitpatternandcontributing tothegeneralunderstandingofgaitarethetwomainmotivationsbehindgaitanalysis.Within instrumentedgaitanalysis,thereisadiverseandbroadspectrumofequipmentandmeasurements usedtocharacterizeagaitpattern.Thereforeanoverviewofthetwomaintheoriesoflocomotion androleofinstrumentedgaitanalysisinresearchandclinicalapplicationsarepresented,witha specialfocusontwosubjectgroupswithimpairedswinglimbadvancement.Thisisfollowedby descriptionsofcommondescriptorsofgaitderivedfrominstrumentedgaitanalysisdataandperformancemeasuresthatcharacterizecertainaspectsofcoordination.Finally,thischapterconcludes withadescriptionofpreviousinvestigationsthatsupporttheuseofdynamicsystemstheorybased measurestocharacterizethecoordinationdynamicsofvariousgaitpatterns. 2.1PhysiologyofLocomotion Bipedalwalkingisafundamentalhumanbehavior,takesyearstodevelop,andisacritical aspectoflifebecauseanindividual'sindependence,interactionswiththeenvironment,health,and qualityoflifearemarkedlycompromisedwhengaitormobilityareimpaired.Successfulexecution ofbipedalgaitrequiressu cientstrength,balance,posturalstability,endurance,andcoordination. Fromasystemsperspective,coordinatedmovementpatternsarisefromself-organizingsubsystemsin relationtobothinternalandexternalconstraintsandaretheresultofdynamicinteractionsbetween thesesubsystems.Thecontrolofgaitrequirestheintegrationofperipheralsensoryinformationand appropriateexecutionandmodulationofamotorplanthroughdescendingsupraspinalpathways. Therefore,coordinationisaconstitutiveelementofgaitthatreliesupondi erentaspectsofthe musculoskeletalandnervoussystems.Thephysiologyoftheselocomotionsystemssignicantly a ectsanindividual'sabilitytoe cientlyperformthetaskofgaitandadapttovarioustaskand 8

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environmentalconstraintsexperiencedduringindependentambulation.Anunderstandingofthe physiologyofthesesystemsandthecorrespondingneurologicalcontroliscrucialforappreciating bipedalwalkingandtheimportantcontributionofinstrumentedgaitanalysisinrehabilitationof variousmovementdisorders. 2.1.1NeurologicControlofMusculoskeletalSystem Althoughneuralactivationofskeletalmuscleprecedesskeletalmuscleactivation,abriefoverview ofthemusculoskeletalsystemisprovidedtosetthestageforamoreindepthdiscussionofcontrol ofthelocomotorsystem.Usingtendons,cartilage,muscles,bonesandconnectivetissuethemusculoskeletalsystemprovidessupport,protection,stability,andtheproductionofforcesandmoments aboutjointsnecessaryformovementofthebodyandperformancedailylivingactivities.Thenervoussystemcontrolsskeletalmusclewithactionpotentials,whicharerapidanduniformelectrical signalsthatpropagatethroughtheexcitablemembranesofnervecellstotheskeletalmuscle.The excitation-contractioncouplingisasequenceofmicroscopiceventsbywhichanactionpotential fromaneuronisconvertedintoamechanicalresponseinamuscleber.Thestriatedappearanceof skeletalmusclewhenviewedwithamicroscopeisduetotherepeatingseriesofsarcomeres,which arethebasicunitofthistissue.Sarcomeresarecomprisedofthickandthinlamentsandthe interactionofthesecontractileproteinsisthemechanismwithinamuscleberresponsibleforthe generationofforce.Althoughmusclesmaychangelengthduringcontraction,theoverlappingmyosin andactinlamentsofsarcomeresslidepasteachotherbythecyclicalformationandreleasingof cross-bridges(e.g.sliding-lamentmechanism).Thenumberofcross-bridgesformedbetweenoverlappingcontractileproteinsandlengthofthesarcomerearetwomechanicalpropertiesofskeletal musclethatinuencetheamountofforce(tension)amuscleiscapableofgenerating[9].Alongwith thislength-tensionrelationship,themaximumforceproductionofskeletalmuscleisalsoinuenced bytheload-velocity,whichisthesigmoidalrelationshipbetweenthevelocityofchangesinmuscle lengthmuscleandforceproductioncapability,andtheforce-timerelationship,whichdescribesthe delayinforcedevelopmentinthemuscle-tendonunitfromthestartofthemotoractionpotential tothepeakmuscletension[9]. Skeletalmusclesareoftenreferredtoasthebody'smotorsbecausetheyconvertchemicalenergy intomechanicalwork.Themechanicalwork(e.g.force)generatedbymusclesistransmittedtothe bonesviatendonsandproducesthejointmomentsnecessaryforwalking.Skeletalmuscleisattached tobonebytendons,whicharemostlycomposedofthestructuralproteincollagen.Inadditionto beingthestructuralconnectionbetweenmuscleandbone,therelativelycompliantphysiologyof 9

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tendonsallowsthistissuetopositivelycontributetotheoverallfunctionofthemuscle-tendonunit [9].Specically,themagnitudeofmuscle-tendondeformationthatoccursduringmusclecontraction isdependentuponthetendon'scomplianceanddirectlya ectsthemuscle'slength-tensionand force-velocityrelationships.Alongwithanatomicalandstructuralpropertiesofthemuscle-tendon unit,thenervoussystemprovidescontinuousresistance(e.g.muscletone)inordertoprevent fullrelaxationofskeletalmusclesandensuretheyarereadytorespondquicklyandsmoothlyto excitation.Inconjunctionwithsensoryinformation,thelocomotorsystemalsointegratesthemotor planandcurrentorientationofsegmentswiththisunderlyingmuscletoneduringtheexecutionof theintendedmotion. Asthesarcomereofskeletalmuscleisthefunctionalunitofforcegeneration,themotorunitisthe functionalunitofmovement.Amotorunitconsistsofone # -motorneuronandtheextrafusalmuscle bersitinnervates.Thecentralnervoussystemcontrolsmuscleforceproductionbyregulatingthe activityofmotorunitswithinamuscle.Theamountofforceexertedbyamuscledependsupon howmanyofitsmotorunitsareactivated(e.g.motorunitrecruitment)andtherateatwhich themotorneuronsdischargeactionpotentials(e.g.ratecoding)[11].Byalteringtheactivation frequencyornumberofactivatedmotorunits,thenervoussystemisabletoelegantlyorchestrate thebiomechanicalinteractionsbetweenmuscles,tendons,andbonesandthuse cientlycontrolthe degreesoffreedominthesystemtoproducethedesiredmotion. Correctdeterminationofthejointpositionsandmovementsduringamotionarefundamental functionsofthelocomotorsystem.Sensoryorganswithintheskeletalmuscledetectperipheral sensoryinformationaboutajoint'spositionandvelocityandchangesinmusclelengthandtension. Thissensoryinformationisrelayedfromthesesensorstothecentralnervoussystemviacorticospinal tractsandisintegratedintothevoluntarymotorscheme.Theskeletalmusclespindleandgolgi tendonaresensoryorgansresponsibleformonitoringskeletalmuscletone.Themusclespindle isanintrafusalmuscleberthatoccursinvaryingnumbersforeachskeletalmuscle.Theyare particularlynumerousinskeletalmusclesthatrequirenecontrol,suchastheintrinsicmusclesof thehand.Musclespindlesareattachedtotheconnectivetissueseptaeandarealignedinparallel withtheskeletalmusclebers.Thisphysiologicalalignmentisimportantbecauseduringcontraction ofthemusclebersthespindlesarekepttautasthemuscleberscontractandthusallowthese sensoryelementstodetectchangesinmuscleberlength. Voluntarycontractionofamusclerequirestheactivationofseveralmotorunits,whicharerecruitedinorderofincreasingsize[12].Studiesinvestigatingpatternsofmuscleactivationrecruited duringposturalcontrolandbalancetaskshaveledtotheproposalthatthecentralnervoussystem 10

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simpliestheenormouscontroldemandsthroughtheuseofmusclesynergies[13,14].Synergiesare exible,emergentpropertiesofasystemthatarethefunctionalcouplingofgroupsofmuscles,which acttogetherasaunitinordertocoordinateredundantelementsandreducethesystem'sdegrees offreedom[1].Theabilitytoadaptthesesynergiesisessentialtomeetanychangingtaskandenvironmentalconstraintswhileexecutingamovement.Thecoordinatedorganizationofmusclesand jointsresultinginasynergyisconsideredthefunctionalunitofmotorbehavior.Theprecisetiming andorderofmuscleactivityandpositionalrelationshipofsegmentsthereforeprovidethedenition ofacoordinatedmovement.Fromthisperspective,coordinationisclearlyanessentialelementof bipedalwalking,whichrequirestheorderedtimingandsequenceofseveralfunctionalsynergies(e.g. extension,exion)amongstthelimbs. Theoutlineprovidedbelowelaboratesuponthegeneralschemeforvoluntarymotorresponses. Thisschemedescribesthesupplementalmotorareasandassociatedareasinthebrainandlists themainstepsinvolvedinthecreation,execution,andmodicationofavoluntarymovementplan. Furtherelaborationofthisgeneralscheme'sstepsisalsopresentedwithanemphasisonthemotor taskofgait. 1.Sensoryinputsaboutthebodyandenvironmentcomeintotheindividual'sconsciousattention. 2.Thesomatosensorycortexusesthesesensoryinputs(e.g.somatosensory,visual,vestibular)to createasensorymap. 3.Fromthissensorymap,amovementplanisdeveloped(parietallobes,supplementarycortex, premotorcortex). 4.Themovementplanissenttothepremotorcortex,wheremusclegroupsnecessaryforthe executionoftheplanarespecied. 5.Theupdatedplanisthensenttothecerebellumandbasalgangliaforfurthermodications andrenement. 6.Thecerebellumandbasalgangliasendtherenedmovementplantothemotorcortexand brainstem. 7.Descendingpathwaysfromthemotorcortexandbrainstemactivatespinalcordnetworksand spinalmotorneuronsthenactivatethepre-selectedmuscles. 8.Spinalreexpathwayscompensateforunexpectedenvironmentalvariablesandactivatemore orfewermotorneuronsaccordingly. 11

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9.Sensoryconsequencesandchangesareevaluatedbythecerebellum,whichcomparestheactual movementwiththeintendedmovementplanandrevisesthemovementplantocorrectforany errors. Thecerebellum,motorcortex,andbasalgangliaareconsideredthethreeimportantbrainareasthat contributetocoordinationofamovementsuchaswalking.Althoughthecerebellumdoesnotplaya primaryroleineithersensoryormotorfunction,lesionsofthecerebellumresultinimpairedmotor output.Similartothecerebellum,lesionsofthebasalgangliadonotresultinlossofmotororsensory functionbutdohoweversignicantlyimpairmotorcontrolandtheresultingmovement.Since voluntarymovementisproducedthroughthecorticospinaltracts,uppermotorneuronlesions(e.g. motorcortex)resultsinlossofmotorcontrolandnegativelya ectstheindividual'sabilitytoperform voluntarymovements(e.g.walking).Uppermotorneuronsareneuronsthatconnectthebrainto thespinalcordandlowermotorneuronsconnectthespinalcordtoskeletalmuscles.Disruptions insensoryinformation,suchasthatneededtomaintainmusclelengthortension,contributeto theaberrantcoordinationcharacteristicoftheunderlyingmotordisorder.Toappreciatetherole ofessentialsubsystemsinvolvedinthegeneralschemeforvoluntarymovementpresentedabove,a briefdiscussionofthesestructuresandtheircontributionfollows. Muscle Spindle.Thecompletefeedbackmechanismofthemusclespindleisalsoknownasthe fusimotorsystem[15].Thefusimotorsystemcontinuallymodulatesthe # -motorneuronsinnervating theextrafusalmusclebersandplaysanimportantroleintheperipheralsensoryfeedbackmechanisms(e.g.stretchreex)usedbythecentralnervoussystemformotorcontrolandmotorlearning. WhenIaa erentreceptorsareexcited,amonosynapticresponseatthespinallevelexcitetheagonistmuscleandapolysynaptic,long-loopresponsewillexciteagonistmusclesanddampen(inhibit) antagonistmuscles[15,16].Themusclespindleislocatedinthebellyofskeletalmusclesandconsists ofintrafusalbersandsensoryneuronendingsthatwraparoundthecentralregionsoftheintrafusal bers.Musclespindlesareinnervatedwithsensoryandmotorneuronsthatsupportthedetection oftheabsolute,staticmusclelengthanddynamicchangesinmusclelength[16].Theextrafusal skeletalmusclebersareinnervatedby # -motorneurons,whichsenda erentactionpotentialstothe centralnervoussystemsandreceiveinputfromuppermotorneuronsviathecorticospinalpathway, thuscontributingtotheinitiationofmusclecontraction.Musclespindlesarealsoinnervatedby -motorneurons,whichrelaybothchangesinmusclelengthandtherateofchangesinmusclelength tothecentralnervoussystem.Additionally, $ -motorneuronsinnervateintrafusalmusclebersand areresponsibleformaintainingappropriatetensioninmusclesspindles.Withouttheco-activation 12

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of # and $ -motorneurons,themuscleberswouldlosetensionduringmusclecontractioncausing themusclespindlestoloosenasthemusclecontracts.Since $ -motorneuronssetthetensionofthe spindlecell,theseneuronsarethoughttocontrolandregulatethesensitivityofthespindlereceptors inresponsetostretchingofthemusclebers. Golgi Tendon Organ.Thegolgitendonorgansareencapsulatedorgansattachedinseriestothe collagenousbersoftendonsatthepointofmuscleinsertionsandalsoexistinthefascialcoverings ofmuscles[11,17].Golgitendonorgansprovidea erentinformationabouttheforces(i.e.tension) betweenamuscleanditstendon[16,18].A erentneuronscomingfromthegolgitendonorgansto thespinalcordarestimulatedbymuscletensionandselectivelyinhibitthe # -motorneuronsofthe agonistmuscleswhilefacilitatingthoseoftheantagonistmuscles.Sincegolgitendonorgansare notinnervatedbye erentneurons,theyarenotsubjecttocontrolfromthecentralnervoussystem. However,thesesensoryorgansdocontributetotheinformationusedbythesomatosensorycortexto createandupdateasensorymapofthebodypriortoandduringamovement.Activationofthegolgi tendonorganreexinhibitsthemuscleinwhichitlivesandexcitestheantagonistmuscle,whichin thepasthasledresearcherstohypothesizethisreexactsasaprotectionmechanismagainstmuscle forcesthatcouldleadtoinjuryofthemuscle-tendonunit.Inthestanceperiodofgait,golgitendon organsofextensormusclesinthelegsareactiveandinhibitexormusclesuntiltheforcesonthe stancelegareremovedduringswing.Morerecentresearchintothefunctionofgolgitendonorgans hasledtoanewhypothesisthatthesesensoryorgansmodulatemuscleoutputwhenthemuscle beginstobecomefatigued. Dorsal Column-Medial Lemniscal Pathway.Thedorsalcolumn-mediallemniscalpathwaysends mostlyproprioceptiveinformationregardingmuscles,tendons,andjointstothesomatosensorycortex,whichintegratesthisinformationandcreatesandupdatesthesensorymap[18].Proprioceptors inthelegshaveaseparatepathwaytothebrainstemviathelateralcolumnwhereitjoinsthedorsal column.Higherbraincenterscanselectivelymodulatetheinformationcomingfromthispathway. Somatosensory Cortex.Thesomatosensorycortexreceivessensoryinformationfromjointreceptors,musclespindles,andcutaneousreceptors(e.g.mechanoreceptors,nocireceptors,thermoreceptors)[18].Thiscortexusescross-modalityprocessingofthesensoryinputstoprovideinformation aboutmovementinagivenbodyareaandistransposeduponanexistingmapoftheentirebody. Thisanalysisisthebeginningofthespatialprocessingthatisessentialtospatiallycoordinating movementsofthebodyanditsinteractionwiththesurroundingenvironment. Cerebellum.Althoughthecerebellumdoesnotprimarilyparticipateinthesensoryormotor functionofmovement,itisconsideredoneofthreecentralnervoussystemstructuresintegralto 13

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movementbecauseitreceivesa erentinformationfromalmosteverysensorysystem,renesthe motorplan,andregulatesmotoroutputbycorrectingforerrors[16,18].Forexample,sensory informationfromthefourspinocerebellartractsrelayinformationfromthespinalcordaboutthe arms,neck,trunk,andlegsandhelpsthecerebellumdetermineifadesiredmovementmatches themotorplan.Additionally,sensoryinformationviathespino-olivo-cerebellartractisusedin theprocessofmotorlearning.Asafunctionofitsneuralcircuitry,thecerebellumitactsasa comparatorthatcompensatesforerrorsinamovementbycomparingintention(e.g.motorplan)with performanceandisthereforearegulatorofmotoroutput.Inconjunctionwithperipheralsensory input,thecerebellumreceivesinformationfromotherbrainstructuresabouttheprogrammingand executionofmovements.Acopyoftheinformationsentfromthemoorcortextothespinalcord isalsosenttothecerebellumandisknownasane erencecopyorcorollarydischarge.Sensory feedback,rea erence,isreceivedbyoneofthethreedeepnuclei(fastigialnucleus,interposednucleus, dentatenucleus)ofthecerebellumbeforecontinuingontothecortex. Basal Ganglia.Therearefourdistinctcircuitsinthebasalgangliathatrunparalleltoeach other.Theskeletomotorcircuit,whichconsistsofbothadirectandanindirectcircuit,isperhaps themostwell-knownofthesesinceitisassociatedwithmovementdisordersasaresultofbasal gangliadysfunction.Thiscircuitreceivesinputfrommanyareasofthecortex.Thesesignals arerelayedthroughthevariousnuclei(e.g.putamen,caudatenucleus,globuspallidus,subthalamic nucleus,andsubstantianigra)ofthebasalgangliaandthencontinueontothethalamusbeforebeing sentbacktocortex.Thedirectpathwayoftheskeletomotorcircuitreceivessensoryinput,often associatedwithpre-movementactivities,andrespondstostimulithathavemotivationalsignicance. Thedirectpathwayincreasescorticalactivity,whiletheindirectpathwaydecreasescorticalactivity. Innormalrestingstate,thetwopathwaysareinbalancewithaslightedgetoindirectpathway[19]. Thereforetheskeletomotorcircuit(comprisedofthepremotorcortex,supplementarymotorcortex, primarymotorcortex,thalamus,basalganglia)contributestoboththepreparationandexecution ofmovement.Thebasalgangliaaremoreinvolvedininternallygeneratedmovementswhilethe cerebellumisinvolvedinvisuallytriggeredandguidedmovements. Motor Cortex.Thereareseveraldi erentprocessingareasinthemotorcortexinvolvedwith voluntarymovement.Alloftheseareasinteractwithinformationfromthesomatosensorycortex, basalganglia,andcerebellumandcontributetothedevelopmentandexecutionofamovementplan. Itishypothesizedthatamotormap,oftenreferredtoasamotorhomunculus,islocatedinthis cortexandissimilartothesensorymapanditshomunculus.Thecorticospinaltract,outputof theprimarymotorcortex,contributestothepyramidaltractthatmakesexcitatorymonosynaptic 14

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connectionsto # -motorneurons,whichcontractmuscles,andpolysynapticconnectionstogamma motorneurons,whichcontrolmusclespindlelength[16].Thistractalsoconsistsofneuronsfrom thesupplementarycortex(controlsmovementsinitiatedinternally),dorsalandventralpremotor areas(controlsmovementsactivatedbyexternalstimuli),andthesomatosensorycortex[16].Ithas beenproposedthatthesupplementaryareaalsoparticipatesintheassemblyofthecentralmotor programorformsamotorsubroutine[16]. Thalamus.Nearlyallsensoryinformation,excepttheolfactorysystem,fromthebodypasses throughthethalamus.Locatedbetweenthecerebralcortexandthemidbrain,thethalamusselectivelyrelayssensoryinformationandmotorsignalstothecerebralcortexandactivatesmotor regionsofthefrontallobe[16,18].Thethalamussendsproprioceptiveinformationtotheprimary somatosensorycortexandthuscontributestothedevelopmentandmaintenanceofthesensorymap. The Muscle Stretch Reex.TheexcitationoftheIaa erentneuronsinmusclespindlesresults inoneoftworesponses:stretchreexorlong-loop(e.g.transcortical)reex.Thestretchreexloop isanegativefeedbackmechanismdesignedtomaintainmusclelengthandissignicantlya ected bytheinherentcomplianceofthemuscle-tendonunit[20].Thestretchreexisinitiatedbya mechanicallengtheningofmuscleberscausesthesimultaneousactivationofterminalbersinthe -motorneuronsofthemusclespindle.Theamplitudeofthesensoryreceptor'sactionpotentialis proportionaltotheintensityofthemusclelengtheningandifitissu cientlylargewillelicitan actionpotentialthatpropagatesalongthe -motorneuronstothecentralnervoussystem.When the # -motorneuronsareexcited,theskeletalmuscleinnervatedbytheseneuronsandsynergistic recruitedmusclesarealsoexcitedandcontract.Additionally,the -motorneuronsexciteIainhibitory interneurons,whichinturninhibit # -motorneuronsoftheantagonisticmuscles. Althoughthestretchreexisnotconsciouslycontrolledduringvoluntarymovement,itcan signicantlyinuenceaperson'sabilitytosuccessfullyexecuteamotorplan.Whentheexcitatory inputfrommusclespindlesisinhibitedorremoved,thesupraspinaldrivetoalphamotorneurons mustincreasetoproducesu cientforcetogeneratethedesiredvoluntarymovement,thuscausing anincreaseinperceivede ort,whichcanleadtofatigue[15].Individualswithspasticcerebralpalsy (neuromuscularmovementdisorders)oftenhaveexcessivespasticity.Spasticity,elicitedbyvelocity dependentchangesinmusclelength,isbroadlydenedbytheSupportProgramforAssembly ofaDatabaseforSpasticityas"disorderedsensory-motorcontrolresultingfromanuppermotor neuronlesion"[22].Thislackofinhibition,whichisnormallytransmittedalongthecorticospinal tract,causesadisruptionofthenegativefeedbackloopthatexistsbetweenmusclespindlesand # -motorneurons.Removalorinhibitionofthisnegativefeedbackresultsinexcessiveandabnormal 15

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muscleactivation[20]. Central Pattern Generators.In1914,GrahamBrown'stheoryproposedthatevenintheabsence ofmusclereexes,rhythmicmotorpatterns(e.g.thoseseeninlocomotion)couldbeproducedby specialneuralnetworks(e.g.centralpatterngenerators)[17].Itishypothesizedthatcentralpattern generatorsatthespinallevel,areanorganizationofintrinsicoscillatorynetworksthatareactivated andmodulatedbycentralnervoussystemstructuresanda erentsensoryinput[18].However,this schemareliesuponamysterious"blackbox"orgeneralhomunculustosupplythedetailsofcoordinationofoscillatorymovementsandleavesaratherunsatisfactorymodelforfurtherdevelopmentand understandingofthiscontrol.Alternatively,thedynamicsystemsapproach(e.g.dynamicpattern generation)proposesthatthereisnotasupremecontrollerbutinsteadmovementproductionis theresultofanintegrationofcentralnervoussystemstructures,externalstimuli,internalsensory information,andenvironmentalfactors.Eventhoughboththeorieso erdi erentadvantagesand disadvantages,coordinationandcontrolofthatcoordinationmustcoexistinordertoaccountfor activecentralgenerationofoscillatorymovements,suchasgait,andcontrolormodicationsof coordinationtoaccommodateinternalandenvironmentalfactors. 2.2ModelingLocomotion AsevidentbytheEdwinSmithSurgicalPapyrusAncientEgyptianmedicaltext(ca.1500BCE) andAristotle'sreections(384-322BCE),humanshavebeeninterestinthephysiologicalelements requiredtoproducemovementandstudiedthemotionofwalkingformillennia[23,24].Baker'sarticlepresentingatimelineandaccountofgaitanalysispriortotheinventionofcomputersprovidesa thoroughhistoryofthisdiscipline[24].TheworkofInmanandEberhartduringthemidtwentieth centuryisoftenconsideredtomarkthebeginningofmoderngaitanalysisbecauseitlaidthegroundworkfortheinvaluablecontributionsbyPerry,Sutherland,andGagewhosee ortsdemonstrated theclinicalutilityforassessingwalkingdisorderswithinstrumentedgaitanalysis[25,26,27,28,29]. Inmanidentiedtwobasicfunctionalrequisitesofgaitthatarenecessaryforanyformofbipedalism,regardlessofthedegreeofimpairment:1)continuinggroundreactionforcesthatsupportthe bodyand2)periodicforwardmovementofeachfootfromonepositionofsupporttothenext[30]. Interestingly,thesetwofundamentalcharacteristicsofbipedalwalkingholdtrueforanyformof bipedalismregardlessoftheseverityorcauseofmovementdisability(e.g.neuromusculardisease, musculoskeletalalteration).ExpandinguponInman'stwofunctionalrequisitesofgait,Perrydivided thegaitcycleintothefollowingthreefunctionalsubdivisionsor"tasks":weightacceptance,single 16

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limbsupport,andswinglimbadvancement[26].ItisworthnotingthatWinteralsoindependently identiedthesethreefunctionaltasks[31].Additionally,Perryidentiedpatternsfromobservational gaitanalysis,electromyography,andkineticsfromacohortofsubjectsfreeofgaitpathologytofurtherelaborateuponthesegaittasksandcreatetheframework(temporalevents)forthephasesofthe gaitcycleandthecriticaleventspresentwithinthesephases(Figure2.2.1).Thisframeworkoutlines thefundamentalaspectsofanunimpairedgaitpatternandformsthepresentworkingdenitionof anormalgaitcycle,whichtemporallyuniesmanyoftheconventionalmeasuresofgait. Figure2.2.1:Periods,task,phases,andimportanttemporalandcriticaleventsoftheunimpaired gaitcycle[26,32]. Althoughseveraldi erencesbetweenanormalandpathologicalgaitpatternscanbedetected withobservationalgaitanalysis,instrumentedgaitanalysisusesvariousinstrumentationandmeasurementstodetectandquantifythesedi erences.Bytrackingandrecordingthemotionofsegments duringthetaskofgait,theabilitytomeasureandanalyzeaspectsofhumanmovement,thatare otherwiseobservationallyundetectable,createsthemeanstoenhancethegeneralunderstandingof walkingandadvancerehabilitativetechniquesforcorrectingatypicalgaitpatterns.Theutilization ofinstrumentedgaitanalysiscanbedividedintotwodi erentyetoftenoverlappingapplications: clinicalandresearch.Clinicalgaitanalysisgeneratesmeasuresthatidentifyfactorscontributing toapathologicalgaitpattern,providessupportingevidenceforclinicalinterventions,andassists intheassessmentoftreatmentoutcomes.Quantitativemeasuresderivedfrominstrumentedgait 17

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analysissupportclinicaldecisionmakingbyprovidingobjective,reproducibledescriptorsofgait pathologythatcanbestratiedbyseverityandcharacterizeoverallgaitperformance.Overthe lastfewdecades,techniquesandinstrumentationforinstrumentedgaitanalysishaveevolvedsignificantlytothepointwhereitisconsideredbymanytobeanintegralcomponentofrehabilitation planningandassessmentoftreatmentoutcomeforindividualswithanaberrantgaitpattern[33]. Sincethereisadiversespectrumofresearchthatinstrumentedgaitanalysiscomprisesofa diverseandbroadspectrum,onlyaselectfewapplicationsthatarerelevanttothisbodyofwork arementioned.Treadmillgaittrainingisanappealingrehabilitationmodalityforpatientswith aneuromuscularimpairmentbecauseito ersameansfortask-specicgaittraining,repetition, manuallyandroboticallyguidedassistance,systematicallycontrolledprogressionofwalkingspeed, andtheoptionforpartialbodyweightsupport.Althoughnumerousstudieshaveexaminedpotential di erencesbetweenoverground(OG)andtreadmill(TM)walkinginordertoassessthevalidityof thisOGwalkinganalogue,thendingsfromthesestudiesareofteninconclusiveandconicting.A challengeinthedevelopmentofprostheticlimbcontrolforindividualswithalowerlimbamputation issimulatingcontrolandfeedbackfromboththee erentanda erentpathwaysofthenervous system.Severalpassivemechanicallypassiveandelectronicallycontrolledprosthesesaredesigned tomimicthekinematicsandkineticsofintact,healthyindividuals.Additionally,usingthisbaseline ofanormativegaitpattern,severalresearchstudiesuseinstrumentedgaitanalysistechniquesto assesschangesinexistingprosthetics,renementofcontrolalgorithms,comparedi erentprosthetics, andevaluatenewprostheticdesigns[34,35,36].Researchusinginstrumentedgaitanalysismeasures hasalsobeenbenecialintheeldofroboticassistedgaittraining,especiallyfortreadmilltraining withactiveorthoses[37,38,39].Normativegaitpatternsandstandarddeviationsfrominstrumented gaitanalysesprovidethebaselinereferencecontrolalgorithmsandsafetylimitsforroboticorthoses andexoskeletons.Researchstudiesoftenuseconventionalmeasuresofinstrumentedgaitanalysisin theirexperimentalprotocoltoteststhesecontrolalgorithms,assessthee ectsofchangesindevice design,ande cacyofsuchrehabilitationdevicesintargetedpatients. Three-dimensionaltrackingofpassiveandactivemarkers,placedonspecicanatomicallandmarks,provideslocationsofsegmentsasanindividualwalksinthemotioncaptureenvironment. Thispositionaldataofsegmentscanbeusedtodeneeachcompletegaitcycle,whichthenprovides thetemporalframeworkthatallowsconventionalmeasuresofgaittobedescribedonthesametime scale.Segmentpositionsareusedtocalculatetemporal-spatialdescriptorsofgait,whichareused todetectasymmetriesandcharacterizeoverallfunctionalperformance.Whensegmentsaretracked withmarkers,thepositionaldataofthesemarkerscanbeusedtocreatecoordinatesystemsforeach 18

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correspondingsegment.Kinematiccurves,quantifyingchangesinjointangleswithrespecttotime, areanglesconstructedfromtheaxesoftwoadjacentsegmentsandseparatedintothethreeplanesof motion.Amoreindepthexplanationoftemporal-spatialandkinematicvariablesisprovidedlater inthischapter.Inadditiontotheseconventionalinstrumentsgaitanalysismeasures,kineticsand dynamicelectromyographyareconsideredtraditionalgaitmeasures.Triaxialforceplatformsmeasurethemagnitudeanddirectionofgroundreactionforceofthestancelimb.Theskeletalhierarchy usedforconstructingkinematicsisalsoused,inaprocessknownasinversedynamics,toestimate theforces,moments,andpowersateachjointinthekinematicchain.Thesekineticvariableso er insightsintopowergeneration/absorptionbythemusculotendoncomplexesastheyactonajoint andprovideinsightsintotherelationshipsbetweentheangularmotionofjoints(kinematics)and themuscleforcesthatgeneratejointmoments.Aspreviouslymentioned,skeletalmusclesarethe motorsofthebodyandtherecruitmentandringrateofmotorunitsbythenervoussystem.An electromyogramisthecumulativemyoelectricactivityofseveralmotorunitactionpotentials,which canberecordedwitheithersurfaceorpercutaneouselectrodesandampliers[23].Sincedi erent combinationsofmuscleactivityduringgaitproduceslowerlimbkinematicpatterns,dynamicelectromyographyisoftenincorporatedintoinstrumentedgaitanalysisbecauseitprovidesarecording ofthephasicmuscleactivityofmonoarticularandbiarticularmusclesusedinwalking.Temporally normalizingkinematics,kinetics,andelectromyographicdatatothegaitcycleaidsintheinterpretationofthisdatabyprovidingacommontimescalebasedonfootstrikesandallowsforintra-subject andinter-subjectcomparisons.Amoreindepthexplanationoftheselectconventionalmeasuresof gaitutilizedinthisinvestigationisprovidedinasubsequentsection.Thisbriefoverviewofcommon equipmentandmeasurementsusedininstrumentedgaitanalysisisbynomeansexhaustive.Fortunately,therearenumeroustextsontheseareasthatprovidemoreextensivecoverageofthevarious typesofequipmentusedtocapturehumanmovementandthemeasurementsderivedfromthedata recordbyvariousinstrumentation[23,29,31,32,40]. Interpretingthevastamountofdatarecordedduringaninstrumentedgaitanalysisandrelating thisinformationtothemultiplephysiologicalinteractionscontributingtoagaitpatterninaclinically meaningfulwaycanbechallenging.AsevidentinPerry'sdivisionsofthegaitcycle,thereareseveral complexmotorbehaviorswhosetimingandorganizationareessentialforcompletingthetaskof gait.Inparticular,thetaskofswinglimbadvancementisacrucialfunctionperformedduring singlelimbstanceandrequiressu cientbalance,strength,andcoordinationtosuccessfullyexecute. Therefore,thefollowingsectionexpoundsuponthisportionofthegaitcycleinthecontextofagait patternfreeofpathology.Establishingthisframeworkforswinglimbadvancementprovidesauseful 19

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referenceforthevariousmathematicalmodelsofgaitusedtoemulatethismotionandthemodel developedinthisdissertation.Lastly,thisreferenceofthefunctionalrequirementsandphysiological interactionsnecessaryforsuccessfullycompletingthisgaittaskassistsinunderstandinghowdi erent physiologicalimpairmentsintheneuromusculoskeletalsystemcannegativelya ecttheinabilityto performthistaske ciently. 2.2.1TaskofSwingLimbAdvancement Thetaskofswinglimbadvancementbeginswiththeoccurrenceofoppositefootstrikeofthe contralateralleg,coincideswiththebeginningofthepre-swingperiodofthegaitcycle,andinvolves fouroftheeightphasesofgait.Swinglimbadvancementincorporatestheswingperiodofgaitand iscompletedwhenthefootoftheswinginglimbmakescontact,ideallyheelrstinitialcontact,with thewalkingsurface.Inanormalgaitpattern,themainfunctionalobjectivesduringthetaskofswing limbadvancementare:properpositioningofthelimbforswing(pre-swingphase),uncouplingof thethigh-footextensionsynergyatfooto ,su cientclearanceabovethegroundbythefoot(initial andmid-swing),forwardadvancementofthelimb(initialandmid-swing),andproperplacementof theleginanticipationofheelrstinitialcontactandloadingresponse(terminalswing). Swinglimbadvancementrequirestheprecisetimingandelegantorganizationofthelegsegments andistheresultingbehaviorofacomplex,dynamicalsystemasevidentbythefollowingsubtle,yet essentialcoordinationmechanisms.Duringpre-swing,thelateralweighttransferfromthestance limbtothecontralaterallimb,atoppositefooton,isrequiredforthenecessarychangesinposture,providesabriefsecondinstanceofdoublelimbsupport,andunloadstheadvancinglimbin preparationforrapidadvancementduringswingphaseattheinstantoffooto .Atfooto ,the simultaneousuncouplingofankleplantarexionandhipextensionisessentialiftheswinginglimb istoe cientlycapitalizeupontheballisticforwardpropulsionprovidedbytheankleplantarexion moment,whichalongwithhipexionwillensuresu cientlimbclearanceandadvancementfrom itstrailinglimbposture.Achievingsu cientkneeexionforuninhibitedfootclearanceandleg swingisanimportantfunctionofthelegduringswinglimbadvancement.Adequatekneeexion, su cientforwardlimbmomentumfromrapidhipexion,andactivationofthebicepsfemorismuscle toreachmaximumkneeexionarethreemechanisms,whoseprecisetimingandmagnitudemustbe accomplishedinordertoliftthefootenoughforunobstructedgroundclearanceandlimbadvancement[26].Inadditiontoidentifyingthesecriticalfunctionsininitialswing,Dr.Perrypresented theparadoxicalrelationshipbetweenthekneeandanklejointswhileliftingthefoot.Passiveknee extensionisnotonlycriticalforfootclearance,butalsoinordertoe cientlyutilizethecompound 20

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pendulardynamicsofthelegswhoseforwardmomentumwilladvancethelimbinpreparationfor theimpendingfootstrike.Oncethefootislocatedaheadofthehipjointcenter,thependular motionofthelegsegmentsandmomentumfromhipexioncontributestocompletionofswing limbadvancement(e.g.passivekneeextension)[26].Finally,duringthelastfewpercentagesofthe gaitcyclethesegmentsarepreciselyorientedfortheimpendingfootstrikeandsubsequentloading response.Activedorsiexionfromtheanteriortibialispositionstheankleneutrallyforaheelrst initialcontact.Simultaneously,preparationforweightacceptanceisachievedbycontractionofthe hamstringmuscles,whichdeceleratestheshankandcreatesslightexionattheknee(preventing hyperextensionofthejointatfootstrike). Pooranticipatoryplanningandimpairedexecutionofamotorprogramduringswinglimbadvancementisexhibitedinindividualswithneurologicalimpairments,whichalsocontributestoan increasedriskoffalling[16].Anticipatoryplanningandexecutionofamotorplanareessentialfor successfullyachievingswinglimbadvancementandpreparationofthelegsegmentsforheelrstinitialcontact.Bipedalgait,especiallyduringsinglelimbsupport,isconsideredaninherentlyunstable motion.Theabilitytoanticipatetheseoscillationsinstabilityandmakeappropriatecorrections isessentialforthepreventionoffallingandadaptationtoanychangesintaskandenvironmental factors[41].Theanticipationoffootfallandthetimeconstraintofswingperioda ectthetemporalorganizationofthelegsegmentsduringtheexecutionofswinglimbadvancement.Thereis anincreasinginterestinunderstandinganticipatorymotorcontrolbecausethiso ersinsightsinto theelaboratecoordinationstrategiesrequiredinthetaskofswinglimbadvancement.Amethod thatquantiescoordinationdynamics,whicharetheresultingbehaviorofappropriateanticipatory planningandunimpededexecutionofthemotorplan,isessentialforunderstandingthesequential organizationoflegsegments.Themodelofcoordinationdynamicspresentedinthisbodyofwork wasusedtounderstandthedynamicalmechanismsunderlyingthistaskbyidentifyingtheexacttimingduringthegaitcyclewhensegmentsarecontributingtoanaberrantcoordinationbehaviorand specifythesegmentsresponsibleforimpairingadvancementoftheswinginglimb.Themethodology presentedo ersameansforquantifyingthetimingandsequencingofmusclesynergies,providing clinicianswithinsightsintohowthenervoussystemiscontrollingthevariouslimbsegmentsinorder toproducethepurposefulandcoordinatedmovementofswinglimbadvancement.Characterizing thisessentialtaskofgaitwillenhancecurrentinstrumentedgaitanalysismethodsandunderstandingofgaitpatternsa ectedbyneurologicalimpairmentsresultingintheinappropriatetimingand interactionsbetweensegments. 21

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2.2.2ModelingSwingLimbAdvancementasaPendulum Amathematicalmodelofasystemprovidesameansfordescribingthesysteminaquantitative form,fromwhichahypothesisaboutthesystemanditsbehaviorcanbeextensivelytested.A majoraimofmodelinggaitistoidentifyandcharacterizethebehaviorofnormalandpathological gaitthroughtheuseofappropriatecomputationaltools.Thecyclicalmotionofthelegsduring gaitisoftencomparedtothemotionofvarioustypesofpendulums,inparticulartoasingleor doublependulum.Thisanalogyhasbeenacornerstoneforassumptionsusedinsoftwareandhardwaremodelingofhumangait,especiallyintherobotics,passivedynamicwalker,andclinicalgait analysisdisciplines.Surprisingly,therehavebeenonlyasmallnumberofstudiesinvestigatingthe validityofthesependularanalogiesbetweennormalhumangaitandtheoreticalpendulummodels.Furthermorethefewexperimentsinvestigatingtherelationshipbetweenthetheoreticalanalogy andactualhumanmovementhavefocusedprimarilyonthestanceperiodofnormalgaitandonly comparedthisrelationshipusingconventionaldescriptorsofgait(i.e.temporal-spatialmeasures, kinematics,kinetics,andenergetics).Thehumangaitdatafromthisstudywascomparedtoan ideal,optimizedtheoreticalpendulummodelinordertoassessthevalidityofthisanalogyandto determinethecorrespondingidealtheoreticaldynamicsforacompoundpendulum.Thereforethe experimentsandanalysisofAim3usedconventionalmeasuresofgaitandnonlinearmeasuresto describethecoordinationdynamicsofvarioustheoreticalpendulumsoftwaremodelsandcompare thetheoreticalpendulardynamicstothoseofsubjectswithnormalandatypicalgaitpatterns. Forsixdecades,twoprevailingtheoriesofwalkinghavebeenusedtomechanisticallydescribe thistask:Inman'ssixdeterminantsofgait(kinematic)andthependulumanalogy(kinetic).In 1966,Elftmanreportedthatenergyexpenditureisminimizedatcertainwalkingfrequencies42.This experimentalndingwasexpoundeduponbyInman,whopresentedsixkinematicdeterminantsof gaitthatheproposedwereemployedtodecreaseenergyexpenditurebyminimizingtheexcursionof thecenterofgravityinboththeverticalandhorizontaldirections.Thesedeterminantsarebased uponthepremisethatdeviationsinthetrajectoryofthecenterofgravityareenergeticallycostly, whichissupportedbystudiestheorizingoneevolutionaryadvantageforhumanswasbipedalwalking requireslowerenergeticcostthanquadrupedalwalking[43,44,45].Thehypothesisthatbipedal walkingisenergye cientisfurthersupportedbystudiesshowingtheswinginglimbconstitutes themajorenergydemandduringwalking[46,47,48]andthereforenecessitatestheoptimization ofthemechanicalmotioninordertominimizeenergycostsandbeevolutionarilyadvantageous. Thesixdeterminantsare:1)pelvicrotation,2)pelvictilt,3)kneeexioninearlystance,4) 22

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anklemechanisminstance,5)footmechanismleadingintofooto ,and6)lateraldisplacement ofthebody/pelvis30.Thesedeterminantsofgaitweremeanttoprovideaninitialframeworkfor deconstructingthekinematicmotionsobservedinnormalandpathologicalgaitpatternsandbegin toestablishamechanisticapproachtounderstandingfundamentalelementsrequiredforanormal gaitpattern;contrarytothecommonmisconceptionthatthesewereintendedtobetakenliterally [49].Whenviewedretrospectively,itbecomesclearhowInman'sinitialapproachtounderstanding kinematicdescriptorsofgaiteventuallydevelopedintotoday'sgaitcycledivisions,criticaland temporalevents,andtasks,whichareusedtodescribethewalkingpatternofhumans,passive dynamicwalkers,andvariouspendula. Inasimilarmotivationtoprovideatheorythataccountsforhowenergeticcostsduringbipedal walkingaree cientlyminimized,pendulartheorieswereproposed[50,51]andusedtogeneratethe initialmathematicalmodelsforpassivedynamicwalkers[51,52,53],whichsignicantlycontributed tothelogicanddesignofmanyoftoday'slowerextremityrobotics,prosthetics,andexoskeletons. Asillustratedinthegurebelow,twopendularsystemsarelikenedtothemotionofthelegsduring walking:aninvertedpendulum(stanceleg)andacompoundpendulum(swingleg). Figure2.2.2:Motionofthelowerlimbsegmentsprogressingthroughthegaitcycleillustratingthe similarityofaninvertedpendulum(left)andcompoundpendulum(right). UnlikeInman'sapproach,pendularmodelstacklethegoalofreducingenergeticcostsduring walkingfromadynamicsandenergeticsperspective.ProponentsofthependulumtheoryoverInman'sdeterminantsofgaitoftennotestudiesshowingthatwhenpeopleareinstructedtoconsciously reducetheverticaldisplacementoftheircenterofmass,thatmoremetabolicenergyisexpended comparedtowhentheindividualsareinstructedtowalkwiththeirusualgaitpattern[54,55,56]. Whileinvertedpendularmodelsofthestanceleg'smotionmayhavekineticandgravitationalpo23

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tentialenergieswithsimilarcenterofmasstrajectoriesasthatinhumangait,pendulummodel theoryoftheswing(andstance)periodofgaitdonotrequireanyenergyexpenditure.Thisposesa disconnectbetweenpendularanalogiesandtheactualmotionofwalkingbecausenumeroushuman gaitstudieshaveusedelectromyographydatatoprovethereismuscleactivityduringthisperiodof gaitandenergyconsumption[26,57,58].Dynamicwalkingmodelshavebeengeneratedtoenhance thesimplepassivependularmodelsofgaitando erameanstomodeldi erentcontrolstrategies (e.g.muscleactivation),notoriouslydi cultmodelingofthetransitionfromstancetoswing,and focusesonthetypesofworkperformedonthemodelasopposedtotheenergyexpenditure[56]. Whilenoneofthesetheoriesaboutwalkingsatisfactorilymodelstheactualperformanceofthistask byhumans,evensimplemodelscanconstructivelycontributetothestudyofwalking.Forexample, thesimplecompoundpendulummodelofswingperiodlimbdynamicscreatedinthisbodyofwork isjustiedbecausetheintentofthismodelwastodemonstratehowdynamicsystemstheorybased measures,whichisrootedinthependularmotionofalimitcycleoscillator,canbeusedtodescribe andcomparethecoordinationbetweenanytwomovingbodies,whethertheyarelegsegmentsor pendulumlinkages. Mathematicalmodelsarenecessarytoolsforstructuringthecurrentbodyofknowledgeand cantransformexistingtheoriesofmotioncontrolintotestablehypotheses.Ifmodelsandtheory areonehalfofadvancingourunderstandingofgait,thenexperimentationistheothersideof thecoinbecauseitistheprimarymechanismforaddingnewinformationtoanexistingbodyof knowledge.Ifthepurposeofstudyinghumanwalkingwithsimpliedpendularmodelsistohelp advancetheunderstandingthegaitpatternsexpressedbyvariouspopulations,thenitisimportant tokeepthesedi erencesinmindandappreciatewhatchangescanbemadetothemodelthatare alsophysiologicallypossibletoexecuteasapersonwalks.Thisapproachtostudyinggaitwitha pendularmathematicalmodelwasafundamentalconsiderationforthedesignofexperimentsand experimentalmethodologiesforAim3.Specically,thedeningpropertiesandinitialconditionsof thesimplecompoundpendulummathematicalmodelwerecalculatedfromtri-planarmotioncapture dataofhumansubjectswhounderwentaninstrumentedgaitanalysis.Furthermore,thevarious permutationsofthependulummodel'sconstitutivebehaviorwerecomparedtotheinstrumented gaitanalysisdatafromdi erentcohortsofsubjectswithvaryingdegreesintheabilitytoperform swinglimbadvancement. 24

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2.2.3GaitPatternswithImpairedSwingLimbAdvancement Successfulande cientexecutionofswinglegadvancementrequirestheelegantcoordination andcontrolofbodysegments,dynamicbalancecontrol,andintegrationofsensoryandenvironmentalinformation.Sincethistaskrequiresthepreciseorganizationandintricateinteractionofmany structureswithinthebody,itcaneasilybeinhibitedbyanumberofbiomechanicalandneurological impairments.Unsuccessfullyperformingswinglimbadvancementnotonlyhindersaperson'sabilitytoachievecriticalgaitevents,butalsoresultsinsuchine cienciesasdecreasedwalkingspeed, alteredstepwidthandlength,andvariablebalance(e.g.increasedriskoffalling).Inorderfor theproposedmodelofcoordinationdynamicstobeincorporatedintotheinstrumentedgaitanalysismeasurementrepertoire,thesemeasuresmustdemonstratethattheyareusefulforanyform ofbipedalismregardlessoftheseverityorcauseofmovementdisability(Aim4).Therefore,two di erentpopulationswithaberrantswinglimbadvancementwerestudied.First,thegaitpatternof subjectswithcerebralpalsywerestudiedtobecausetheyprovideexamplesofhowneuromuscular impairmentscanleadtoimpairedswinglimbadvancement.Second,thegaitpatternsofsubjects withalowerlimbamputationwerestudiedtheirdi cultywiththetaskofswinglimbadvancementstemsfromtheinabilitytocontroltheirlimbbelowthelevelofamputationduetolossof neuromusculoskeletalelementsasopposedtoaninappropriateexecutionofamovementplan. 2.2.3.1SpasticCerebralPalsy Cerebralpalsyisamovementdisorderresultingfromastatic,non-homogeneousencephalopathythatoccursinthebrainofapretermorterminfant.Approximately3per1000livebirths havecerebralpalsy,makingthisconditionthemostcommonpediatricmovementdisorder[59].Althoughcerebralpalsyisnotaprogressivedisease,asindividualswithcerebralpalsygrowolderthey arereportingpervasivehealthissuesandsecondaryimpairmentssuchasdiminishingindependent ambulation,musculoskeletalpain,chronicfatigue,andsignsofprematureaging[60].Theselifealteringimpairmentscostthenationupwardsof$11billioninmedicalexpenseseachyearandthere isgrowingevidencethatlackofcoordinationbroughtonbyneuromusculardiseaseislinkedtothese impairments.Thissuggeststhereisaprofoundandoftenoverlookedneedforimprovingexisting rehabilitationstrategiesinane orttoreducelong-termhealthproblemsinthispopulation. Thesubjectswithspasticcerebralpalsystudiedinthisdissertationwereclassiedwiththe followingcategories:a)Physiology(e.g.spastic)b)Anatomicallocationoftheinjuryresultingin eitherorunilateral(e.g.hemiplegic)orbilateral(e.g.diplegic)involvementc)Gaitpattern(e.g. 25

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sti knee,crouch)Spastic,ataxic,andathetoid(ordyskinetic)arethethreemainclassicationsof cerebralpalsyandarebaseduponthetypesofmotorimpairmentanda ectedareasofthebrain61. Spasticcerebralpalsy,henceforthreferredinterchangeablywithcerebralpalsy,occursin70%ofall cases,makingitthemostcommontype[62].Thevastmajorityofindividualswithcerebralpalsy haveeitherhemiplegia(22%ofpretermbirths,44%oftermbirths)ordiplegia(66%ofpreterm births,29%oftermbirths),withtheremaininghavingquadriplegia(7%ofpretermbirths,10%of termbirths)[61].Sincethisbodyofworkexaminedthegaitpatternofindividualswitheitherone orbothlegsa ectedbyimpairedselectivemotorcontrol,theclassicationofdiplegiaalsoincludes individualswithquadriplegia. Impairedselectivemotorcontrolisaclassiccharacteristicofspasticcerebralpalsythatisdened asanegativemotorsignduetotheinsu cientcontrolofmuscleactivity.Motorsignsthatleadto anincreaseinthefrequencyormagnitudeofmusclecontractionormovementpatternsaredened aspositivemotorsigns[63].Tremorandhypertoniaareexamplesofpositivemotorsigns.Negative motorsignsarenotoriouslymoredi culttoquantify,especiallysincebothpositiveandnegative motorsignsareoftenpresentinamotordisorderandarethoughttobeconnectedratherthan independent.Forexample,thediplegicgaitpatternofachildwithspasticcerebralpalsymaybe duetotheinabilitytogeneratesu cientvoluntarymuscleforceaboutajoint(positivemotorsign) aswellasaninabilitytoisolatetheactivationofspecicmuscles(negativemotorsign).Reduced selectivemotorcontrolisdenedastheinabilitytoselectivelyactivatespecicmusclesynergiesto generateamovementpattern,whichinthecaseofgaitleadstoanundesirableresponseincertain phasesofthegaitcycle,lackofexibilitytoadapttochangesintaskandenvironmentaldemands, andanoverallaberrantgaitpattern. Variousneuralimagingmodalitieshaveshedfurtherlightontothephysiologicalcharacteristics leadingtothenegativeandpositivemotorsignspresentinindividualswithcerebralpalsy.Brain scansofchildrenwithspasticcerebralpalsyhaverevealedthemostcommonlocationofdamagewas tothecorticospinaltractsintheperiventricularwhitematter[64].Damagetothecorticospinaltracts hindersanindividual'sabilitytocontrolforceproduction,speed,timing,andmovementpatterns, thusresultinginimpairmentofsuchvoluntarymovementsaswalking.Correlationsbetweeninjury tothecorticospinaltractsandmotordisabilityinindividualswithspasticcerebralpalsyhavebeen foundinoverone-thirdofthosewithhemiplegiaandquadriplegia[64,65]. Increasedmuscleexcitationduetospasticityresultinginpathologicalco-contractionofmuscles isahallmarkcharacteristicofcerebralpalsythatcontributetooverallfunctionalmotordecits. Ingait,thesemotordecitsinterferewiththesuccessfulexecutionofamovementpatternandare 26

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particularlyevidentduringthetaskofswinglimbadvancement.Lance(1980)denedspasticity as"...amotordisordercharacterizedbyavelocity-dependentincreaseintonicstretchreexes, withexaggeratedtendonjerksresultingfromhyper-excitabilityofthestretchreex...".When spasticityistheprimaryimpairmentcontributingtoanaberrantgaitpattern,excessiveactivityof aspasticmuscleoccursattimesinthegaitcyclewhenthemuscleisbeinglengthened.Forexample, thequadricepsmusclesarelengthenedinearlystanceduringweightacceptanceandatfooto as thekneeexes.Spasticityintherectusfemorismusclepreventspassivekneeexioninpre-swing andforcestheindividualtoadoptcompensatorymovementsinordertoadvancetheswinglimb. Spasticityinthehamstringmusclesinhibitssu cientkneeextensionduringterminalswingwhich isnecessaryforpreparationofinitialcontactandcorrespondstotheonetimeinthegaitcyclewhen thismuscleislengthened. Althoughtheprimarylesionleadingtospasticityislocatedinthecentralnervoussystem,numerousstudieshavedemonstratedthatthestructureofskeletalmuscleinpatientswithspasticity isdramaticallyalteredandabnormal[10,67].Furthermore,abnormalbonegrowthastheresultof atypicalforcesandloadsgeneratedfrommusclespasticityandtheexaggeratedofthestretchreex contributetothismovementdisorder.Co-contractionofmusclesaboutjoints(e.g.simultaneous exionofthehip,knee,andanklejoints)isalsoassociatedwithspasticgaitpatterns.Leonard etal.(1991)foundthatcomparedtochildrenwithoutcerebralpalsy,childrenwithcerebralpalsy retainedpathologicco-contractionaboutjointsandwereunabletodissociatecertainsynergiesdue tospasticity[68].Secondaryimpairmentsofuppermotorlesions,suchaschangesinskeletalmuscle mechanicalpropertiesandinappropriateactivationofmusclesasaresultofspasticity,illustrate manyfactorscancontributetoanaberrantgaitpatternassociatedwithcerebralpalsyandreveal thecomplexitiesinhowagaitpatternisuniquelya ectedineachindividual.Eventhoughthegait patternofanindividualwithcerebralpalsyisuniqueduetothelocationoftheuppermotorneuronlesion,therearegeneralcharacteristicsandcombinationsofmovementpatternsidentiedwith measuresofinstrumentedgaitanalysisthathavebeencategorizedintopathologicalgaitpatterns. Inparticular,asaconsequenceofspasticity,co-contractures,andaberrantmuscleexcitationtwo ofthemostcommonabnormalgaitpatternsassociatedwithcerebralpalsyoccurintheplaneof progression(sagittal)aboutthekneejoint:sti kneegaitandcrouchgait[69]. Sti Knee Gait Pattern.Asti kneegaitpatterncanbepresentineitherhemiplegicordiplegic patientsandisoneofthemostcommongaitpatternsassociatedwithcerebralpalsy[112].The sti kneegaitpatternisassociatedwithexcessivekneeextensionthroughouttheswingperiodof gait,especiallyduringinitialswingandmid-swingphases.Contractureaboutthekneeiscaused 27

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byaninabilitytoceaseexcitationoftherectusfemorismuscleduringswinglimbadvancement andthereforecausesadelayinboththetiming(after72%ofthegaitcycle)andmagnitudeof maximumkneeexion(lessthan45 ¡ )[69].Inabilitytodissociatethisextensionsynergyatfoot o delaysinitiationoflimbadvancement,interfereswithfootclearance,disruptsthesmoothstance toswingtransitionandresultingcompoundpendularmotionofthesegmentsinswing,andforces theindividualtoadoptine cientcompensatorymovementsusingthecontralateral(stance)limbin ordertoavoidtrippingandachieveforwardmovementoftheswinginglimb[26,70,113]. Crouch Gait Pattern.Acrouchgaitpatterndisplaysexcessivehip,knee,andankleexion throughoutthegaitcycle.Theseexcessivejointanglepositionscanbetheresultofthecontractures, spasticity,leverarmdysfunction,andbonedeformitieseitherindividuallyorinanycombination [32,71,72].Contracturesofthehamstringandiliopsoasmusclesmanifestsasaninabilitytogenerate su cienthipextensionandinadequatekneeextensioninterminalswing.Spasticityinthehamstring musclesresultsinexcessivekneeexionandpreventsthedesiredkneeextensioninpreparationfora heelrstinitialcontact.Inconjunctionwithinsu cienthipextension,excessiveankledorsiexion asaresultofweaktricepssuraemusclesisoftenpresentandcontributestoadecreasedabilityto generatesu cientanklemomentsandpowersatfooto foradvancementoftheswinglimb[69]. Weakquadricepsmusclesarealsooftenpresentinacrouchgaitpatternandasaconsequencefurther contributetoexcessivekneeexionthroughoutthegaitcycle.Thesealteredjointanglepatternsand weaknessofcertainmusclesmanifestinthetemporal-spatialvariablesasdecreasedstridelengthand decreasedwalkingspeed.Acrouchgaitpatterncanbepresentinpatientswitheitherhemiplegia orquadriplegia,butismorecommonlyassociatedwithdiplegia.Dependinguponthelocationofan individual'suppermotorneuronlesion,asti kneegaitpatternmayalsobepresentwithacrouch gaitpattern. 2.2.3.2LowerLimbAmputation In2005,itwasestimatedthat1.6millionAmericanswerelivingwiththelossofalimb,65%of whichhadalowerextremityamputation,andbytheyear2050thistotalpopulationofindividuals withanamputationisexpectedtoreach3.6million[73].AmongtheseAmericanslivingwiththeloss ofalimb,themainreasonsforamputationaredysvasculardisease(54%),trauma(45%),andcancer (lessthan2%)73.Thelargehealthcarecostsassociatedwithalowerlimbamputation,inpartdueto concomitantillnesses[74],secondarydisabilitiesresultingfromamputation(e.g.pain,degenerative arthritis,osteoporosis,re-amputation)[75,76],anddecreasedqualityoflifeandmobility[77,78] rendersthispopulationwithsignicantambulatoryimpairmentsandthusisanidealbeneciary 28

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ofinsightsgainedfrominstrumentedgaitanalysis.Thereareseveralreasonsforanamputation, butsincethepurposeofthisworkistoinvestigatetheneurologicalcontroloftheresiduallimbby anintactandunimpairednervoussystem,onlyacquiredamputationstotreattrauma,congenital limbdeciencies,andmanagementoftumorswereconsidered.Inconjunctionwithaprosthetic's mechanicalqualityandproperties,thelevelofamputationsignicantlycontributestotheoverall alteredgaitpattern.Longitudinallowerlimbdecienciesrefertothereductionorabsenceofabone withinthelongaxisoftheleg,asillustratedinthegurebelow[79]. Figure2.2.3:Diagramoflongitudinallevelsofamputationforthelowerextremity. InresponsetothelargenumberofsurvivingWorldWarIIveteransreturninghomewithlower limbamputations,InmanandEberhartuseinstrumentedgaitanalysistoenhancetheunderstanding ofnormalandlowerlimbamputationgaitpatternsandimproveprosthesisdesignwithknowledge gainedfromtheirstudies[30,80,81].Sincethen,manystudieshaveusedkinematics,kinetics,electromyography,andtemporal-spatialmeasurestoevaluatethefunctionale ectsofvariousprosthetics andlevelofamputationontheindividual'sgaitpattern[78].Ageneralconsensusexiststhatthere aresignicantdi erencesinthegaitofindividualswithanamputationcomparedtohealthyindividualsfreeofgaitpathologyorlimbamputation.Prinsenetal.(2011)performedasystematic reviewofIGAstudiesinvestigatingindividualswithalowerlimbamputationandfoundthatindividualswitheitheratranstibialortransfemoralamputationusedsimilarcompensatorystrategies atthehiptocompensateforinsu cientpowergenerationattheankleduringfooto andforlimb advancementinswing[82].Also,thetiminganddurationofcriticalgaiteventshasbeenfoundin numerousstudiestobedelayedandsignicantlyelongatedwhencomparedtonormalgait[78].Since 29

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amajorgoalofprostheticinterventionistoprovidethepatientwiththemoste cientgaitpossible andemulateanunimpairedgaitpatternascloselyaspossible,theuseofinstrumentedgaitanalysis measurestoidentifyasymmetriesanddeviationshasprovidedvaluableinsightsandquantitative dataforimprovingrehabilitationprogramsandinformingprostheticdesign. Afteranamputation,thelocomotorsystemischallengedtorelearnthetaskofwalkingwithout thea erentsensorymotorinputbelowthelevelofamputationandadapttothealteredmechanicalpropertiesoftheprosthetic.Duringtheinitialphaseofrehabilitation,theindividualwithan amputationcompensatesfortheneuromusculoskeletalchangesbyadoptingvariousgaitcompensationsthatplaceagreatrelianceupontheintactlimb.Tofacilitatelimbclearanceandadvancement duringswingperiod,theprostheticlegistypicallymadeslightlyshorterthanthenon-amputated leg.Inconjunctionwithanincreaseintimespentontheintactlimbandshiftofloadbearing responsibilityincreasingontheintactlimb[80],thisintentionalleglengthdiscrepancymayalso contributetoincreasedforcesontheintactlimbandexplaintheprevalenceofosteoarthrosisthat occursinthenon-amputatedlimb[75].Ingeneralindividualswithalowerlimbamputationspend moretimeinstanceontheintactlimb[83,84,85],loadtheintactlimbmorewhiledecreasingloads ontheprostheticlimb[85,86,87],andhavehigherforcesontheintactlimbwhichcombinedhave beenshowntoleadtoincreaseddegenerativejointdisease,pain,anddecreasedmobility[75,88,89]. Numerousstudieshavereportedthemetabolicenergycostduringwalkingforanindividualwith anamputationissignicantlygreaterthanenergyexpenditureofhealthyindividualswithoutan amputation[58,90,91,92,93].Althoughmetabolicenergyexpenditureishighlydependentuponan individual'sphysicalcondition,thegeneraltrendofanincreasedmetaboliccostofwalkinghasbeen showntosignicantlyincreasewithhigherlevelsofamputationandforbilateralamputations[58]. Changesinwalkingspeedhasbeencorrelatedtoincreasinglevelsofamputationandistherefore commonlyusedtodescribeanindividual'soverallabilitytoe cientlyperformthetaskofgait[82]. Unlikemetaboliccost,walkingspeediseasilycalculatedfromthreedimensionalsegmenttrajectories, whicharecapturedandusedtodescribeotherconventionalinstrumentedgaitanalysismeasures, anddoesnotrequireadditionalequipment.Walkingspeedandasymmetriesintemporal-spatialand kinematicvariableshavebecomethestandardmeansusedtoassessthegaitpatternofanindividual withanamputation,especiallyingaitrehabilitation[94]. ThemajorityofstudiesexaminingthegaitofindividualswithaLLAassumethelegactslike apassivecompoundpendulum.Evenstudiesinvestigatingmechanicallypassiveandelectronically controlledprostheticsfocustheirinvestigationonthetaskofweightacceptanceandswinginitiation (e.g.pre-swing).ThemajorityofprostheticsusedbyindividualswithaLLAarepassive,mechanical 30

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devicesthattrytoemulateanormalgaitpattern.Improvementsinmaterialqualityandinsightsfrom IGAhavehelpedtoadvanceandrenethedesignsofsuchmechanicalmechanisms,howeverbecause theyarepassivethesedevicesarestillunabletocompletelyaccountforsmoothweightacceptance, adequatepowergenerationforfooto ,andadapttodi erentwalkingconditions(e.g.speed).To addressthee ectsoflostneurologicalcontrolofajointbeloworatthelevelofamputationand provideagaitpatternmoreanalogoustothatofanindividualfreeofgaitpathology,electronically controlledprostheticsweredesigned.Forexample,themicroprocessoroftheC-Leg ¨ isableto identifytheinitiationofswingphaseandminimizekneeresistancesinordertoassistintheinitiation ofswingphasekneeexionforindividualswithatransfemoralamputation[95].Activecontrolof thisprosthetic'sotherwisepassivependularmotionhasbeenshowntoshiftkinematiccurvesand temporal-spatialmeasuresclosertowardnormalkinematiccurvesofnon-amputatedlegs[35,78]. However,severalgaitabnormalitiespersistedwithbothelectronicallycontrolledandmechanically passivedeviceswithaxedankleangleduringswing[84].Measuresofcoordinationdynamicsmay revealadditionalinsightsintoapatient'scontrolofthea ectedlimbthatcouldbeusedtoprovide real-timeadjustmentstotheelectronicalgorithmscontrollingtheprostheticjointsoastomore closelyemulateanormalgaitpattern. Limbamputationleadstomajorchangeinbiomechanicalandneurophysiologicalrelationships thatalsoinuencethephysiologicalqualityoftheresiduallimbandcontributetotheindividual's overallwalkingability.Severalresearchstudieshavefoundthatamajorreorganizationofboth a erentande erentprojectionsoccursinsuchpatientsandthatthisneurologicalreorganization contributestothechangesinmotorpatternsseeninpersonswithlowerlimbamputations[96]. Thesetheoreticalmodelssuggestthemotorcontrolsystemcanre-organizeafterthereductionor removalofbiomechanicalconstraintsandresultinachangeincoordination.Compensationfor lossofproprioceptivecues,whichnormallyhelpsignaltheinitiationandterminalofcertaingait events,andalteredinertialpropertiescanbeachievedinindividualswithaLLAwhoarefreeof neuromuscularpathology.Describingmovementatthelevelofcoordinationinthispopulationhas thepotentialtoenhancethee cacyofapatient'srehabilitationbyprovidinginsightsintohowthe nervoussystemisadaptingtoandcontrollingthealteredbiomechanicalpropertiesoftheresidual limbandprosthetic.Thereforeitwasanticipatedthatsubjectswithalowerlimbamputation wouldadoptdistinctlydi erentcoordinationpatterns,dependinguponthelevelofamputation, thantheothertwopopulationsstudiedandthatthesealternativeSLAstrategiesarebedetectable withthecoordinationdynamicsmeasuresutilizedinthisinvestigation.Asthelevelofamputation increases,thesemeasuresofcoordinationdynamicswerealsoexpectedtofollowsimilartrendsas 31

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theconventionalmeasuresofgaitandshowgreaterdeviationsfromanunimpairedgaitpattern. Individualswithalowerlimbamputationandanunimpairednervoussystemconstitutethethird populationstudiedinthisbodyofwork.Similartoindividualswithcerebralpalsy,individualswith alowerlimbamputationhaveanaberrantswinglegmotionandalteredswinglimbadvancement. However,unliketheaberrantneurologicalcontrolcharacteristicofindividualswithcerebralpalsy, swinglimbadvancementisalteredinanindividualwithalowerlimbamputationduetotheinabilitytocontroljointsatorbelowthelevelofamputationasaresultofthephysicalremovalof essentiallocomotorsystemelements.Gaitrehabilitationstrivestowardhelpingthepatientachieve asymmetricalgaitpatternbyfocusesonreducingcoordinationimpairments.Conventionalinstrumentedgaitanalysismeasures(e.g.temporal-spatial,kinematic)areoftenusedtohelpidentify asymmetriesandtrackchangesduringandaftertherapeuticinterventions.However,sinceanamputatedleghasinherentlydi erentfunctionalabilities(e.g.insu cientanklepowergenerationat footo )andhasdi erentphysiologicalcapabilitiescomparedtotheintactlimb(e.g.lossofankle plantarexormuscles)thenitseemsunfairtoholdthesetwolimbs(intactandamputated)tothe samefunctionalperformancecriteria.Perhapsbyincludingmeasuresofcoordinationdynamics, insightsintotherelationshipsbetweenthecontrolstrategiesoftheintactandamputatedlimbs canhelprehabilitationinterventions(e.g.behaviorofmusclesynergiesatspecicinstancesingait cycle)byfacilitating/enablingmaximumpossibleadaptabilityofeachlimb.Whenconsideringa person'sabilitytore-organizecoordinationstrategiesandthebiomechanicaldesignofaprosthesis, itbecomesclearthesuccessofapatient'srehabilitation,idealprostheticbehavior,andadoptionof optimizedcoordinationpatternsnecessitatesameasureforcoordinationdynamics.Therefore,the gaitpatternsofindividualswithalowerlimbamputationwerestudiedandhavebeenclassiedinto twogeneralcategories:transtibial(belowknee)andtransfemoral(aboveknee). Transtibial Amputation Gait Pattern.Transtibialamputationsarethemostcommonlowerextremityamputationsandaccountfor55%ofallindividualswithlossofalowerlimb[97].Thegait taskofweightacceptanceandpre-swingperiodlimbadvancementaresignicantlyimpactedbythe lossoftheanklejointandfoot.Thegastrocnemius-soleuscomplexisthemajormusclegroupresponsibleforgeneratingtheplantarexionmomentatfooto andcombinedwiththehipexorsprovides theballisticpowertopropeltheswinginglimbforward.However,forindividualswithatranstibial amputationthehipexorsbecomethedominantmotortoprovidesu cientpowergenerationfor swinglimbadvancement.SeveralIGAstudieshavebeenconductedtocharacterizethegaitpattern associatedwithatranstibialamputation,manyofwhichhavereportedthefollowingcharacteristics: decreasedwalkingspeedcomparedtounimpairedgait[78,90],kneeexioncontracturesgreaterthan 32

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10 ¡ [98],delayedandinsu cientpeakkneeexion[37,78],increasedenergyexpenditure[90],persistentankledorsiexionduetoprostheticanklejoint'sinabilitytoplantarex[90],andacorrelation betweendecreasedwalkingspeedandreducedmusclestrength[100].Aclassicexampleofearly stancedeviationsinsubjectswithatranstibialamputationisareducedanddelayedkneeexion curvewithprolongedheelsupportanddelayedforefootcontact.Ensuringappropriatekneeexion inanindividualwithatranstibialamputationisnotoriouslyoneofthemostchallengingaspectsof thedynamicalignmentprocess.Electromyographyactivationpatternsofsubjectswithatranstibial amputationwereobservedtobedi erentthanthoseinsubjectswithanintactlimb[101],suggesting anexplanationtotheunderlyingcauseofanattenuatedanddelayedstancepeakkneeexionliesin thesubject'smotorcontrolstrategiesorcoordination.Whenalowerlimbamputationremovesthe gastrocnemius-soleusmusclecomplex,thehipexormusclesnotonlybecomethesourceofswing limbadvancementbutalsoplaceanincreaseinenergyexpenditure[78,90].Presently,themajority ofe ortstoreduceenergycostofprostheticgaithavefocusedonimprovingstanceperiodevents andpowergenerationatfooto [78].Itisproposedthate ortstoimproveswinglimbadvancement mechanics,whichareaprecursortoinitialcontactandweightacceptance,maycontributetoimprovingtheorientationofsegments/prostheticatinitialcontactandthetaskofweightacceptance. Insightsintolimb-prostheticcompensatorycoordinationdynamicsoftheamputatedlimbduring swinglimbadvancementmayhelpelucidatemotorcontrolstrategiesadoptedbyanindividualwith aLLAthatcouldhelpassistinrehabilitationtechniquesandelectronicallycontrolledprosthetics. Transfemoral Amputation Gait Pattern.Inadditiontolosingneurologicalcontrolattheankle, atransfemoralamputationremovesneurologicalcontrolatthekneeaswellleavingthehipasthe lowestintactjointtocontrolthedistalprostheticlinkages.Theincreaseddemandonthehipmuscles, limitationsofprostheticfeet,andrelianceoncompensatorymovementsintheintactlimb,trunk, andpelvismakeswalkingwithatransfemoralamputationevenmorechallengingthanwalkingwith atranstibialamputation.Aspreviouslymentioned,walkingspeedhasbeenshowntobeagood indicatorofwalkingabilityandthushasbeenshowntohavegoodcorrelationswithgaitdisability [26,58,90,102].Therefore,itisperhapsofnogreatsurprisethatindividualswithatransfemoral amputationhavebeenreportedtohaveaslowerwalkingspeed,slowercadence,andshorterstride lengthcomparedtoindividualsfreeofgaitimpairmentandindividualswithatranstibialamputation [78].Whateverweightacceptancepeakremainedinthesagittalkneekinematiccurveofanindividual withatranstibialamputation,isnownoneexistentinthekneekinematiccurveofanindividualwith atransfemoralamputationbecausekneeexioninstanceisusedtoavoidcollapsingoftheprosthetic limb.Thesagittalhipkinematiccurveofanindividualwithatransfemoralamputationlosesthe 33

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smooth,roundedtransitionsbetweendi erenttasksinthegaitcycleandbecomesmoreabrupt, thuscausingthisgaitdescriptortobesignicantlydi erentfromthatofanindividualwithout anamputation.Adecreasedamountoftheamputatedlimb'shiprangeofmotioncomparedtothe ipsilateralintactlimbhasalsobeenreported[78].Comparedtoanindividualwithoutanamputation andlowerlevelsofanamputation,increasedmuscleactivitymagnitudeanddurationintheresidual limb,increasedandasymmetrictri-planardisplacementofthetrunkandpelvis,andincreasedenergy expenditureareseeninindividualswithatransfemoralamputation[78]. 2.2.4ConventionalMeasuresofInstrumentedGaitAnalysis Conventionalmeasuresderivedfrominstrumentedgaitanalysisdatatypicallydescribetheorientationofjoints,timingofmuscleexcitation,groundreactionforcesproducedatjointsbycontractions ofskeletalmuscles,andoverallgaitperformanceinregardstothedurationofwalkinganddistance covered.Abriefoverviewoftheconventionalmeasurescalculatedinthisbodyofworkfollows. 2.2.4.1Temporal-SpatialVariables Temporallynormalizingthegaitcycle(GC)allowsforintra-subjectandinter-subjectcomparison ofgaitcycles.UsingPerry'sdivisionsofthegaitcycle,thedurationofperiods,phases,tasks,and instancesofsingleanddoublelimbsupportareexamplesoftemporaldescriptorsofagaitcycle. Asymmetriesinoneorbothsidesofanindividual'sgaitpatterncanbedetectedbyunequaldurations ofthesegaitcycledivisions.Sincethegaitcycleistemporallynormalized,thedivisionsofthegait cycle(e.g.periods,tasks,phases,etc.)canbemappedontoaunitcircle,makingtheseasymmetries easilydetectable,asshowninthefollowinggure[114]. 34

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Figure2.2.4:Divisionsofthegaitcycledepictedonaunitcircle,readclockwise,foractitious subject'sleft(red)andright(green)gaitcycleswithreferencetoanormativecontrol(grey)using thevaluesdisplayedinFigure2.2.1. Typically,onegaitcycleisdenedasthetimeintervalbetweentwosuccessivefootstrikesof thesameleg.Thedistancetraversedbythatlegcanbeusedtocalculatespatialdescriptors.Step length,stridelength,andbaseofsupportarevariablesusedtodescribethespatialrelationshipsof theplacementofthefeetonthewalkingsurfaceandaredepictedinthefollowinggure[40]. Figure2.2.5:Isometricviewdepictingvariablesusedtodescribespatialrelationshipsbetweenthe feet(typicallyusingthecentroidlocationoftheheelmarker)andtheirplacementontheground (greyrectangles).A=rightsteplength,B=rightstridelength,C=leftsteplength. 35

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Walkingspeedisdenedasthetimerequiredtotravelacertaindistance,oftenmeasuredas therstfootstrikeandlastfootstrikeinatrial,andisthereforeatemporalandspatialdescriptor commonlyusedasanoverallgaitperformancemeasure[40].Stridewidth,alsoknownaswalking baseandbaseofsupport,isoftenusedasadescriptorofanindividual'sdynamicbalanceand coordination.Balance(e.g.posturalcontrol)iscommonlydenedastheabilitytomaintainthe body'sprojectedcenterofmass(e.g.centerofgravity)withinthebaseofsupport[16].However, whenwalkingthebodycontinuallyoscillatesbetweenstatesofbalance(doublelimbsupport)and imbalanceastheforwardprogressionofbodysegmentscausethecenterofmasstofalloutsideof thebaseofsupport.Advancementoftheswinginglimbandsu cientforwardandlateralplacement ofthefootwithrespecttothecenterofmasspreventsfallingandallowsforthesystemtoregain stability.Increasewideningandvariabilityofthebaseofsupporthavebeenassociatedwithvarious neuromusculardisorders[16].Additionally,tandemwalkingorheel-to-toewalkingisacommon variationofgaitthatisdi culttoperformwhenanindividualhaspoorbalanceand/orimpaired coordination.Decreasesinspatialmeasuressuchassteplengthandstridelength,whichcharacterize theforwardprogressionduringagaitcycle,canbeattributedtospasticity(cerebralpalsy)and adoptionofcompensatorymotionstoaccountforbiomechanicallimitationsinthecontralateral limb(lowerlimbamputation). 2.2.4.2Kinematics Threedimensionaltrackingofmotioncapturemarkersplacedonspecicanatomicallocationsof segmentscanbeusedtoconstructananatomicalcoordinatesystemforthesegmentbeingtracked. Theseanatomicalcoordinatesystemscanthenbeexpressedwithrespecttoeachotherandthemotioncaptureenvironment'sglobalcoordinatesystem.Kinematiccurvesarecreatedfromaparentchildsegmentrelationship,inwhichthechildsegment'scoordinatesystemisexpressedwithrespect totheparentsegment'slocalcoordinatesystem.Kinematiccurvesaregeneratedbytransforming onesegment'scoordinatesystemintoanotherandcalculatedfromtheangleformedbetweentwo axesofthesecoordinatesystems.Forexample,thekneeexion/extensionkinematiccurveisthe angleformedinthesagittalplanebetweentheshank'slongaxisandthethigh'slongaxis.Kinematiccurvesaretypicallybaseduponaskeletalhierarchy(distalsegmentwithrespecttoadjacent, ipsilateralproximalsegment)andprovideameansfordescribingchangesinjointanglesthroughout agaitcycle.Themagnitudeandtimingofkinematiccurvefeatures,suchasextrema,areoftenused tocharacterizehowanindividual'sgaitpatterndivergesfromanormalreference.Additionally,deviationsfromthenormalrangeofkinematiccurvescanbeindicativeofgaitpathology(e.g.cerebral 36

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palsy)andfunctionallimitationscausinganaberrantgaitpattern(e.g.lowerlimbamputation). Inane orttoprovideclinicianswithamultivariatethatcouldbeusedtodescribeanindividual's overallgaitpathology,agaitdeviationindex(GDI)wascreatedhelpconsolidatethevastamount ofmultidimensionaldatafromaninstrumentedgaitanalysis[103].TheGDIisconstructedfrom nineofthetwelvekinematiccurvesusingtechniquesofprinciplecomponentanalysis.Application oftheGDIiscontinuingtogrowininstrumentedgaitanalysisasameasureofhowcloseasubject's jointanglesaretoanormativereference.Byscalingthekinematicdi erencesbetweenalarge normativereference,aGDIscorecanbecalculatedforanindividualandthusprovideameansfor quantifyingandstratifyingtheseveritygaitpathologyandcomparisonofmultiplegaitpatterns causedbydi erentpathologies.AnotherbenetoftheGDIcalculationmethodologyisthatitcan beconstructedfromvariableswithdi erentunits.Onedisadvantagetothisparticulartechnique isthatthefeatureanalysisstepsusedtoconstructthenormativereferencefeaturesmustoriginate fromalargedatasetofnormativegaitdata.Ifthismethodistoreliablycalculatedandconstructed fromdi erentgaitmeasures(e.g.kinetics)orformovementtasks(e.g.running)thensimilarlylarge referencedatasetarerequired. 2.2.5ConventionalMeasuresofCoordination Dependinguponthecontext,coordinationcanhaveseveraldi erentdenitionsandiscomprised ofnumerouselementssuchasinformationprocessing,balance,selectivemotorcontrol,postural control,musclesynergies,attention,andmemory.Presently,agoldstandardforquantifyingcoordinationduringthetaskofgaitdoesnotexistbecausecoordinationisaninherentlyabstractconcept thatcannotbedirectlymeasuredlikestrengthorenduranceandisacomplexsensorimotorprocess involvingseveralsystems.Severaloftheconventionalmeasuresofcoordinationthatarerelevantto thisbodyofworkarepresentedbelow. 2.2.5.1PerformanceMeasures Clinicalperformancemeasureso erinsightsintospecicaspectsofcoordinationwhileperforming isolatedmotionsortasks.Numerousfunctionalscaleshavebeencreatedtoprovideastandardized meansofdetectingandscoringthepresenceandseverityofaberrantcoordinationandareused invariousclinicalassessments.Thefollowingperformancemeasureswereusedtocharacterizethe di erentsubjectpopulationsstudiedandspecicallyaddressthehypothesesofAim2. Assessment of Selective Motor Control.Aspreviouslydiscussed,impairedselectivemotorcontrol contributingtofunctionalmotordecitsischaracteristicofthegaitpatternofindividualswith 37

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spasticcerebralpalsy.Fowleretal.(2009)createdandvalidatedaclinicalmethodforassessing selectivevoluntarymotorcontrolofspecicmotionsofthehip,knee,ankle,subtalar,andtoe joints[104].Theassessmentratestheindividual'sabilitytomoveeachjointindependentlyat thesamespeedanddirectionsasthecorrespondingdemonstratedmotion.Theassessmentalso accountsforinvoluntarymovementsareotherjointswhileperformingtheisolatedselectivevoluntary movement.Withtheexceptionofhipexion,allofthetasksareperformedwhiletheindividualis seated.Thisassessmenthasbeenvalidatedforindividualswithcerebralpalsyandfoundtocorrelate withinter-jointmeasuresofcoordinationduringgaitthatweregeneratedfromphaseportraitsand continuousrelativephasediagramsbasedinalocalcoordinatesystem[105].Whilethepresence ofadditionalimpairmentsa ectingfunctionalmobilitysuchasbalance,spasticity,weakness,and skeletaldeformitymayalsocontributetoaperson'sSCALEscore,thisclinicalperformancemeasure waschosenforcharacterizingselectivevoluntarymotorcontrolbecauseoftheassessment'ssimplicity, shortadministrationtime,andminimalrequiredtraining.Lastly,thisparticularsetofselected voluntarylowerextremitytasksisperhapsthebestsetofperformancemeasuresthatrelatestothe coordinationconstructinthetaskofgait.Therefore,comparisonsofprospectivesubject'sSCALE scoresandtheircoordinationdynamicswhilewalkingareexpectedtoreectsimilartrendsinmotor controldecitsrelatingtoimpairedselectivemotorcontrol.Thissetofperformancemeasureswere usedtocharacterizethedegreeofselectivemotorcontrolimpairmentsintheprospectivesubjects (Aim2,Hypothesis2B). Assessment of Cerebellar Inuence in Gait.TheInternationalCooperativeAtaxiaRatingScale (ICARS)andScalefortheAssessmentandRatingofAtaxia(SARA)aresemi-quantitativeassessmentsforvariousactivitiesofdailyliving,gait,posture,speech,andoculomotorskillsthatcanall beimpairedinpatientswithcerebellardisease[106,107].Thesestandardizedclinicalratingsystems wereoriginallydesignedtoprovideastandardizedratingsystemforcerebellardisease.Although thesetwoassessmentshavepredominantlybeenappliedtosubjectswithspinocerebellardisease (e.g.ataxia),Tisonetal.(2002)studiedtheICARSassessmentforvaryinglevelsofseverityof cerebellarsignsinpatientswithmultiplesystematrophyandparkinson'sdisease,whichareboth neurodegenerativediseases[108].Althoughneitherofthetwoatypicalgaitpopulationsinthisstudy haveaneurodegenerativedisease,thelowerextremitytasksfromtheICARSandSARAassessments o erameansofcharacterizingthecoordinationofanindividualwhileperformingthesegaitrelated andlowerextremitytasks.Eventhoughneitherofthesetwopopulations(e.g.cerebralpalsy,lower limbamputation)havecerebellardegeneration,theydohaveanalteredabilitytosmoothlyand e ectivelyperformvoluntarymovement.Theseassessmentsofoverallcoordinationcantherefore 38

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beusedasareferenceforassessingoverallgaitperformanceabilityando eranothermeansfor characterizingcoordination.Therefore,motioncapturedataofprospectivesubjectsinthisstudy wascollectedduringthefollowingICARS/SARAbasedtasks:over-groundwalkingataself-selected speed,tandemwakingataself-selectedspeed,andwalkingataself-selectedspeedwith90 ¡ turnsto theleftandright.Additionally,eachsubject'sabilitytoperformthevoluntarymovementofsliding theheeldowntheopposinglimb'sshininasstraightofalineaspossiblewasrecordedwithhigh denitionvideo.Inane orttoprovidegreaterdelitytothesemeasures,additionalquantitative measureswerecalculatedfromthemotioncapturedataasthesubjectsperformedthesewalking tasksandareprovidedindetailwiththestudy'sothermethodsinChapter4. Speed-Accuracy Tradeo .FromtheBernsteinperspective,thecentralnervoussystem'sorganizationofindividualvariablesintoalargergroup(e.g.synergy)duringamovementdecreases thedegreesoffreedominthesystemandallowsforsimplercontrolstrategies,whichinthecase ofbipedalgaitresultincomplexoscillatorypatterns[1,2,4,5].Aresultantmotorbehavioristhe culminationoffactorsfromenvironment,taskconstraints,andindividual'sabilitytoprocessthis informationandthenexecutethemotorplanwithconsiderationtoalltheseelements[109].The abilitytoidentifyinternalandexternalstimulirelevanttoexecutionofthemotorplan,selection oftheappropriateresponse,andpreparefortheexecutingofthemodiedthemotorprogramare themainstepsofinformationprocessing[110].Informationprocessingisoneaspectofcoordinated movementbecauseitcontributestohowanindividualplansandcontrolsforamovement,especially inresponsetochangesinoneormoreoftheenvironmental,task,orpersonalconstraints.In1954, Fittsperformedaseriesofupperextremityexperimentsthatexempliestheinuenceofinformationprocessinginamotionbysystematicallychangingonetaskconstraintatatime,elucidating thesubject'sdecisionmakingprocessandresultingrelationshipbetweenspeedandaccuracy[111]. Consideringthemovementlimitations(e.g.endurance,strength,etc.)ofthisstudy'ssubjectswith gaitpathology,itwasnotfeasibletoperformafulllowerextremityreplicationofthenumerous variationsanditerationsinFitts'originalexperiments.Therefore,avariationofFitts'experiment wasdesignedtoexploretherelationshipbetweenthemeasuresofcoordinationdynamicsandtheaccuracyofmovingtheleginarepetitive,reciprocalmimickingthemotionofswinglimbadvancement ingaitduringaxedtime.Additionally,thecomparisonsbetweenanindividual'sselectedspeed ofthelimbduringthistaskandtheswingperiodofgaitwerealsocompared.Whilethea ectsof informationprocessingduringgaitarenotthefocusofthiswork,thisexperimentforprospective subjectsprovidesanothermeansforcharacterizingtheimpairmentsinthespeedandaccuracyof voluntaryreciprocalmovements(Aim2,Hypothesis2A). 39

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2.3InvestigationsPriortoPre-doctoralWork Priortothecommencementofandintandemwiththispre-doctoralwork,thefollowingthree investigationsintotheutilityandclinicalsignicanceofthesecoordinationdynamicsmeasureswere conducted.Alloftheseinvestigationssupporttheoverallsignicanceofthedissertationwork, especiallyinregardstoAims1and4. Thesepreviousinvestigationsprovidedtheopportunitytorenethemethodologyforcalculating thesemeasuresofcoordinationdynamics,applythesemeasurestodi erentpathologicalgaitpatterns,anddemonstratebenetsforincorporatingthesemeasuresintotheinstrumentedgaitanalysis repertoire.Additionally,ndingsfromthesepriorinvestigationsprovidesu cientevidencetojustify thispre-doctoralinvestigationintothevalueandabilityofthesenonlinearmeasurestodescribethe coordinationdynamicsemployedindi erentgaitpatternsandthemotionofswinglimbadvancementthroughmathematicalandphysicalexperiments.Thenextchapterdiscussestherationalefor whythedynamicsystemstheoryperspectiveisideallysuitedforcharacterizingthecoordination dynamicsinthecyclicaltaskofgait,especiallyinregardstoswinglimbadvancement.Anexplanationofthetwodynamicsystemstheorybasedmeasuresthatwereusedtoquantifycoordination dynamicsofbothretrospectiveandprospectivesubjectsduringswinglimbadvancement(Aims1,2, 4)andthependularmotionofthemathematicalmodelofadoublecompoundpendulumdeveloped (Aim3).Ajusticationandrationaleforimplementingthesenonlinearmeasuresisprovidedand comparedtoothermeasuresofcoordinationderivedfrominstrumentedgaitanalysisdata. Changes in Coordination and Functional Outcomes After Rectus Femoris Transfer Procedure in Children with Spastic Cerebral Palsy.Thepurposeofthisongoingretrospectivestudyistodetermine iffunctionalgaitoutcomesaftertherectusfemoristransferprocedureareassociatedwithimprovementsininter-segmentalcoordinationinchildrenwithspasticcerebralpalsy.Preliminaryndings fromthisstudyhaverevealedtherearesignicantchangesininter-segmentalcoordinationforthese childrenandre-organizationofmotorcontrolstrategiesaftertheremovalofthebiomechanicalconstraint(e.g.inappropriateringoftherectusfemorismuscle).Findingsfromthisinvestigationwere reportedinapodiumpresentationandconferencepaperatthe2010jointconferencefortheGait andClinicalMovementAnalysisSociety(GCMAS)andEuropeanSocietyforMovementAnalysis inAdultsandChildren(ESMAC.Postersandconferencepapersofreferencesubjectndingswere presentedattheGCMAS2011conferenceandthe2013ColemanInstituteConferenceforCognitive Disabilities. Use of Nonlinear and Conventional Gait Analysis Methods to Model Gait Abnormalities Associated 40

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with Spastic Cerebral Palsy.Thepurposeofthisretrospectivestudywastodetermineifintersegmentalcoordinationmeasuresaboutthekneejointaresignicantlycorrelatedtoconventional gaitperformancemeasuresandifthesecoordinationmeasurescanbeusedtohelpdetermineifa subjecthasoneofthefourgaitabnormalitiesconsideredinthisstudy.Thefourpathologicalgait patternsexaminedinthisstudywere1)sti knee,2)crouch,3)recurvatum,and4)jumpknee. Ourresultsindicatedinter-segmentalcoordinationmeasuresaresignicantlycorrelatedtoconventionalgaitmeasuresandprovidespecicanduniquemovementpatternsthatarecharacteristicof movementabnormalitiesassociatedwiththefourpathologicalkneecenteredgaitpatterns.Additionally,novelinsightsintothecoordinationdynamicsofwalkingwithoneoftheabnormalgait patternsweregainedfromusingnonlinearmeasures.Theseinsightsarenotrevealedwithconventionalinstrumentedgaitanalysismeasures.Findingsfromthisinvestigationweredisseminatedas apodiumpresentationattheNorthAmericanSocietyforthePsychologyofSportandPhysical Activity(NASPSPA)2010conferenceandpublishedasaconferencepaperinthe2010Journalof SportandExercisePsychology. Inter-segmental Coordination and Ankle-Foot Orthoses during Gait in Children with Spastic Cerebral Palsy.Thepurposesofthison-goingretrospectivedescriptivestudyareto:1)characterizethelowerextremityinter-segmentalcoordinationduringover-groundwalkingofchildrenwith spasticcerebralpalsywhoexhibitanequinusgaitpattern;2)examinechangesininter-segmental coordinationassociatedwithuseofanankle-footorthosis;and3)examinerelationshipsbetween changesininter-segmentalcoordinationandchangesinselectkinematicandfunctionalgaitparametersassociatedwiththeuseofanankle-footorthosis.Theinitialndingsfromthisstudysupport thehypothesisthatbyprovidinganinterventionatdistalsegments,coordinationdynamicsareimprovedformoreproximalsegmentsthatarenotdirectlyimpactedbytheinterventionandtherefore, demonstratesthisintervention(e.g.ankle-footorthosis)a ectsasubject'scoordinationdynamics. Thesepreviousinvestigationsprovidedtheopportunitytorenethemethodologyforcalculating thesemeasuresofcoordinationdynamics,appliedthesemeasuresofcoordinationtodi erentpathologicalgaitpatterns,anddemonstratedsomeofthebenetsforincorporatingthesemeasuresinto theinstrumentedgaitanalysisrepertoire.Additionally,ndingsfromthesepreviousinvestigations providesu cientevidencetojustifythispre-doctoralinvestigationintothevalueandabilityofthese nonlinearmeasurestodescribethecoordinationdynamicsemployedindi erentgaitpatternsand themotionofswinglimbadvancementthroughmathematicalandphysicalexperiments.Thenext chapterdiscussestherationaleforwhythedynamicsystemstheoryperspectiveisideallysuitedfor characterizingthecoordinationdynamicsofthelegsegmentsduringthecyclicalofwalking,espe41

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ciallyinregardstothegaittaskofswinglimbadvancement.Anexplanationofthetwodynamic systemstheorybasedmeasuresthatwereusedtoquantifycoordinationdynamicsofthisinvestigation'sprospectiveandretrospectivesubjectsduringswinglimbadvancement(Aims1,2,4)and thependularmotionofthemathematicalmodelofacompoundpendulumdeveloped(Aim3).A justicationandrationaleforimplementingthesenonlinearmeasuresisprovidedandcomparedto othermeasuresofcoordinationderivedfrominstrumentedgaitanalysisdata. 42

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3AModelfortheCoordinationDynamicsofWalking Thischapterbeginswithabriefoverviewofdynamicsystemstheoryandhowcoordinationdynamicsofwalkingcanbequantiedbytwononlinearmeasuresderivedfromthiseldofmathematics. Furtherdiscussionofthesecoordinationmeasuresandtheirspecicapplicationtogaitdetailshow theycomplementconventionalgaitanalysismethodsbyprovidingcoordinationdynamicsinsights thatarenotascertainedfromtraditionalinstrumentedgaitanalysismeasures.Areviewofalternativemodelsandmeasuresofcoordinationdynamics,alsoderivedfrominstrumentedgaitanalysis data,ispresented.Lastly,assumptionsandlimitationsfortheproposedmodelofcoordination dynamicsandarationaleforthechosenmethodologyisdiscussed. 3.1DynamicSystemsTheoryApproachtoCoordination Dynamicssystemstheoryisaeldofmathematicsthatmodelsthebehaviorofasystemthroughoutthecourseoftime[4,5,7].Adynamicalsystemisacomplexsystemcomprisedofmanyconstitutiveelementsdenedbyasetofvariables,who'sphysicalbehavior(e.g.state)canbedescribed withmathematicsasitchangesstate(e.g.behavior)intime.Analyticalmethodsderivedfromdynamicalsystemstheoryprovidestoolsthatcanbeusedtoanalyzemovementpatternsthatemerge fromasystem'sself-organization.AsChapter2discussed,humanmovementisanetworkofcodependentsubsystemsworkingtogethertowardafunctionaloutcome.Thesesynergisticorganization ofamovementpatternisbaseduponmanyfactors:morphological(e.g.muscle-tendonproperties), biomechanical(e.g.Newtonianlawsofphysics),environmental(e.g.walkingsurfaceandincline), andtaskconstraints(e.g.di erentwalkingspeeds,treadmill,obstacleavoidance)[7,109].Aspresentedinthepreviouschapter,beingabletointerpret,combine,anddeterminewhichinstrumented gaitanalysismeasurescapturethestateoftheneuromuscularsystemisquiteachallengingtask. Fortunately,toolsderivedfromdynamicsystemstheoryarelowdimensionaldescriptorsthatconsolidatethecomplex,multifactorialvariablesofasystemandcanbeusedtocreatesimplermodels ofanotherwisecomplexphysiologicalbehavior. Instrumentedgaitanalysis(IGA)quantitativelydescribesthepathologicalgaitpatternofan individualwhosewalkingisnegativelya ectedbyneuromuscularimpairments.TraditionalIGA measuresidentifyfactorscontributingtoapathologicalgaitpattern,providesupportingevidence forclinicalinterventions,andassistinassessmentoftreatmentoutcomes.Duetothemethodsfor constructingconventionalIGAmeasuresandnatureoftheactionsorrelationshipstheyquantify 43

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(e.g.jointangles,jointkinetics,temporal-spatial),thesemeasuresdescribethemotionoflimbs orjointbutareunabletocharacterizetheunderlyingdynamicsofthemotion.Thecoordinated behavioroflegsegmentsingaitistheresultofacomplexdynamicalsystemthatrequiresorganized neurologicalcontrolofthemusculoskeletalsystem.Thephaseportrait(PP)andcontinuousrelative phasediagram(CRPD)fromdynamicsystemstheory(DST)usethesamemotioncapturedataas IGAmeasures,butareinherentlydesignedtodescribetheorganizationoflimbsegmentsresulting inagaitpattern.TheseDSTbasedmeasuresaremoresuitableforcharacterizingselectivemotor controlstrategiescontributingtoagaitpattern,quantifyorganizationofindividualsegments,identifymechanismsofchange,andlociofimpairment.Sincethefundamentalorganizationoftheleg segmentsduringgaitislinkedtogaitpathologyandguidestherationaleforinterventions,itisproposedthataddingPPsandCRPDstoIGAwillopennewavenuesforunderstandingthecomplexity ofcoordinationandallowcliniciansthemeanstomoree ectivelyande cientlytreatpatientswith neuromusculargaitimpairments.Afundamentalobjectiveofthisbodyofworkwastoprovidea contextfortheutilityofthesemeasuresasacomplementtoconventionalIGAmeasuresandpresent anormativedatasetthatcanbeusedinresearchortheclinic. AbriefdiscussionoftheconstructionofcommonIGAmeasuresandunderstandingofthevariablestheydescribeisessentialforrecognizingwhythesemeasuresareunsuitableforquantifyingcoordination.ConventionalIGAusesthree-dimensionaldatatocreatekinematic,kinetic,and temporal-spatialdescriptorstoanalyzetherecordedmovement.Kinematiccurvesarecreatedfrom aparent-childsegmentrelationship,inwhichthechildsegment'smotionisexpressedwithrespect totheparentsegment'slocalcoordinatesystem.Thereforekinematiccurvesdescribethechanges injointanglesusingalocalcoordinatesystemandkineticmeasuresarebaseduponthisskeletal hierarchy.Electromyographicdataprovideinformationabouttiminganddurationofmuscleactivity,butareusuallynotquantitativelypairedwithotherIGAdata.Whiletheseconventional measuresareessentialforunderstandingcertainaspectsofgait,duetothehighdimensionalnature ofcoordination,theabilitytoe ectivelydescribethecomplexityandnumberofvariablesofthisbehaviorislostusingtypicalIGAmeasures.Thesecustomarytechniquescannotisolateanindividual segment'scontributiontothemotionorlocatethetimingandsequencingofasegmentorsegment pairs.Therefore,itisproposedthatconventionalIGAmeasuresdonotprovidetheappropriate perspectiveandlevelofanalysisnecessarytounderstandtheunderlyingmotorcontrolmechanisms responsibleforgeneratingtheresultinggaitpattern.Furthermore,coordinationstrategiesbetween segmentsoftenconsistofnon-adjacentsegmentrelationshipsinadditiontotheinterplaybetween adjacentsegments4.Thesenonlinearmethodsareinherentlyconducivetopairinganycombination 44

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ofsegmentsandareidealforinvestigatinginter-segmentalcoordinationdynamicsofnon-adjacent segments.Thisdissertationalsocontendsthatbymaintainingthesegmentsinaglobalcoordinate system,theDSTtoolspresentedinthisdissertationaremoreakintotheperspectiveinwhich cliniciansobserveandevaluateanindividual'scharacteristicgaitpattern. ToappreciatetheidealpairingbetweenDSTandcoordinationfromamotorcontrolperspective,adenitionofcoordinationandreviewofpreviouspivotalinvestigationsthatcontributedto theapplicationofDSTinIGAispresented.Coordinationofthelegsduringwalkingrequiresthe elegantorganizationoftheneuromuscularsystem'smanyelementsandappropriateconsolidation ofthesystem'sredundantdegreesoffreedomwhileconsideringtaskandenvironmentalconstraints [1].Thisconstitutiveelementofbipedalismhaslongbeenrecognizedasanimportantfactorof motion,especiallyincaseswhencoordinationofthelegsegmentsduringgaitisadverselya ected inindividualswithselectivemotorcontrolimpairmentsresultingfromneuromuscularpathology. However,theabilitytoemployamethodthate ectivelycapturescoordinationandpresentsthe behaviorinaconcisemannerhasoftenbeenaselusiveastheconceptofcoordination.Theapplicationofangle-anglediagramswasanimportantprecursorbecausethesemeasuresdescribethe relationshipbetweentwojointsasalowdimensionaldescriptor[3,115].SimilartoconventionalIGA measures,angle-anglediagramsareconstructedfromaskeletalhierarchyandthereforethesejoint basedmeasuresproveunsuitabletoolsfordelvingdeeperintothebehaviorofindividualsegmentsor non-adjacentsegments.Theneedforquantitativedescriptorsofcoordinationwasidentiedinthe developmentofmotorcontroltheoryandthemathematicaleldofDSTwasproposedasasolution4. Clarketal.(1993)appliedDSTbasedmeasurestomotioncapturedataofinfantsduringtheirrst yearofindependentwalking,demonstratingtheelegantpairingofDSTconceptstothedynamical systemofgait[116].Withconsiderableadvancementsinmotioncapturesystemsandcomputational performance,themarriagebetweenmovementanalysisandDSTwaslaterrevisitedbyStergiouetal. (2004)whodemonstratedDSTbasedmeasurescanbeeasilycalculatedfromsegmentmarkertrajectoriesrecordedfrommotioncapturedata[7].DSTprincipleshavebeenabsorbedintocurrentmotor controlpracticeandre-introductionofthesetechniquesappliedtomotioncapturedatahaso ered ameanstobridgethesetheoreticalconstructswithpracticalapplicationsinIGA.Itisproposed thelackofaunifyingmethodology,normativereference,andclinicallymeaningfuldemonstrations ofthepracticalbenetsandimportantmotorcontrolinsightso eredbythesenonlinearmeasures haveslowedtheirincorporationintoIGA.Inane orttocontinueadvancingtheapplicationofDST techniquestolocomotion,thisdissertationpresentsarenedmethodologyfortwoDSTmeasures appliedtomotioncapturedatafromalargecohortofindividualswithoutgaitpathology. 45

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AconceptualframeworkforhowPPsandCRPDsquantifythecomplexbehaviorofcoordinationisestablishedusinganoverviewoftherelationshipsbetweenDSTprinciplesandaspectsof conventionalmotorcontroltheory.Thebehaviorofcoordinationcanbecharacterizedbythetiming andpositionofanindividualsegmentandpairsofsegmentsthroughoutthecyclicaltaskofgait. Sincethecyclicaloscillationsofthelegsegmentsduringgaitareanalogoustothemotionofvarious pendula,thismotioncanbemodeledasalimitcycleinphasespace.Asalimitcycle,thetrajectory ofalegsegmentcanberepresentedinaPP,providingasuitablevehicleforexaminingthemotion ofanindividualsegment.ForIGA,thismovesthelevelofanalysisfromkinematicspacetostate spaceofthelimitcycleoscillator. FromtheBernsteinperspective,theorganizationofindividualvariablesintoalargergroupis denedasasynergy[4].Employingsynergiesduringamovementessentiallydecreasesthedegrees offreedominthesystem,thusallowingforsimplercontrolstrategies[2].Synergiesarethecentral nervoussystem'spartialsolutiontothedegreesoffreedomproblemandinthecaseofgait,generate complexandoscillatorypatterns[5].TheCRPDprovidesimportantcluesintotheorganizational strategiesgoverningtheconstitutiveoscillators(e.g.segmentpairs)andconversely,thePPsdescribe propertiesofindividualoscillators(e.g.segment)a ectingthecoordinatedbehaviorofthisdynamic system.Phaseportraitsprovideclinicallymeaningfulinsightsabouthowanindividualsegment's oscillationscontributetotheoverallmotionofthelimb.Therelativephaseangleisacollective variablethatconciselycapturesbothspatialandtemporalpatternsbetweentwosegments.The CRPDpresentsthislowdimensionalmetricthroughoutthegaitcycleanddescribesthecoupling anduncouplingofsegments'oscillations.Consolidationofthedynamicsystem'snumerousvariables intotherelativephaseangleallowsforinferencestobemadeabouttheunderlyingcontrolprocesses. Whentemporallynormalizedtothegaitcycle,thesemeasureso erconcise,easilycalculated,and clinicallymeaningfuldescriptorsofindividualsegmentandinter-segmentalbehaviorasaresultof selectivemotorcontrol. Investigationsintointra-limbcoordinationofgaithavebeenconductedbyafewresearchersinthe pastusingvarietyofmethods,rangingfromtheearlierapplicationofangle-anglediagramstomore recentDSTbasedmethods[117,118].Thesestudieshavecontributedtoanincreasingawarenessin thegaitcommunityabouttheimportanceofexpandingtraditionalmeansofcharacterizinggaitand servedasinitialstepsinunderstandingcoordinationincertainatypicalgaitpatterns.Themajority ofstudiesreportedsmallsamplesizesandasisoftenthecaseinstudiesofsubjectswithcerebralpalsy orstroke,theuna ectedlimbservedasacomparisontothea ectedlimb'smotion[119].While comparisonsbetweenasubject'sa ectedanduna ectedlegshedinsightsintothecompensatory 46

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strategiesemployedbytheindividual,becauseoftheasymmetryofsuchgaitpatternstheuseofan una ectedlimbisnotatrueanaloguetoanormativereference. ThisbodyofworkdemonstrateshowPPsandCRPDscomplementconventionalIGAmeasures andbydescribingmovementatthelevelofcoordination,howtheseDSTbasedmeasuresexplainthe mechanismsunderlyingtemporal-spatialandkinematicdi erencesobservedintypicalandatypical gaitpatterns.Thefollowingsectionsprovideanexplanationofthetwodynamicsystemstheorybased measuresthatareusedinthismodelandanexplanationoftheinsightsandvaluefordescribing gaitwitheachofthesemeasures. 3.1.1PhasePortrait AsdiscussedinChapter2,themotionofthelegsegmentsduringgaitresultsfromtheelegant organizationoftheintricatemusclesynergiesandhasbeencomparedtothedynamicsofacompound pendulum'slinkages.Thiscoordinatedcouplinganduncouplingoflegsegmentscanbemodeledusing principlesofdynamicalsystemstheory[6,7]andisareectionofaperson'svoluntarymotorcontrol. Thisanalogyoftheleg'smotioninthiscontextprovesusefulandappropriatebecauseindynamics systemstheory,thestateofthesystemisinuencedbychangesinenergy(e.g.kinetic,potential) thatoccurswithinthesystemduringeachorbit(e.g.gaitcycle).Usingthistheoreticalconstruct, theoscillatory,cyclicalmotionofapendulumcanbedescribedasalimitcycle.Alimitcycleisthe two-dimensionaltrajectoryofanoscillatorysystem'svariables,whicharerepresentedasaperiodic orbitinphasespace.Phasespacedescribesallpossiblestates(e.g.behaviors)ofadynamical systemandportrayshowthesestatesevolveintime[4,5,7].Thelimitcycletrajectoryofasimple, frictionlesspenduluminphasespacewouldbeanellipticalwhoseclosedpathcompletelydescribes therelationshipbetweenpositionandvelocityasafunctionoftime.Intheapplicationofgait,a phaseportraitcanbeconstructedtodescribetherelationshipbetweentheangulardisplacement andangularvelocityofasegmentthroughouteachgaitcycle(e.g.limitcycle).Asshowninthe followingphaseportrait,readinaclockwisedirection,issimplyasetoftrajectories(e.g.limit cycles)inphasespaceandcancontainanynumberoflimitcycles(Figure3.1.1). 47

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Figure3.1.1:Diagramofanideal,closedorbitlimitcycle(blue)withdi erenttrajectories(green)of atheoreticaldynamicalsystem.Astablelimitcycleisanalogoustoanormalgaitpatternbecause itreturnstoapreferredstateevenafterperturbationsorchangesininitialconditions.Anunstable limitcycleisanalogoustoanirregularpathologicalgaitpatternbecausethesubjectisunableto returntothesamestateafterperturbationorfromonegaitcycletothenext. Theapplicationofthistheoryhasbeentestedforthetaskofgaitinpreviousinvestigations. Severalinvestigationsusingphaseportraitsandinstrumentedgaitanalysishavedemonstratedthat phaseportraitscaptureasystem'sstateanditsstabilitywhenanindividual'sgaitisperturbed [120,121].Additionally,ClarkandPhillips(1993)demonstratedthatpreferredlowerextremity movementscanbemappedontoaphaseportraitasalimitcycleoscillatorandhavedi erentshapes andcharacteristicsfordi erentgaitpathologies116.Furthermore,numerousotherinvestigations haverevealedthatchangesinthephaseportrait'strajectoryshapearecorrelatedtonewmovement behaviors,eitherpathologicalortypical[117,119,122].Sincetheshapeofphaseportraitsforlower extremitysegmentsprovidesvisualevidencevalidatingthatthebehaviorofsegmentsduringgaitcan bedescribedaslimitcycleoscillators,thedi erenttrajectoryfeaturesanddeviationsfromanellipse orcircleareindicativeoftheactivemodulationandchangesofthesegmentbythenervoussystem. Thesechangesinphaseportraittrajectorycapturethedi erentenergyexchanges(e.g.acceleration, deceleration)ofasegmentthroughoutthegaitcycle[123].Phaseportraitcurvefeatures(e.g.zero crossings,extrema)canbeidentiedandusedtoquantitativelydescribedi erencesinphaseportrait trajectoriesandthusmotorbehaviorsforthesameindividualordi erentsubjects.Therefore,phase portraitscanprovideclinicallymeaningfulinsightsabouthowanindividualsegment'soscillations contributetotheoverallmotionofthelimb. 48

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Figure3.1.2:Phaseportraitconstructionfromtri-planarmarkerdata. Tri-planarmarkerbasedtrajectoriesandsegmentcoordinatesystems(A)frominstrumentedgait analysisprovideangulardisplacementandangularvelocity(B),withrespecttothehorizontal,and areusedtoconstructphaseportraits. Atthistime,theproposedmodelofcoordinationdynamicsusestheangulardisplacementand angularvelocityfromasegment'smarkertrajectorytogeneratethecorrespondingsegment'sphase portrait.However,phaseportraitscouldbeconstructedfromothersystemvariablessuchasangularaccelerationandprovidedi erentinsightsintothesystem.Forreasonsthatwillbefurther elaboratedinafollowingsectionofthischapter,theangulardisplacementandangularvelocity wasresampledandnormalizedtoeachvalidgaitcycleinthemotioncapturetrial.Althoughthis modelallowsforexibilityinselectingasegment'sdeningmarkers,jointcenterscalculatedfrom theconventionallowerbodymarkerset[124]wereusedbecausetheywerealreadycalculatedforthe standardinstrumentedgaitanalysismethods.Additionally,whilethismodeliseasilyadjustableto di erentcoordinatesystemdenitions,thesagittalplaneforbothmotioncaptureenvironmentswas denedbytheoor(horizontal)andperpendiculartotheoor(vertical)andthereforemaintained asthiswork'sdeningglobalsagittalplaneaxes. 3.1.2ContinuousRelativePhaseDiagram TheproposedmodelofcoordinationdynamicsusesPPstocharacterizetheindividualbehaviors ofasegmentwithrespecttotheglobalcoordinatesystem.ForsagittalplanePPs,theglobal referenceisthesameasthelevelwalkingsurface(e.g.over-ground,treadmill).Thephaseangle iscalculatedfromasegment'sPP,isalow-dimensionalparameterthatconsolidatesasegment's spatio-temporaloscillatorybehavior,andrepresentstheprogressionofthelimitcycle'strajectory 49

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throughoutthegaitcycle.Theunalteredarctangentfunctionwasusedtocalculatethephaseangle ofasegmentforeachpercentofthegaitcycle.Thephaseangleisdenedastheanglebetween thephaseportrait'shorizontalandthevectorformedfromthephaseportraitorigin(0,0)tothe coordinatesofthephaseportraittrajectoryforeachpercentgaitcycle(Figure3.1.3). Figure3.1.3:Diagramofhowasegment'sphaseangleiscalculatedwithrespecttothehorizontalof thephaseportrait,foronecompletegaitcyclefromanormalreferencesubject'sthigh(leftcolumn) andshank(rightcolumn).Vectorsfromtheorigin(0,0)tothephaseportraitcoordinatesforeach percentgaitcycle(A).Zoomed-inviewofthevectorsandphaseportraittrajectory(B).Phaseangle foronepercentgaitcycleonthethighandshank(C). Phaseportraitsforthepelvis,thigh,shank,andfootweregeneratedandthefollowingequation 50

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wasusedtocalculatethecorrespondingphaseangles( % seg )foreachsegment[7]. Algorithm3.1 PhaseAngle (% GC ) seg =tan 1 x (% GC ) x (% GC ) Foreachsegmentpairing(i.e.pelvis-thigh,thigh-shank,shank-foot,thigh-foot),thephaseangles fromanytwosegments'PPswereusedtocalculatethepair'srelativephaseangles( & )foreach instanceintime(e.g.eachpercentgaitcycle).Thismodelofcoordinationdynamicscalculates therelativephaseusingthefollowingequationandgeneratesCRPDsbyplottingtherelativephase angleswithrespecttoeachpercentgaitcycle[7]. Algorithm3.2 RelativePhaseAngle (% GC )= (% GC ) Distal (% GC ) Proximal Therelativephaseangleisalow-dimensionaldescriptorbecauseitencompassestheangular displacementsandangularvelocitiesfromtwosegmentsandisafunctionoftime.Therefore,the magnitudeandtimingoftherelativephaseangleprovidesasimplescalarvaluequantifyingthe multifactorialelementsofinter-segmentalcoordination(e.g.temporalandspatialorganization) betweenanytwosegments.Inadditiontooverallspatio-temporalpatternsofCRPDs,characteristics ofCRPDsshapecanbequantiedbycalculatingsuchcurvefeaturesaszero-crossings,extrema, slopes,andinectionpoints.Thesecurvefeaturesprovideinformationaboutcertaincoordination eventsandthesegmentalrelationships.AnextremumonaCRPDindicatestheinstancewhen therelationshipbetweenthetwoconstitutivesegmentsisthemostout-of-phase(e.g.instanceof reversal).SinceDSTassumesthatthemotionsofsegmentsapproximateasinusoid,thenitcanbe assumedthatwhentherelativephaseangleequals0 ¡ thesegmentsarein-phasewitheachother [4-7,132].ThisCRPDzero-crossingindicatestheinstantwhenthetwosegments'phaseanglesare changingatthesameratewithrespecttoeachother.Similarly,whentherelativephaseangle equals180 ¡ theoscillatingsegmentsareout-of-phasewitheachother[4-7,132].BothoftheseCRPD featuresrefertothesegments'phaseportraittrajectoriesandtherelationshipinphasespace,not Euclideanspace.InectionpointsonaCRPDindicatetheinstantwhenthephaseanglesofthe twosegmentsbeginchangingtheirrelationshiptoeachother.Forexample,aninectionpointona thigh-shankCRPDcouldindicatetheinstantwhenthethigh'sphaseanglebeginschangingmoreor haslargervaluesthantheshank'sphaseangle.TheslopeofaCRPDgivesinsightsintohowtherate ofthesegment'sphaseanglesaremovingwithrespecttoeachother.Forexample,anegativeslope indicatestheproximalsegmentischangingitsphaseangle(e.g.angulardisplacementandangular 51

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velocity)atafasterratethanthedistalsegmentandthushasagreaterinuenceonthecalculation oftherelativephaseangle.TheinverseistrueforapositiveslopeonaCRPD.Lastly,thetemporal normalizationoftherelativephaseangletothetogaitcyclealsoallowsforintra-subjectandintersubjectcomparisons.Bymaintainingthiscommontemporalscalewithconventionalmeasuresof instrumentedgaitanalysis,curvefeaturesfromothermeasuresandcriticalandtemporalgaitevents canbemappedontothesemeasuresofcoordinationdynamics. Theabilitytoquantitativelyinvestigatecoordinationdynamicsbetweenanytwosegmentsisan inherentadvantageofCRPDs.TheCRPD'slowdimensionalrelativephaseanglecapturestherelativecouplinganduncouplingbetweensegments,thuscapturinganindividual'sabilitytodi erentiate jointmovementsoutofexionorextension(e.g.voluntarymotorcontrol).CRPDsquantitatively describefunctionalsynergiesingaitandprovideanexcellentmeansformakinginferencesabout selectivemotorcontrol,aprimaryimpairmentinindividualswithneurologicaldiagnoses.Throughouttheevolutionofeachgaitcycle,aCRPDcapturesthetransitionfromonepatterntoanother (e.g.stancetoswing).OnegoalofusingIGAinrehabilitationistoidentifyimpairedcoordination usingconventionalIGAmeasures(e.g.temporal-spatialvariables,kinematics)andreducethosecoordinationimpairmentsbyimprovingintraandinter-limbcoordination.CRPDsconciselydescribe theorganizationalstrategies(e.g.symmetries,synergies)oftwolegsegmentsando erinsightsinto howthenervoussystemisimposingfunctionalconstraintsonthelimbs.Theorganizationalchanges betweentwosegments,throughtheuseofsynergies,thataccountforfunctionalactionscanbeidentiedusingcommoncurvefeaturessuchasextrema,zero-crossings,andinectionpoints.Sincethe CRPDencapsulatesbothtemporalandspatialsymmetriesanddynamicsofthelegsduringgait, thedegreetowhichtwosegmentsmoveinandoutofvarioussynergiesiseasilyquantiedbythe percentgaitcycleandmagnitudeoftherelativephaseangle.Previousinvestigationsmentionedin Chapter2havedemonstratedthisCRPDfunctionalitybymodelingthegaitofchildrenwithspastic cerebralpalsyexhibitingasti kneegaitpatternbeforeandafterarectusfemoristransfer(Valvano et.al,2010).InthepreviousinvestigationsmentionedinChapter2,benecialinsightsfromPPsand CRPDshavealsoprovidedthemeanstoexploretemporalconstraintsassociatedwiththedynamics offootfallandnon-adjacentsegmentsduringswinglimbadvancement. 3.2ModelAssumptions&Limitations Eventhoughwalkingistypicallydescribedandcharacterizedbythegaitcycleandsubsequent subdivisions,thismotortaskisconsideredacontinuoustaskasopposedtoadiscreteone.A 52

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continuoustaskisdenedasacoordinatedmovementthatdoesnothaveanarbitrarystartand endandcandependuponthecontextofthemovement.Giventhisdenition,walkingandrunning aretwoexamplesofacontinuoustask.Intheexampleofgait,thepreviousgaitcyclesinuence thesubsequentonesaswellastheeventswithinagaitcycle,whichareinuentialprecursorsto theremainingphaseswithinthatgaitcycle.Discretetasks(e.g.hop,jump,orreachtograsp)are coordinatedmovementsthathavedenitivestartandendpoints[110].Dynamicsystemstheory assumesthatstablemovementpatternsemergefromadynamicsystemandthevariabilityasystem containsreectschangesinstatesandembodiesthesystem'ssearchforstability.Opponentsof DSTviewvariabilityinasystem'smotorcontroltobealineardeclineine ciencyasopposedto theimpetusforanonlinearchangetoadi erentmovementpatternreectingthesystem'sprocess ofself-organization[110,135].Furthermore,somehavearguedthatsincetheproposedmeasuresof coordination(e.g.PPs,CRPDs)aregroundedintheassumptionthatsegmentsmoveaslimitcycle oscillators,thesemeasuresofcoordinationmaynotbeappropriatefordiscretetasksandthatother motorcontrolparadigms(e.g.generalizedmotorprograms)aremoresuitablefordiscretetasks[110]. Fortunately,thisbodyofworkbypassesthisissuebecauseitexaminesthecontinuous,oscillatory taskofgait,whichsupportstheapplicationoftheDSTparadigm. Sincethismodel'smeasuresarederivedfromtri-planarmarkertrajectories,themeasuresare unabletoidentifythecontributionofspecicmusclesinamovement,whichsomemayargueisamore directmeasureoftheneurologicalactivity,andthusmotorcontrolemployedduringgait.Advantages anddisadvantagesofthispositionandalternativemethodologyareaddressedinthefollowingsection. Giventheprovideddenitionofcoordination,whichisconsideredanemergentspatiotemporalmotor behaviorculminatingfromnumerousinteractionswithintheneuromusculoskeletalsystemasopposed toasinglephysiologicalelement(e.g.heartrate,muscleforceproduction,actionpotential)thatcan bemeasureddirectly,theexplorationofbehavioralmeasures(e.g.PPs,CRPDs)maintainstheir relevanceandapplicability. Lastly,inspiteofe ortstakentolimittheinuenceofhumanerrorinexperiments,itisnot possibletocompletelyeliminatesucherrors.Furtherdetailsofe ortstakentoreduceanycontributionsfromhumanerrorandvalidatevariouscalculationsandanalysesareprovidedinChapter4. Althoughtherehavebeensignicantimprovementsandadvancementsinmotioncaptureinstrumentation(e.g.cameras),thereareinherenterrorsandassumptionswithinstrumentedgaitanalysis, suchasmarkerplacement,motionartifact,andmotioncapturemodelassumptions(e.g.jointcenter estimation),whicharecurrentlyunavoidable.Aswithotherconventionalgaitanalysismeasures, thePPsandCRPDsusedinthismodelarenotimmunetotheseassumptionsandpotentialerrors. 53

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3.3AlternativePerspectivestoModelingCoordinationinGait Justastherearedi erenttheoriesandmodelsofhumangait(Chapter2),therearealsonumerousdenitionsofcoordination,evenwithinthecontextofgait,andmodelsforcharacterizingeach theory.Everymodelhasitsuniquesetoflimitationsandissubjecttochangeasresearchrevealsnew informationandtechnologicaladvancesexpandmeasurementcapabilities.Itisnottheintentofthis bodyofworktodeclareonetheoryormodelisthedenitivemeansforcharacterizingcoordination ingait,becauseitistheauthor'sbeliefthatmodelsandcorrespondingmeasuresshouldbeselected baseduponthedrivingquestionsthatwillbeansweredbythesedescriptors.Inthecontextofcoordinationdynamicsderivedfrominstrumentedgaitanalysisdata,modelandmeasurementselection shouldbemadewithconsiderationtothecorrespondinglevelofmotioncapturedataanalysisthat bestcharacterizesthesefactors(e.g.denitionofcoordination)andgoalsfordescribingmovement performance.Tosetthestageforthefollowingsectionofthischapterontheproposedmodel's methodologicalrationale,thefollowingsubsectionsprovideabriefoverviewofothercoordination models. 3.3.1CentralPatternGenerators&MotorPlanTheories Theneurophysiologicalconstructofcentralpatterngenerators(CPG)andthemotorprogram aretwotheoriesofmotorbehaviorinanimalsthatdespitetheirdominancefailtoprovideasatisfactoryexplanationofmovement.Thelenproposedthatthemainreasonthesetwotheoriesare insu cientisbecausetheyapproachmotorcontrolasacomputercontrollinganelectronicdevice andthereforeviewtheexecutionofamotorplanasbeinggeneratedonlyfromneuralcommands [5].However,itisapparentfromeventhegeneraloverviewofthelocomotorsystempresentedin Chapter2thatmovementistheorchestrationofacomplexsystemcomprisedofintrinsicelements (e.g.neuromusculoskeletalsystem,segmentmass,energyexchange,etc.)andextrinsicfactors(e.g. walkingsurface,taskconstraints,etc.).Whenmotorcontrolisviewedasaconstantxed(e.g. CPGs)andpredeterminedpatterns(motorprogram),severalshortcomingsarisefromthesetheories becausetheyareunabletoexplainhowapersonisabletowalkindi erentdirections,avoidobstacles,thevariabilityinnormalandpathologicalmovements,andadapttochangesinenvironmental ortaskconditionsandconstraints[5,110].Dynamicsystemstheoryprovidesamoresatisfactory explanationtotheseshortcomingsbecauseitisbasedupondynamicpatterns,whicharenotxed toahierarchy,thatcharacterizechangesinasystem'sbehaviorovertimeasitsearchesforastable state. 54

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3.3.2UsingElectromyographytoQuantifyCoordination Ithasbeenproposedthatmusclesynergiesaremotorcontrolstrategythatsimpliestheredundantdegreesoffreedominthebodyandallowsforthelow-dimensionalorganizationofthelocomotor system,whichisnecessarytoproducee cientmovements[1,13,14].Severalstudieshavetherefore useddynamicelectromyography(EMG)datatoidentifypatternsofmusclesynergiesusedduring di erentwalkingconditionsandbydi erentpopulations[125,126,127].Modelsofcoordinationproposedusingmusclesynergiesaregroundedinthelength-tensionandforce-velocityrelationshipsof skeletalmuscle.Thesestudiesproposethatmusclerecruitmentfordi erentsynergypatternsis variableandmodulatedbythenervoussystemasafunctionofthemuscle'slength[125].Furthermore,thesemuscle-forcerelationshipsareoftenemployedinmusculoskeletalcomputersimulations [128],whichcanbeusedtoestimatefunctionalimpactsofdi erentmusclesynergiesbasedupon kinematic,kinetic,andEMGdata[127].AlthoughEMGdatacollectedduringinstrumentedgait analysiscomprisesofboththeamplitudeandtimingofmuscleactivity,therelationshipbetween muscleforceproductionandEMGamplitudewhileperformingadynamicmovementlikegaitis notareliable,linearrelationship.AsmentionedinChapter2,thereisanoptimallengthatwhich amusclecanproducethemaximumforce(e.g.length-tensionrelationship)andoptimalspeedfor forcegeneration(e.g.force-velocityrelationship).Theserelationshipsaregeneratedfrommuscle forcesduringastaticpositionandthereforebreakdownduringadynamicmotionbecauseofthe propertiesoftheslidinglamentmechanismdiscussedinChapter2[23].UseofdynamicEMGdata isfurtherconfoundedbythenoiseinherenttothisdata(oftenrequiringconsiderableltering)and changesinthemuscle'srelationshiptotheelectrodeasitcontracts[23].Usingtri-planarmarker basedtrajectoriestogeneratemeasuresofcoordinationdynamicsavoidstheseissuesandsimplies thedatacollectionandanalysisprocess.However,markerbaseddescriptorsofcoordinationdynamicsarenotabletoidentifythecontributionofindividualmuscles.Thereisgreatpotentialforfuture collaborationbetweenandcombinationofmeasuresfromthesetwomodelsofmotorcontrol. 3.4RationaleforModel'sMethodology Aspreviouslymentioned,thedynamicsystemsperspectiveofgaitseparatesitselffromconventionaldualisticapproachesofmovement(e.g.structurevs.function,brainvs.behavior)andinstead embracesvariabilityasanessentialelementdescribingasystem'sstateandspatiotemporalchanges, considerspatternchangesoccurringindi erenttimescales,andconsiderstheuniqueexpressionof movementforeachindividualinsteadofgeneralizationsbasedsolelyondemographics(e.g.gender, 55

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age,etc.).Thetaskofgaitisuniquelyexpressedineachindividual,withvariabilityfromgaitcycle togaitcycle[130].Thereforeusingdynamicsystemstheorytodevelopamodelofthecoordination dynamicsofwalkingisanidealpairingbecausethistheoryofmovementembracestheindividualistic variabilityofgait,theemergentbehaviorresultingfromthevariousaspectsandinteractionsofthe locomotorsystem,environmentalandtaskfactors[109],andwhosemeasures(e.g.PP,CRPD)are rootedintheseprinciplesandthusideallysuitedtodescribethecoordinationdynamicsofgait. OneadvantagetotheproposedmethodsforgeneratingPPsandCRPDsisthatthesearederivedfromthree-dimensionalmarkertrajectoriesplacedonsegmentsduringamotioncapturesession.Clinicalinstrumentedgaitanalysistypicallyusesstandardized,well-documentedmarkersets todenesegments[124].Byusingmarkertrajectories,theneedforadditionalinstrumentation (e.g.electromyography)andtheassociatedcosts,placementtime,andanalysesareremoved.As previouslystated,bytemporallynormalizingthePPsandCRPDstothegaitcycle,intra-subject andinter-subjectcomparisonsusingthesemeasuresofcoordinationcanbemade,justasisstandard practiceforconventionalinstrumentedgaitanalysismeasures.Bymaintainingthesesimilaritiesto conventionalgaitanalysismeasures'markerlocations,processingmethodsformotioncapturedata, andtemporalscale,thisproposedmodelofcoordinationdynamicsrequiresminimalworktoadopt intoinstrumentedgaitanalysispractice. AlthoughotherinvestigationsintocoordinationdynamicsusingDSTbasedmeasureshavebeen conducted,themannerinwhichthesemeasureshavepreviouslybeengeneratedvariesandessential detailsaboutPPscalculationsareoftenmissing.Ifcomparisonsbetweenstudiesusingcoordination dynamicsaretobeunied,asitisforconventionalIGAmeasures,itisimperativetoestablisha standardizedmethodofgeneratingtheseDSTmeasures.Toaddressthisdiscontinuityintheliteratureandjustifythismodel'smethodology,thefollowingrationalediscussesthenormalizationof thesemeasures,selectionofanarctangentfunction,andpracticalityofcoordinatesystemtransformations.Markertrajectoriesandderivednonlinearmeasureswerekeptinglobalcoordinatesinstead oflocalcoordinatesystemsusedinthetraditionalskeletalhierarchyofjointbasedvariables(e.g. kinematics)forthefollowingreasons. First,maintainingglobalcoordinatesallowsforatrulyindividualsegmentbehaviordescription. Whenmeasuresaretransformedintoajointbasedcoordinatesystemthevariablelosestheability todistinguishwhichsegmentofajointiscausingachangeinthemeasureoridentifytheamount eachofthesegmentscontributestothephaseangleorrelativephaseangles.Numerousstudieshave reportedCRPDcalculationswithvariousdi erenttechniquesandquiteoftenusejointanglesin thecalculationofphaserelationships[105,132,133,134].Itisproposedtheuseofjointanglesinthe 56

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calculationofphaserelationshipsisaninappropriatemethodologybecauseitdoesnotevaluatethe coordinativerelationshipsbetweenthesegmentsofinterest.Thefaultofthisstrategyisrevealed inthephasecomparisonoftwojointangles.Anexampleofusingthehip-kneeanglerelationship togenerateaCRPDispresentedtodemonstratetheawwithajointanglemethodology.The hipangleisgeneratedfromthepelvisandthighsegments,wherethethighistransformedintothe localcoordinatesystemofthepelvis.Similarly,thekneeangleistraditionallyconstructedfroma skeletalhierarchywheretheshankisdescribedwithrespecttothethigh'slocalcoordinatesystem. Forthecalculationoftherelativephaseangle,eachofthephaseanglesthatarecalculatedthen containasimilarbodysegment,thethigh.ThereforewhencalculatingtheCRPDfromthehip-knee anglerelationship,thethighsegmentisusedtwiceinthecalculationoftherelativephaseangle. Calculatingtherelativephaseinthiswaydoesnotlendauthoritytotheinterpretationusedand directlyinhibitsthevalidityofdescribingmotionsduringmovement.Theclassicparadigmpresented byKelsowheresegmentalanglesareusedprovidesfurtherjusticationforthismethodology4.When twongersmoveinthesamedirectionandwiththesamevelocitytheyarein-phasewitheachother andareout-of-phasefortheconverse.Thissegmentalmotionisanalogoustoasimplependulumand aspreviouslydiscussed,PPsarerootedinthisoscillatorypendularmotion.Thetrademarkpaper byClarkandPhillips(1993)[116]providedaneloquentguideforthedevelopmentandanalysisof segment-segmentanglesandpresentedcorrectinterpretationofthesemeasuresusingtheframework ofthedynamicalsystemstheoryasinitiallylaidoutbyKelso[4],Kugler[131],Turvey[6],and laterbyThelen[5],andutilizedbyStergiou[7,130]andothers[129].Calculatingvariablesinthe segmentanglemannerprovidesmeaningfulandinterpretableresultsthatcanbeusedtodescribe phaserelationshipsproperly. Second,retainingglobalcoordinatesallowsforidenticationofasegment'scoordinationevents andeliminatesgratuitouscoordinatesystemtransformationswhenquantifyingnon-adjacentsegmentcoordinationpatterns.Theclinicalvalueofthismethodologicalexibilitybecomesespecially apparentduringswinglimbadvancement.Thekneeispassivelyexingduringtheinitialphases ofswingasaresultofactivehipandanklemomentgeneration.Thereforetheabilitytostudythe relationshipsbetweennon-adjacentsegments,suchasthethighandfoot,providesvaluableinsights intotheuncouplingandcouplingofvarioussegmentcombinations.Third,maintainingmeasuresin theglobalcoordinatesystemallowforamoredirectcomparisontothemotionviewedbyclinicians duringobservationalgaitanalysis.Additionally,thearctangentfunctionusedwasnotnormalized butkeptintheoriginalquadrants,range,anddomain,thusadheringtothistrigonometricfunction's originaldenition.AfterperformingPPcalculationswithMatlab'salternativearctangentfunctions, 57

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itwasfoundthatnoiseisinducedintothephaseanglecalculationwhenusingalternativearctangent functionsthatforcethedomainoftheoutputsintodi erentoradditionalquadrants(AppendixD). Notonlyisthenormalizationofthearctangentunnecessaryandanextraneouscalculationbutthe inducednoisefromsuchalterationsisundesirablewhenconsideringtheresultofthesee ortsonly presentsthephaseanglesabouttheoriginofthePP'scoordinatesystemandincreasesthedi culty indiscerninginducednoisefromphysiologicallysignicantvariationsinthesecurves.Thisdecision tonotapplyadditionalnormalizationtechniquestothephaseanglesisfurthersupportedinthe paperbyKurz(2002)[129]. Thischapterprovidedanoverviewoftwodynamicsystemstheorybasedmeasuresandtheir abilitytosimplifyandquantitativelydescribethecomplexcoordinationdynamicsrequiredduring walking.Themodelofthecoordinationdynamicsduringswinglimbadvancementpresentedinthis dissertationprovidesaquantitativemeanstouncoverandunderstandtheorganizationalstrategies employedtosolveoneofthefundamentalaspectofmovementscience:Bernstein'sdegreesoffreedom problem.Thenextchapterwillpresentthevariousmathematicalpendulummodels,experiments forprospectivesubjects,andaccompanyinganalysesofprospectiveandretrospectivesubjectdata thatwillbeusedtotestthedissertation'shypotheses. 58

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4ExperimentalMethodology 4.1PurposeofExperiments Ithasbeenveriedthatkinematiccurvesareavalidmeansforquantifyingtheanglecreatedby twoadjacentsegmentsbecauseeachsegmentformsavectorandtheanglebetweenthetwovectors canbecalculatedusingbasicgeometry.Todate,thereisnotagoldstandardmethodforquantifying aindividual'scoordinationdynamicswhileperformingthecyclicaltaskofgait.Sincethereisnot anestablishedreferencetocomparetheproposedmeasures(e.g.PP,CRPD)ofcoordination,these nonlinearmeasureswillbecomparedtothebestavailableanalogues:performancemeasuresfrom aselectivemotorcontrolexam,instrumentedgaitanalysisdata,performancemeasuresofspeedaccuracyduringacyclicallegmotion,walkingtasksthatchallengeasubject'sdynamicbalance, andamathematicalmodelofapendulumwhoseinitialconditionsandparametersarebasedupon instrumentedgaitanalysismeasuresfromhumansubjects.Thefollowingsectionsofthischapter describetheexperimentalmethodology,analysistechniques,andhoweachexperiment'sdatawill beusedtotestthehypothesesandaimsofthisdissertation. Thepurposeoftheexperimentsdetailedinthischapteristocollectexperimentalevidencefor testingofthehypothesesassociatedwitheachaim.WhileAim1doesnothaveanyhypotheses, thecollectionandanalysisofexperimentaldataforalargecohortfreeofgaitpathologywasused toestablishanormativereference,whichprovidesthenecessaryfoundationfortheotheraimsand hypotheses.Aim2'shypothesesexaminetherelationshipbetweenfunctionaldescriptorsofother aspectsofcoordinationandtheproposedmeasuresofcoordinationdynamicsandserveasmeans tocharacterizethesubjects.ThehypothesesforAim3useasoftwarebasedmathematicalmodel ofadoublependulumtomodelthemotionofthethighandshankduringswingperiodandthus testtheconstructvalidityofthelongheldanalogythattheselegsegmentsmimicthemotionofa passivecompoundpendulum.Lastly,thehypothesisofAim4wasdesignedwiththeclinicalutilityof thesemeasuresinmindbydeterminingifthemeasuresofcoordinationcouldbeusedtodistinguish betweendi erentgaitpatternsandthusdemonstrateanothervaluableclinicalapplicationofthese gaitmeasures. 4.2Subjects Thisstudyconsistsofgaitdatafromsubjectswithanunimpairedgaitpatternandsubjectswith anatypicalgaitpatternresultingfromeithercerebralpalsy(e.g.sti kneeorcrouchgaitpattern) 59

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oralowerlimbamputation(e.g.transtibialortransfemoral).Retrospectivesubjectmotioncapture datawasaccessedfromtheCenterforGaitandMovementAnalysis(CGMA)subjectdatabases andconsistsofunimpairedsubjects,subjectswithspasticcerebralpalsy,andsubjectswithalower limbamputation.Prospectivesubjectdatawascollectedbytheexperimenterforthisstudyand consistsofmotioncapturedataforsubjectsfreeofgaitpathologyandsubjectsdiagnosedwithspastic cerebralpalsy.ApprovaltoconductthisresearchwasgrantedbytheColoradoMultipleInstitutional ReviewBoard.Consentforallprospectivesubjectsandassentforparticipantsunder14yearsof agewasobtainedintheprivacyoftheCGMAlaboratory'sclinicalexamroom.AHealthInsurance PortabilityandAccountabilityAct(HIPAA)waiverwasgrantedtoreviewallretrospectivesubjects, meetingthestudy'sinclusioncriteria,whoseinstrumentedgaitanalysisdataisstoredontheserver atCGMA.ProspectivesubjectswererecruitedfromDenver,Coloradoandsurroundingareas. ProspectiveparticipantswererstscreenedwiththescriptprovidedinAppendixAandaninitialvisitatCGMAwasscheduledfortheinterestedparticipantsthatsatisedthisinitialscreening. Attheparticipant'svisit,thestudywasexplainedtotheindividualandifaftermeetingtheinclusioncriteriaandiftheparticipantagreedtobeenrolledinthestudy,theconsent(assentwhen applicable)formswerecompleted.Theprospectivesubjectthenwasassignedastudynumberfor de-identicationofallmotioncapturedata(Table4.1). Forthestudy'sretrospectivesubjects,allpersonalhealthinformation(PHI)wasobtained,stored, andaccessedfromthesecuredatabaseserverofclinicalgaitanalysesperformedattheCGMA,which isonlyaccessibletoCGMAsta .Onlytheprincipalinvestigatorandco-investigatorshadaccessto asubject'sPHIpriortode-identication.Inordertoidentifyretrospectivesubjectsforthisstudy, aretrospectivesubject'smedicalrecordswerereviewedsoastoobtainasubject'sname,medical recordsnumber(MRN),diagnosis,age,andanthropometrics.Anypatientfoundtobeineligible wasnotconsideredinthisstudyandnosinglepatientexceptionswerepermitted.Aretrospective subject'smotioncapturedata(e.g.markerdata,kinematicgraphs,andvideo)wasthenexaminedto verifythediagnoses(e.g.sti kneegait,crouchgaitpattern)andwalkingability(e.g.unassisted)of thesubject,asdocumentedinthesubject'smedicalrecordsandIGAclinicalreport.Afterconrming themotioncapturetrialsmetthestudy'sinclusioncriteria,thenthesubjectwasthenenteredinto thestudy. Onceithadbeendeemedthatasubjectsatisedthestudy'sinclusioncriteria,allofthesubject's motioncapturedatawasimmediatelyrelabeledandde-identiedwiththesubject'sstudynumber. Toprotectsubjectprivacy,eachsubjectwasassignedanumberandaletterdesignationassociated withthecorrespondinggroup,asshowninthetablebelow. 60

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Table4.2.1:Study'sprospectiveandretrospectivesubjectdesignations ProspectivePopulationLetterNumbering UnimpairedN1000-1019 LowerLimbAmputationB1000-1019 CerebralPalsyC1000-1019 RetrospectivePopulationLetterNumbering UnimpairedN1020-1300 LowerLimbAmputationB1020-1300 CerebralPalsyC1020-1300 4.2.1UnimpairedSubjects Maleandfemalesubjectsfreeofgaitpathologybetweentheagesof7and100yearsofagewere eligibleforparticipatinginthisstudyaspartofthereferencecohort.Allunimpairedsubjectswhose datamettheinclusioncriteriaforthisstudyfromtheCGMAnormativemotioncapturedatabase wereincorporatedintothisstudyasretrospectivereferencesubjects.Additionally,prospectively captureddatafrom20unimpairedsubjectswhosatisedthefollowinginclusionandexclusioncriteria.ProspectivesubjectswererecruitedfromtheDenverColoradoarea.Noexceptionstothese criteriaweremadeforanyofreferencesubjects. UnimpairedSubjectInclusionCriteria: Malesandfemalesbetweentheagesof7and100yearsofage. Abilitytowalk,unassistedcontinuouslyfor3minutes. Ifundertheageof18,parentconsentandsubjectassent. Cumulativetimeforover-groundwalkingtrialsmustbeatleast3minutes UnimpairedSubjectExclusionCriteria: Orthopaedicsurgeryatahip,knee,oranklewithinthelast2years. Anacutetraumaticinjurytoalowerextremitya ectingthesubject'sgait. Leglengthdiscrepancygreaterthan2cm. Diagnosisofaneuromuscularorcardiovascularimpairmentthata ectsgait. Medicationsormedicaldevicesthata ectgait. Paininthehip,knee,and/oranklejoints. 61

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4.2.2SubjectswithCerebralPalsy Thesubjectsinthisinvestigationconsistofbothprospectivelycapturedmotioncapturedata andretrospectivemotioncapturedatafromtheCGMAdatabase.Allgaitdatafromsubjectswith cerebralpalsy,whosatisedthefollowingcriteria,intheCGMAsubjectmotioncapturedatabase wereincorporatedintothisstudyasretrospectivesubjectswithspasticcerebralpalsy(CP).Subjects withspasticcerebralpalsywhowerebetweentheagesof7and100yearsofagewereeligiblefor participatinginthisstudyaspartoftheatypicalgaitgroup.Allretrospectivesubjectswithcerebral palsysatisedthefollowinginclusionandexclusioncriteria.Anypotentialsubjectswhodonot satisfythesecriteriawerenotincorporatedintothestudy;noexceptionsweremade. SubjectwithSpasticCerebralPalsyInclusionCriteria: Malesandfemalesbetweentheagesof7and100yearsofage. Retrospectivegaitdatamustcontainacompletelowerbodymarkersetandvalidkineticdata. Onlygaitdatatrialsofthesubjectwalkingunassistedwillbeused. Diagnosisofspasticcerebralpalsy. Exhibitseithersti kneegaitpattern,characterizedbyinsu cientanddelayedpeakknee exionduringswing(lessthan45 ¡ ),orcrouchgaitpattern,characterizedbyexcessivehip exionandkneeexion(greaterthan30 ¡ throughoutstance)[69]. SubjectwithSpasticCerebralPalsyExclusionCriteria: Orthopaedicsurgeryatahip,knee,oranklewithinthelast2years. Leglengthdiscrepancygreaterthan2cm. Medicationsormedicaldevicesthata ectgait. Subjectusedassistanceduringwalking(e.g.orthoses,walkers,crutches,canes,etc.) Paininthehip,knee,and/oranklejoints. 4.2.3SubjectswithaLowerLimbAmputation Allgaitdatafromsubjectswithalowerlimbamputation,whosatisedthefollowingcriteria, intheCGMAsubjectmotioncapturedatabasewereincorporatedintothisstudy.Subjectswith alowerlimbamputationwhowerebetweentheagesof7and100yearsofagewereeligiblefor 62

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participatinginthisstudyaspartoftheatypicalgaitgroup.Allprospectiveandretrospective lowerlimbamputationsubjectsinthisstudymetthefollowinginclusionandexclusioncriteria.Any potentialsubjectswhodonotsatisfythesecriteriawerenotbeincorporatedintothestudy;no exceptionsweremade. SubjectwithLowerLimbAmputationInclusionCriteria: Malesandfemalesbetweentheagesof7and100yearsofage. Abilitytowalkcontinuouslyandunassistedfor3minutes. Ifundertheageof18,parentconsentandsubjectassent. Hasbeenusingtheprostheticlimbforatleast6monthsforindependentambulationpriorto gaitanalysisatCGMA. Belowkneeorabovekneeamputation. SubjectwithLowerLimbAmputationExclusionCriteria: Orthopaedicsurgeryatahip,knee,oranklewithinthelast2years. Diagnosisofaneuromuscularorcardiovascularimpairmentthata ectsgait. Medicationsthata ectgait. Hasbeenusingtheprostheticlimbforlessthan6monthsforindependentambulationprior togaitanalysisatCGMA. 4.3Equipment Theequipmentdescribedinthissectionofthechapterpertainstotwomotioncapturedata collectionenvironments:anover-groundenvironmentandatreadmillenvironment.Thematerial inthissectionappliestobothmotioncaptureenvironments.Followingtheconventionalgaitmodel [136],passiveretro-reectivemarkerswereplacedonlowerextremitybonylandmarksandlocationsofallsubjectsbycliniciansandsta experiencedinIGA.Markertrajectorieswererecorded usingViconMXmotioncapturesystem,whosedetailsforthetwomotioncaptureenvironments areprovidedinthefollowingsections.Additionally,groundreactionforcesanddynamic,surface electromyographydatawerecollectedsimultaneouslyfrommostretrospectivesubjectsbutwerenot usedinthisanalysis.Aftermanuallyidentifyingfootoorcontactevents,llinganymarkertrajectorygaps,applyingaWoltringlterwithmeansquareerrorof17toallmarkertrajectories,and 63

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applyingtheViconPlug-in-Gaitmodelforeachsubject'strialsintheViconNexussoftware,the mostrepresentativetrialforeachsubjectwasselectedfromthevetrialscapturedforeachsubject usingacustomMatlabprogram.Usingthekinematicsandtemporal-spatialmeasuresfromthegait cyclesofeachtrialfromasubject,theprogramcalculatedthevarianceratioforeachtrial.The subject'srepresentativetrialhadthelowestvarianceratioandwasusedforallanalyses.Thecustom Matlabprograms,describedinsection4.3.3Software,extractedandusedthenecessaryinformation fromeachc3dletocalculatethestudy'skinematic,temporal-spatial,andnonlinearvariables. BothCGMAmotioncaptureenvironmentsareroutinelycheckedtoensurethecamerasprovide thesamelevelofaccuracyindetectionandmarkercentroidcalculations.Duetothiscontinual practiceofqualityassurance,thereishighcondenceinthevalidityofcomparingmotioncapture datafromthesetwoenvironments. 4.3.1Over-groundMotionCaptureEnvironment ThemainmotioncaptureenvironmentattheCGMAlaboratoryutilizesthirteeninfraredcameras oftheViconMX-40motioncapturesystemtorecordthethreedimensionalpositionofpassiveretroreectivemarkers.MarkertrajectorieswererecordedbytheViconsystemat120Hz.Allprospective subjectstraverseda362cmwalkwayinthismotioncaptureenvironment,withadditionalroomat eachofthewalkwayforgaitinitiationandtermination.Twohighdenitionvideocamerasrecorded thesagittalandcoronalplanevideoofeachprospectiveandretrospectivesubject.Topreservea prospectivesubject'sprivacyandcondentiality,allbi-planarvideoonlyrecordedthesubjectfrom theshouldersdown,therebyautomaticallyde-identifyingallvideouponcollection. Retrospectivesubjectdatafromtheoldermotioncaptureenvironmentwasalsoincorporated intothestudy.TheoldermotioncaptureenvironmentusedeightCCDanalogcamerasoftheVicon PulnixTM-6710motioncapturesystemtorecordthethreedimensionalpositionofpassiveretroreectivemarkers.AllmarkertrajectorieswererecordedbytheViconsystemat120Hz.Thesame motioncapturemarkersetsandmotioncapturedataanalysis(e.g.ltering,models)wereusedfor bothover-groundmotioncaptureenvironments. 4.3.2TreadmillMotionCaptureEnvironment ThetreadmillcaptureenvironmentattheCGMAlaboratoryutilizesasplitbeltinstrumented Bertectreadmill,Medtronicbodyweightsupportsystem,andeightinfraredViconMX-40motion capturecamerasystemtorecordthethreedimensionalpositionofpassiveretro-reectivemarkers. MarkertrajectorieswererecordedbytheViconsystemat120Hz.Twostandarddenitionvideo 64

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camerasrecordedthesagittalandcoronalplanevideowhileeachprospectivesubjectwalkedonthe treadmill.Topreserveaprospectivesubject'sprivacyandcondentiality,allbi-planarvideoonly recordedthesubjectfromtheshouldersdown,therebyautomaticallyde-identifyingallvideoupon collection.Inthetreadmillmotioncaptureenvironment,therewasadditionalequipmentusedto modifytheswinglimbadvancementandimposerangeofmotionlimitationsfortheunimpaired prospectivesubjectsinordertomimicthebiomechanicallimitationsseeninsubjectswithcerebral palsy.Furtherexplanationsaboutthisadditionaltreadmillroomequipmentareprovidedinthe followingsub-sections. 4.3.2.1BodyWeightSupportSystem Asasafetyprecautionduringalltreadmillwalkingtrials,everyprospectivesubjectworewearing asafetyharnessthatwasattachedtoabodyweightsupportsystem(BWSS).Intheeventthe subjectbegantofall,theBWSSwouldengageandcatchthepersonbeforehittingthegroundand preventanyfallrelatedinjuries.Toreducediscomfortandprovideanoptimalt,theharnesswas selectedtomatchthesizeofeachsubject.TohelpreduceBWSSrelatedvariablesthatcouldalter theirgaitpattern,noneoftheprospectivesubjectsheldthehandrailsduringtheTMtrials. 4.3.2.2SwingLimbAssistDevice Thelegswingextensionassistivedevice(LSEAD)isanon-invasivepieceofrehabilitationequipmentthatwasattachedtothesubject'sshoesduringtreadmillwalking(Figure4.3.1).TheLSEAD deviceassistsswinglimbadvancementbyusingalinearspringandpulleysystemtopullthesubject'slegforward(whenfacingthedevice)duringswingandtherebyprovideanassistiveforce.The devicewasalsousedwhenthesubjectswalkedintheoppositedirection,thusprovidingresistance toswinglimbadvancement. 65

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Figure4.3.1:Legswingextensionassistivedeviceprovidingswinglimbassistance(A)andresistance (B)whenaprospectivesubjectwalksonthetreadmillwiththebodyweightsupportsystem. 4.3.2.3RestrictingRangeofMotion Twodi erentbraceswereusedtosimulatetherestrictedrangeofkneeandanklejointmotion commonlyseeninindividualswithsti kneeandcrouchgaitpatterns.Thebraceswereonlyapplied tothedominantlegoftheprospectiveunimpairedsubjects. Knee Brace. Alockingkneebracewithwraparoundthighandshankattachmentpointswas usedtorestricttherangeofmotionfortheprospectivesubjectsfreeofgaitpathologyastheywalked onthetreadmill.Thekneeangledialandlockingpinswereusedtopositionandxthekneebrace intoafullyextendedposition(180 ¡ extension)andaexedposition(60 ¡ exion).Tosimulatethe sti kneegait(fullextension)andcrouchgait(exion)patternsandstudyhowsubjectsadapted tothesexedkneepositions,thekneebracewaswornonthesubject'sdominantleg.Thebrace wasttoeachsubjectusingthegenericsizesofsmall,medium,andlarge.Sincethelateralknee, thigh,andshankmotioncapturemarkersweremovedtoputthebraceonthesubject'sleg,anew statictrialwastakenforthekneebracecondition.Byconstrainingmovementatajoint,suchas theknee,inindividualsfreeofgaitpathology,theresultingchangesincoordinationduetolimiting thedegreesoffreedomatthekneewerestudied. Ankle Brace. Ananklebrace,whichxedtheankleinaneutralposition,wasusedtorestrict ankledorsiexionandplantarexionduringwalkinginsubjectsfreeofgaitpathology.Thebrace wasttoeachsubjectusingthegenericsizesofsmall,medium,andlarge.Sincethelateralshank, 66

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ankle,andfootmarkersmotioncapturemarkersweremovedtoputthebraceonthesubject'sleg, anewstatictrialwastakenfortheanklebracecondition.Solidankle-footorthosesarecommonly prescribedbyclinicianstoaddressexcessiveplantarexionduetospasticityinthemusclesofthe leg'sposteriorcompartment.Otherstudieshaveshownthatconstrainingjointmotionattheankle hasasignicantimpactonthetimingandsequencingofmuscleactivation.Thereforebyproviding restrictionattheanklejoint,itwasexpectedthatsubjectsfreeofgaitpathologywouldadopta di erentwalkingstrategybychangingthecoordinationofmoreproximalsegments. 4.3.3Software Allmotioncapturedatalesandinitialmotioncaptureleprocessingwasperformedusingthe ViconLifeSciencesSoftwareSuite.Aftermanuallyidentifyingfootoorcontactevents,applyinga Woltringlterwithmeansquareerrorof17toallmarkertrajectories,andapplyingtheViconPlugin-Gaitmodelforeachsubject'strialsintheViconNexus1.8.5software,themostrepresentative trialforeachsubjectwasselectedfromthevetrialscapturedforeachsubjectusingacustom Matlabprogram.Usingthekinematicsandtemporal-spatialmeasuresfromthegaitcyclesofeach trialfromasubject,thisMatlabprogramcalculatedthevarianceratioforeachtrial.Asubject's representativetrialhadthelowestvarianceratio.AowchartofthecustomMatlabcode'salgorithm forselectingasubject'srepresentativetrialislocatedinAppendixE.Onlytherightlegsegments fromeachunimpairedsubject'srepresentativetrialcontributedtodatasetandonlya ectedlegsin theothersubjectpopulationswereusedtocreatethoserespectivedatasets. AcustomBodyBuilderprogramwaswrittentocreatethevirtualtargetboundariesforthe speed-accuracytask(prospectivesubjectsonly)andusedtovalidatethevirtualtargetboundaries generatedbycustomMatlabprogram(CERBERUS),whichanalyzedthismotioncapturetask. NumerouscustomMatlabprogramswerewrittentocalculatethevariablesforthevariousaimsand theirhypotheses.Table4.2providesalistofthemaincustomMatlabprograms,theircorresponding aims,andprimarypurpose. Table4.3.1:ListofcustomMatlabprogramsusedfordataanalysis. ProgramAimPurpose DIONYSOSAim1,4GeneratePPsandCPRDsfromc3dle(s)orpendulummodel GAMSAim1,4GenerateconventionalIGAmeasures PEGASUSAim3Compoundpendulummodel CERBERUSAim2Analyzesspeed-accuracy,tandemwalking,and90 ¡ turningtasks CDIAim1,4Generatescoordinationdynamicsindexfromc3dle CPSAim1,4Generatescoordinationperformancescorefromc3dle SAPAi1,2,3,4Calculatesdescriptivestatisticsandcorrelationmatrix 67

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Asdetailedmoreinthefollowingsections,statisticalanalyseswereperformedinMicrosoftExcel, JMP,Minitab,SAS,orMatlabandalldescriptivestatisticalanalyseswereperformedinatleasttwo di erentsoftwareprogramstoreducetheoccurrenceoferrorsandserveasaninternalvalidationof calculations. 4.4ExperimentalProtocols Thefollowingexperimentalprotocolsaredescribedfortwoclinicalpopulations:unimpaired subjectsandsubjectswithanatypicalgaitpattern(e.g.cerebralpalsyorlowerlimbamputation). Therearetwoseparatedatasetsforthesesubjects,oneconsistingofonlyprospectivesubjectsand asecondconsistingofonlyretrospectivesubjects.Theprospectivesubjectdatasetisdistinguished fromtheretrospectivesubjectdatasetbyabatteryofclinicalmeasuresanddonningofshoestoenable multipletaskvariationsforboththeover-groundandtreadmillmotioncaptureenvironments.The followingexperimentalprotocolmainlyfocusesontheprospectiveexperimentalprocedures. Priortoanymotioncaptureexperiments,theanthropometricsofeachprospectivesubjectwas measuredandrecordedwithatapemeasure,calipers,andscale.Theseanthropometricvalueswere enteredintothemotioncapturecomputersandusedtocreateauniqueskeletalcoordinatesystem foreachsubject.Thisvirtualskeletalcoordinatesystemwasusedbyconventionalandnonlinear methodstocalculatevariousmeasuresofgait.Table4.3providesalistoftheanthropometricsthat weremeasuredfromeachprospectivesubject. Table4.4.1:Anthropometricsmeasuredfromeachsubject,where*indicatesprospectivesubject measurements. Anthropometrics Height(cm) Bodymass(kg) Left&rightleglength(cm) Left&rightkneewidth(cm) Left&rightanklewidth(cm) Left&rightelbowwidth(cm)* Left&rightwristthickness(cm)* Left&righthandthickness(cm)* Forallprospectivelycaptureddata,eachsubjectworeafullbodymarkersetandhisorherown shoes(Figure4.4.1,Figure4.4.2).Allretrospectivesubjectsworealowerbodymarkerset,which isidenticaltothefullbodymarkersetsshownbelowbutdoesnotincludethehead,torso,orarm markers. 68

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Figure4.4.1:Anterior(left)andposterior(right)viewsoffullbodystaticmarkerset. 69

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Figure4.4.2:Anterior(left)andposterior(right)viewsofthefullbodydynamicmarkerset. Allretrospectivesubjectswithunimpairedgaitorcerebralpalsywerebarefootduringovergroundwalking.Retrospectiveandprospectivesubjectswithalowerlimbamputationworeshoes onboththeprostheticandintactlimbduringallmotioncapturetrials. 4.4.1UnimpairedProspectiveSubjectExperimentalProtocol Thefollowingtable(Table4.4)outlinestheorderofexperiments,datacaptureprocedurefor eachunimpairedprospectivesubject,andcorrespondinginstrumentationassociatedwitheachexperiment/task.Priortoplacingmarkersonaprospectivesubject,theinvestigatormeasuredeach subject'santhropometricdata(Table4.3). 70

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Table4.4.2:Overviewofthelocationandinstrumentationusedforexperimentsfortheunimpaired prospectivesubjects. LocationTaskInstrumentation ClinicalExamRoomAnthropometricDataCalipers,tapemeasure,scale OGMoCap 1.WalkatVss 2.Speed-AccuracyTask 3.ModiedICARSTasks 1-3.Fullbodymarkerset BiplanarHDVideo TMMoCap 4.LevelwalkingatVss 5.SpeedTasks 6.AssistiveTask 7.ResistiveTask 8.Knee/AnkleRangeofMotionTasks 9.SCALE&ICARSTasks 4-9.Fullbodymarkerset BiplanarHDVideo 4.4.1.1ProspectiveUnimpairedSubject:Over-groundWalkingTask Toestablisheachsubject'sbaselinegaitforover-groundwalking,eachsubjectwalkedinthemain motioncapturelaboratory(over-ground)whilewearingafullbodymarkerset(Figure4.3).Each subjectwillwalkataself-selectedwalkingspeed(Vss)onthelevelover-groundsurfaceuntilatleast 3minutesofgaitdatahasbeencollected.Themotioncapturesoftware(ViconLifeSciencesSuite) willbeusedtoprovidethemeanwalkingspeedandmeansteplengthforeachsubject. 4.4.1.2ProspectiveUnimpairedSubject:Speed-AccuracyTask Eachprospectivesubjectperformedalowerextremityspeed-accuracytasktocharacterizeany impairmentinasubject'saccuracyofvoluntaryreciprocalmovements.Thistaskisamodied versionoftheupperextremityspeed-accuracytaskthatadaptsthisclinicaltaskfortheanteriorposteriorswingingmotionofthelowerleg,similartotheswingperiodmotionduringthegaitcycle [14,15].Squarefoottargetsweresizeforeachsubject,usingthedistancebetweenthesubject's rstandfthmetatarsalhead.Theseanatomicalboneylocationswereidentiedbypalpation andthedistancewasmeasuredwithcaliperswhilethesubjectworethesameshoesinwhichall motioncapturedatawasconducted.Threesetsoffoottargetswerecreated:100%ofthesubject's shoe/footwidth,80%oftheshoe/footwidth,and120%oftheshoe/footwidth.Forconsistency andinconsiderationofthebi-planarvideocameras,onefoottargetwasplacedwitha10cmo set fromeitherforceplatenumber6orforceplatenumber3ofthemainlab'stenforceplatearray, dependingonthesubject'sdominantleg(Figure4.4).Themeansteplengthwascalculatedfrom therstthreeover-groundwalkingtasksandusedasthedistancebetweentheleadingedgeofeach foottargetandprovidedthelocationofthesecondfoottarget.Foottargetsweresecuredtothe oorusingtapeandaclearprotectivecoating.Priortostartingeachtrial,thetargetlocationwas 71

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doubledcheckedbythisinvestigatortoensurenomovementhadoccurredasaresultoftheprevious trial. Forthistask,thesubjectstoodononelegwhileontheforceplatearrayintheover-ground motioncaptureenvironment.Thesubjectthenusedtheswinglimbtoalternatetappingofthefoot betweentheforwardtarget(locatedonaforceplate)andbackwardtarget(locatedonadi erent forceplate)asquicklyaspossiblewhilemaintainingaccuracyoftappingthefootoneachtarget. Subjectswereinstructedtopositionthemselvesinordertoseeeachtargetpriortoafoottapand soastoreducetheinuenceofobscuredvision,whichcouldhinderthesubject'saccuracy.Subjects performedthetaskwiththesmallesttargetrstandthenallsubsequenttargetswerepositioned overtheprevioussmallertargetsoonlythecurrenttargetwasvisible.Thetargetswereplacedina plasticprotectivesheet,whichwastapedsecurelytotheoor,inordertoreducewearonthetarget andensureplacementofeachtargetwasconsistent. 72

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Figure4.4.3:Speed-Accuracytasktargetsetupandsizing.A)Targetsetupforarightleg,B)target setupforaleftleg. Forsafetyandsubjectstability,allsubjectsusedbothhandstoholdontoaxedsupportbar whileperformingthetask.Thefollowinggureprovidesaschematicofthespeed-accuracytaskto beperformedbyeachprospectiveunimpairedsubject. 73

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Figure4.4.4:Functionaldiagramofthelowerextremityspeed-accuracytask. Thedurationofeachtrialwasxedto30seconds.Thistemporalconstraintwasselectedwith considerationtothepotentiallimitedenduranceofsubjectswithanatypicalgaitpatternandwas looselybasedupontheFitts'experimentalparadigm[110].Thepurposeofthisexperimentisto characterizeanyprospectivesubject'sspeedandaccuracyimpairmentsduringthereciprocalleg movementsandexploretherelationshipbetweenthisexperiment'soutcomesandthemeasuresof coordinationdynamics.Toprovideenoughsamplesforstatisticalcomparisonofthesedi erenttask conditions,eachsubjectperformedthistaskthreetimesforeachsetoffoottargets,totaling9trials. 4.4.1.3ProspectiveUnimpairedSubject:ModiedICARS/SARATasks ProspectivesubjectsperformedselectwalkingtasksfromtheInternationalCooperativeAtaxia RatingScale(ICARS)andScalefortheAssessmentandRatingofAtaxia(SARA)exams.In themainmotioncaptureenvironment,allprospectiveunimpairedsubjectsperformedthetandem walkingand90 ¡ turningtasks.Forthetandemwalkingtask,eachsubjectwasinstructedtowalk whiletouchingtheadvancefoot'sheeltothelaggingfoot'stoe(Figure4.4.5).Subjectswereallowed 74

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tofreelypositiontheirarmsforbalanceduringthistask.Eachsubjectperformedthistaskfour timesonthesamewalkwayastheover-groundwalkingtasks. Figure4.4.5:Functionaldiagramofover-groundtandemwalkingtask. Nextasimple"T"constructedfromwhitepapertapewasplacedonforceplate9,whichis approximatelythelocationofleastparallaxfromthesagittalplanevideocameraandhalfwayin thewalkway(Figure4.4.6).Thesubjectwasinstructedtowalknormallyataself-selectedspeed towardthe"T"anduponreachingthemark,madea90 ¡ turntoeithertheleftorright.Eachsubject performedaminimumofoneandmaximumthreeturnsperside. Figure4.4.6:Diagramof90 ¡ walkingtasksetupwiththeT'tapetargetindicatingwheretoinitiate theturn(transverseview). 75

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4.4.1.4ProspectiveUnimpairedSubject:TreadmillWalkingTask Todetermineeachprospectivesubject'spreferredwalkingspeedforthetreadmilltasks,themean over-groundwalkingspeedfromthreetrialswascalculatedforeachsubject.Thisaverageovergroundwalkingspeedwasthenusedtosetthetreadmillbeltspeedforthistask.Eachprospective subjectwalkedforatleast3minutesonthetreadmillwiththebeltspeedsetatthismeanVss. 4.4.1.5ProspectiveUnimpairedSubject:ChangesinWalkingSpeedTask Thee ectsofchangesinwalkingspeedoncoordinationdynamicswereexaminedforleveltreadmillwalking.Thesubject'saverageVsswasusedtocalculatewalkingspeedsthatare10and20 percentslowerandfasterthanVss(Table4.5).Alternativelydescribed,thesubjectwalkedonthe treadmillwithabeltspeedof80%,90%,110%,and120%.Walkingspeedsfasterthan120%were notincludedinordertoadequatelyavoidthetransition(andthereforechangeingaitpattern)from walkingtorunning,whichoccursatapproximately130-140%ofVss[13]. Table4.4.3:Changesinwalkingspeedconditionsforunimpairedprospectivesubjects. BeltSpeedTaskDuration 80%ofVSSLeveltreadmillwalking3minutes 90%ofVSSLeveltreadmillwalking3minutes 110%ofVSSLeveltreadmillwalking3minutes 120%ofVSSLeveltreadmillwalking3minutes 4.4.1.6ProspectiveUnimpairedSubject:ChangesinAssistiveForcesTask Thee ectofaddingassistiveexternalforcestotheadvancingswinglegduringthetaskofswing limbadvancementoncoordinationwasperformedonthetreadmillusingalegswingextensionassist device(LSEAD).TheLSEADdeviceassistsswinglimbadvancementbyusingalinearspringand pulleysystemtopullthesubject'slegforwardduringswingandtherebyprovidinganassistiveforce. Eachsubjectwalkedfor3minuteswiththeLSEADdeviceattachedtothesubject'sshoes.Ifthe 5lbflinearspringwastoomuchforceforthesubjecttowalksafelyandfortheallottedtaskduration, thenthe3lbflinearspringwasusedinstead. 4.4.1.7ProspectiveUnimpairedSubject:ChangesinResistiveForcesTask Thee ectofaddingresistiveexternalforcestotheadvancingswinglegduringthetaskof swinglimbadvancementoncoordinationwasperformedonthetreadmillusingtheLSEAD.Inthis condition,theLSEADattachestothesubject'sshoesasthesubjectwalksintheoppositedirection fromthepreviousLSEADwalkingtask.Whenwalkinginthisdirection,theLSEADdeviceresists 76

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swinglimbadvancementbyusingalinearspringandpulleysystemtopullthesubject'slegbackward duringswing.Thesamelinearspringforceasintheassistiveconditionwasalsousedinthisresistive condition.Eachsubjectwalkedfor3minuteswiththeLSEADdeviceattachedtothesubject'sshoes. 4.4.1.8ProspectiveUnimpairedSubject:ChangesinJointRangeofMotionTasks Thee ectslimitingtherangeofmotionforkneeandanklejointsoncoordinationweresimulated byhavingtheunimpairedsubjectwearpassivebracesonthekneeandanklejointsduringlevel treadmillwalkingatVss.Thiscommonlyemployedmethodofcreatingatemporaryimpairment inanunimpairedsubjectwasincludedinordertosimulatesti kneeandcrouchgaitpatterns insubjectswithanintactnervoussystem.Priorinvestigationsofpathologicalgaithaveshown signicantchangesinkinematicsandtemporalspatialmeasuresinsubjectsbeforeandaftersurgical interventionsthata ordedsubjectswithanincreasedrangeofmotion[7]. Limitationofthekneejoint'srangeofmotionwasaccomplishedbyhavingeachsubjectwear ahingedkneebracewhilewalkingonthetreadmillfor3minutes.Thetwokneerangeofmotion limitationswillsimulateasti kneegaitpattern(xedat180 ¡ extension)andacrouchgaitpattern (xedat60 ¡ extension)[11].Thekneebracepinswereusedtosettheexionandextensionranges foreachconditionandensuredthebraceremainedxedinthedesiredposition.Limitationofthe anklejoint'srangeofmotionwasaccomplishedbyhavingeachsubjectwearasolid(non-articulating) walkingankleboottopreventplantar/dorsi-exion(0 ¡ dorsi/plantar-exion).Thefollowingtable providesasummaryofthistask'sconditions,rangeofmotion,andapplicableside(s). Table4.4.4:Jointrangeofmotionlimitationsforunimpairedprospectivesubjects. JointTaskSide&Duration A.Knee A1.180 ¡ A2.60 ¡ A1.Dominantleg,3minutes A2.Dominantleg,3minutes B.Ankle B1.0 ¡ B1.Dominantleg,3minutes Amongtheavailablebracesizes,eachsubjectwasttedtoanappropriatelysizedbraceforthese treadmillwalkingtasks.Thekneeandanklebracesutilizedforthistaskwereobtainedfromthe OrthopedicClinicatChildren'sHospitalColorado(pediatricsizes)andtheDepartmentofPhysical TherapyattheUniversityofColorado(adultsizes). 4.4.1.9ProspectiveUnimpairedSubject:SCALEExamandModiedICARSTask PriortoperformingtheSelectiveControlAssessmentoftheLowerExtremity(SCALE)exam onanyprospectivesubjects,Ireviewedtheclinicaltrainingvideos,accompanyingworksheet,and 77

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presentationtolearnhowtoproperlyinstructasubjectandperformeachtask.Thisinvestigator reviewedthetrialstoverifyeachprospectivesubject'sSCALEscoreandachievedproceduraldelity withaclinicaladvisorandco-investigatorexperiencedinneurologicalphysicaltherapy.Althougha detaileddescriptionoftheSCALEtasksandscoringcriteriaisprovidedinAppendixB,thefollowing generaldescriptionso eranoverviewofthetasksandexperimentalprotocolforallprospective subjects. Afterremovingallpassiveretro-reectivemarkers,eachprospectivesubjectlayonhis/herside andsatonanexamtableinthetreadmillmotioncaptureenvironmentfortheseperformancemeasures.Eachsubjectperformedtheselectivevoluntarymovementtasksatthehip,knee,andankle aftertheexaminerdemonstratedeachjoint'staskbypassivelymovingthejointthroughthedesired motion.Eachtaskwasverballyexplainedanddemonstratedtothesubjectpriortothesubject performingthetask.Thesubjectwasthengivenaverbalcuetoperformthetaskalongwitha three-secondverbalcadencebytheexaminer.Thesubject'scomfortwasalsomonitoredthroughout thepassivedemonstrationofthesetasksbyaskingeachsubjectifhe/shewasexperiencinganypain. Thefollowinggureprovidestheowchartusedforthisportionoftheprospectivesubjectdata capture. Figure4.4.7:FlowchartoftheSCALEtasksperformedforeachprospectivesubject. 78

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Thesubject'shiprangeofmotionforexionandextensionwaspassivelydemonstratedbythe examinerandthenactivelyperformedbythesubjectwhilelyingonhis/herside.Thistaskwas performedforeachleg.Theexaminerassessedthesubject'spassivehipabductionrangeofmotion whilethesubjectlayonhis/herside.TheThomastestwasperformedtoassesthetightnessofthe musclesinvolvedinore ectinghipexion(e.g.rectusfemoris,illiopsoas)[141].Nextthesubject's kneeexion/extensionrangeofmotionwaspassivelyandactivelyassessedwhilethesubjectsaton theedgeoftheexamtable.Lastly,thesubject'sankleplantarexion/dorsiexionpassiverangeof motionwasassessedbytheexaminerandthenactivelyperformedbythesubject. Videoofthetaskwasrecordedandusedafterthesubject'sdatacapturevisittoscorethe subject'sabilitytoperformthevariousSCALEexamtasks.WhiletheoriginalSCALEexam includesmeasuresforthesubtalarjointandtoes,thesesegmentswerenotincludedbecausethisbody ofworkisexaminingsegmentalcoordinationdynamicsandcharacterizedthefootasonesegment. Furthermore,sincetheprospectivesubjectsworeshoesforallwalkingconditionstheabilityto accuratelydistinguishamulti-segmentedfootwouldnotbepossiblewiththecurrentlyavailable andvalidatedmotioncapturemodels.ASCALEscoreforeachlimbisobtainedbysummingthe pointsassignedtoeachjoint.Sinceonlythehip,knee,andankle,jointsarebeingmeasuredforthis researchproject,amaximumlimbscoreof6pointsispossible. Theknee-tibiaslidetestfromtheICARS/SARAexamswasthenperformedinasupineposition (layingontheexamtable)withtheheadtiltedsothatvisualinputwaspossible.Beforethesubject performedthetaskitwasrstexplainedanddemonstrated.Afterreceivingaverbalcuetobegin thetask,thesubjectraisedplacedtherightheelontheleftknee,andthenslidtherightheeldown theanteriortibialcrest/surfaceoftherestingleftleguntilreachingtheleftankle.Oncetheright heelwasattheleftankle,thesubjectraisedtheheelo theleftlegandrepositionedtherightheel ontheleftknee.Thesubjectrepeatedthisknee-heelslidingmotionthreetimeswiththerightleg andthenthreetimeswiththeleftleg.Videoofthetaskwasrecordedandusedafterthesubject's datacapturevisittoconrmthescoreforthistask,whichreectedthesubject'sabilitytoperform thetask.Thetaskwasscoredbytwodi erentrequirements,whichtotalamaximumpossiblescore of8.Therstrequirementscoredthesubjectonhisorherabilitytoperformthetask(0=unable toperformand4=noimpairment)andthesecondrequirementscoredthesubjectontheamount ofactiontremorduringthetask(0=uninterruptedtremorand4=notremor).Amoredetailed descriptionforthescoringcriteriaislocatedinAppendixB. 79

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4.4.2ExperimentalProtocolforProspectiveSubjectswithanAtypicalGaitPattern Thefollowingtableoutlinestheorderofexperiments(detailedbelow),datacaptureenvironment foreachprospectivesubjectwitheitheralowerlimbamputation(LLA)orcerebralpalsy(CP)and correspondinginstrumentationassociatedwitheachtask.Priortoplacingmarkersonaprospective subject,theinvestigatormeasuredeachsubject'santhropometricdata. Table4.4.5:Overviewofthelocationandinstrumentationusedforexperimentsfortheprospective subjectswithanatypicalgaitpattern. LocationTaskInstrumentation ClinicalExamRoomAnthropometricDataCalipers,tapemeasure,scale Over-groundMoCapEnvironment 1.WalkatVss 2.Speed-AccuracyTask 3.ModiedICARSTasks 1-3.Fullbodymarkerset BiplanarHDVideo TreadmillMoCapEnvironment 4.LevelwalkingatVss 5.SCALE&ICARSTasks 4-5.Fullbodymarkerset BiplanarHDVideo 4.4.2.1ProspectiveAtypicalSubject:Over-GroundWalkingTask Eachprospectivesubjectwalkedinthemainmotioncapturelaboratorywhilewearingafullbody markersettoestablishthebaselineover-groundgaitpattern.Eachsubjectwalkedataself-selected walkingspeed(Vss)onthelevelover-groundsurfaceforapproximately3minutes.Ifasubjectwas unabletowalkforacumulativeamountof3minutes,thenthesubjectwasaskedtowalkuntil he/shebegantofeeltired.Restsweretakenasneededtotrytoreducefatigue.Asidefromthe subjectdependentmodicationsmentionedhere,theprocedures,measures,andequipmentforthese subjectswerethesameasthatdetailedbythesubjectswithanunimpairedgaitpatternabovefor thistask. 4.4.2.2ProspectiveAtypicalSubject:Speed-AccuracyTask Eachprospectivesubjectwithanatypicalgaitpatternperformedthelowerextremityspeedaccuracytasktocharacterizeanyimpairmentinthesubject'saccuracyofvoluntaryreciprocal movements.Intheeventasubjectwasunabletophysicallyreachthetargetswhenplacedadistance apartequaltothemeansteplength,thetargetdistancewassystematicallyreduced(incrementsof 1cm)untilthesubjectwasabletoreachbothfoottargets.Subjectswereinstructedtoposition themselvesinordertoseeeachtargetpriortoafoottapandsoastoreducetheinuenceof obscuredvision,whichcouldhinderthesubject'saccuracy.Forsafetyandsubjectstability,all subjectsusedbothhandstoholdontoaxedsupportbarwhileperformingthetask.Theduration 80

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ofeachtrialwasxedto30seconds.Dependingontheseverityofgaitimpairmenteachsubject performedthistaskaminimumofoneandmaximumofthreetimesforeachsetoffoottargets.Aside fromthesubjectdependentmodicationsmentionedhere,theprocedures,measures,andequipment forthesesubjectswerethesameasthatdetailedbythesubjectswithanunimpairedgaitpattern aboveforthistask. 4.4.2.3ProspectiveAtypicalSubject:ModiedICARS/SARATasks Inthemainmotioncaptureenvironment,allprospectivesubjectsperformedthetandemwalking and90 ¡ turningtasks.Eachsubjectperformedthistaskamaximumoffourtimesonthesame walkwayastheover-groundwalkingtasks.Ifsubjectswereunabletosafelywalkindependently,the investigatorheldtheirhandstopreventfalling.Ifsubjectswereunabletotouchaheeltoatoe, theywereinstructedtogetascloseaspossible.Asidefromthesubjectdependentmodications mentionedhere,theprocedures,measures,andequipmentforthesesubjectswerethesameasthat detailedbythesubjectswithanunimpairedgaitpatternaboveforthistask. Aswiththeunimpairedprospectivesubjects,asimple"T"constructedfromwhitepapertape wasplacedonforceplate9,atapproximatelythelocationofleastparallaxfromthesagittalplane videocameraandhalfthelengthofthetotalmotioncapturewalkway.Thesubjectwasinstructedto walknormallyataselfselectedpacetowardthe"T"anduponreachingthemark,makea90degree turntoeithertheleftorright.Dependingonthesubject'swalkingability,eachsubjectperformed aminimumofoneleftandrightturntoamaximumofthreeleftandthreerightturnsforthis task.Asidefromthesubjectdependentmodicationsmentionedhere,theprocedures,measures, andequipmentforthesesubjectswerethesameasthatdetailedbythesubjectswithanunimpaired gaitpatternaboveforthistask. 4.4.2.4ProspectiveAtypicalSubject:TreadmillWalkingTask Themeanover-groundwalkingspeedfromthreetrialswascalculatedforeachprospectivesubject. Thisaverageover-groundwalkingspeedwasthenusedtosetthetreadmillbeltspeedforthis task.Eachsubjectwalkedforaminimumof30secondsandamaximumof3minutesonthe treadmillwiththebeltspeedsetatthismeanself-selectedwalkingspeed(Vss).Forindividualswho wereunabletowalkonthetreadmillatthesamespeedastheirover-groundwalkingtrials(asis commonforindividualswithcerebralpalsy),thetreadmillbeltspeedwassystematicallylowered in10%incrementsuntilthesubjectwasabletowalksafely,inacontrolledmanner,andwithout theassistanceofthebodyweightsupportharness.Insuchsituations,thereducedbeltspeedwas 81

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recorded.Asidefromthesubjectdependentmodicationsmentionedhere,theprocedures,measures, andequipmentforthesesubjectswerethesameasthatdetailedbythesubjectswithanunimpaired gaitpatternaboveforthistask. 4.4.2.5ProspectiveAtypicalSubject:SCALEandModiedICARSTasks PriortoperformingtheSCALEexamonanyprospectivesubjects,thisinvestigatorreviewedthe clinicaltrainingvideos,accompanyingworksheet,andpresentationtolearnhowtoproperlyinstruct asubjectandperformeachtask.Aswiththeunimpairedprospectivesubjects,thisinvestigator reviewedthetrialsoftheprospectivesubjectswithanatypicalgaitpatternandachievedprocedural delitywithaclinicaladvisorandco-investigatorexperiencedinneurologicalphysicaltherapy. 4.4.3RetrospectiveSubjectMotionCaptureData Aspreviouslymentioned,themotioncapturedataoftheretrospectivesubjectsinthisinvestigationwasobtainedfromtheretrospectivesubjectdatabaseatCGMA.Themotioncaptureforall retrospectivesubjectsfromtheCGMAdatabasecontainsasubject'santhropometricdata,biplanar video,andtri-planarlowerbodymarkertrajectories.Toestablisheachretrospectivesubject'sbaselineover-groundmeasuresofgait,allunassistedwalkingtrialswereconcatenatedusingfootstrike asthecommonjoiningtemporalevent.Thesubject'srepresentativewalkingtrialwasthenassessed withthesamemotioncapturemodelandMatlabanalysesastheprospectivesubjectsover-ground walkinggaitdata.ClinicalIGAfromtheCGMAretrospectivedatabaseusuallyonlycontainsmotioncapturedataforthetaskofover-groundwalking.Therefore,over-groundwalkingistheonly commonmotioncapturetaskbetweenallretrospectiveandprospectivesubjectsinthisdissertation andcomparisonsoftheotherprospectivemotioncapturetaskstoretrospectivesubjectswerenot possible. 4.4.4MathematicalSoftwareModelofaCompoundPendulum TheLagrangianapproachwasusedtosolveforadoublependulum'sequationsofmotion.Initially,theequationsofmotionwerecalculatedforapendulumwithoutdampingorinertiaterms andthenagainincludingtheseterms(AppendixC ) .ThelatersetofequationsofmotionwasimplementedintotheMatlabmodelandusedforallanalyses. Thebaselinemathematical,two-dimensionalpendulummodelconsistsofaxedpivotandtwo linkages.Thispendulummodelprovidedatheoreticalanaloguetothesagittalmotionofthethigh andshanksegmentsduringlevelover-groundwalking.Thelength,centerofmasslocation,initial 82

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angulardisplacement,initialangularvelocity,andmassforthependulumlinkageswerecalculated fromthemeanofthecorrespondingvariablesfromtheretrospectiveunimpairedsubjects,allsubjects withsti kneegaitandcrouchgaitpatterns,andallsubjectswitheitheratranstibialortransfemoral amputation.Thesesubject-derivedvariableswereusedinane orttocreateapendulummodelthat isbasedupontheinitialconditionsofhumansubjectsatthebeginningofswingperiod.The pendulummodelwascreatedinMatlabusingthecodeprovidedinAppendixCtosolveforeach linkage'sangulardisplacementandangularvelocity. 4.4.4.1CompoundPendulumSoftwareModel Amathematical,two-dimensionalcompoundpendulumsoftwaremodelconsistingofaxedpivot andtwolinkagesprovidedatheoreticalanaloguetothesagittalmotionofthethighandshank segmentsduringlevelover-groundwalking.Theresultingmotionsofthispendulummodelfor variousdampingcasesservedasatheoreticalcomparisontotheswinglimbadvancementdynamics ofthevarioussubjectcohortsinthisstudy.Thevariablesfortheinitialconditionsofthesoftware modelweregeneratedfromeachcohort'smeanofthevariableslistedinTable4.8.Thesubject cohortsusedforthependulummodelconsistedofallunimpairedsubjects(N),allsubjectswitha sti kneegaitpattern(SKG),allsubjectswithacrouch(C)gaitpattern,allsubjectswithabelow kneeamputation(BK),andallsubjectswithanabovekneeamputation(AK). Table4.4.6:Pendulummodelparameters,model'sinitialconditions,andthesubjectinstrumented gaitanalysisdatafromwhichtheyarederived.Thesubjectdatavariablesaremeanvaluesforeach ofthestudy'scohortsandFOindicatestheinstanceoffooto duringthegaitcycle. ModelVariablesSubjectData 1.Lengthofproximallinkage1.Thighlength 2.Lengthofdistallinkage2.Shanklength 3.Massofproximallinkage3.Thighmass 4.Massofdistallinkage4.Shankmass 5.Centerofmasslocationofproximallinkage5.Thighcenterofmasslocation 6.Centerofmasslocationofdistallinkage6.Shankcenterofmasslocation 7.Initialangulardisplacementofproximallinkage7.ThighangulardisplacementatFO 8.Initialangularvelocityofproximallinkage8.ThighangularvelocityatFO 9.Initialangularaccelerationofdistallinkage9.ShankangularaccelerationatFO 10.Initialangulardisplacementofdistallinkage10.ShankangulardisplacementatFO 11.Initialangularvelocityofdistallinkage11.ShankangularvelocityatFO 12.Initialangularaccelerationofdistallinkage12.ShankangularaccelerationatFO 13.Durationofmodelsimulation13.Swingperiodduration Thependulummodelwasrunforfourdi erentdampingconditionsforeachsubjectcohort, totalingtwentysimulations.Theproximalanddistallinkages'dampingcoe cientforeachcondition weresetequaltoeachother.Table4.9liststhefourclassicaldynamicsdampingcasesusedforeach 83

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cohort'spendulumanalysis. Table4.4.7:Descriptionofthefourdampingconditionsandcorrespondinglinkagedampingcoe cientvalues. DampingCoe cientDampingConditionCohortComparison 1. # Prox = # Dist =0 1.Un-damped1.N,SKG,C,BK,AK 2. # Prox = # Dist =0 5 2.Underdamped2.N,SKG,C,BK,AK 3. # Prox = # Dist =1 3.Criticallydamped3.N,SKG,C,BK,AK 4. # Prox = # Dist =1 5 4.Overdamped4.N,SKG,C,BK,AK Thependulummodel'sinitialconditionswerecalculatedfromeachsubject'srepresentativetrial usingtheMatlabalgorithmdetailedinAppendixE.Acohort'sensembleaveragewasthencalculated usingeachsubject'sinitialconditionsandthisensemblecohortaverageprovidedthependulum model'sinputforeachgaitpatternsimulation.Agaitpatternsimulationforthependulummodel wasrunfortheretrospectivenormativecohort,allsubjectswithasti kneegaitpattern,allsubjects withacrouchgaitpattern,allsubjectswithabelowkneeamputation,andallsubjectswithanabove kneeamputation. Themodelusedacohort'sinitialconditionsandtheequationsofmotionprovidedinAppendixB tosolvethecompoundpendulum'sdi erentialequationswithMatlab'sode45function.ThisMatlab functionappliestheRunge-Kutta4,5methodtosolvethemodels'ordinarydi erentialequationsof motion.Thisordinarydi erentialequationsolverreturnstheangulardisplacement,angularvelocity, andangularaccelerationofthetwopendulumlinkagesinthePEGASUSmodel'scoordinatesystem (Figure4.5.2).Theresultingpositionsofthelinkageswerethenusedtocalculateaphaseportrait foreachlinkageandtheresultingCPRDforthetwolinkages,whichareintheDIONYSOSmodel's coordinatesystem(Figure4.5.2).Thependulummodel'sPPsandCPRDsforeachcohortandeach cohort'sdampingcasewerethencomparedtotheactualcohort'smeanPPsforthethighandshank andthethigh-shankCRPD.Allphaseportraitsandcontinuousrelativephasediagramsforthis experimentwerenormalizedtoswingperiod,whichhad100timeepochs(e.g.points). Foreachdampingcondition,thenormalizedrootmeansquareerror(NRMSE)oftheresidual betweentheangulardisplacementandangularvelocityofthependulummodel'slinkagesanda cohort'sthighandshankangulardisplacementandangularvelocitywerecalculatedforeachtime epochinMatlab.ThesummationoftheNRMSEvaluesforallcurveswerethencalculatedand usedtorankthedampingcasesforeachcohort.Thedampingconditionwiththesmallestsummed NRMSEforacohortwasdeemedastheclosestofthefourdampingconditionstothatcohort's actualmotion.Inadditiontorankingthedampingconditionsforeachcohort,thecohortswerealso rankedwithrespecttoeachotherforthefourdampingconditions.Todetermineiftherewasa 84

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signicantdi erencebetweentherankingsbetweencohortsandintra-cohortrankings,aWilcoxon signed-ranktestwasperformed. 4.4.4.2AdditionalInvestigationsofthePendulumModel Anonlinearapproachtosolvingthecompoundpendulum'sdi erentialequationsandvariable dampingcoe cientsusedanumericalsolutionateachpercentageofswingperiodbycallingthe Matlabode45function,whichappliestheRunge-Kutta4,5solver.Thisadditionalinvestigation intothependulummodelwasimplementedtodetermineifthedampingcoe cientforeachofthe pendulum'slinkagescouldbecalculatedforeachpercentofswingperiodinsteadofusingaconstant dampingcoe cientfortheentiresimulation. Asecondlinearapproachtosolvingthecompoundpendulum'sdi erentialequationsandvariable dampingcoe cientsusedtheanalyticsolutionfor proximal and distal bycallingtheMatlabfunction lsqcurvet.ThisbuiltinMatlabfunctionenablesthecodetotparameterizedlinearfunctionsto dataeasily.Thisapproachrequirestheparameterizationofthependulum'sequationsofmotion. Unfortunately,itisnotpossible(refertoequationsofmotioninAppendixB)toparameterizethe twoequationsofmotionforthesetwovariablesbecauseoftheinherentcouplingbetweenthetwo linkagesinadoublependulum. 4.5HypothesisTestingandDataAnalysis Table4.10liststheprimaryoutcomemeasuresforthisdescriptiveresearchstudyandtheaims andhypothesestowhichtheydirectlyrelate.Also,thesourceofthedataandmotioncapture environmentfortheseprimaryoutcomemeasuresisprovided. Table4.5.1:Primarysagittalplaneoutcomemeasures,theircorrespondingaimsandhypotheses,and motioncapture(MoCap)environment(OG=over-ground,TM=treadmill)thatprovidesthesource dataforthesemeasures. PrimaryOutcomeMeasureAims&HypothesesSource PPs:Pelvis,Thigh,Shank,&Foot Extrema Zero-crossings Aim1 Aim3,H3A,H3B,H3C Aim4,H4A OG/TMMoCap CRPD:Pelvis-Thigh,Thigh-Shank, Shank-Foot,&Thigh-Foot Extrema Zero-crossings Slopes Inectionpoints Aim1 Aim3,H3A,H3B,H3C Aim4,H4A OG/TMMoCap Table4.11listsallthesecondaryoutcomemeasuresforthisdescriptiveresearchandthecorrespondingaimsandhypotheses.Additionally,thesourceofthedataforthesesecondaryoutcome 85

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measuresisalsoprovided. Table4.5.2:Secondaryoutcomemeasures,theircorrespondingaimsandhypotheses,andsourceof thedataforthesemeasures(e.g.motioncaptureenvironment=MoCap). SecondaryOutcomeMeasureAims&HypothesesDataSource Speed-AccuracyTask %ofsuccessfultargettaps advancinglimb'sforwardspeed Aim2,H2AOGMoCap SCALEScoreAim2,H2BExamroomvideo ICARS/SARAScore Turncurvature Baseofsupportwidth Aim2,H2COGMoCap Temporal-spatialMeasures Cadence Walkingspeed Stridelength,stridetime,steptime Gaitcyclephases,tasks,periods,events Aim1 Aim3,H3A,H3B,H3C Aim4,H4A OG/TMMoCap Sagittalplanekinematiccurves Pelvis,hip,knee,ankle Aim1 Aim4,H4A OG/TMMoCap Angulardisplacement&angularvelocity Pendulummodel'sproximallinkage Pendulummodel'sdistallinkage Thighsegment Shanksegment Aim3,H3A,H3B,H3COG/TMMoCap 4.5.1Aim1DataAnalysisMethodsandMeasures ThepurposeofAim1wastoconstructanormativereferencefortheotheraimsanddemonstrate theproposedmeasuresofcoordinationdynamicscharacterizeanunimpairedgaitpattern.Since theunimpairedretrospectivesubjectswerebarefootandtheprospectivesubjectsworeshoes,two normativereferencedatasetswereconstructedfromthesetwogroups. MeansagittalPPsandensembleCRPDsforthelowerextremitysegmentswerecreatedfrom thetwounimpairedcohortsusingthemethodsdescribedinChapter3fortheentiregaitcycle. Thecoe cientofvariance(CV)foreachofthecohorts'segmentPPsandCRPDsvariableswas calculatedusingthefollowingequation(Winter,1983).TheCVwascalculatedtoquantifytheextent ofvariabilityforeachofthecoordinationcurves'variableswithrespecttothemeanofthesecurves acrossalltimeintheensembleaverageandisshownwithineachPPandCRPD. Algorithm4.1 Coe cientofvariation(CV). CV = # 1 N N i =1 !" 2 i 1 N N i =1 | X i | Thegroup'smeanpercentgaitcycleforfootstrike,oppositefooton,oppositefooto ,and footo werealsocalculated.Thecorrespondingrelativephaseangleforeachoftheseessential 86

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footfalleventswasfoundanda95%condenceinterval(CI)foreachrelativephaseanglevaluewas calculatedtoprovideanestimateofthenormallimitsforapopulationfreeofgaitpathology. 4.5.2Aim2DataAnalysisMethodsandMeasures TheexperimentsassociatedwithAim2anditshypothesesaredesignedtoexploretherelationship betweentheproposedmeasuresofcoordinationdynamics(e.g.PP,CRPD)andselectclinical performancemeasuresthatcharacterizeaspectsofcoordination.Thesearenotdirectanaloguesto themeasuresoftheproposedcoordinationdynamicsduringgaitandareinsteadusedasdescriptive performancemeasures. Hypothesis2Ausesthevoluntaryreciprocalmovementsinaspeed-accuracytasktocharacterize asubject'sselectivemotorcontrolinrelationtoanytaskspeciccoordinationdecits.Twomeasures werecalculatedtotestthishypothesis.First,toquantifyasubject'sabilitytosuccessfullytapa footontheatarget,thenumberoffoottapsthatwereonatargetwasdividedbythenumberof foottapsoutsideofafoottargetandusedasthepercentageofhits(e.g.tappingaccuracy).It wasanticipatedthatsubjectswithanatypicalgaitpatternwouldhavedecreasedtargetaccuracy comparedtotheunimpairedsubjects.Secondly,thespeedoftheswinginglimbwhenitmovedfrom theafttoforwardtargetwascalculatedbythedistancecoveredbetweenfoottapsanddividedby thetimeittooktheswinginglegtotraversethatdistance.Ameanforwardswinginglimbspeed forthistaskwascalculatedforeachsubject.Thisforwardswinginglimbspeedwasthencompared tothemeanswinglimbadvancementspeedduringthesubject'srepresentativeover-groundwalking trial.Sincesubjectswithimpairedswinglimbadvancementareknowntohaveslowerwalking speeds,thenitwasanticipatedthatthespeedoftheswinginglimbwouldbeslowerforindividuals withacoordinationdecitcomparedtotheunimpairedsubjects.Thetimingandmagnitudeof coordinationevents(minimumnearfootof,zerocrossing,inectionpoint,maximuminstantaneous slope)fromeachprospectivesubject'sthigh-shankandthigh-footCRPDswereextractedsincethese eventscapturethedissociationoftheextensionsynergyatfooto .Student'st-testswerecalculated totestforsignicantdi erencesbetweenthemeanaccuracyandforwardswinglimbspeedforthe unimpairedprospectivesubjects'andprospectivesubjectswithcerebralpalsy. Hypothesis2BusestheSCALEassessmenttocharacterizethedegreeofselectivemotorcontrol impairmentsinasubject'slowerextremities.Aspreviouslydiscussed,theSCALEscoreforeach prospectivesubject'slegonlyincludedthehip,knee,andanklejointtasksandthusresultedinatotal possiblelimbscoreof6.ForretrospectivesubjectswithanatypicalgaitpatterntheSCALEscore wascalculatedforeacha ectedlimb.Fortheunimpairedprospectivesubjects,althoughtheleftand 87

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rightlimbsperformedtheSCALEtasks,onlytherightlimb'sscorewasusedforanalysis.Sincecurve featuresfromCRPDs(e.g.extrema,slope,inectionpoint,zerocrossing)capturevariousaspects ofinter-segmentalcoordination,theCRPDcurvefeaturesnearfooto forthethigh-shankand thigh-footCRPDswereexaminedinanexploratoryanalysis.Theabilitytodissociatethethighfootextensionsynergyatfooto duringgaitisanimportantmotorcontroltasktosuccessfully achieveswinglimbadvancement.SincetheSCALEscorecharacterizesanindividual'sabilityto voluntarilydissociatesegments,thenitwashypothesizedthatthissameabilityduringwalkingshould becapturedbyvariouscurvefeaturesfromCRPDs.ThetimingandmagnitudeofaCRPDextremum quantiesthedissociationofsynergiesbetweentwosegments.Thereforethetimingandmagnitude oftheminimumnearfooto onthethigh-shankandthigh-footCRPDswereextractedfromeach prospectivesubject'sa ectedside(rightsideonlyforunimpairedsubjects).Additionally,therate atwhichthesesegmentsdissociatedfromthisminimumtothenextlocalmaximum(maximum instantaneousslope)wascalculated.Lastly,thetimingandmagnitudeoftheinectionpointand zerocrossingthatoccurredfromthisminimumtothenextlocalmaximumwerecalculatedforeach subject.Itwasanticipatedthatthetiming,magnitude,andslopeofthesecurvefeatureswould followasimilartrendtoasubject'sSCALEscore.T-testswereusedtotestiftherewasasignicant di erencebetweenprospectivecohorts'meantiming,magnitude,andslopeforthesecoordination events.At-testwasalsousedtodetermineiftherewasasignicantdi erenceintheSCALEscores fortheprospectiveunimpairedsubjectsandprospectivesubjectswithcerebralpalsy. Hypothesis2CusesgaittasksfromtheICARSandSARAassessmentstocharacterizeaprospectivesubject'sspatialaccuracyduringamovementanddynamicbalance.Whiletherearenumerous methodsforcharacterizingdynamicbalanceduringgait,thefollowingtwomeasureswerecalculated fortotestthishypothesisandcharacterizethisaspectofgait.First,aMatlabspecialfunctionwas writtentocalculatethecurvatureforthe90 ¡ turnsfromasubject'scenterofmasstrajectorywith thefollowingequation.Aplanecurvecreatedbysubject'scenterofmass(CoM)trajectoryin R 2 spacecanbeparametricallydenedinCartesiancoordinatesforeachtimeepochwiththefollowing equation. Algorithm4.2 Parametricequationforcenterofmass(CoM)two-dimensionaltrajectory. r CoM ( t )=( CoM x ( t ) ,CoM y ( t )) Thecurvature( )ofthistransverseplaneCoMcurve(e.g.trajectory)wasthencalculatedwith therstandsecondderivativesoftheCoMxandytrajectoryusingthefollowingequation. 88

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Algorithm4.3 Curvaturefortwo-dimensionalparametriccurve. = | x y y x | ( x 2 + y 2 ) 3 / 2 Alongwithjointcenters,thecenterofmasstrajectoryisautomaticallycalculatedinVicon's Plug-In-Gaitmotioncapturefullbodymodel.Thetransverseplanetrajectorycoordinates(zeroed height)forthisvirtualmarkerwereusedtocalculateasubject'scurvatureduringeachofthe90 ¡ turningtasks.Ameancurvaturewascalculatedforallturnsassociatedwithasubject'sa ectedsides orinthecaseofunimpairedsubjects,therightsideonly.Itwasanticipatedthatalargercurvature wouldcorrespondedtoanincreaseddynamicbalanceimpairmentbecausesubjects.Acorrelation matrixwascalculatedusingeachprospectivesubject'smeanleftandmeanrightcurvatureandmean cadence,meanstridelength,andmeanwalkingspeedfromthesubject'srepresentativeover-ground walkingtrial. Secondly,acustomMatlabfunctionwaswrittentocalculatethemeanbaseofsupport(BoS)for eachsubject'sover-groundwalkingtrialsandtandemwalkingtrial(s).Otherresearchstudieshave reportedthebaseofsupportasameasureofdynamicbalanceduringwalkingandthetrendthata largerbaseofsupportcorrespondstoincreaseddi cultywithdynamicbalanceandthusactsasa compensatorymechanismtoprovidemorestability.Thereforeitwasanticipatedthatthestudy's subjectswithanatypicalgaitpatternwouldhavealargerbaseofsupportthanthesubjectsfreeof gaitpathology.Thefollowinggureillustratesthedenitionofbaseofsupportwidthusedforthis analysis. 89

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Figure4.5.1:Denitionofthebaseofsupportwidthduringdoublelimbsupport. Thewidthofthebaseofsupportwascalculatedforeachinstanceofdoublelimbsupportduring asubject'srepresentativeover-groundwalkingtrial.Doublelimbsupportisdenedastheinstance inthegaitcyclewhenbothfeetareincontactwiththeground.Thetransverseplaneheelmarker locationsduringtheonsetofeachdoublelimbsupportwereusedtocreatethebaseofsupport rectangle(shownaboveinFigure4.5.1).Themeanwidthofthisrectangularbaseofsupportwas calculatedforeachsubject.Acohortmeanbaseofsupportwidthwascalculatedfortheprospective andretrospectivesubjectswithcerebralpalsy,freeofgaitimpairment,andallretrospectivesubjects withalowerlimbamputation.T-testswerecalculatedtotestforsignicantdi erencesbetweenthe cohorts'smeanbaseofsupportwidth.AsareferencetothetandemwalkingtaskBoScalculations, theBoSwascalculatedforeachprospectiveandretrospectivesubject'srepresentativeover-ground walkingtrial. 90

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4.5.3Aim3DataAnalysisMethodsandMeasures ThepurposeofAim3anditscorrespondinghypothesesistocomparethemotionofacompound pendulumtothemotionofthethighandshankforvariousgaitpatternsduringtheswingperiodof gait.Themeasuresofcoordinationdynamicsusedinthisinvestigationwerederivedwithrespectto theglobalcoordinatesystemofthemotioncaptureenvironmentandarecalculatedwithrespectto thehorizontal(DIONYSOS).Thesoftwarependulummodelwasdenedwithrespecttothevertical ofatwodimensionalcoordinatesystem(PEGASUS).Thedi erencesinthesetwomodelsandtheir outcomemeasuresaredepictedinfollowinggure. Figure4.5.2:Comparisonofcoordinationsystemsfornonlinearmeasures(left)andpendulummodel (right). AspecialfunctionwaswritteninMatlabtoconvertbetweenthecoordinatesystemssothe phaseportraitsandcontinuousrelativephasediagramofthedoublependulumcouldbecompared tothecohort'scoordinationmeasures.However,aftergeneratingthesePPsandCRPDsfromthe pendulummodelforthedi erentensemblecohortbasedinitialconditionsanddampingconditions, itwasrealizedthatbecausethependulum'spivot(i.e.virtualpelvis)wasstationaryanddidnot oscillatelikeanactualsubjectwalkingthemagnitudeofthesePPsandCPRDswouldnotbethe sameasthehumanmotioncapturedata.Therefore,theangulardisplacementandangularvelocity ofthecohort'sthighandshanksegmentsfortheentiredurationofswingperiodwerecalculated usingthePEGASUScoordinatesystemconvention.Thisprovidedameanstocomparethetwo models(e.g.subjectbasedandtheoreticalpendulum)anddidnotrequireadditionalscalingor coordinatesystemtransformations. 91

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Therootmeansquareerror(RMSE)betweenthetheoreticalpendulumlinkages'motionsandthe actualsubjectensemblecohortmotionswascalculated.Sincethisanalysis'outputvariables(e.g. angulardisplacementandangularvelocity)havedi erentunits,theRMSEwasnormalizedtothe meanofthecohort'svariable.ThefollowingequationforthenormalizedRMSEisalsocommonly knownasthecoe cientofvariationoftheRMSE.ForthisapplicationofNRMSE,thenumber oftimeepochsinswingperiod(n)was100,thepredictedvalues(y PEND )werethependulum model'sangulardisplacementorangularvelocityofbothlinkagesinPEGASUScoordinates,and thereferencevalues(y SUBJ )fromacohort'sactualmeanangulardisplacementorangularvelocity ofthethighandshankduringtheswingperiodofgait.Aspreviouslydiscussed,theNRMSEwas calculatedforeachdampingcondition( # )foreachsubjectcohortcomparison. Algorithm4.4 Normalizedrootmeansquareerror(NRMSE) NRMSE d = (1 /n ) # ( y PEND y SUBJ ) 2 y SUBJ Thesumofthefouroutputvariablesfromeachpendulumversuscohortsimulationwascalculated andthenusedtorankthedampingconditionswithineachcohortandamongstthecohorts(Figure 4.5.3). 92

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Figure4.5.3:Flowchartoftheoreticalpendulummodeltoagaitpatterncohort'sactualthighand shanksegmentmotionsduringtheswingperiodofgait. TherankingofthesummedNRMSEvariablesforeachcohort'sdampingconditionwasusedto testhypothesesforthisaim.AWilcoxonsigned-ranktestwasrunontherankingsforeachdamping conditiontodetermineassesswhetherthecohort'srankswerestatisticallydi erentfromeachother. 4.5.4Aim4DataAnalysisMethodsandMeasures ThepurposeofAim4anditshypothesiswastodemonstratetheproposedmeasuresofcoordinationdynamicsareabletodistinguishbetweendi erentgaitpathologiesandpatternsassociated withalteredlimbadvancementduringtheswingperiodofgait.However,sincethereiscurrentlynot agoldstandardmeasureforcoordinationdynamicsnoristhereavariablethatencompassesthese eightcoordinationcurvesitwasdeterminedthatametricthatsatisesthisneedmustbecreated. Additionally,duetothenumberofcurvesforeachcohort,variablescharacterizingacurve,andthe numberofsubjectgroupsthatthenumberoft-testswouldincreasethechancesofahypothesis beingsignicant(typeIIerror)whenitactuallyisfalse.Twodi erentapproachesweretakento generateanindexofcoordinationdynamicssothatthevarioussubjectgroupscouldbecompared andtestthisaim'shypothesis:thegaitpatternsstudiedinthisbodyofworkaredistinguishablewith 93

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thenonlineardynamicsystemstheorybasedmeasures(e.g.PPs,CRPDs).Thetwocoordination indiceswerecalculatedforallsubjectsandprospectiveexperimentalwalkingtasks.Comparisons betweenthetwoindiceswereperformedusingpairedt-tests.Theresultsfromtheset-testsandthe additionalanalysesforregressionmodelbasedindexwereusedtotestthisaim'shypothesis.In regardstosatisfyingtheobjectiveofAim4andtestingitshypothesis,thetwonovelcoordination indiceswereusedtoshowhoweachgaitpathologyconsideredinthisstudyisdi erentfromthe unimpairedcohort,aswellashowthevariouscohortsaredi erentfromeachother. 4.5.4.1CoordinationDeviationIndex(CDI) Applicationofthegaitdeviationindex(GDI)iscontinuingtogrowininstrumentedgaitanalysis asameasureofhowcloseasubject'sjointanglesaretoanormativereference[103].Sincethe GDIquantieschangesinanoveralljointanglepattern,itisavaluablemetricespeciallywhen consideringthehypothesisthatonebehavioralgoalofambulationistomaintainjointanglepatterns[137].Inordertoquantifyhowchangesinsegmentpositionsandtimingscontributetoagait pattern,anotherlevelofanalysisformarker-baseddatathatcharacterizestheunderlyingcoordinationdynamicsandenrichesexistinggaitpatterndescriptorswasincorporated.Employingthe GDImethodology,acoordinationdeviationindex(CDI)wascreatedthatusessagittalplanephase portraitsandcontinuousrelativephasediagramsinsteadofjointangles.Thisportionoftheanalysis usedtheCDItoexaminethecoordinationdynamicsinthetwoclinicalcohortswithdistinctgait impairmentsa ectingtheirabilitytosuccessfullycompleteswinglimbadvancementwithreference toagroupofhealthysubjectsfreeofgaitpathology(N).Inadditiontotheunimpairedsubjects, CDIscoresweregeneratedforsubjectswithspasticcerebralpalsy(CP)witheitherthehemiplegic (H)ordiplegic(D)distributionandeithersti kneegait(SKG)orcrouch(C)gaitpattern,and lowerlimbamputees(LLA)withanamputationeitherabove(AK)orbelow(BK)thekneeTable 4.12. Table4.5.3:Subjectclassicationforcoordinationdeviationindexanalysis. PopulationDesignation UnimpairedN CerebralPalsyCP HemiplegiaH DiplegiaD Sti KneeGaitSKG CrouchGaitC LowerLimbAmputationLLA BelowKneeAmputationBK AboveKneeAmputationAK 94

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Theoverallobjectiveofthissub-investigationwastoexploretheapplicabilityoftheCDIin describinggaitpathology.Thespecicobjectivesofthisanalysiswereto1)generateacoordination deviationindexusingtheGDImethodologyforthesegroups,2)compareCDIscoresofthegroups usingtheGDIasabenchmarktodescribevaryingdegreesofgaitperformanceinthesedistinct groups,and3)demonstratethatthemagnitudeofcoordinationimpairment(CDI)correspondsto themagnitudeofjointangleimpairment(GDI). CreatinganindexfromPPsandCRPDs,whichdescribesmovementatthelevelofcoordination, providescliniciansandresearcherswithametricthatmaybemoremeaningfulandappropriatewhen studyingagaitpattern'sunderlyingcoordinationdynamics.Additionalinsightsprovidedbythe CDIcomplementstheGDIbyelucidatingunderlyingindividualsegmentpositionsandtimingthat contributestoagaitpattern.Forexample,inter-segmentalcoordinationdescribesselectivemotor controlimpairmentsinindividualswithCPandquantiescoordinationstrategiesthatareadopted andreorganizationofsegmentsbyindividualswithaLLAasaresultoftheinertialconsequences duetoanamputationandwearingaprosthetic. AcustomMatlabprogramwaswrittentoreproducethecalculationsoftheGDIdetailedin thearticlebySchwartzetal.,2008.Theaccompanyingnormativegaitfeaturesreferencefromthis articlewasusedforeachsubject'sGDIcalculation.AGDIwascalculatedforeacha ectedleginthe subjectswithCPoraLLAandonlytherightlegwasusedforeachunimpairedsubject.Additional sta atCGMAandaco-authoroftheoriginalarticlethatpresentedthismethodologyvalidatedthis GDIMatlabprogram.Anexplanationofthemethodologyforthisfeaturebasedanalysis,originally providedbySchwartzetal.,2008,thatusesthecoordinationdynamicsmeasuresinsteadofthe GDI'skinematiccurvesfromallthreeplanesofmotionisprovidedinthefollowingparagraphsand AppendixE. Althoughdisplayedasatwo-dimensionalcurve,thesegmentPPswereseparatedintotwocurves, oneforangulardisplacementandtheotherforangularvelocity.Thuseachsubject'scoordination dynamicsvectorwasconstructedfromeightphaseportraitcurvesandfourCRPDcurves.Sagittal planePPs(pelvis,thigh,shank,foot)andCRPD(pelvis-thigh,thigh-shank,shank-foot,thighfoot)werecalculatedin2%incrementsthroughouttheentiregaitcycleandformthecoordination dynamicsvectorforeachsubject.Onecoordinationdynamicsvectorcontainstwelvecurvesthatare sampledat51pointsandthuscreateavectoroflength612.Thecompleteprocessandequations usedtoconstructthenormativecontrolfeaturesandasubject'sCDIarelocatedinAppendixE. Theoretically,anindividualwithoutanydeviationsfromthenormativereferencewouldhavea perfectCDIscoreof100.Every10-pointincrementbelowthetheoreticalperfectscorecorrespondsto 95

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anincreasingnumberstandarddeviationsawayfromthenormativereference.Therefore,asubject's CDIvaluecanbeinterpretedasfollows: CDI $ 100indicatesthesubject's(sagittalplane)coordinationdynamicsisatleastasclose totheunimpairedaverageasthatofarandomlyselectedunimpairedsubject.ACDIgreater thanorequalto100indicatestheabsenceof(sagittal)coordinationpathology. Every10pointstheCDIfallsbelow100correspondstoonestandarddeviationawayfromthe unimpairedmean.Forexample,asubjectwithaCDIof75meansthecoordinationdynamics ofthatsubject(s)is2.5standarddeviationsawayfromtheunimpairedmean. ACDIscorewascalculatedforallprospectiveandretrospectivesubjectsa ectedside(rightlegonly forunimpairedsubjects)andlikethesubjects'GDIscoresrepresentsthecoordinationdynamicsfor theentiredurationofthegaitcycle(e.g.stanceandswing).Thegroups'meanCDIandGDIscores werethencomparedusingpairedt-teststodetermineifthereweresignicantdi erencesbetween thesubjectclassications. Whilethemanifestationofmotordisordersinindividualswithcerebralpalsyiscomplexand uniquelyexpressed,therearecommongaitpatterns[69]usedtodescribethisgroup'sinabilityto achievevariousspatialandtemporalaspectsofgait(e.g.gaiteventsandtasks[26,143],decreased steplengthandwalkingspeed[26,29,143]).Motordecitsinindividualswithalowerlimbamputation,whilefromadi erentetiologythanCP,aresimilarlyexpressedinvisuallyrecognizablegait patterns[78,82,98].Duetothelackofneurologicalcontrolbelowthelevelofamputation,these subjectsalsostruggletoachievecriticalgaitevents[78,82].Molloyetal.,2010evaluatedtherelationshipoftheGDIandgrossmotorfunctionbyusingtheGrossMotorFunctionClassication System(GMFCS)anddemonstratedtheGDIdistinguishesbetweendi erentGMFCSlevelsinindividualswithCP.ToevaluatetheCDI'sabilitytostratifygaitpathologyrelatedtocoordination,we alsoanalyzedtherelationshipbetweentheGMFCSlevelsforindividualswithCP.Sinceincreasing amputationlevelforindividualswithaLLAhasbeenshowntodecreasefunctionalgaitabilities[82], theCDI'sabilitytodetectdi erencesincoordinationduetoamputationlevelwasalsoexamined. Therefore,aone-wayanalysisofvariance(ANOVA)testwasperformedonthecohort'smeanCDIs, GDIs,andGMFCSlevels(forsubjectswithCP).Matlab'sbuilt-inKolmogorov-Smirnovfunction wasusetoverifytheassumptionofnormalityintheGDIandCDIvaluesforallunimpairedsubjects. 96

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4.5.4.2CoordinationPerformanceScore(CPS) EmployingasimilarmethodologytothegaitperformancescorepresentedbyBakeretal,2008, statisticallysignicantcurvefeaturesfromPPsandCRPDswereidentiedandusedtocreatea secondindex:thecoordinationperformancescore(CPS).Additionally,thesesignicantcoordinationeventswereusedtocreatetwonominalregressionmodelscapableofdistinguishingbetween unimpairedandimpairedgaitpatternsforindividualswithcerebralpalsy. Thegaitperformancescore(GPS)usesanalternativeinterpretationoftheEuclideandi erence measuresfromtheGDImethodologyandcreatesanun-scaledindexfromninekinematiccurve features(e.g.maximumsagittalkneeexion)thathavebeenfoundtosignicantmeasuresofgait pathologyinnumerousgaitstudies[138].Followingthislogic,acoordinationperformancescore (CPS)wasthencalculatedwithacustomMatlabprogramforeachsubject'sa ectedlimb(right onlyforunimpairedsubjects).NostatisticalanalysiswaspresentedbyBakeretal.,2008,inregards tothestatisticalsignicanceforselectingtheninekinematiccurvefeaturesusedtocreatethe GPS.Sinceamajorobjectiveofthisdissertationistoestablishanormativereference(Aim1)and ndmeaningfulmeasuresfromthismodelofcoordinationdynamics,thendeterminingifessential orcriticalcoordinationeventsexistisalogicalanalysis.Twodi erentprecursoryanalyseswere performedonswingperiodcoordinationeventsfromthesagittalplanePPs(pelvis,thigh,shank, foot)andCRPDs(pelvis-thigh,thigh-shank,shank-foot,thigh-foot)todeterminewhich(ifany) coordinationeventswerestatisticallysignicantandthusjustifytheirinclusioninthecalculationof thecoordinationperformancescore. Perry'scriticalandtemporalgaiteventshavebeenusedtodelineatetheessentialphases,tasks, andjointmotionsofthegaitcyclenecessarytoachieveanormalgaitpatternandprovideaframeworkforconventionalinstrumentedgaitanalysismeasures[26,137].AsPerry'sgaiteventsprovide aframeworkforconventionalinstrumentedgaitanalysismeasures,theexistenceofessentialcoordinationeventsfromthecohort'smeannormalgaitpatterncanserveasaninitialnormativereference forimportantcurvefeaturesandframeworkforclinicalandresearchapplicationsusingPPsand CRPDsinadditiontoservingasameanstocreateacoordinationdynamicsindex.Byidentifying criticalcoordinationeventsduringtheswingperiodofgaitforalargecohortofunimpairedsubjects, thesemethodsprovideameanstoenhancetheunderstandingofvariousmotorcontrolstrategiesemployedintheswingperiodgait.Also,extractingspeciccurvefeaturesfromthesenonlinearcurves toidentifycoordinationeventsdemonstratestheclinicalutilityofthesemeasuresasacomplement toconventionalinstrumentedgaitanalysismeasures. 97

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Thefollowingtwosectionsdescribetwodi erentmethodologicalapproachestoidentifyingcritical coordinationeventsonphaseportraitsandcontinuousrelativephasediagramsduringtheswing periodofgait.Usingcriticalcoordinationeventstoconstructaconsolidatedindexofanindividual's PPsandCRPDso ers1)aquantitativemeanstosatisfyAim4andtestitshypothesis,2)showhow eachgaitpathologyconsideredinthisstudyisdi erentfromtheunimpairedcohort,and3)ametric thatcanbeusedtocharacterizehowthecoordinationdynamicsofthevarioussubjectcohortsare di erentfromeachother. First Approach to Identify Critical Coordination Events. TherstapproachtoidentifyingcriticalcoordinationeventsbeganwithgeneratingthesagittalplanePPs(pelvis,thigh,shank, foot)andCRPDs(pelvis-thigh,thigh-shank,shank-foot,thigh-foot)foreachunimpairedprospectiveandretrospectivesubject.Thenthreecategoriesofcurvefeatureswerechosenascoordination eventsinswing:extremum,zero-crossing,andinectionpoint.Thebuilt-inMatlabfunctionsfor identifyingthemaximumandminimumofavariablewereusedtoidentifythepercentgaitcycleof eachextremum.AnothercustomMatlabfunctioncalculatedzero-crossingsofCRPDsandinection pointsonCRPDsastheinstantwhenthecurve'sderivativeequalszero.Incaseswhenazerocrossingdidnotfallexactlyonasampledpercentgaitcycle,thefunctionselectedthepreviousclosest percentgaitcycleastheinstanceofthezero-crossing.Thepercentgaitcycleatwhichthesethree curvefeaturesoccurredoneachsubject'ssetofcoordinationdynamicscurveswasfound.Ofthe forty-fourpossiblecoordinationevents,thirty-sevenwerefoundtoalwaysexistintheunimpaired cohort'scoordinationcurves.Thesethirty-sevencoordinationeventswereusedfortheremainderof thisanalysis. Thequestionofwhetheranyofthesethirty-sevencoordinationevents(CE)wereindependent andinvariantforanunimpairedwalkingpatternforvariousdemographics/anthropometricswas thenposed.TodetermineifanyoftheCEswereindependentandinvariantforanunimpaired walkingpattern,thecohortwassortedintothefollowingdemographiccategoriesforeachgender individuallyandbothgenderscombined:age(2yearincrements),weight(10kgincrements),andleg length(50mmincrements).Foreachoftheseninedemographiccategories,ther-squarevalueand correspondingPearsoncorrelationcoe cient( ( )werecalculatedforthepercentgaitcyclewhen eachofthethirty-sevencoordinationeventsoccurred.Ther-squareand ( valuesforcomparing eachdemographicandanthropomorphiccategorytoacoordinationeventwascalculatedusingthe correspondingMiniTabfunctions.Acoordinationeventwasdeemed"critical"ifthepercentgait cycleatwhichitoccurredwasinvariantifr 2 2.5%andindependentifthePearsoncorrelation coe cientthresholdofwasequaltoorlessthan0.2forallofthesedemographic/anthropomorphic 98

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categories. Subsequentanalyseswerethenperformedonthisdatasettoinvestigatethepotentialinuences ofbarefootversusshodwalkingontheinitialresults.Thebarefootover-groundwalkingtrials (e.g.retrospectivenormativesubjects)andtheshoeover-groundwalkingtrials(e.g.prospective normativesubjects)wereseparatedintotwocohortsandthisanalysiswasrepeatedforthesetwo subgroups.Next,condenceintervalsforthecriticalcoordinationeventsfromthesetwonormative cohortswerecalculatedtodetermineifagehadana ectonthetimingofthesecoordinationevents. Thethirdsubsequentanalysis,themeansandstandarddeviationsofthetimingforthesecritical coordinationeventsandthetimingofcriticalgaitandtemporaleventswerecalculatedandcompared todetermineifanycoordinationeventsoccurredatthesametimeasconventionalgaitevents. Afterexaminingthesagittalplanecoordinationdynamicscurvesforthevarioussubjectcohorts, itisqualitativelyclearthereareessentialcurvefeaturespresentindi erentgaitpatterns.Asecond approachtoidentifyingsignicantcoordinationeventswasperformedandformedthebasisforthe secondcoordinationdynamicsindex.Additionally,thissecondapproachisappealingbecauseit capturesthenumberofmeasuresrepresentedintheselowdimensionalPPsandCRPDsandit accountsforboththetimingandmagnitudesofpointsonthesecurves.Therstapproachto identifyingcriticalcoordinationeventsonlyaccountsforthetimingofthepointsinthePPand CRPDcurves. Second Approach to Identify Critical Coordination Events. Thesecondapproachto ndingthepotentialexistenceofcriticalcoordinationeventsusedtwosetsofregressionmodels: 1)astepwisebackwardregressionwasusedtodetermineifasubsetofcoordinationeventscould distinguishbetweenpathologicalandpathologyfreegaitand2)anominalregressionmodelto determineifthissubsetofcoordinationeventscoulddistinguishbetweendi erentgaitpatterns.This secondapproachdenedthesamethreetypesofcoordinationdynamicscurvefeatures(extrema, zerocrossings,andinectionpoints)ascoordinationevents.Thirty-sevencoordinationeventswere foundintheswingperiodofthesagittalplanePPsandCRPDsofallunimpairedsubjects.The timingandmagnitudeforeachofthesethirty-sevencoordinationeventswereextractedfromall prospectiveandretrospectivesubjects.Onedatasetwascreatedforthetimingofthesecoordination eventsandasecondwascreatedforthemagnitudeofthesescoordinationevents.Abackward stepwiseregressioninJMPwasrunoneachdatasetwiththefollowingparameterstodetermineif anyoftheseeventswerestatisticallysignicant(p 0.05)indistinguishingwhetherasubject'sgait patternwasunimpairedoratypical.Thefollowingtableliststhevariablesusedinthisbackward stepwiseregression. 99

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Table4.5.4:Variablesusedtocreatethebackwardstepwiseregressionmodels. ModelVariableTypeDescription GaitPathologyDependent0=No,1=Yes GenderControlF=female,M=male LegLengthControlValue(mm) WeightControlValue(kg) CoordinationEventsIndependentTiming(%GC)orMagnitude Theremainingcoordinationeventsfromeachstepwiseregressionmodel(timing,magnitude) thatwerestatisticallysignicantwerethenusedtocreateanominalregressionmodel.Thenominal regressionmodelfromthesesignicantcoordinationeventswascreatedtodetermineifthismodel couldbeusedtodistinguishbetweendi erentgaitpatterns.Thefollowingtableprovidesthe parametersusedtocreatethenominalregressionmodels. Table4.5.5:Variablesusedtocreatethenominalregressionmodels. ModelVariableTypeDescription GaitPatternDependent0=N,1=SKG,3=C,4=BK,5=AK GenderControlF=female,M=male LegLengthControlValue(mm) WeightControlValue(kg) SignicantCoordinationEvents(p 0.05)IndependentTiming(%GC)orMagnitude Thisprocessofgeneratingaregressionmodelwasconductedforathirdtimetodetermine ifallofthesignicantcoordinationevents(bothtimingandmagnitude)fromtheprevioustwo stepwiseregressionmodelswerenecessarytoaccuratelypredictthepresenceofgaitpathologyand distinguishdi erentgaitpatterns.Theresultingninesignicantcombinedcoordinationeventsthat werestatisticallysignicant(p 0.05)werethenusedtocreateathirdnominalregressionmodel, whichwasusedtodeterminehowwellthesecoordinationeventswereabletodistinguishbetween di erentgaitpatterns.Forclarityofthismethodology,Figure4.5.4providesaowchartdepicting alltheregressionmodelscreatedforthisportionoftheCPSanalysis.Theninecoordinationevents werethenusedasthevariablesfortheCPS. 100

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Figure4.5.4:Flowchartofprocessusingregressionmodelstoidentifysignicantswingperiod coordinationevents. UnlikeconventionalIGAmeasures,therehasnotbeenaninvestigationtodeterminewhich coordinationcurvefeaturesaresignicantduringgait.Therefore,werstdenedacoordination event(CE)asoneofthethreefollowingcategoriesofcurvefeatures:extremum,zero-crossing,or inectionpoint.Built-inandcustomMatlabfunctionswereusedtoidentifythepercentgaitcycle andmagnitudeofallpossibleswingperiodCEsonthesagittalplanePPsandCRPDs,yielding thirty-sevenCEstotal.UsingJMPsoftware,abackwardstepwiseregressionmodelswascreated usingthetimingandmagnitudeoftheseCEsasthemodel'sindependentvariables.Thesubjects' age,gender,leglength,andweightwereprovidedascontrolvariablesforthisregressionmodel.The presenceofgaitpathologywasusedasthemodel'snominalpredictorbydesignatingeachunimpaired subjectastypicalandeachsubjectwithCPasatypical.Theminimump-value(probabilitytoleave) of0.05wassetasthethresholdforwhichaCEwasremovedfromthemodelduringabackward 101

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step.NinesignicantCEswereidentiedusingthisstepwiseregressionmodel. Thevarianceinationfactor(VIF)andtolerancefortheseninesignicantCEswerecalculated inSAS9.4todeterminethepotentialpresenceofmulticollinearitybetweentheseCEs.ACEwitha tolerancelessthan0.4and/oraVIFgreaterthan2.5wasdeemedasindicativeofmulticollinearity. Theunimpairedcohort'smeantimingofallnineCEswascalculatedandusedtodetermineifany oftheCEsoccurredatthesametimeinswing.OftheCEswithVIFandtolerancevaluesabove thegiventhresholds,threewerefoundtooccuratthesametimeasotherCEsinthesetofnine signicantCEs.ThesethreeCEswereremovedandtheVIFandtolerancewererecalculatedto ensuretherewasnomulticollinearityassociatedwiththeparameterestimatesoftheremainingsix CEs. Calculation of the Coordination Performance Score. Thefollowingprocedureswere adaptedfromthearticlebyBakeretal,2008usingthenalsixsignicantCEs.TheGDIis fundamentallybasedontherootmeansquare(RMS)di erencebetweenthecoordinationdynamics vectorandtheaveragecoordinationdynamicsvectorforindividualsfreeofgaitpathology.The Euclideandistance(e.g.di erence)betweenacoordinationeventofanysubject( CE S )andthe meannormativereferencecoordinationevent( CE N )canbecalculatedwiththefollowingequation, usingsimilarnotationfromtheCDIsection. Algorithm4.5 Di erenceofcoordinationeventbetweensubject(s)andmeannormativereference (N). CE s,N = CE s CE N Thisdi erencecanbeusedtocalculateasimilarquantityforasinglecoordinationdynamics variableratherthantheentirecoordinationdynamicsvector.Theaveragerootmeansquareofall thecoordinationvaluescores(CVS)foraparticularsideequaltheCPScalculatedfromatheentire coordinationvectorusingeachofthesignicantcoordinationevents( n CE ). Algorithm4.6 Equationforasubject'sCoordinationPerformanceScore(CPS). CPS s = $ 1 n CE ( CVS 2 CE 1 + CVS 2 CE 2 + ... + CVS 2 CEn ) TheCPSwascalculatedforeachsubject'sa ectedsideandtherightsideonlyforallunimpaired subjects.Themeanandstandarddeviationforeachsubjectcohortclassier(N,CP,LLA,SKG, C,H,D,BK,AK)wascalculated.T-testswereusedtotestforstatisticalsignicancebetweenthe cohorts'meanCPSscores.Lastly,theCPSwassubtractedfrom100foreaseofcomparisontothe CDIandGDIsubjectscoresandtodisplaythesescoresinthesamescale. 102

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Algorithm4.7 Scaledcoordinationperformancescore(*CPS). CPS =100 CPS s ItisimportanttonotethatthisscalingoftheCPSdoesnotfollowthesameconventionasthe CDIandGDI,whereevery10-pointdecrementawayfrom100isequaltoastandarddeviationaway fromthenormativemean.Insteadthefurtherasubject'sscaledCPSscoreisfromthemaximum (100),thenthefurtherawaythesubject'scoordinationeventsarefromthemaximum.Byscaling theCPS,theindicesconventionof"biggerisbetter"ismaintained,asistheconventionfortheCDI andGDIscores. Regression Models for Distinguishing Coordination of Di erent Gait Patterns. The rstregressionmodeldeterminedwhichofthesixsignicantCEswerenecessaryfordistinguishing betweenanunimpairedandimpairedgaitpattern.Asecondregressionmodeldeterminedwhichof thesixCEseventswerenecessarytodistinguishbetweenasti kneeorcrouchgaitpattern.These tworegressionmodelso eranadditionalmeanstodemonstratehoweachgaitpathologicalpattern consideredinthisstudyisdi erentfromtheunimpairedcohortandthesemodelscanbeusedto characterizehowthecoordinationdynamicsofthevarioussubjectcohortsaredi erentfromeach other(Aim4).Unfortunately,duetothesmallsamplesizeoflimbswithanamputation(n=19), itwasnotpossibletobuildasatisfactoryregressionmodelfordistinguishingthegaitpatternsof eitherabelowkneeorabovekneeamputation.Therstregressionmodelwasdesignedtodistinguish betweenthepresenceorabsenceofgaitpathologyandthesecondmodelwasdesigneddistinguish betweenasti kneegaitorcrouchgaitpattern. Todeterminewhichofthesixsignicantcoordinationeventswerenecessaryforthetworegression models,thea ectsonthemodelfortheadditionofeachcoordinationeventwasassessedandfor allcombinations.Inorderforacoordinationeventtobeaddedtoamodelthefollowingcriteria hadtohavebeenmeet.First,theadditionofaCEmustincreasethesignicancerelatedtothe outcomeofinterest.Second,theadditionofaCEmustimprovetheareaunderthecurveofthe receiveroperatorcharacteristiccurve.Andthird,theadditionofaCEmustnotviolateanderrors (e.g.varianceinationfactor,tolerance).Thecorrelationmatrixp-valuesofthesixcoordination eventswasusedtoranktheimportanceofthecoordinationeventsandensuretherewasn'tany multicolinearitybetweencoordinationevents.Afterassessingtheinclusionofcoordinationevents intoeachofthetworegressionmodels,theinclusionofnuisance(e.g.control)variableswereused toassessiftheadditionofthesevariablesimprovedtheoverallmodel.Leglength,age,weight,and genderofallsubjectswereusedasnuisancevariables. 103

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Theareaunderthecurve(AUC)fromthereceiver-operatorcurvesforthetwonominalregressionmodels(timingandmagnitudeofsignicantcoordinationevents)wascalculatedinJMPand StatisticalAnalysisSoftware(SAS)alongwiththeconfusionmatrixandcondenceintervals.The leave-one-outmethodinSASwasusedtocreatearandomlyselectedsubsetoftheavailable226 samplesandcomparetheareaunderthecurve(AUC)ofthereceiveroperatorcharacteristic(ROC) curvetotheROCofallthesamples. 4.5.4.3CurveFeatureTrendsbyGaitPattern Whilevisuallyexaminingthevariouscohorts'coordinationcurvesgeneratedforthedi erent experimentsandaimsdiscussedabove,thereappearedtobetrendsinwhichcertaingaitpatterns weremissingcertainPPandCRPDcurvefeatures.Similartothevisualuseofkinematiccurves toidentifyaparticulargaitpattern,itwaspostulatedthatcertaincurvefeaturesfromPPsand CRPDscouldbeusedtoidentifycertaincoordinationimpairments.Additionally,itwaspostulated thattheremightbetrendsinwhichcommoncurvefeatures(e.g.zero-crossing,inectionpoint, extremum)weremissingforvariousatypicalgaitpatterns.Portionsofthisdissertationhasbeen presentedatprofessionalconferencesandoftenmembersofthegaitcommunityhaveexpresseda commonreasonforthehesitancytoadoptingPPsandCRPDsisthatthesecurvesareunfamiliar andthatthecorrelationsbetweenthesenonlinearcurves'featuresandasubject'sgaitpatternare unknown.Therefore,thissecondaryanalysis,designedtoaddressAim4,wasconductedinane ort toresolvetheunfamiliarityofthesecoordinationmeasuresandprovideaprimerforcurvefeatures forsagittalplanePPsandCRPDsinthefollowinggaitpatterns:unimpaired,sti kneegait,crouch, belowkneeamputation,andabovekneeamputation. First,thetimingandmagnitudeofeverysubject'sthirty-sevenswingperiodcoordinationevents wasmanuallycheckedtoensurethealgorithmsfordetectingtheseeventshadsu cientcriteria foridentifyingtheseevents,evenforthemoreextremeaberrantgaitpatterns.WhentheMatlab programdidnotdetectacoordinationevent,thismanualprocessofcheckingthetimingsand magnitudesofallcoordinationeventsalsoservedasameanstoconrmifaneventtrulydidnot existforaparticularsubject.Oncethetimingsandmagnitudesofallthirty-sevenswingperiod coordinationeventswereconrmedforallprospectiveandretrospectivesubjects(n=265legs),they werethencodedaseitherpresent(1)orabsent(0)andorganizedtopographically(e.g.hemiplegia ordiplegiaforsubjectswithCP),bygaitpattern(e.g.SKGorCrouchforsubjectswithCP),level ofamputation(e.g.belowknee,aboveknee),andbynumberofa ectedsides(e.g.unilateralor bilateralforsubjectswithaLLA).Thepercentageofsubjectsmissingoneormorecoordination 104

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eventsforeachgaitpatterncategory,includingtheunimpairedgroup,wasthencalculated.These percentageswereusedtodetermineiftherewasatrendforthesubjectsmissingacoordination event(s)andtheirgaitpatternordiagnosis.Next,thepercentageofsubjectsinagaitcategory thatwereunabletoachieveamissingcoordinationeventwascalculated.Thesepercentageswere usedtodetermineifagaitpatternordiagnosiswasassociatedwiththeinabilitytoachievespecic coordinationevents. 4.6ExperimentalLimitationsAssociatedwithHumanSubjects RecallingtheoverviewpresentedinChapter2ofthesubsystemsinvolvedwithwalkingandcomplexphysiologicalinteractionsrequiredtoperformthiselegantmotortask,itbecomesapparentthat instrumentedgaitanalysisiscurrentlyunabletomeasurealloftheseelements.Theuseofhuman subjectsprovidesmoreaccuratedatathanmodelsevenmorecomplexthanthetheoreticalpendulum modelcreatedforthisdissertation.Theoreticalforwardmodelingprogramsarechallengedevenmore whentaskedwithpredictingthegaitpatternofasubjectwithacomplexanduniquelyexpressed neuromuscularimpairment,suchascerebralpalsy.Althoughmanyofthemoreadvancedmodeling programsareincreasingtheuseofsubjectdatafrominstrumentedgaitanalysistoenhancetheir outcomemeasures,therearestillsignicantlimitations,oftenduetothesimplifyingassumptions,to thesemodels.Thustheneedforcollectinghumanmotioncapturedataremainsvaluableandsecond tonone,especiallyforclinicaldecisionmakingandpatientcareapplications.Whilemotioncapture dataforasubjectistypicallyfarmoreaccuratethanamodel,therearestillsignicantchallenges associatedwithhumansubjects. Numerousfactorsassociatedwithusinghumansubjects(e.g.endurance,strength,time)for prospectiveexperimentsa ecttheexperimentalprotocol,duration,andvariablesthatcanbemeasured.Instrumentedgaitanalysisrequiresaconsiderableamountoftimefordatacaptureand signicantlyevenmoretimetoprocessthemotioncapturedatatothepointwhereitcanbeusedto generatemeasuresofgait(e.g.kinematics,temporal-spatial,coordination).Onaveragetheprospectiveunimpairedsubjectprotocolinthisbodyofworkrequiredon3hoursofasubject'stime,from consenttocompletionofdatacapture.AsitishopefullyclearfromthediscussioninChapter3,itis alsonotpracticaltomeasureallvariablesassociatedwithwalkingoreventheconstitutiveelement ofcoordination,whichitselfishighlycomplexandcontainsnumerousvariables.Thegaitmeasures andproposedcoordinationmeasuresselectedinthisbodyworkdescribetheresultingbehaviorof numeroussubsystemsandareintendedtodescribethesystemofwalkingatamoremacroscopic,sys105

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temlevel.However,futureworkmayrevealpromisingndingswhenthesemeasuresofcoordination arepairedwithmorespecicmeasuresofhumanperformance(e.g.surfaceelectromyography). Experimentallimitationsassociatedwithhumanperformancearefurtherconfoundedinsubjects withagaitimpairment.AsdiscussedinChapter2,duetothenatureofcerebralpalsyeachsubject presentsdi erentfunctionallimitationsandthusrequiresexibilitytobeincorporatedintothe designofexperiments.Oftensubjects'withimpairedgaithavediminishedenduranceandstrength, thusplacingalimitonthedurationofanexperimentandthesubject'svisit.Thedatacapture durationforaprospectivesubjectwithagaitimpairmentlastedanaverageoftwohours.Although thesubjectsweregivenbreaksforrestwhenevertheyneeded,itisclearamotioncapturevisit longerthantwohourswouldhavesignicantlydiminishedthequalityofmotioncapturedatadue tosubjectfatigue,bothmentallyandphysically.Otherexperimentalconsiderationsmustbetaken forsubjectswithagaitimpairment.Forexample,asubjectwithcerebralpalsymaybeablewalk independentlyover-groundforatleast6minutes,butthatsamesubjectmaynotbeabletosafely walkonatreadmillatthesamespeedordurationduetothenatureoftheneuromuscularimpairment. Althoughane ortwasmadetoanticipatelimitationsinasubject'sabilitytoperformanyofthe prospectiveexperiments,afewadaptiveadjustmentsweremadetotheprotocolsothesubjectscould performthetask.Theseadjustmentsarereectedintheprevioussections.Mostsignicantly,was thereductionofthetreadmillbeltspeedfortheprospectivesubjectswithcerebralpalsy.Allthe retrospectivenormativesubjectswalkedbarefootover-ground.However,theprospectivenormative subjectswalkedwithshoesforallmotioncapturetrialsbecauseofthetreadmillwalkingtask. Additionally,havingtheprospectivenormativesubjectswalkwithshoesmadeforamoreconsistent comparisontotheprospectivesubjectswithanatypicalgaitpatternbecausetheyalsoperformed allmotioncapturetaskswithshoes.Comparisonsbetweenthepotentialdi erencesofbarefootand shodwalkingaredetailedaboveandtheresultspresentedinChapter5. Theretrospectivedatabaseconsistsofmotioncapturedatafromtwodi erentmotioncapture laboratories.TherstandolderlabwaslocatedattheChildren'sHospitalinDenver,Coloradoprior tothehospital'srelocationtotheFitzsimmonscampusin2008.Thesecondsetofretrospective subjects'motioncapturedatawascollectedatthenewChildren'sHospitalcampusinAurora, Colorado.Onlysubjectswiththesamemakersetsforbothmotioncapturelocationswereincluded inthestudy.Mostofthesta memberswhocollectedtheretrospectivenormativesubjectdataset atbothlocationsalsohelpedtrainmyself,whowasthesolepersonresponsibleforallprospective subjectsmarkerplacement.Thesubjectofmarkerplacementandassociatederrorisatopicof considerabledebateinthemotioncapturecommunityandnumerousarticleshavebeenpublished 106

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thatinvestigatedi erentmarkersets,checkstovalidateplacement,errorcorrectionalgorithms, andmarkerplacementprotocols.Theknowledgeandexperiencegainedfromparticipatinginsuch discussionsandexperimentsattheCenterforGaitandMovementAnalysislaboratorypriorto startingthisdissertationwasofsignicantbenetandinuencetomymarkerplacementtraining andprotocolusedintheprospectiveexperiments.Greatcarewastakentoensuremarkerplacement foreachsubjectwasasaccurateaspossiblesinceallofthestudy'smotioncapturebasedvariables arederivedfrommarkertrajectories.Forexample,clinicalsta memberswithmanymoreyearsof markerplacementandgaitanalysiso eredtraininginmarkerplacement,demonstratedpalpation techniquestocorrectlyidentifybonylandmarks,andvalidationofmarkerplacement(e.g.statictrial markerplacement)forseveralprospectivesubjects.Inadditiontothesee orts,eachprospective subject'sstatictodynamictrialtransitionwascheckedtoensurethethighandshankrotationo sets werewithinacceptablelimitsandthattherewasnocrosstalkbetweenthesagittalandcoronalplanes ofmotionatthekneejoint. 107

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5Results AfterapprovaltoconductthisresearchwasgrantedbytheColoradoMedicalInternalReview Board(COMIRB),prospectivesubjectdatacaptureoccurredfromJuly2013toNovember2014. Identicationandanalysisofretrospectivesubjectdatawasconductedintandemwithprospective subjectdatacaptureandanalysis.Thischapterreportstheresultsfromtheprospectivesubjectexperiments,retrospectivesubjectanalyses,analysescombiningprospectiveandretrospectivesubject cohorts,andtheanalysesforthefouraimsandtheirrespectivehypotheses. 5.1SubjectDemographics Eachprospectiveunimpairedsubject'smotioncapturestudywasapproximately3hoursinduration,fromconsent/assenttocompletionofdatacapture.Thestudyvisitforprospectivesubject withanatypicalgaitpatternlastedanaverageof2hours,fromconsent/assenttocompletionof datacapture.Table5.1providestheaveragetimespentforeachprospectivesubject'sdatacapture, motioncapturedataprocessing,andMatlabprocessingnecessarytogeneratePPsandCRPDs. ThesetimeestimatesdonotincludetheadditionalanalysesinMatlabfortestingthevariousaims andhypothesesorsecondaryinvestigations. Table5.1.1:Averagetimesforprospectivesubjectdatacaptureandanalysis. ProspectiveSubjectDataCaptureViconProcessingMatlabProcessingTotal Unimpaired3hours15hours2hours20hours CerebralPalsy2hours10hours1hour13hours Whileeachretrospectivesubjectdidnotrequiretimefordatacapture,themotioncapturetrials capturedfromeachretrospectivesubject'sinstrumentedgaitanalysiswasreprocessedtoensurethe samemotioncapturemarkerset,motioncapturemodel(e.g.Plug-in-Gait),gaitevents,andltering methodswereconsistentwiththoseusedforallprospectivesubjects.Additionally,thediagnosisof eachprospectivesubjectwasveriedbyexaminingandconrmingconsistencybetweenthediagnosis listedineachclinicalpatient'sinstrumentedgaitanalysisclinicalreportwiththepatient'sdiagnosis inhis/herelectronicmedicalrecords.Furthervisualconrmationofaretrospectivesubject'smotion capturedatawasperformedbyexaminingeachretrospectivesubject'smultimediainstrumentedgait analysisreport(e.g.ViconPolygon),whichincludesbi-planarvideo,kinematics,kinetics,temporalspatial,andwhenapplicable,dynamicsurfaceelectromyographicdata.Onaveragetimespent identifying,conrming,andofprocessingmotioncapturedataforretrospectivesubjectwithan atypicalgaitpatternwas3hours. 108

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Asanyonefamiliarwithprospectiveexperimentswithhumansubjectscanattest,oneofthe challengesinthisareaofbiomedicalresearchisrecruitingalargenumberofsubjectswhomeetthe study'sinclusioncriteriaandareinterestinparticipatinginresearch.Numerouse ortsweremadeto recruitprospectivesubjectswitheitherspasticcerebralpalsyoralowerlimbamputationbyapplying newtechniquesandlessonslearnedfrompreviousexperiencewithrecruitingprospectivesubjects. Potentialprospectivesubjectswererecruitedbyattendingfourcerebralpalsyclinicsandvelower limbamputeeclinicsateitherthemaincampusofChildren'sHospitalColoradooroneofthesatellite locations.Flyerswerepostedthroughoutthecommunity,FitzsimmonsMedicalCampus,Children's HospitalColoradoclinicalareas,andonseveralelectronicresearchsites/emaillistings.Duringthis phaseofsubjectrecruitment,fourindividualswithalowerlimbamputationwereidentied,but canceledtheirscheduledstudyvisitduetorecentdevelopmentofmusculoskeletalimpairments(2 individuals)a ectingtheirabilitytowalk,cardiovascularproblemslimitingendurance(1individual),andpersonalschedulingconicts(1subject).Therewereseveralindividualswithcerebralpalsy whowereinterestedinparticipatingasaprospectivesubjectbutdidnotmeetthestudy'sinclusion criteriaduetoconcomitantneurologicaldisordersa ectinggait(4individuals),inabilitytoambulate independentlywithoutanassistivedevice(2individuals),recentmusculoskeletalsurgery(1individual),andorthopaedicinjurya ectinggait(1individual).Additionally,oneindividualwithcerebral palsyhadtocancelascheduleddatacapturevisitduetoincreasedpainthatsignicantlya ected his/hergaitpatternandduration,whichalsopreventedreschedulingofthedatacapturevisit.The followingthreetablesprovidethegeneralsubjectdemographicsofthethreesubjectcohortsstudied inthisbodyofwork:unimpaired,cerebralpalsy,andlowerlimbamputation. Table5.1.2:Prospectiveandretrospectivedemographicsforallsubjectsfreeofgaitpathology,with mean(standarddeviation)valuesreported. UNIMPAIREDRetrospectiveProspective Males569 Females6411 Age(yr)21.03(12.58)25.95(10.69) Range(yr)7to669to54 LegLength(mm)851.41(94.26)877.45(80/25) Weight(kg)59.25(19.49)65.43(17.34) #Subjects12020 #Legs12020 109

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Table5.1.3:ProspectiveandRetrospectivedemographicsforallsubjectswithcerebralpalsy,with mean(standarddeviation)valuesreported. CEREBRALPALSYRetrospectiveProspective Males322 Females232 Age(yr)11.73(4.89)21.25(13.94) Range(yr)7to667to36 LegLength(mm)716.28(96.25)735.83(99.62) Weight(kg)33.21(12.74)50.73(22.38) #Subjects554 #Legs1006 SKG(#Legs)546 Crouch(#Legs)460 Hemiplegic(#Subjects)102 Diplegic(#Subjects)452 Table5.1.4:Retrospectivedemographicsforallsubjectswithalowerlimbamputation,withmean (standarddeviation)valuesreported. LOWERLIMBAMPUTATIONRetrospective Males9 Females6 Age(yr)17.33(8.35) Range(yr)7to66 LegLength(mm)832.37(147.74) Weight(kg)53.59(24.31) #Subjects15 #Legs19 Transtibial(#Legs)9 Transfemoral(#Legs)6 Unilateral(#Subjects)11 Bilateral(#Subjects)4 5.2ProspectiveExperimentalResults WhilePPandCRPDarelow-dimensionaldescriptors,sincetherearefourPPsandfourCPRDs foreachexperimentalconditionthereisstillalargeamountofdataassociatedwtihthesemeasures andconditions.Thereforedevelopingameanstoreducethesemeasuresofcoordinationandprovide asimplemetrictodescribethedeviationofacohortorexperimentalconditionfromareference becomesdesirable.Developingaquantitativemeansoffurtherconsolidatingtheinformationin thesecurveswassolvedbycreatedtwoindicesbaseduponelementsofthesecoordinationcurves.In additiontousingthesetwocoordinationindices,thegaitdeviationindexwasalsocalculatedfora comparisontoacommonlyusedjointangledescriptor.Thejusticationandanalyticalresultsfrom testingthesenewcoordinationindicesisaddressedinsection5.3.4aspartoftheAim4hypothesis testing.Althoughthefocusofthisbodyofworkandprospectiveexperimentsistoexaminechanges incoordinationdynamicsforvarioussubjectgroupsandwalkingconditions,conventionalswing 110

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periodtemporal-spatialmeasures,temporalevents,andcriticaleventswerealsocalculatedforall subjectsandprovidedforreferenceinAppendixG. 5.2.1ProspectiveSubjects:Over-GroundWalkingTask Toestablisheachprospectiveunimpairedsubject'sbaselinegaitforover-groundwalking,each subjectwalkedinthemainmotioncapturelaboratorywhilewearingafullbodymarkerset.The meanphaseportraitsandensemblecontinuousrelativephasediagramsforthiscohortarepresented inFigure5.2.1withtheretrospectiveunimpairedcohort'smeancoordinationcurves. Figure5.2.1:Unimpairedprospectivesubjects'(blue)meanphaseportraitsandensemblecontinuous relativephasediagramswiththeretrospectiveunimpairedcohort'smeancoordinationcurves(grey). InAppendixG,TableG1.1providesthemeanover-groundwalkingspeed,meansteplength, conventionaltemporal-spatialmeasures,andtimingofcriticalandtemporalgaiteventsforthe unimpairedsubjects,subjectswithcerebralpalsy,andsubjectswithalowerlimbamputation.The meanandstandarddeviationsfortheGDI,CDI,andscaledCPSvaluesforeachsubjectgroupwere 111

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calculatedandlistedinthetablebelow. Table5.2.1:MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSoftheunimpaired subjects,subjectswithCP,andsubjectswithalowerlimbamputationforover-groundwalking. Cohort#SubjectsGDICDICPS* N(Retro)120101.87(8.38)98.17(8.48)97.15(1.25) N(Pro)2092.67(5.00)92.37(7.74)97.08(0.68) CP(Pro)475.95(10.16)84.25(5.44)87.557(9.12) CP(Retro)5570.43(17.46)84.73(6.52)82.56(8.79) LLA(Retro)1578.79(12.68)85.69(7.21)89.03(5.86) Table5.2.2:Thecoe cientofvariation(CV)andvarianceration(VR)fortheangulardisplacement (AD),angularvelocity(AV)andcontinuousrelativephasediagramsforallunimpairedretrospective (n=120)andprospective(n=20)subjectsduringover-groundwalking. CoordinationCurve CVVR RetroProRetroPro PelvisAD2.71202.061.00471.05 PelvisAV365.5103913.420.92201.03 ThighAD4.11433.630.06020.04 ThighAV31.703027.980.06260.05 ShankAD5.40484.520.03080.02 ShankAV26.172821.960.04400.03 FootAD4.02833.650.07830.07 FootAV55.898554.490.15040.14 Pelvis-ThighCRPD27.250425.640.05170.05 Thigh-ShankCRPD36.052933.070.07300.06 Shank-FootCRPD50.521842.380.13880.10 Thigh-FootCRPD43.786338.270.11730.10 5.2.2ProspectiveSubjects:TreadmillWalkingTasks Allunimpairedprospectivesubjectswalkedover-groundataself-selectedwalkingspeedandthen onthetreadmillatslowerandfasterwalkingspeeds(Vss).ThenexttableprovidestheGDI,CDI, andscaledCPSforeachcondition'srepresentativetrialwasusedtocalculatethecohort'smean andstandarddeviationindexvalues.Markerdropoutforonesubjectduringthe80%Vsswalking conditionwasunabletobelledandthusresultedin19subjectscontributingtotheindexmeans. Table5.2.3:MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSoftheunimpaired prospectivecohortforvariouswalkingconditions. Task#SubjectsGDICDICPS* Over-groundWalk2092.67(5.00)92.36(7.74)97.08(0.68) Treadmill80%Vss1978.53(8.07)85.27(5.98)92.15(1.31) Treadmill90%Vss2078.31(7.67)88.24(6.67)91.99(0.61) Treadmill100%Vss2077.38(8.44)96.98(12.17)92.32(0.58) Treadmill110%Vss2078.91(9.23)97.44(9.44)92.09(0.71) Treadmill120%Vss2080.74(9.02)100.29(9.76)92.09(0.61) ThesagittalplanePPsandCRPDsfortheunimpairedprospectivecohort'sdi erenttreadmill walkingconditionsareprovidedinthegurebelow.AzoomedinviewofthesagittalplanePPsand 112

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CRPDsfortheunimpairedprospectivecohort'sdi erenttreadmillwalkingconditionsareprovided inAppendixG. Figure5.2.2:Phaseportraitsandcontinuousrelativephasediagramsfortreadmillwalkingconditionsoftheunimpairedprospectivesubjects(green=80%Vss,purple=90%Vss,blue=100%Vss, orange=110%Vss,red=120%Vss). AllprospectivesubjectswithCPwalkedover-groundataself-selectedwalkingspeedandthen onthetreadmillatasclosetotheover-groundwalkingspeed(Vss)aspossible.Thetablebelow providestheGDI,CDI,andscaledCPSforeachcondition'srepresentativetrialwasusedtocalculate thecohort'smeanandstandarddeviationindexvalues. Table5.2.4:MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSoftheprospective subjectswithCPforover-groundandtreadmillwalkingconditions. Task#SubjectsGDICDICPS* Over-groundWalking478.79(12.68)85.69(7.21)82.56(8.79) TreadmillWalking365.10(3.58)82.74(10.87)88.41(7.25) ThesagittalplanePPsandCRPDsforover-groundandtreadmillwalkingconditionsareprovided 113

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infollowinggurefortheprospectivesubjectswithcerebralpalsy.Thesagittalplanekinematics fortheprospectivesubjectswithCPforover-groundandtreadmillwalkingconditionsareprovided inAppendixG.Additionally,atableofconventionalinstrumentedgaitanalysismeasuresforthe subjectswithCPisprovidedinAppendixG. Figure5.2.3:Phaseportraitsandcontinuousrelativephasediagramsforover-ground(OG)and treadmill(TM)walkingconditionsofprospectivesubjectswithCP(blue=OG,red=TM). 5.2.3UnimpairedProspectiveSubjects:ChangesinAssistive/ResistiveForcesTask ThefollowingtableliststhemeanandstandarddeviationfortheGDI,CDI,andscaledCPS valuesforthetreadmillwalkingtaskswithswinglimbassistanceandswinglimbresistancewere calculated.Markerdropoutfortwosubjectsduringthebothofthesetreadmillwalkingconditions wereunabletobelledandthusresultedin18subjectscontributingtotheindicesmeans.Forboth ofthesetreadmillwalkingconditions,thetreadmillbeltspeedwassettotheaverageover-ground walkingspeedforeachsubject. 114

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Table5.2.5:MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSoftheunimpaired prospectivecohortfortwowalkingtreadmillconditions. Task#SubjectsGDICDICPS* SwingLimbAssist1890.99(13.72)94.07(9.32)92.72(1.35) SwingLimbResist1891.36(9.85)94.04(1.41)89.98(1.70) 5.2.4UnimpairedProspectiveSubjects:Over-groundvs.TreadmillWalking Comparisonsbetweentheprospectiveunimpairedsubjects'over-groundandtreadmillwalking weremadeusingconventionalinstrumentedgaitanalysismeasures,thetwonovelindicesofcoordinationdynamics,phaseportraits,andcontinuousrelativephasediagrams.Thegurebelowcontains meanensemblesagittalkinematiccurvesweregeneratedfromtheprospectiveunimpairedgroup's OGandTMwalkingtrials. Figure5.2.4:Sagittalplanekinematiccurvesforprospectiveunimpairedsubjectsduringover-ground (OG,blue)andtreadmill(TM,red)walkingconditions,withcoe cientsofvariation(CV). Theconventionaltemporal-spatial,gaitevents,andkinematicdescriptorsofgaitforthesetwo walkingconditionsisprovidedinthefollowingtable. 115

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Table5.2.6:ConventionalTemporal-Spatial,GaitEvents,andKinematicDescriptorsofGaitThe mean,standarddeviation,andp-valuesfortemporal-spatial,kinematic,andcriticalgaiteventsfrom thecohort'sover-ground(OG)andtreadmill(TM)walkingconditions.*Signicantlydi erent fromover-groundwalking,p 0.05.1Calculatedasdistancewalkeddividedbytimetowalk correspondingdistance. GaitMeasureOGTMp-value Cadence(steps/min)110.6(7.19)113.43(7.61)0.2339 WalkingSpeed(m/min)181.20(11.35)71.60(11.20)*0.0105 StepLength(m)0.73(0.08)0.64(0.09)*0.0009 StepTime(sec)0.54(0.04)0.53(0.04)0.1566 StrideLength(m)1.47(0.16)1.28(0.17)*0.0011 StrideTime(sec)1.09(0.07)1.06(0.07)0.2739 StanceTime(sec)0.70(0.05)0.69(0.05)0.8838 SwingTime(sec)0.39(0.03)0.37(0.02)*0.0074 FootO (%GC)64(1.65)65(1.45)*0.0015 FeetAdjacent(%GC)78(1.35)79(1.14)*0.0178 TibiaVertical(%GC)86(1.50)82(6.53)*0.0222 Kneeto40 ¡ Flexion(%GC)65(1.33)66(1.84)*0.0046 PeakRateofAnkleFlexion( ¡ /%GC)-2.10(0.39)-1.78(0.52)*0.0312 MaxKneeFlexion(%GC)73(1.43)74(1.41)0.1021 MaxKneeFlexion( ¡ )59(4.47)55(5.27)*0.0009 MaxHipFlexion(%GC)92(5.66)93(4.06)0.4936 MaxHipFlexion( ¡ )25.12(7.47)21.20(5.14)0.0724 KneetoNeutral(%GC)95(2.24)92(4.76)*0.0429 AnkletoNeutral(%GC)84(5.81)82(7.54)0.0700 MinimumAnkleDorsiexion( ¡ )-21(5.74)-19(7.57)*0.0231 HipRangeofMotion( ¡ )46.02(4.74)41.87(5.07)*0.0484 KneeRangeofMotion( ¡ )65.52(5.34)60.83(5.19)*0.0162 AnkleRangeofMotion( ¡ )33.42(4.90)31.67(5.83)0.4244 Pairedt-testswerecalculatedforthetimingandmagnitudeofthethirty-sevencoordination eventsintheswingperiodofgait.Falsediscoverrate(FDR)isamultiplehypothesiserrormeasures thatwasusedtoreducethelikelihoodoffalsepositivendings.FDRisthequantityofexpected proportionoffalsepositivendingsamongalltherejectedhypotheses.SinceFDRdoesnotsu er fromtheoverlystrictcriteriaintheBonferroniadjustedsignicancelevel,itisamoreappropriate errorratetocontrolinthetestingofmultiplehypotheses.Ofthethirty-sevencoordinationevents, thefollowingtableslistthefourcoordinationeventsthatwerefoundtobesignicantlydi erence usingthefalsediscoveryratemethodandadjustedp-valueslessthanorequalto0.0091. 116

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Table5.2.7:Swingperiodcoordinationeventswithsignicantchangesintimingandmagnitude. Themean,standarddeviation,andp-valueforthemagnitudeand/ortiming(percentgaitcycle= %GC)ofswingperiodcoordinationeventsthatweresignicantlydi erent(adjustedp 0.0091) betweenthecohort'sover-groundandtreadmillwalkingconditions.EachCEisalsoassociatedwith amechanismcategory. CoordinationEventOGTMAdj.pvalue 1.FootmaxAD( ¡ )178.45(0.54)175.15(1.44)0.0000 2.FootminAV(%GC)88(1.79)91(1.10)0.0000 FootminAV( ¡ /%GC)-444.18(58.93)-375.59(61.26)0.0009 3.Shank-Footabs.swingmin(%GC)88(1.77)91(1.17)0.0000 MeansagittalPPsandensembleCRPDsfortherightthigh,shank,andfootweregenerated fromthecohort'sOGandTMwalkingtrials(Figure5.2.5).Thefourcoordinationeventsthatwere signicantlybetweenthesetwowalkingconditionsareindicatedinthegurebelow.Thenumbering ofstatisticallysignicantcoordinationeventslistedinTable5.11correspondstothenumbersshown inthePPsandCRPDs. Figure5.2.5:Meanphaseportraitsandcontinuousrelativephasediagramsforunimpairedprospectivesubjectsover-ground(OG,blue)andtreadmill(TM,red)walkingconditionsandsignicant coordinationevents. 117

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Thecoe cientofvariation(CV)foreachPPvariableandCRPDarealsoprovidedingure above. 5.2.5UnimpairedProspectiveSubjects:ChangesinAssistive/ResistiveForcesTask ThenexttableliststhemeanandstandarddeviationfortheGDI,CDI,andscaledCPSvalues forthetreadmillwalkingtaskswithswinglimbassistanceandswinglimbresistancewerecalculated. Markerdropoutfortwosubjectsduringthebothofthesetreadmillwalkingconditionswereunable tobelledandthusresultedin18subjectscontributingtotheindicesmeans.Forbothofthese treadmillwalkingconditions,thetreadmillbeltspeedwassettotheaverageover-groundwalking speedforeachsubject. Table5.2.8:MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSoftheunimpaired prospectivecohortfortwowalkingtreadmillconditions. Task#SubjectsGDICDICPS* SwingLimbAssist1890.99(13.72)94.07(9.32)92.72(1.35) SwingLimbResist1891.36(9.85)94.04(1.41)89.98(1.70) 5.2.6UnimpairedProspectiveSubjects:ChangesinJointRangeofMotionTasks ThefollowingtableprovidesthemeanandstandarddeviationfortheGDI,CDI,andscaledCPS forthetreadmillwalkingtasksakneebracexedtofullextension(180 ¡ ),akneebracexedto 60 ¡ ofexion,andananklebootxedtoneutraldorsiexionwasalsocalculatedforallunimpaired prospectivesubjects.Markerdropoutforonesubjectduringthesetreadmillwalkingconditionswas unabletobelledandthusresultedin19subjectscontributingtotheindicesmeans.Forthesethree treadmillwalkingconditions,thetreadmillbeltspeedwassettotheaverageover-groundwalking speedforeachsubject. Table5.2.9:MeanandstandarddeviationvaluesfortheGDI,CDI,andscaledCPSoftheunimpaired prospectivecohortfortwowalkingtreadmillconditions. Task#SubjectsGDICDICPS* KneeFixed180 ¡ 1973.69(7.86)80.72(5.24)86.25(3.27) KneeFixed60 ¡ 1975.53(7.08)85.08(7.00)84.95(4.35) AnkleFixed0 ¡ 1989.92(10.56)89.35(8.12)90.99(1.37) Sincethepurposeoftheexperimentwithoneoftheunimpairedsubjectskneesbeingxedinfull extensionwastocomparethecoordinationdynamicsoftheunimpairedsubjectstothecoordination dynamicsofsubjectswithasti kneegaitpattern,thesagittalplanePPsandCRPDsforthesetwo subjectgroupsareprovidedinthegurebelow. 118

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Figure5.2.6:Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjectswalkingonthetreadmillwithxed180 ¡ kneeextension(lightred),over-groundwalkingof allsubjectswithasti kneegaitpattern(darkred),andover-groundwalkingforallretrospective unimpairedsubjects(grey). Similarly,thepurposeoftheexperimentwithoneoftheunimpairedsubjectskneesbeingxed inexionwastocomparethecoordinationdynamicsoftheunimpairedsubjectstothecoordination dynamicsofsubjectswithacrouchgaitpattern.ThesagittalplanePPsandCRPDsforthesetwo subjectgroupsareprovidedinthefollowinggure. 119

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Figure5.2.7:Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjectswalkingonthetreadmillwithxed60 ¡ kneeexion(orange),over-groundwalkingofall subjectswithacrouchgaitpattern(red),andover-groundwalkingforallretrospectiveunimpaired subjects(grey). Similarly,thepurposeoftheexperimentwithoneoftheunimpairedsubjectsanklesbeingxed inneutraldorsiexionwastocomparethecoordinationdynamicsoftheunimpairedsubjectstothe coordinationdynamicsofsubjectswithabelowkneeamputation.Phaseportraitsandcontinuous relativephasediagramsforthesevarioussubjectgroupsarepresentedinthenextgure. 120

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Figure5.2.8:Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjectswalkingonthetreadmillwithxedankledorsiexion(lightgreen),over-groundwalkingof allsubjectswithatranstibialamputation(darkgreen),andover-groundwalkingforallretrospective unimpairedsubjects(grey). 5.3AimsandHypothesesTestResults 5.3.1Aim1Results AsdiscussedinChapter1and3,thepurposeofAim1wastoconstructanormativereferencefrom alargecohortofindividualsfreeofgaitpathology,whichwouldserveasthereferencefortheother threeaims.AsmentionedinChapter4,twonormativereferencedatasetswereconstructedbecause theunimpairedretrospectivesubjectswerebarefootandtheprospectivesubjectsworeshoes.Mean sagittalPPsandensembleCRPDsforthelowerextremitysegmentswerecreatedfortheprospective andretrospectiveunimpairedsubjectsusingthemethodsdescribedinChapters3and4(Figure 5.2.1). Thefollowingtableprovidesthecoe cientofvariation(CV)andvarianceratio(VR)were 121

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calculatedtoquantifytheextentofvariabilityfortheangulardisplacement(AD),angularvelocity (AV),andrelativephaseanglewithrespecttothemeanofthesecurvesacrossalltimeinthe ensembleaverage. Table5.3.1:Coe cientofvariation(CV)andvarianceratio(VR)forunimpairedretrospective cohort'smeanangulardisplacement(AD),meanangularvelocity(AV),andrelativephaseangles. CoordinationCurve CVVR RetroProRetroPro PelvisAD2.71202.061.00471.05 PelvisAV365.5103913.420.92201.03 ThighAD4.11433.630.06020.04 ThighAV31.703027.980.06260.05 ShankAD5.40484.520.03080.02 ShankAV26.172821.960.04400.03 FootAD4.02833.650.07830.07 FootAV55.898554.490.15040.14 Pelvis-ThighCRPD27.250425.640.05170.05 Thigh-ShankCRPD36.052933.070.07300.06 Shank-FootCRPD50.521842.380.13880.10 Thigh-FootCRPD43.786338.270.11730.10 Thefollowingtableprovidesthemean,standarddeviation,and95%condenceintervalsforthe relativephaseanglesfromeachCRPDatthefouressentialfootfallconditionsofthenormalgait cyclefromtheunimpairedretrospectivecohort. Table5.3.2:Mean,1standarddeviation,and95%condenceintervalsfortherelativephaseangles (degrees)atcommontemporalgaiteventsforunimpairedprospectivesubjects.Theprospective cohort'smeanand1standarddeviationforthepercentgaitcycleforeachtemporalgaiteventis alsoreported. CRPDFootStrike0%( 0.00%)OppositeFootO 10%( 2.49%) Pelvis-Thigh0.70(SD11.23)-1.28to2.68-32.17(SD7.43)-33.48to-30.86 Thigh-Shank-48.05(SD19.16)-51.44to-44.66-23.29(SD9.78)-25.02to-21.56 Shank-Foot98.12(SD17.76)94.98to101.2657.30(SD14.68)54.71to59.89 Thigh-Foot50.07(SD10.77)48.17to51.9734.01(SD13.20)31.68to36.34 CRPDOppositeFootOn49%( 0.92%)FootO 60%( 2.14%) Pelvis-Thigh-27.17(SD12.73)-29.42to-24.9262.20(SD6.35)61.08to63.32 Thigh-Shank-40.14(SD15.24)-42.83to-37.45-137.69(SD7.51)-139.02to-136.36 Shank-Foot19.29(SD9.02)17.70to20.885.81(SD10.07)4.03to7.59 Thigh-Foot-20.85(SD20.87)-24.54to-17.16-131.88(SD10.69)-133.77to-129.99 5.3.2Aim2Results AspresentedinChapter1and3,thepurposeofAim2anditshypotheseswastoexplorethe relationshipbetweentheproposedmeasuresofcoordinationdynamics(e.g.PP,CRPD)andselect clinicalperformancemeasuresthatcharacterizeaspectsofcoordination.Recallfromthemethods discussioninChapter4,thattheresultsfromthesetestsandanalysesareonlyforthestudy's 122

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prospectivesubjects. 5.3.2.1Hypothesis2AResults Hypothesis2Awastestedbytwomeasuresderivedfromthevoluntaryreciprocalmovements ofeachsubject'slegsinthespeed-accuracytask,whichwasdesignedtocharacterizeasubject's selectivemotorcontrolinrelationtoanytaskspeciccoordinationdecits.Theaveragepercentage offoottapsthatwerewithinatarget'sboundary(e.g.hitaccuracy)fortheprospectivesubjects withcerebralpalsyandanunimpairedgaitaredisplayedwithatrendlineinthefollowinggure. Figure5.3.1:Meanpercentageofhits(accuracy)fortheprospectiveunimpairedsubjects(blue)and subjectswithcerebralpalsy(red)forthethreefoottargetsizes(80%,100%,120%).Alineartrend lineisprovidedand*indicatesasignicant(p<0.05)di erencebetweenthetwosubjectgroups. Foreachofthethreetargetsizes,Student'st-testswereconductedtotestiftherewasasignicant di erencebetweentheunimpairedsubjects'meanaccuracyandthemeanaccuracyofthesubjects withcerebralpalsy.Asindicatedinthegureabove,therewasastatisticallysignicant(p<0.05) di erencebetweenthetwosubjectgroups'abilitytoaccuratelytapthetarget. Thesecondmeasureusedtotestthehypothesis2Awasthespeedoftheswinginglimbwhen itmovedfromtheafttargettotheforwardtarget.Foreachofthethreetargetsizes,Student's t-testswereconductedtotestiftherewasasignicantdi erencebetweentheunimpairedsubjects' meanswinglegforwardspeedandthemeanforwardspeedoftheswinginglegofthesubjects withcerebralpalsy.Asindicatedinthegurebelow,therewasastatisticallysignicant(p<0.05) di erencebetweenthetwosubjectgroups'abilitytoaccuratelytapthetarget. 123

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Figure5.3.2:Meanspeedoftheforwardswinginglegfortheprospectiveunimpairedsubjects(blue) andsubjectswithcerebralpalsy(red)forthethreetargetsizes(80%,100%,120%).Alineartrend lineisprovidedand*indicatessignicant(p<0.05)di erencesbetweenthetwosubjectgroups. Sincetheforwardmotionoftheswingingleginthisreciprocaltappingtaskmimicstheforward motionoftheswinglegduringgait,coordinationeventsrelatedtoasubject'sabilitytodissociatethe hipextensionandankleplantarexionsynergynearfooto andduringinitialswingwerecompared toeachprospectivecohort'sswinginglegspeed.AsmentionedinChapter4,t-testswerecalculated foreachcohort'smeantiming(%GC)andmagnitudeforcoordinationeventsduringinitialswingon thethigh-shankandthigh-footcontinuousrelativephasediagrams.Thecoordinationeventswerea minimum,maximuminstantaneousslope(MiS),inectionpoint(IP),andazerocrossing(0x).The timingandmagnitudeofthemaximuminstantaneousslopeofthethigh-shankCRPDwastheonly statisticallysignicantcoordinationevent.Thefollowingtableprovidesthemeansandstandard deviationsforthisthigh-shankCRPDcoordinationeventininitialswing. Table5.3.3:Meantiming(%GC)andmagnitudeofthemaximuminstantaneousslope(MiS),withits standarddeviation,forthetwoprospectivecohorts'thigh-shankcontinuousrelativephasediagram. Pro.Groups Thigh-ShankCRPDThigh-ShankCRPD MiS(%GC)MiS( ¡ /%GC) N(n=20)70( 1.28)52.00( 5.55) CP(n=6)74( 5.04)21.85( 11.42) Additionally,belowisaplotofthetwomeanensemblethigh-shankCRPDsforthetwoprospectivesubjectcohorts.Asthetwoblackarrowsonthegureindicate,themaximuminstantaneous slopeforthesubjectswithCPisconsiderablyshallower,delayed,andoverallattenuated. 124

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Figure5.3.3:Meanensemblethigh-shankCPRDfortheunimpairedretrospectivesubjects(grey), unimpaired(blue)prospectivesubjects,andprospectivesubjectswithCP(red)withthesignicant coordinationevent.Verticallinesindicatethemeanoccurrenceoffooto foreachgroup. 5.3.2.2Hypothesis2BResults AllprospectivesubjectsweregivenascoreforeachlimbbasedontheSelectiveControlAssessmentoftheLowerExtremity(SCALE)tocharacterizeeachsubject'sdegreeofselectivemotor controlimpairment.Amaximumof6pointsforeachlimbwerepossible;2pointsperjoint.The SCALEscoresforallprospectivesubjectswithCPareprovidedinAppendixG.Alloftheunimpairedprospectivesubjectsscoreamaximumpossiblescoreof6points.ThesubjectswithCPhad variousscoresrangingfromthemaximumpossibleto2pointsperlimb.Therewasasignicant di erence(p=0.013)betweenthemeanunimpairedsubjectsSCALEscoreandthemeanSCALE scoreforthesubjectswithCP. Todetermineiftherewasasignicantrelationshipbetweenasubject'sabilitytoperformthe selectvoluntarymotorcontroljointtasksoftheSCALEandasubject'sabilitytoperformswing limbadvancementwhilewalkingover-ground,theSCALEscoreswerecomparedtocoordination eventsininitialswingthatarerelatedtoasubject'sabilitytodissociatethehipextensionandankle plantarexionsynergynearfooto andinitiateahipexorsynergy.Asmentionedinchapter4, t-testswerecalculatedforeachcohort'smeantiming(%GC)andmagnitudeforcoordinationevents duringinitialswingonthethigh-shankandthigh-footcontinuousrelativephasediagrams.The coordinationeventsanalyzedwereaminimum,maximuminstantaneousslope,inectionpoint,and azerocrossing.Threecoordinationeventswerefoundtobesignicantly(p<0.05)di erentbetween 125

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thetwosubjectgroups.Whilecompletetablesoftheset-testsforalltheconsideredcoordination eventsareprovidedinAppendixG,thefollowingtableprovidesthemeansandstandarddeviations forthesethreecoordinationevents. Table5.3.4:Meantiming(%GC)andmagnitudeofthemaximuminstantaneousslope(MiS),minimum(Min),andinectionpoint(IP)withstandarddeviation,fortheprospectivecohorts'thighshankandthigh-footcontinuousrelativephasediagrams(CRPDs). Pro.Group Thigh-ShankCRPDMin(%GC)Thigh-ShankCRPDMiS(deg/%GC) (%GC)( ¡ )(%GC)( ¡ ) N(n=20)64( 1.21)-142.53( 4.03)52.00( 5.55)69( 1.67) CP(n=6)70( 6.0)-85.57( 44.32)21.85( 11.42)76( 5.92) Thefollowingplotofthemeanensemblethigh-shankandthigh-footCRPDsforthetwoprospectivesubjectcohortswiththethreecoordinationeventsthatweresignicantlydi erent(p<0.05) forthesetwocohorts. 126

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Figure5.3.4:Meanensemblethigh-shank(top)andthigh-foot(bottom)CPRDfortheunimpaired retrospectivesubjects(grey),unimpaired(blue)prospectivesubjects,prospectivesubjectswithCP (red),andthesignicantcoordinationevents.Verticallinesindicatethemeanoccurrenceoffooto foreachgroup. Sinceallunimpairedprospectivesubjectsscoredthemaximumpossiblepointsforthismetric, correlationsforthesesubjects'SCALEscoresandothermeasureswerenotcalculated.However,a correlationmatrixfortheprospectiveunimpairedsubjects'signicantcoordinationeventsisprovided inAppendixG.Additionally,acorrelationmatrixforthesamevariablesandSCALEscoreforthe prospectivesubjects'withCPisprovidedinAppendixG. 5.3.2.3Hypothesis2CResults GaitrelatedtasksfromtheInternationalCooperativeAtaxiaRatingScale(ICARS)andScale fortheAssessmentandRatingofAtaxia(SARA)examswereusedtocharacterizecerebellarbased 127

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impairmentsinspatialaccuracyofmovementanddynamicbalanceforallprospectivesubjects.A maximumof40pointsforeachlimbwaspossibleforthismetric.WhileFigure5.12providesa scatterplotoftheprospectivesubject'sscores,theICARS/SARAscoresforallprospectivesubjects withcerebralpalsyareprovidedinAppendixG.Therewasnotastatisticallysignicantdi erence (p=0.1040)betweentheunimpairedprospectivesubjectsandsubjectswithcerebralpalsy.Thismay bepartiallyduetothefactthatallunimpairedprospectivesubjectsscoredthemaximumpossible valueforthismetricandthesmallsamplesizeofsubjectswithCP. Figure5.3.5:ICARS/SARAscoresforallunimpairedprospectivesubjects(bluecircle)andall prospectivesubjectswithcerebralpalsy(redsquare). AsdetailedinChapter4,twoadditionalanalyseswereconductedonthemotioncapturedata fortheexperimentsrelatedtothishypothesis.First,themeanbaseofsupport(BoS)wascalculated foreachprospectivesubject'srepresentativeover-groundwalkingtrialandmeanofalltandem walkingtrial(s).Ofthefourprospectivesubjectswithcerebralpalsy,onlyonesubjectwasableto completethetandemwalkingtask.Theotherthreesubjectswereunabletocompletethistaskfor variousreasons:requiredassistance(1subject),heel/toemarkerskeptfallingo duetowalking pattern(1subject),andunabletoperformtask(1subject).Therewasnotastatisticallysignicant di erence(p=0.0672)betweentheover-groundBoSwalkingtrialsfortheprospectivesubjectswith CPandtheBoSfortheunimpairedprospectivesubjects.However,whencomparingtheBoSfor over-groundwalkingofallthestudy'ssubjects,bothprospectiveandretrospective,therewere signicantdi erencesbetweentheunimpairedsubjectsandsubjectswithCP(p=2.96E-12)and betweensubjectswithCPandsubjectswithaLLA(p=0.01).Therewasnotasignicantdi erence intheBoSwidthbetweentheunimpairedsubjectsandsubjectswithaLLA(p=0.27). Secondly,thecenterofmasscurvatureduringtheturningtaskswascalculatedforallprospective 128

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subjectsandt-testswereruntodetermineifthereweresignicantdi erencesbetweenthecohorts. Recallalargercurvature( )correspondstoatighterturn.Therewerenotanystatisticallysignicant di erencesbetweenthemeanmaximumcurvatureforeachprospectivecohort'srightandleftturns (gurebelow).Again,thiscouldinpartbeduetothesmallnumberofprospectivesubjectswith CP.Also,itisimportanttonotethatofthefourprospectivesubjectswithCP,twosubjectswere a ectedonbothsides(e.g.diplegic)andtwowerea ectedononlyoneside(e.g.hemiplegic). Therefore,ofthefourlegscorrespondingtothefourrightturns,allofthelegswerea ectedandof thefourlegscorrespondingtothefourleftturns,onlytwowerea ected. Figure5.3.6:Meanmaximumcurvature(K)forleft(red)andright(green)turnsforallunimpaired prospectivesubjects(n=20)andprospectivesubjectswithCP(n=4). Thenextguredepictsthemeancenterofmass(CoM)trajectoryfortheleftandrightturns ofbothprospectivesubjectgroups.Thisgureclearlyshowstherearedi erencesintheturning curvatureandtheinuenceofsubjectswithhemiplegiaanddiplegiaontheseresultsandobserved turningstrategiesforthesetwocohortswillbediscussedinChapter6. 129

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Figure5.3.7:MeanCenterofMass(CoM)trajectoriesforleft(red)andright(green)turningtasks ofprospectivesubjects. Sinceallunimpairedprospectivesubjectsscoredthemaximumpossiblepointsforthismetric,correlationsforthesesubjects'ICARS/SARAscoresandothermeasureswerenotcalculated.However, acorrelationmatrixfortheprospectiveunimpairedsubjects'maximumcurvatureandconventional temporal-spatialmeasuresofgaitisprovidedinAppendixG.Additionally,acorrelationmatrixfor thesamevariablesandICARS/SARAscorefortheprospectivesubjects'withCPisprovidedin AppendixG. 5.3.3Aim3Results AspresentedinChapter1and3,thepurposeofAim3wastoconstructamathematicalsoftware modelofadoublependulum,usinginitialconditionsandmodelparametersderivedfromsubject motioncapturedata,andcomparethemotionofthemodel'stwolinkagestothesagittalplanmotion ofthethighandshankfromactualsubjectdata.RecallingfromthemethodologyoutlinedinChapter 4,therstversionofthemodelusedtheMatlabfunctionode45tosolvetheequationsofmotion andcomparethefourdi erentdampingcasestotheactualmotionofeachcohort'sthighandshank sagittalplanetrajectories.Thetablebelowpresentstherankingofthegeneralsubjectcohorts(e.g. N,CP,LLA)foreachdampingcase.Alargersummednormalizedrootmeansquareerror(NRMSE) indicatesagreaterdi erencebetweenthependulummodel'smotionandthecohort'smotion,thus resultinginalowerranking. 130

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Table5.3.5:Rankingsofthethreegeneralsubjectcohortsfor4di erentpendulummodeldamping conditions.Thesubjectgroupwiththelowestrankingforeachdampingcaseisindicatedwitha rectanglesurroundingthesummednormalizedrootmeansquareerror( NRMSE).Threesubject cohortswereconsidered:unimpaired(N),cerebralpalsy(C),andalowerlimbamputation(LLA). Group UndampedUnderDampedCriticallyDampedOver-Damped NRMSERank NRMSERank NRMSERank NRMSERank N23.322 25.581 26.301 26.171 C31.57335.80334.52334.563 LLA 19.971 26.58226.81226.372 ThenexttableprovidesthesummedNRMSErankingforeachofthefourdampingconditions thatwascalculatedforthevegaitpatternsconsideredinthisbodyofwork. Table5.3.6:Gaitpatterncohortrankingsfor4di erentpendulummodeldampingconditions. Fivegaitpatternswereconsidered:unimpaired(N),sti kneegait(SKG),crouch(C),belowknee amputation(BK),andabovekneeamputation(AK). Group UndampedUnderDampedCriticallyDampedOverDamped NRMSERank NRMSERank NRMSERank NRMSERank N23.32325.58226.30226.173 SKG35.30433.02430.66430.694 C38.52538.39538.11538.135 BK 20.451 26.38326.34325.772 AK22.442 24.451 25.341 25.361 ThesummedNRMSEandcorrespondingrankingsforeachsubjectcohortforeachofthefour dampingconditionsareprovidedinAppendixG.Todetermineifthevariousrankingsforthethree di erentsubjectgroupsweresignicantlydi erent,aWilcoxonsigned-ranktestwasconductedin Matlab.Noneofthep-valuesfromthevariousWilcoxonsigned-ranktestsweresignicantlydi erent. Asindicatedinprevioustable,asubjectwithalowerlimbamputation,specicallythosewith atranstibialamputation,hadcoordinationdynamicsmeasureswiththesmallestresidualwhen comparedtoapassivedoublependulum(Hypothesis3A).Andwhenconsideringsubjectswith alowerlimbamputationasagroup,thiscohorthadthelowestresidualwhencomparedtoan un-dampedpendulum(Table5.13).Ingeneral,theresidualbetweenthecoordinationdynamics measuresofsubjectswithcerebralpalsyandanover-dampeddoublependulumwerethelargestof thethreegroups(Hypothesis3B).However,whendividingsubjectsfurtherintogaitpattern,the subjectswitheithersti kneegaitorcrouchwerethefurthestfromanyofthependuladamping conditions.Ingeneral,theunimpairedsubjectgrouphadthesmallestresidualwhencompared toacriticallydampedpendulum(Hypothesis3C),buttheyalsohadthesmallestresidualforall dampingcases.Whencomparedtothevariousgaitpatterns,thiscohorthadeitherthesecondor thirdsmallestresidualforalldampingcases. 131

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5.3.4Aim4Results RecalltheobjectofAim4wastodemonstratetheproposedmeasuresofcoordinationdynamics areabletodistinguishbetweendi erentgaitpathologiesandpatternsassociatedwithalteredlimb advancementduringtheswingperiodofgait.Inane orttoconsolidatethelargeamountofvariables anddataassociatedwiththeproposedmeasuresofcoordinationdynamicstwonovelindiceswere created.Theseindiceswereusedtodetermineiftherearestatisticallysignicantdi erencebetween thecoordinationdynamicsforunimpairedsubjectsandsubjectswitheitherasti knee,crouch,and mechanicallyalteredgaitpattern.Thefollowingsectionpresentstheresultsforvariousanalyses testingthevalidityofthesenewindicesandthehypothesistestresults. 5.3.4.1CoordinationDeviationIndexResults TwonovelindiceswerecreatedtoaddressAim4anditshypothesis.Therstindex,thecoordinationdeviationindex(CDI),wascalculatedforallprospectiveandretrospectivesubjectsand comparedtotheGDIandGrossMotorFunctionClassicationSystem(GMFCS)levelofindividuals withvaryingdegreesofmotorimpairment.Theoverallobjectiveofthisinvestigationwastoexplore theapplicabilityoftheCDIindescribinggaitpathologyfortwoclinicalcohorts(CP,LLA)with di erentreasonsforcoordinationdecits.Thespecicaimsofthisindex'sinvestigationwereto 1)generateacoordinationdeviationindexusingtheGDImethodologyforthesubjectgroups,2) compareCDIscoresofthegroupsusingtheGDIasabenchmarktodescribevaryingdegreesof gaitperformanceinthesedistinctgroups,and3)demonstratethatthemagnitudeofcoordination impairment(CDI)correspondstothemagnitudeofkinematicimpairment(GDI). InAppendixG,TableG.4.1providesthemeansandstandarddeviationsofdemographiccharacteristics,GDIs,andCDIsforthesubjects.UsingtheequationofvarianceaccountedforinSchwartz etal,2008sixcoordinationfeatureswerefoundtobenecessaryforreconstructingthecoordination curveswith98%reconstructionquality(AppendixG,Figure1).Figure5.3.8Adisplaysthemean GDIandCDIvaluesforthedi erentsubjectcohortcategories.Forallofthesubjectgroups,there wasasignicantdi erence(p 0.001)betweentheirGDIandtheunimpairedgroup'sGDIsanda signicantdi erence(p 0.001)betweengroup'sCDIandtheunimpairedgroup'sCDIs.Except fortheAKsubjectgroup,therewasasignicantdi erence(p 0.001)betweenagroup'sCDIsand GDIs.NotethepatternforreducedCDIinclinicalgroupsfollowsasimilardownwardtrendasthe GDI.Figure5.3.8BpresentsthemeanGDIsandCDIsfortheunimpairedsubjectsandsubjects withCPwhenorganizedbyGMFCSlevel.Thereweresignicantdi erences(p 0.05)between 132

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themeanCDIsandeachGMFCSlevelandbetweenthemeanCDIsforGMFCSlevelsIandIII. Figure5.3.8:A)ComparisonofGDI(greysquare)andCDI(bluesquare)meanscoresforeach subjectgroup:unimpaired(N),lowerlimbamputation(LLA),belowkneeamputation(BK),above kneeamputation(AK),cerebralpalsy(CP),hemiplegia(H),diplegia(D),sti kneegaitpattern (SKG),andcrouchgaitpattern(C).B)MeanGDI(grey)andCDI(blue)valuesforNandCP subjectswithcondenceintervalswith95%condenceintervalsarepresentedbyGMFCSlevel. Signicantdi erencesbetweengroups(p 0.05)andbetweenGMFCSlevelsIandIII. Figure5.3.9AshowstherelationshipbetweentheGDIandCDIvaluesforallofthestudy's subjects,withadashedlineindicatingtheidealunimpairedsubjectindexvalue.Figure5.3.8B illustratestheempiricalnormaldistributionoftheGDIandCDIscoresinrelationtoatheoretical cumulativedistributionfunction.TheKolmogorov-SmirnovtestconrmedtheGDIandCDIvalues forthisstudy'ssubjectswerenormallydistributed. 133

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Figure5.3.9:A)ScatterplotofallGDIscoresagainstallCDIscoreswiththelineofbestt(red). B)Cumulativedistributionfunctions(CDF)fortheGDI(black)andCDI(blue)incomparisonto thetheoreticalnormalCDF(red). 5.3.4.2CoordinationPerformanceScoreResults RecallfromChapter4thatsixcoordinationevents(CEs)duringswingperiodwereidentied usingabackwardstepwiseregressionmodelassignicant.Table5.20providesalistofthesix signicantCEs,abriefdescriptionofeachCE,themean,standarddeviation,and95%condence intervalsfromtheunimpairedsubjects. Table5.3.7:Descriptionofthesixsignicantcoordinationeventslistedinorderofoccurrenceduring swingperiodwiththenormativecohort'smean(standarddeviation)valueforeachCE,and95% condenceinterval(CI)fromthenormativecohort.Thegaitcyclewasindexedfrom1to101%. CoordinationEventDescriptionMean(SD)95%CI 1)Thigh-FootCRPDAbsoluteminimum(%GC)-137.14 ¡ (6.38)-149.65 ¡ to-124.63 ¡ 2)ThighPPMaxangularvelocity(%GC)67%(1.70)64.05%to70.41% 3)PelvisPPMaxangulardisplacement( ¡ )173.59 ¡ (4.61)164.56 ¡ to182.62 ¡ 4)PelvisPPMinangulardisplacement( ¡ )171.51 ¡ (4.54)162.62 ¡ to180.41 ¡ 5)FootPPMaxangulardisplacement( ¡ )89%(1.83)85.00%to92.16% 6)Thigh-FootCRPDLastinectionpointinswing( ¡ )98%(1.25)95.29%to100.19% Ofthesixsignicantcoordinationeventsidentied,threeswingperiodcoordinationeventswere usedforthisrstregressionmodel(atypicalvs.typicalgaitpattern).Themagnitudeofthe thigh-footCRPDminimumnearfooto (TF1),themagnitudeofthepelvisPP'sminimumangular displacement(P1),andthepercentgaitcycleofthefootPP'smaximumangulardisplacement(pF2). Alloftheavailable246observations(legs)wereusedintheconstructionofthetworegressionmodels baseduponthecoordinationeventsusedtoconstructtheCPSmetric.Thenalregressionmodelfor distinguishingbetweenanimpairedandunimpairedgaitpatternisprovidedintheequationbelow. 134

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Theareaunderthereceiveroperatorcharacteristic(ROC)curvewas0.9767.AppendixGcontains additionalresultsfromthismodel'sanalysesinSAS. Algorithm5.1 Regressionmodelfordistinguishingbetweenanunimpaired(N)andcerebralpalsy (CP)gaitpattern. Y CPvN =8 74246 0 04577 X P 1 +0 03298 X TF 1 +0 03815 X F 2 Usingthisequation,itispossibletosolvefortheprobabilitythatasubject'sgaitpatternis atypical.Thisfurthersupportstheabilityoftheproposedmeasuresofcoordinationdynamicsto distinguishbetweenvariousgaitpatterns(Aim4).Noneofthenuisancevariablesconsidered(e.g. leglength,weight,age,gender)hadasignicantinuenceonthismodelandwerenotincluded becausetheydidnotstrengthenthemodelorimprovetheareaunderthecurveofthereceiver operatorcharacteristiccurve. Ofthesixsignicantcoordinationeventsidentied,twoswingperiodcoordinationeventswere usedforthissecondregressionmodel(sti kneegaitvs.crouchgaitpattern).Thenalregression modelfordistinguishingifasubjectwithcerebralpalsyhaseitherasti kneegaitorcrouchgait patternisprovidedinthefollowingequation.Theareaunderthereceiveroperatorcharacteristic(ROC)curvewas0.6377.Noneofthenuisancevariablesconsidered(e.g.leglength,weight, age,gender)hadasignicantinuenceonthismodelandwerenotincludedbecausetheydidnot strengthenthemodelorimprovetheareaunderthecurveofthereceiveroperatorcharacteristic curve.AppendixGcontainsadditionalresultsfromthismodel'sanalysesinSAS. Algorithm5.2 Regressionmodelfordistinguishingbetweenasti kneegait(SKG)andacrouch (C)gaitpattern. Y SKGvC =7 8164 0 0564 X TF 1 0 0147 X P 1 MeansagittalPPsandensembleCRPDswiththesixsignicantcoordinationeventswerecreated fortheretrospectiveunimpairedsubjectsandsubjectswitheitherasti kneegaitorcrouchgait pattern(Figure5.3.10).PPsarereadinaclockwiseprogressionthroughthegaitcyclestartingat footstrike,indicatedwithasoliddownwardarrow.Footo isindicatedwithasolidupwardarrow oneachPPandverticallineontheCRPD.Forvisualclarity,standarddeviationbandsforthePP curvesarenotdepicted.EachpercentgaitcycleisindicatedwithacircleonthePPs. 135

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Figure5.3.10:ThesixsignicantCEsareindicatedoneachcohort'scorrespondingPPsandensemble CPRDs,wheregreycorrespondstotheunimpairedsubjects,redcorrespondstosubjectswithaSKG pattern,andorangecorrespondstosubjectswithacrouchgaitpattern. Themean(unscaled)CPSscoreforeachgaitpatternandsubjectgrouparedepictedinthe followinggure. 136

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Figure5.3.11:Abox-plotofeachcohort'sCoordinationPerformanceScore(CPS)isprovided,where outliersareindicatedwithared+andablack*indicatesmeancohortCPSsthatweresignicantly (p<0.001)fromtheunimpairedcohort'smeanCPS. 5.3.4.3ComparisonofTwoNewCoordinationIndices Theprocessesdiscussedinsection5.3.4.1werealsousedtoassesstheCDIthescaledcoordination performancescore(CPS).Figure5.3.12AdisplaysthemeanGDI,CDI,andCPSvaluesforthe di erentsubjectcohortcategories.Forallofthesubjectgroups,therewasasignicantdi erence (p 0.001)betweentheirGDIandtheTDgroup'sGDIsandasignicantdi erence(p 0.001) betweengroup'sCDIandtheTDgroup'sCDIs.ExceptfortheAKsubjectgroup,therewasa signicantdi erence(p 0.001)betweenagroup'sCDIsandGDIs.Notethepatternforareduced CDIandCPSinclinicalgroupsfollowsasimilardownwardtrendastheGDI.Figure5.3.12B presentsthemeanGDI,CDI,andCPSvaluesfortheunimpairedsubjectsandsubjectswithCP whenorganizedbyGMFCSlevel.Thereweresignicantdi erences(p 0.05)betweenthemean scaledCPSvaluesandeachGMFCSlevelandbetweenthemeanscaledCPSforGMFCSlevelsI andIII. 137

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Figure5.3.12:A)ComparisonofGDI(greysquare),CDI(bluesquare),andscaledCPS(yellow square)meanscoresforeachsubjectgroup:unimpaired(TD),lowerlimbamputation(LLA),below kneeamputation(BK),abovekneeamputation(AK),cerebralpalsy(CP),hemiplegia(H),diplegia (D),sti kneegaitpattern(SKG),andcrouchgaitpattern(C).B)MeanGDI(grey),CDI(blue), andCPS(yellow)valuesforTDandCPsubjectswithcondenceintervalswith95%condenceintervalsarepresentedbyGMFCSlevel.Signicantdi erencesbetweengroups(p 0.05)andbetween GMFCSlevelsIandIII. Figure5.3.13AshowstherelationshipbetweentheGDIandscaledCPSvaluesforallofthe study'ssubjects,withadashedlineindicatingtheidealunimpairedsubjectindexvalue.Figure 5.3.13BillustratestheempiricalnormaldistributionoftheGDI,CDI,andscaledCPSvaluesin relationtoatheoreticalcumulativedistributionfunction.TheKolmogorov-Smirnovtestconrmed theGDI,CDI,andscaledCPSvaluesforthisstudy'ssubjectswerenormallydistributed. 138

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Figure5.3.13:A)ScatterplotofallGDIscoresagainstallscaledCPSvalueswiththelineofbest t(red).B)Cumulativedistributionfunctions(CDF)fortheGDI(black),CDI(blue),andscaled CPS(green)incomparisontothetheoreticalnormalCDF(red). 5.3.4.4MissingCoordinationEventsbyGaitPattern Inane orttodetermineiftherewerecertaingaitpatterns,diagnoses,orgaitcategoriesassociatedwiththeinabilitytoachievespeciccoordinationevents,aninvestigationintomissing coordinationeventsforallsubjectswasperformed.Whilethisinvestigationdidnotdirectlyaddress Hypothesis4A,itdoescontributetotheutilityofthesecoordinationmeasures,theirinterpretation forvariousgaitpatterns,andabilitytoisolatespeciccoordinationdynamicscriticalforthecompletionofswinglimbadvancement.Thepercentageofsubjectsmissingoneormorecoordination eventsforeachgaitpatterncategory,includingtheunimpairedgroup,wascalculated. Forallunimpairedsubjects,threedi erentswingperiodcoordinationeventsdidnotexistfor 6.34%(or9subjects)ofthis140-subjectcohort.Thethreemissingcoordinationeventsforthis cohortwasthezero-crossingafterabsolutemaximuminlateswingonthepelvis-thighCRPD(e.g. PelvThi3),inectionpointbetweenoppositefootonandtheswingmaximumonthepelvis-thigh CRPD(e.g.PelvThi4),andzero-crossingaftertheswingmaximumonthethigh-shankCRPD (e.g.ThiSha4).Itisinterestingtonotethatthesethreecoordinationeventswerealsofound missinginseveralofthesubjectswithCPandsubjectswithaLLA.Foursubjectsweremissingthe PelvThi3coordinationevent,threesubjectsweremissingthePelvThi4coordinationevent,andtwo subjectsweremissingtheThiSha4coordinationevent.Thefollowinggureprovidesthepercentages unimpairedsubjectsthatdidnothavethesethreecoordinationevents.Theimpactofnothaving thesecurvefeaturesisdiscussedinthenextChapter.Itisworthnotingthatnoneofthemissing 139

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coordinationeventswereselectedbytheregressionmodelsforuseintheCPSindex. Figure5.3.14:Percentageofcoordinationevents(CE)missingfromallunimpaired(N)subjects. ForallsubjectswithCP,thesubjectswereorganizedbygaitpattern,topographically,andasa group.ThepercentageofsubjectswithCPthatweremissingatleastonecoordinationeventfor eachofthesecategorieswascalcula t edandpresentedinthenextgure. Figure5.3.15:ThepercentageofsubjectswithCPmissingatleastonecoordinationevent(CE)are displayedforeachgaitcategory:allsubjectswithCP,hemiplegic(hemi),diplegic(dipl),sti knee gaitpattern(SKG),andcrouchgaitpattern. 140

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Whilefurtherelaborationintothesignicanceofthesetrendsandmissingcoordinationevents forthiscohortwillbeprovidedinthenextchapter,itisinterestingtonotethatover70%ofsubjects ofwithCPweremissingaleastonecoordinationevent,regardlessofgaitcategory.Forthesubjects withCP,tencoordinationeventswerefoundtobemissingandarepresentedinthetablebelow. Table5.3.8:DescriptionofthetenswingperiodcoordinationeventsmissinginsubjectswithCP, whereasuperscriptLandNindicatethiscoordinationeventisalsomissinginsubjectswithaLLA andunimpairedsubjects,respectively. CoordinationEventAbbreviationDescription 1)Pelvis-ThighCPRDPelvThi21st0xinSwing 2)Pelvis-ThighCPRD N,L PelvThi31st0xafterabs.maxinSwing 3)Pelvis-ThighCRPD N PelvThi4Inectionpointbtwnoppositefootonandmax 4)Thigh-ShankCRPDThiSha31st0xafterfooto 5)Thigh-ShankCRPD N,L ThiSha41stoxafterswingmax 6)Shank-FootCRPDShaFoot3Inectionpointafterswingabs.min 7)Shank-FootCRPD L ShaFoot4Lastzero-crossinginswing 8)Thigh-FootCRPDThiFoot32ndzero-crossingafterfooto 9)Thigh-FootCRPDThiFoot4Abs.maxbetween1st&2nd0xpostFO 10)Thigh-FootCRPDThiFoot6Lastzero-crossinginswing Thenextgurepresentsthedistributionofmissingcoordinationeventsforthevariousgait categoriesofsubjectswithcerebralpalsy. Figure5.3.16:PercentagesofcoordinationeventsmissingfromsubjectswithCPwhoareorganized byvegaitcategories:allsubjectswithCP,hemiplegic(hemi),diplegic(dipl),sti kneegaitpattern (SKG),andcrouchgaitpattern. 141

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SubjectswithaLLAwereorganizedintothefollowingvecategories:allsubjectswithaLLA, unilateralamputation,bilateralamputation,belowkneeamputation,andabovekneeamputation. ThepercentageofsubjectswithaLLAthatweremissingatleastonecoordinationeventforeach ofthesecategorieswascalculatedandprovidedinthenextgure. Figure5.3.17:ThepercentageofsubjectswithaLLAmissingatleastonecoordinationevent(CE) aredisplayedforeachgaitcategory:allsubjectswithaLLA,belowkneeamputation(BK),above kneeamputation(AK),bilateralamputation(Bilat),andunilateralamputation(Unilat). Furtherelaborationintothesignicanceofthesetrendsandmissingcoordinationeventsforthis cohortwillbeprovidedinthefollowingchapter.Asdepictedinthefollowinggure,forthesubjects withaLLA,threecoordinationeventswerefoundtobemissing:PelvThi3,ThiSha4,andShaFoot4. Thegurebelowpresentsthedistributionofthesethreemissingcoordinationeventsforthevarious gaitcategoriesofsubjectswithalowerlimbamputation. 142

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Figure5.3.18:PercentagesofcoordinationeventsmissingfromsubjectswithaLLAwhoareorganizedbyvegaitcategories:allsubjectswithaLLA,belowkneeamputation(BK),aboveknee amputation(AK),bilateralamputation(Bilat),andunilateralamputation(Unilat). 5.3.4.5ExploratoryInvestigationtoIdentifyCriticalCoordinationEvents Asdiscussedinsection4.5.4.2.1ofChapter4,threeadditionalanalyseswereconductedtodetermineifthereweresalientcoordinationeventsintheswingperiodofgait.Resultsfortheseanalyses areprovidedinAppendixG.Therstoftheseanalysesdividedtheunimpairedprospectivesubjects (n=20),whowalkedover-groundwithshoes,andtheunimpairedretrospectivesubjects(n=120), whowalkedbarefootover-ground.Outofthirty-sevenpossiblecoordinationevents,fourcritical coordinationevents(Table5.17)metthecriteriaforbeingbothindependent(P 0.2)andinvariant(r 2 2.5%).Themeantiming,withstandarddeviation,andvarianceforeachofthesecritical coordinationeventsisprovidedinthetablebelowandwascalculatedfromthe120unimpaired retrospectivesubjects. Table5.3.9:Themeantiming(standarddeviation)andvarianceforthe120unimpairedretrospective subjects'fourcriticalcoordinationeventsareprovidedalongwithadescriptionofeachevent. CoordinationMeasureCoordinationEventMean(SD)Variance 1)FootPPTimingofmaximumangularvelocity83%( 3%)13.12% 2)Thigh-FootCPRDLastlocalminimum89%( 2%)4.60% 3)Thigh-FootCRPDLastzero-crossing98%( 1%)1.38% 4)ShankPP1stzerocrossingafterfooto 98%( 1%)1.34% Itisworthnotingthatthelastinectionpointofthethigh-footCRPDwasidentiedasacritical 143

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coordinationeventbythismethodologyandthestepwiseregressionmodelusedinthecoordination performancescoremethods.TheresultssupportingthefollowingndingsfromtheadditionalanalysesofthecriticalCEsareprovidedinAppendixG.ThetimingofthesefourcriticalCEswasnot foundtobeclinicallydi erentbetweenthesetwounimpairedgroupsamples.Secondly,itwasfound thatagedoesnota ectthetimingofthesefourcriticalCEs.Thirdly,thefourcriticalCEswere foundtobeuniqueanddidnotcoincidewithothergaitevents(e.g.temporal,critical). 5.3.5Hypothesis4AResults ReferringtoFigure5.3.8A,whenorganizedbygaitpattern,levelofamputation,andtopographicallytherewasasignicantdi erence(p 0.001)betweenacohort'smeanCDIandGDI,exceptfor thesubjectswithatransfemoralamputation.Additionally,whenorganizedbygaitpattern,level ofamputation,andtopographicallytherewasasignicantdi erence(p 0.001)betweenacohort's meanscaledCPSvalueandtheunimpairedcohort'smeanscaledCPSvalue.Therefore,asaconsolidatedindexoftheproposedmeasuresofcoordinationdynamics,theCDIandscaledCPSdetect statisticallysignicantdi erences(p 0.05)betweenthecoordinationdynamicsofindividualswith unimpaired,sti knee,crouch,andmechanicallyalteredgaitpatterns(Hypothesis4A).Thephase portraitsandcontinuousrelativephasediagramsforthethreegeneralsubjectgroups(unimpaired, CP,LLA)areprovidedbelowingurebelow.Thephaseportraitsandcontinuousrelativephase diagramsforadditionalsubjectcomparisonsandorganizations(e.g.a ectedside,amputationlevel, topographical)areprovidedinAppendixG. 144

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Figure5.3.19:Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingforall subjectswithCP(red),allsubjectswithaLLA(green),andallretrospectiveunimpairedsubjects (grey). 5.4TranstibialAmputationCaseStudyResults ResultsforthiscasestudyarelocatedinAppendixG. 145

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6Discussion Themaingoalsofthisbodyofworkwereto1)createanormativedatasetfortheproposed measuresofcoordinationfromanunimpairedcohort,2)comparetheproposedmodelofcoordination tothreeclinicalperformancesmeasuresthatdescribeaspectsofmotorcontrol,3)comparethe motionofatheoreticalcompoundpendulumtoactualhumangaitdata,and4)usetheproposed measurestostudyandcomparethecoordinationdynamicsofdi erentclinicalpopulationswhohave varyingabilitiestosuccessfullyande cientlyperformswinglimbadvancement.Inadditiontothe retrospectivesubjectmotioncapturedata,prospectivemotioncapturedatawascollectedforthe di erentexperimentsdiscussedinChapter4.Theprospectiveexperimentsweredesignedtostudy thepotentiale ectsonthecoordinationstrategiesoftheunimpairedsubjectsbyvaryingtemporal andspatialconstraintsduringwalkingtasks.Additionally,potentialdi erencesincoordination strategieswerestudiedforbothover-groundandtreadmillwalkingconditionsintheprospective subjectswithanatypicalgaitpattern.InreferencetotheresultspresentedinChapter5and AppendixG,thefollowingsectionsdiscusstheresultsforthesefourdi erentaimsandtheadditional prospectiveexperiments. 6.1DiscussionofProspectiveExperiments 6.1.1Over-GroundWalkingTask Theunimpairedsubjectcohortconsistedofover-groundwalkingdataforbothretrospective andprospectivesubjects.Themeasuresofcoordinationdynamicsweregeneratedfortheentire unimpairedcohort,theretrospectivesubjectswhowerebarefootfortheirover-groundwalking,and theprospectivesubjectswhoworeshoesfortheirover-groundwalking.Thecontinuousrelativephase diagrams(CRPD)fortheprospectivesubjectswerewithinonestandarddeviationbandofthelarger retrospectiveunimpairedcohort,indicatingthattherewerelittletonodi erencesinthecoordination strategiesforbarefootandshodwalkingemployedbythesetwogroups.Whiletherearesomesubtle di erencesthebetweenprospectiveandretrospectivesubjectsPPsandCRPDs,perhapsthemost strikingdi erenceisinthepelvisphaseportraitcenterlocation.Thisdi erenceincenterlocationof thepelvisphaseportraitismostlikelyduetodi erencesinplacementofthesacralmarker.While themarkerplacementofseveralrandomsubjectswasconrmedbycliniciansexperiencedinmotion capture,thesacrummarkercouldhaveeasilybeenplacedafewmillimetersbelowthesacrum, thusresultinginanincreaseinafewdegreesofposteriorpelvictilt.Itwasoriginallyspeculated 146

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thatsomeoftheothermoresubtledi erencesintheprospectiveandretrospectivesubjectsPPs andCRPDsmaybeduetothefactthattheprospectivesubjectsworeshoesandtheretrospective subjectswerebarefoot.Theresultsfromsubsequentinvestigationsintopotentialdi erencesinthese twounimpairedsubjectgroupsisaddressedlaterinthisChapterinsection6.3.1. TableG.1.3inAppendixGprovidethemean,standarddeviation,and95%condenceintervals fortherelativephaseanglesatcommonfootoorcontacteventsfortheunimpairedprospective subjects.Notalloftheunimpairedprospectivecohort'smeanCRPDvaluesatessentialfootcontact conditionsfellwithinthe95%condenceintervalsoftheunimpairedretrospectivesubjects'CRPD footcontactevents.WhenexaminingtheCRPDplots,itseemslesslikelythattheCRPDvaluesfrom theprospectivesubjectsthatwereoutsideoftheselimitswerebecauseofadi erentcoordination strategyemployedwhilewalkingbarefootverseswithshoes.Thedi erenceinsubjectsamplesize mayskewthesevaluesanditwouldbeinterestingtoseeiffuturecollectionofmoreprospective subjectsmightbringthesevalueswithintheretrospectivesubject'scondenceintervals. TheCDIandscaledCPSvalueswerecalculatedfortheunimpairedprospectiveandretrospective subjectsasanothermeansforcomparingtheircoordinationcurves.TheGDIandCDIvaluesfor theunimpairedprospectiveandretrospectivesubjectswerewithinonestandarddeviationaway fromthenormativereference,indicatingthatanydeviationsfromthereferencearestillwithinthe "unimpaired"range.Similarly,thescaledCPSvaluesforthesetwounimpairedsubjectsubgroups variedonlyasmallamountfromeachotherandwereclosetothenormativereference.When consideringthecoordinationandgaitindices,coordinationcurves,andadditionalanalysesbelow comparingcoordinationeventsbetweenthesetwounimpairedsubjectgroups,theredoesnotappear tobeanyclinicallysignicantdi erencesinthecoordinationdynamics.AsmentionedinChapter 4,theprospectivesubjectsneededtowearshoesbecauseofthetreadmillwalkingtasks.Therefore, havingdi erentunimpairedsubjectsgroupsallowsformoreconsistentcomparisonsandreferences fortheprospectiveexperimentsandotheranalysesconductedtoaddressAims2,3,and4. 6.1.2TreadmillWalkingTasks Ingeneral,thedi erenceintheprospectivesubjects'pelvisphaseportraitrangeofmotion andangularvelocitymayinpartbeduetothefacttheywerewearingaharnessandattachedto thebodyweightsupportsystem.Thedi erencesintheCPRDsforthesetwowalkingconditionsis indistinguishableintheunimpairedsubjects,indicatingthatthesesubjectswereabletoadapttothe changingtaskconstraintsofwalkingonatreadmillversesover-groundandmaintainthesameintersegmentalcoordinationdynamics(e.g.spatio-temporalorganization).Fortheunimpairedsubjects, 147

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thesubtledi erences(e.g.reducedswingperiodlimitcycleradius,divergetoasmallerphase portraitorbitinswing)inthethigh,shank,andfootPPsappeartobethecompensatorychanges atthesegmentlevelthatallowedthesubjectstomaintainasimilarinter-segmentalcoordination dynamicsbetweenthesetwowalkingconditions.Thefollowingsectionsdelveintomorespecic di erencesforthevariousprospectivesubjectcohortsandwalkingtasks. 6.1.3ProspectiveUnimpairedSubjects:Over-groundandTreadmillWalking Oneoftheexperimentsforthe20unimpairedprospectivesubjectswastowalkover-groundwith shoesataself-selectedspeedandthenwalkonasplitbeltinstrumentedtreadmillatabeltspeed equivalenttoeachsubject'sover-groundwalkingspeed.Oneofthemotivationsforthisexperiment wastousePPsandCRPDs,whicho eranalternativelevelofanalysisandperspectiveofmarker basedmotioncapturedata,tocharacterizetheunderlyingcoordinationstrategiesemployedby healthyindividualsastheymaintainanormativegaitpatternforthesetwosimilar,yetdi erent walkingconditions.Treadmillgaittrainingisanappealingmodalityforrehabilitationofpatients withaneuromuscularimpairmentbecauseito ersameansfortask-specicgaittraining,repetition, manuallyandroboticallyguidedassistance,systematicallycontrolledprogressionofwalkingspeed, andtheoptionforpartialbodyweightsupport.Althoughnumerousstudieshaveexaminedpotential di erencesbetweenover-ground(OG)andtreadmill(TM)walkinginordertoassessthevalidityof thisOGwalkinganalogue,thendingsfromthesestudiesareofteninconclusiveandconicting[145150].Therefore,themotivationforthisexploratorycomparisonwastousetheproposedmeasures ofcoordination,whicho eranalternativelevelofanalysisandperspectiveofmarkerbasedmotion capturedata,tocharacterizetheunderlyingcoordinationstrategiesemployedbyhealthyindividuals astheymaintainanormativegaitpatternforthesetwosimilar,yetdi erentwalkingconditions. FromtheBernsteinperspective,thecentralnervoussystem'sorganizationofindividualvariables intoalargergroup(e.g.synergy)duringamovementdecreasesthedegreesoffreedominthe systemandallowsforsimplercontrolstrategies,whichinthecaseofbipedalgaitresultincomplex oscillatorypatterns[7-10].Afundamentalprinciplefromthedynamicsystemstheoryperspective ofmotorcontrolisthatthetask,environment,andindividualallinuencetheresultantmotor behavior[109].Smallchangesinanyoftheseelementscanresultinanalteredmovementpattern. Forexample,duringtreadmillwalkingthemovingbeltdrivesthesupportlimbbackwardsunderthe relativelystationarycenterofmassasopposedtoover-groundwalkingwherethecenterofmassis rotatedoverthestancelimb,muchlikeaninvertedpendulum[56].Inadditiontodi erencesintask constraints,environmentalchangescontributetodi erencesinsensoryinformation(e.g.opticow 148

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information)andhavebeenshowntoalteranindividual'sgaitpattern[151,152].FindingsfromLee etalproposedthechangesinmuscleactivationsandkineticscouldbeattributedtohowsubjectsare abletoachieveawalkingpattern,characterizedbytemporalgaitparametersandkinematics(i.e. jointangles),thatissimilarbetweenover-groundandtreadmillwalking.Whilewalking,individuals withanintactnervoussystemareabletointegratethislargeamountofinformationaboutthe orientationoflimbsegments,task,andenvironmentanddevelopamotorplanthatconsolidates theseelementsandorganizesthepositionandtimingofthelegintoacoordinatedgaitpattern. Carollo,etal(2002)proposedthehypothesisthatonebehavioralgoalofambulationistomaintainkinematicpatterns.WhenconsideringthishypothesisandtheBernsteinperspectiveofmotor control,itisthenperhapsofnogreatsurprisethatoftenlittletonostatisticallysignicantdifferencesinkinematiccurvesbetweenover-groundandtreadmillwalkingforhealthyindividualsare reported.Incorporationofdynamicsystemstheorymeasuresasacomplementtotraditionalinstrumentedgaitanalysismeasuresprovidesvaluableinsightsinintotheunderlyingcoordination strategiesthatcontributetoanasymmetricaloratypicalagaitpattern.Aspreviouslydiscussed inChapter3,phaseportraitsandcontinuousrelativephasediagramsfromdynamicsystemstheory provideadi erentperspectiveforstudyingagaitpatternbydescribingindividualsegmentsinphase spaceandcoordinationdynamics(e.g.positionandtiming)betweenanytwosegments;adjacentor non-adjacent[137].Toquantifythecomplexcoordinationdynamicsusedtomaintainanormative gaitpatternduringthesetwodi erentwalkingconditions,lowdimensionalmeasuresencapsulating thepositionandtimingofbothindividualandmultiplesegmentsarerequired.Measuresthatquantifytheunderlyingcoordinationdynamicscontributingtoanaberrantgaitpatternareessentialto capitalizeupontherehabilitativebenetsoftreadmillgaittraining. Thekinematiccurvesfortheseprospectivesubjectsarewithintheexpectrangesforanormalgait pattern.Thecoe cientofvariationvaluesforthisgroup'skinematiccurvessimilartothosereported byWinter(1983),supportingthehypothesisthatsubjectstrytomaintainanormativekinematic patternduringthesetwowalkingconditions.Ingeneral,themagnitudeofkinematicvariablesduring treadmillwalkingwerereduced,whichsupportsthepositionthatchangesinamplitudeofspatial variablesweremadebythesubjectsinordertocomplywiththereducedswingtime.Whilethere arestatisticallysignicantdi erencesbetweensomeoftheseconventionalmeasures,itisdi cultto determineifdi erencesarealsoclinicallysignicant.Consistentwithpreviouslyreportedstudies, thesubjectshadshortersteplengths,shorterstridelengths,reducedswingtimeduration,andslower walkingspeedsduringTMwalking[146,153].Changesinthesubjects'gaitpatternsdescribedby conventionalinstrumentedgaitanalysismeasuresareproposedtobeaccomplishedbyalteringthe 149

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timingandorganizationofthefollowingfourmechanisms,elucidatedbycoordinationdynamics, thatareessentialforsuccessfulcompletionofswinglimbadvancement. TheremainingparagraphsofthissectiondiscusshowtheinclusionofPPsandCRPDstoexamine thegaitoftheseindividualsforthesetwodi erentwalkingtasksprovidesanalternativelevelof analysisandperspectiveintotheunderlyingcoordinationdynamicsofagaitpattern.Asthethigh PPtrajectoryrateofchangedecreasesandapproachesanabscissazero-crossing(e.g.maximum angulardisplacement),thefootPPtrajectoryisacceleratingasthefootapproachesahorizontal orientationwithrespecttotheoorandtransitionsfromplantarexiontodorsiexion(e.g.near anklekinematiczero-crossing).Thischangeinrelationshipbetweenthesetwosegmentsmanifestsas alocalmaximumonthethigh-footCRPD,whichispredominantlyinuencedbythefootPPphase anglebecausethethighPPphaseangleisapproximatelyzero.Theattenuationofthisextremum duringtreadmillwalkingmeansthesubjectsincreasedtherateofchangeinthefootPPtrajectory (e.g.positionandvelocity)inordertosu cientlyadvancethefootintimefortheup-comingfoot strikeandcompensateforanoverallreducedswingperiodduration. Oncethefootislocatedaheadofthehipjointcenter,thependularmotionofthelegsegments andmomentumfromhipexioncontributestocompletionofswinglimbadvancement(e.g.passive kneeextension)[26].Asignicantreductioninthemagnitudeoftheshank'smaximumangular velocityduringtreadmillwalkingcoincideswiththePPtrajectorybeginningtonoticeablydiverge toasmallerorbitfromtheover-groundtrajectorycausingareducedpendularvelocityanddisplacementoftheshankfortheremainderofswingperiod.Otherstudiesreportingshorterswing perioddurationhavealsoobservedincreasedcadenceandshortersteplength,allofwhichcanbe attributedtodecreasedhipandkneeextension,inpartasaresultofthealteredpendularmotion ofthecontralateralsupportlimbasmovesbackwardbythetreadandrotatesaboutthehipinstead oftheinvertedpendularmotionabouttheankleduringOGwalking[143,145,153].Considering thesealteredpendularmechanicsofthelegs,thetemporal-spatialandkinematicsofthelegsegmentsduringterminalswingcanbefurtherexpoundeduponbytheabatedshankPPtrajectory duringtreadmillwalking.ThediminishedPPtrajectoryrevealedtheshankphaseanglecausedan attenuationoftheshank-footCRPDabsolutemaximum,thigh-footCRPDlocalminimum,andfoot PPmaximumangulardisplacementandminimumangularvelocity.Thesignicantlydelayedand reducedfootminimumangularvelocityandmaximumangulardisplacement,occurringjustafter thefootisorientedhorizontally,ispredominantlyduetotheshank'spendularmotionbecausethere isasmallamountofchangeintheanklejointangleduringterminalswing.Sincetherewasageneral trendofdelayedandattenuatedswingeventsduringtreadmillwalking,therewaslesstimetoswing 150

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thetibiaforwardfromverticalandthesubjectscompensatedbyincreasingthephaseanglerateof change(e.g.spatialadjustmentoftheshanktomeettemporalconstraintofimpendingfootstrike). FindingsfromthisprospectiveexperimentdemonstratehowsagittalplanePPsandCRPDs quantifycoordinationdynamicsandrevealtheinherentmechanismsunderlyingtheswingperiod gaitpatternsof20unimpairedsubjectsduringover-groundandtreadmillwalking.Itwasproposed thatiftheunderlyingcoordinationdynamicsofhealthysubjectscouldbeusedtoexplainhowthese individualsmaintainedanormalgaitpatternforthesetwodi erentwalkingconditions,thenPPs andCRPDsmayalsoprovideclinicallymeaningfulinsightsandvaluableinformationfortherapeutic modalitiesthatstrivetouseatreadmillfortherehabilitationofindividualswithneurologicallybased gaitimpairments. ThisprospectiveexperimentdemonstratedhowPPsandCRPDscomplementconventionalIGA measuresandbydescribingmovementatthelevelofcoordination,thesedynamicsystemstheory (DST)basedmeasuresexplainthemechanismsunderlyingtemporal-spatialandkinematicdi erences observedbetweenOGandTMwalking.Whilendingsfromthisstudyindicatetherearedi erent coordinationdynamicsemployedduringthesetwowalkingtasks,ageneraldecisionastowhetheror notTMwalkingisasuitableanaloguetoOGwalkingisintentionallyleftunansweredbecausethe investigatorfeelssuchadecisionshouldconsidereachpatientandroleofTMusageinrehabilitation beforeselectingthecorrespondinglevelofmotioncapturedataanalysisthatbestcharacterizes thesefactorsandgoals.Forexample,ifTMwalkingisutilizedtoaddressasymmetriesandoverall gaitperformanceorimprovetherangeofjointanglesduringthetaskofgaitthentemporal-spatial measuresorjointanglesareappropriatedescriptorsfortheseaspectsofgait.Ifinter-segmental coordination,changesinmotorcontrolstrategies,ormotorlearningarethegoalsofTMwalking thenusingPPsandCPRDstoquantifytheorganizationofsegmentsatthelevelofcoordination satisesthisperspectiveofgait.Thealternativeperspectiveofmotioncapturedatao eredbythese nonlineartools,providesameanstounderstandtheunderlyingmechanismsadoptedbyhealthy subjectstomaintainanormalgaitpatternwhenpresentedwiththealteredtemporalandspatial constraintsofTMwalking.Theenhancedperspectiveofgaito eredbyPPsandCRPDsmay providevaluableclinicalinsightsforpatientswhostrugglewithachievingthecriticalmechanisms ofswinglimbadvancement,contributingtoanatypicalgaitpattern,andhelpdeterminehowTM walkingmightbeusedtoaddresssuchaberrantcoordinationdynamics. 151

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6.1.4ProspectiveSubjectswithCerebralPalsy:Over-groundvs.TreadmillWalking Guidedtreadmilltrainingforindividualswithcerebralpalsyhasbeenadoptedinane ortto improveatypicalmotorpatternsusingpracticeandexperiencebyexpandingtherangeofmovementoptionsfortheindividuals[16,154].Severalresearchershaveproposedthemotorbehaviorof individualswithCPduringtreadmilltrainingemergefromthedynamicalinteractionofthecentralnervoussystem,biomechanicalelements,psychologicalfactors,andtheenvironment[155-158]. Therefore,thedevelopmentofmeasuresthatcapturethemotorbehaviorofthisdynamicalsystemis importanttoimproveandoptimizetheconnectionbetweenclinicalresearchandclinicaltreatment. Asithaspreviouslybeenproposedthroughoutthisbodyofworkandbyothers,theapplicationof dynamicsystemstheorymeasures(e.g.PP,CRPD)o eraframeworkforcharacterizingsegmentalinteractionsandinter-segmentalcoordination[155-158].Thisprospectiveexperimentcomparing theover-groundandtreadmillwalkingcoordinationofindividualswithcerebralpalsyprovidesone exampleapplicationofhowscienticallyvalidatedndingsfromthesemeasuresmayprovidesuch aconnectionandlltheneedformeasuresofcoordinationdynamicstohelpstudyatypicalmotor patterns. Individualswithcerebralpalsy(CP)oftenhavedi cultywalkingonatreadmillwhenthebelt speedissettotheindividual'spreferredover-groundwalkingspeed.Therefore,manytherapeutic interventionsonthetreadmilltrytoincrementallyincreasingthetreadmillspeedtochallengethe individual'smotorlearningsystemwiththegoalofobtainingimprovedcoordinationatawalking speedcomparabletotheindividual'sover-groundwalkingspeed.Thistrendwasconsistentforthe treadmillbeltspeedusedforthreeprospectivesubjects. Ingeneral,allofthephaseportraitorbitsweresignicantlyreducedwhentheprospectivesubjects withCPwalkedonthetreadmill.Mostnotableweretheshiftinposteriorpelvictilt,reducedthigh speed,reducedthighextension,diminishedfootspeed,andmorecircularandreducedfoottrajectory.Therewasnotadetectibledi erenceinthepelvis-thighCRPDduringswingandtheremaining CRPDcurvesareattenuatedfromthesubjects'over-groundwalking.Conventionalgaitmeasures showthesubjectshaddecreasedwalkingspeed,shortenedsteplength,reducedsteptime,ItisproposedthatthePPsandCRPDsforthesetwowalkingconditionsrevealtheunderlyingmotorcontrol strategiesthatresultedinthesealteredkinematicsandtemporal-spatialmeasures.Specically,the subjectsincreasedpelvictilttocompensateforreducingtheamountofthighextensionandinstead ofmodulatingthethighspeedthroughoutswinglimbadvancementthesubjectsextendedthethigh atamoreconstantrate.AsdiscussedinChapter2,hiphikingandcircumductionaretwocommon 152

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compensatorygaitadaptationsemployedbyindividualswithSKGandCgaitpatternstoadvance andcleartheswinginglimb.TheprospectivesubjectswithCPinthisexperimentalsoadopted thesecompensatorystrategies.Specically,theinter-segmentalcoordinationbetweenthethigh-foot andshank-footcapturethesemechanismsinthenoticeableattenuationoftheseCRPDs.Recalling theequationforcalculatingtherelativephaseangleandpreviouslydiscussedcurvefeatures,itis proposedthatthereducedtheinvolvementofthefootforthesecompensationsmanifestsinthese CRPDs'as1)attenuatedcurveindicatinglessinteractionbetweenthesegments,and2)shifttoward zeroindicatingthesegmentsaremovingmorein-phasewitheachother.Whileonlythreeofthefour prospectivesubjectswithCPwereabletowalkonthetreadmill,therewasaconsiderablerangein theiroverallfunctionalabilities.Futureinvestigationsthatexaminethetreadmillandover-ground gaitandcoordinationstrategiesforalargersubjectsize,perhapsorganizedbyfunctionalability,is warranted.Whilethisexperimentisnotdirectlyconnectedtoahypothesis,thesendingssupport theoverallproposalthatthesemeasuresdetectchangesinsegmentalspatio-temporalorganization andinter-segmentalcoordination. 6.1.5ProspectiveUnimpairedSubjects:TreadmillWalkingatVariousSpeeds Similartotheotherprospectiveexperiments,themaingoalsofthisexploratoryprospective experimentwasto1)determineiftheunimpairedsubjectsalteredtheirgaitpatterntocompensate forthetemporalchangesofthewalkingtaskimposedbyincreasingtheTMbeltspeedand2)use theproposedmeasuresofcoordinationtoidentifychangesinthesegmentalorganizationandintersegmentalcoordinationstrategiesadoptedbythisunimpairedcohort.AspresentedinChapter3, coordinationinthecyclicaltaskofgaitrequirestheelegantbalancebetweenboththespatialand temporalorganizationofthesegments.Therefore,itwasproposedthattheunimpairedsubjects wouldbeabletoaccountforchangesinspatialdemandsofwalkingonatreadmillatvariousspeeds andadoptanormativegaitpatternsimilartotheirtreadmillgaitpattern. Theunimpairedsubjectswereabletoadapttothechangesintemporalconstraintsofwalking onthetreadmillatvariousspeedsbyadjustingthespatialandtemporalrelationshipofsegments. Asthetreadmillbeltspeedincreased,thesubjectsincreasedtheswingperiodvelocityofthethigh, shank,andfoot,whilemaintainingclosetothesamesegmentangulardisplacementsatfooto andfootstrike.Bychangingthetemporalconstraintsofthewalkingtask,thesubjectsresponded bychangingthetimingofthesegments'positionsbyalteringthetemporalorganization(velocity). Interestingly,theCRPDdiagramsforthesevarioustreadmillwalkingspeedsshowedlittledi erences inshapeorcurvefeatures.Asthetreadmillbeltspeedincreased,therateofdissociatingthe 153

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thigh-footextensionsynergynearfooto (thigh-shank,thigh-footCRPDs)increasedreectingthe reducedtimethesubjectshadduringswingtoinitiateswinglimbadvancementandplacethe segmentsinanorientationthatresembledthegaitpatternduringaself-selectedwalkingspeed. Additionally,thetimingofthelocalmaximumontheshank-footCRPDshiftedsoonertowardfoot o andalsocapturesthisreducedtimetoclearthefootduringswinglimbadvancementasaresult ofthedecreasedswingperiodtimewhenthetreadmillbeltspeedincreased.Theresultsfromthis experimentnotonlysupporttheoverallproposalthatthesemeasuresdetectchangesinsegmental spatio-temporalorganizationandinter-segmentalcoordination,buttheyalsodemonstratethese measuresareabletodetectchangesinonlythetemporalelementsofcoordinationwhensubjects areimposedwithtemporaltaskconstraints. 6.1.6ChangesinAssistive/ResistiveForcesTask Themaingoalsofthisexploratoryprospectiveexperimentwasto1)determineiftheunimpaired subjectsalteredtheirgaitpatterntocompensateforthee ectsofanassistiveforceandaresistive forceontheadvancinglimband2)usetheproposedmeasuresofcoordinationtoidentifythesegmentalorganizationandinter-segmentalcoordinationstrategiesadoptedtoachievethesechangesin theirgaitpatterns.Ingeneral,itwasobservedduringdatacapturethatinapproximatelylessthan 30secondsthesubjectswereabletondamotorprogramthatresultedinthe(subjectperceived) themoste cient(leastperceivedexertede ort)gaitpatternthatmostcloselyresembledtheir preferredtreadmillwalkingpattern.Allofthesubjectschosetoreducethemotionofthethigh, shank,andfootwhilealsoincreasingtrunkinvolvement(exionforresistiveforces,extensionfor assistiveforces).Additionally,theratethesegmentsadvancedandmoved(PPtrajectory)became moreconstantandexhibitedlessofthenelymodulatedratesintheirregulartreadmillandovergroundwalkingtrials.Asreportedbythegaitandcoordinationindicesinthecorrespondingresults sectionforthisexperiment,thesubjectswereabletomaintainarelativelynormalgaitpatternby modulatingthespatio-temporalinteractionoftheirlegsegmentsanddrawuponanintactnervous systemtondanalternativegaitstrategy.Perhapsthemostimportantandexcitingndingfrom thisparticularexperiment,inregardstotheaimsandoverallgoalsofthisbodyofwork,isthat thesesubjectsadoptedadi erentwalkingstrategywhenpresentedwithspatialconstraintsandthese measuresofcoordinationdynamicswereabletodetectthosechanges. 154

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6.1.7ChangesinJointRangeofMotionTasks Itwasproposedthatthesedynamicsystemstheorybasedmeasuresaremoresuitableforcharacterizingmotorcontrolstrategiescontributingtoagaitpattern,quantifyorganizationofindividual segments,identifymechanismsofchange,andlociofimpairment.Sincethefundamentalorganizationofthelegsegmentsduringgaitislinkedtogaitpathologyandguidestherationalefor interventions,itwashypothesizedthatincorporatingPPsandCRPDsintoinstrumentedgaitanalysiswillopennewavenuesforunderstandingthecomplexityofcoordinationandallowclinicians themeanstomoree ectivelyande cientlytreatpatientswithneuromusculargaitimpairments. Thepurposeofthissetofprospectiveexperimentswastorestricttherangeofmotionfortheknee andankleinsubjectsfreeofgaitpathologyandexploredcoordinationstrategiesadoptedbythe unimpairedcohortinrelationtothecoordinationdynamicsofindividualswithpathologicalgait patterns.Theresultsfromthissetofexperimentsprovideacontextfortheutilityofthesemeasures asacomplementtoconventionalIGAmeasures.Theresultsfromthesethreeexperimentsnotonly supporttheoverallproposalthatthesemeasuresdetectchangesinsegmentalspatio-temporalorganizationandinter-segmentalcoordination,buttheyalsodemonstratethesemeasuresareableto detectchangesinboththetemporalandspatialelementsofcoordinationwhensubjectsareimposed withonlyspatialtaskconstraints(e.g.restrictedjointrangeofmotion). 6.1.7.1FixedKneeExtension Theunimpairedsubjectsmadeseveralgaitpatterncompensationstoadapttotheunilateral restrictedrangeofmotionaboutthekneejointimposedbyakneebrace.Whenthekneebracewas xedinfullextension,theshapeofthepelvis-thighandthigh-shankCRPDsfortheunimpaired subjectsisdelayedduringswing,muchlikeindividualswithasti kneegaitpattern(SKG).Similar tosubjectswithSKG,theCRPDsfortheunimpairedsubjectsareconsiderablyattenuated.These spatio-temporalchangesdepictedintheCRPDscapturethecohort'schangesinmotorcontrol strategiesduringgait.Theunimpairedsubjectschosetorestrictthedynamicrangeofmotionof thefootandthighwhilewalkingandinsteaduseacombinationofhipcircumductionandhiphike tocleartheadvancingswinglimb.IndividualswithaSKGpatterncommonlyemploythesesame compensatorystrategiesforswinglimbadvancement.Alsothechangeinhip(e.g.thigh)motionis capturedbythethighphaseportrait'sshifttowardincreasedextension(thighangulardisplacement closerto90 ¡ withrespecttoglobalhorizontal).Itisproposedtheselimbadvancementstrategiesare partiallycapturedinthesagittalplanecurvesbytheleftwardshiftofthethighphaseportrait.This 155

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shiftindicatesthethighremainedslightlymoreinexionthanwhenthesubjectswalkingwithout xedkneeextension.Thislateralshiftmayalsoreectthecompensatorymotionsinthecoronal plane,butsincethefocusofthisinvestigationissagittalplanecoordinationdynamicsitisdi cult todistinguishtri-planarcompensatorymotionsandanye ectonsagittalplanemotion. Althoughtheanklewasnotdirectlya ectedbythekneebrace,theunimpairedsubjectsalso restrictedrangeofmotionattheankle.Thisfootcompensatorystrategyiseasilydetectedonthe foot'sphaseportrait,whichhasareducedlimitcycleradiusandmissinglocalminimumjustafter footo ontheshank-footCRPD.Therestrictedrangeofmotionforthethigh,shank,andfoot adoptedbytheunimpairedcohortisreectedinthereducedcircumferenceofeachsegment'sphase portrait. Sincethephaseportraitsarenormalizedtothegaitcycleandplottedtoshoweachpercentage ofswingwithacircle,itisalsointerestingtonotetherateofchangeforthethighandshank phaseanglesisfairlyconstantthroughoutswingasopposedtovaryingtheratethesetwosegments advancedinpreparationforfootcontact.Duetothenatureoftheexperiment,itisdi cultto determineifanydi erencesinspatio-temporalcurvefeaturesareduetowalkingonatreadmill (unimpairedcohort)versesover-groundwalking(subjectswithSKG).Thedi erencesinpelvisPP magnitudesandcenterlocationbetweenthesubjectswithaSKGandtheunimpairedsubjectswith xedkneeextensionmaybebecausetheunimpairedsubjectsdidnothaveanyrestrictionsatthe hipjointthatoftenoccursinindividualswithcerebralpalsy.Overall,itisexcitingtonotethat theseproposedmeasuresofcoordinationdynamicscapturedchangesinmotorcontrolstrategies, quantiedthereorganizationofindividualsegments,andcanbeusedtoidentifymechanismsof change. 6.1.7.2FixedKneeFlexion Theunimpairedsubjectsmadeseveralcompensationstotheirgaitpatterntoadapttothe restrictedrangeofmotionaboutthekneejointwhenthekneebracewasxedat60 ¡ ofexion. Whenthekneebracewasxedinexion,theshapeofthepelvis-thighCRPDfortheunimpaired subjectsisalmostidenticaltothesubjectswithacrouchgaitpattern.Aswiththecondition withxedkneeextension,thethigh-shankandshank-footCRPDswereconsiderablyattenuated andlocalcurvefeatureswereattenuated.ThesechangesdemonstratetheabilityoftheCRPDto captureorganizationalchangesofsegments(e.g.inter-segmentalcoordination). Eventhoughtheanklewasnotdirectlya ectedbythekneebrace,theunimpairedsubjectschose torestrictthedynamicrangeofmotionwhilewalkingwiththeirdominantleginxedkneeexion. 156

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Tocompensatefortheimposedmechanicalconstraintatthekneetheunimpairedsubjectsreduced theirsteplengthandrelieduponincreasedhipexiontoadvancethelegandprolongeddorsiexion clearthelimbduringswing.Theseindividualsegmentalcompensationsareseeninthethighand footPPs'shiftrighttowardmoreexion(angulardisplacementcloserto180 ¡ withrespecttoglobal horizontal)andreducedlimitcycleradius.Alsothisselfimposedrestrictedrangeofmotionatthe ankleiseasilydetectedbythelackofalocalminimumjustafterfooto ontheshank-footCRPD. Overall,itisexcitingtonotethatthisexperimentdemonstrateshowtheproposedmeasuresof coordinationdynamicscapturedchangesinmotorcontrolstrategies,quantiedthereorganization ofindividualsegments,andcanbeusedtoidentifymechanismsofchange. 6.1.7.3FixedAnkleDorsiexion Individualswithatranstibialamputationhavelosttheabilitytoactivelycontrolthemotionof jointsbelowthelevelofamputationandmustrelyuponthepropertiesoftheprosthesisatfoot o andduringswinglimbadvancement.Byxingtheanklemotiontoneutralintheunimpaired prospectivesubjects,itwasproposedtherewouldbecompensatorystrategiesproximaltothisxationthatmaybesimilartothegaitpatternofindividualswithatranstibialamputation.Byusing theproposedmeasuresofcoordinationdynamicstocomparethegaitpatternoftheunimpaired prospectivesubjectsduringthisconditiontothegaitpatternoftheretrospectivesubjectswith anamputation,theopportunitytoexamineanydi erencesatthelevelofcoordinationwouldbe possible. Similartothesubjectswithatranstibialamputation,thefootPPcharacteristicsoftheunimpairedsubjectswasalmostidenticalandsupportstheexperiment'sabilitytomimicthe"foot"motion oftheindividualswithanamputationusingtheanklebraceintheunimpairedsubjects.Ascanbe seeninthePPsforthesetwosubjectgroups,thedi erencesinasegment'spositionandvelocity fromtheunimpairedretrospectivereferenceincreasedasthedistanceofasegmentincreasedfromthe restrictedjoint.Additionally,thepelvisandthighPPrevealtheunimpairedsubjectsrelieduponincreasedanteriorpelvictilt(morehorizontalwithrespecttotheglobalhorizontal)andincreasethigh extensiontoadvancetheswinginglimb.Thisreorganizationabouttheankleforthemoreproximalsegmentswasalsodetectedbythesemeasuresofcoordinationdynamicsinthepre-doctoral investigationdiscussedinChapter2.Thendingsfromthisprospectiveexperimentfurthersupport theproposalthatindividualswithalowerlimbamputationwhoarefreeofneurologicalpathology areabletore-organizethespatio-temporalinteractionsbetweentheresiduallimb'ssegmentsand theprosthesis,asdetectedbytheproposedmeasuresofcoordinationdynamics.Furthermore,by 157

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analyzingthegaitpatternwiththesecoordinationmeasuresanalternativeperspectiveintoanindividual'smovementstrategiesmayo ervaluableclinicalinsightsthatcouldenhancetherapeutic interventions.Sincethisgroupofindividualswithalowerlimbamputation(freeofneurological pathology)areabletodrawupontheremainingdegreesoffreedom,accountfortheinertialpropertiesoftheirprosthesis,andndanothermotorsolutiontogaitinordertoadoptarelativelynormal gaitpattern,thesestrategiesandchangesmaynotbedetectablewithconventionalIGAmeasures thusfurthersupportingtheinclusionofPPsandCRPDswheninvestigatingthecoordinationofa subjectsgaitpattern.Thelowerlimbamputationcasestudypresentedthroughoutthisbodyof workelaboratethispositionandprovideanadditionalinvestigationintotheproposalthatthese IGAmeasures(PP,CPRD)aredetectingdi erentaspectsofgaitthanconventionalIGAmeasures. 6.2DiscussionofAimsandHypotheses Thefollowingsectionofthischapteraddressestheresultsfromtheexperiments,models,and analysescorrespondingtothefouraimsandtheircorrespondinghypotheses. 6.2.1Aim1 Capabilitiesoftheindividualandconstraintsofthetaskandenvironmentalallinuencethe emergingcoordinationpatternsofanymovement.Duetotheenormousnumberofvariablesassociatedwiththesethreefactors,alowdimensionalnormativereferencebecomesessentialinassisting withtheidenticationofaberrantmotorcontrolstrategiesinsubjectswithatypicalgaitpatterns resultingfromaneuromuscularimpairment.Thetwodynamicsystemstheorybasedmeasurespresentedinthisbodyofwork(e.g.PP,CRPD)complementtraditionalinstrumentedgaitanalysis measuresbysharingacommonoriginofmarkertrajectoriesandconsolidatethecomplexrelationshipsandorganizationalstrategiesofthelegsegmentsintrinsictogait.Similartohownormative kinematicsandkineticso ersacomparativeframeworkforresearchandclinicalinstrumentedgait analysis,hopefullybysharingthisnormativedatasetofcoordinationdynamicswillbemorereadily consideredandembracedbybothcommunities.AsdiscussedinChapter1,theobjectiveoftherst aimwastogenerateareferencedatasetofcoordinationmeasuresinthesagittalplanecoordinationforthepelvis,thigh,shank,andfootsegmentsandsegmentpairings(pelvis-thigh,thigh-shank, shank-foot,thigh-foot)fromalargegroupofindividualsfreeofgaitpathology.Thisreferencedataset wasthenassessedtodetermineiftheproposedmeasuresofcoordinationdynamicscharacterizea normalgaitpattern. 158

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WhilePPsandCRPDsarecalculateddi erentlythanjointkinematics,thecoe cientsofvariation(CVs)foreachPPandCRPDareofsimilarmagnitudetothekinematicCVspublishedby Winter(1983).ThisndingislogicalbecausetheCVdescribestheextentofvariabilityinthese trajectory-basedmeasuresthatarederivedfromthesamemarkerset.Thesamplesize,demographic ranges,lowCVs,narrowcondenceintervalsforfootcontactconditions,andsmallCRPDstandard deviationbandsareevidencethatthesecurvescharacterizethebehaviorofnormalcoordination dynamicsingait.Thesendingsdemonstratetherobustnessofthesecoordinationpatternsacross thiscohort'sconsiderabledemographicsandcapturethesubject-to-subjectvariabilityinherentin gait.Elaborationanddevelopmentofthedynamicsystemstheorymethodsusedtogeneratethis normativedatasetprovidethenextstepnecessarytomakethesetechniquesclinicallyusefuland becomeintegratedwithexistinginstrumentedgaitanalysismeasures. Inadditiontodevelopinganormativereferenceforthefollowingaimsandhypotheses,theresults andunimpaireddatasetcontributetothegeneralunderstandingofhealthygait.Whileinstrumented gaitanalysistechniqueshaveadvancedgreatly,thereisstillaneedformoreenlighteningtechniques toimproveourunderstandingofgaitstrategiesandcoordination.Healthygaitdataisoftenpresented inliteratureasanafterthoughtorasacontrolgroupforpathologicalapplications.Rarelyarethere concertede ortstoimproveourunderstandingofthenaturalvariabilityingaitpatterns,sothatwe maythenbegintoimproveourunderstandingofpathology.Creatinganormativereferenceofthese measuresofcoordinationdynamicsduringwalkingisessentialforimprovingourunderstandingof atypicalgaitpatternsbecauseitprovidesthemeanstodiscoverinsightsintohowthenervoussystem isimposingfunctionalconstraintsonthelimbs.Thereforeanormativereferencefromalargecohort ofindividualswithunimpairedgaitiscriticalforinterpretingcoordinationndingsinindividuals withneurologicaldisorders(Aim2,4). Itwasalsoproposedthatthelackofaunifyingandconsistentmethodology,normativereference,andclinicallymeaningfuldemonstrationsoftheimportantmotorcontrolinsightso eredby thesenonlinearmeasureshaveslowedtheirincorporationintoinstrumentedgaitanalysis.Anormativereferencefromalargecohortofindividualsiscriticalforunderstandingnormalgaitand forinterpretingcoordinationndingsinindividualswithneurologicaldisorders.Therefore,inan e orttocontinueadvancingtheapplicationofdynamicsystemstheorytechniquesinlocomotion andfollowingtherationalefordevelopingaclinicallyusefulnormativereference,aswasconducted forconventionalinstrumentedgaitanalysismeasures,thisaimprovidedanormativereferencefor coordinationdynamicsconstructedfromalargecohortofsubjectsfreeofgaitpathology. 159

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6.2.1.1PPandCRPDCurveFeatures Thenormativereferencesetofcoordinationcurvesprovidesthefoundationfordelineatingspecic curvefeaturesofatypicalandtypicalgaitpatterns.Extremaoftheabscissaandordinatemeasures inaPPassistinidentifyinganindividualsegment'spositionandvelocityatthatinstanceinthegait cycleandprovideinsightsintohowonesegmentiscontributingtotheorientationoftheentirelimb. CRPDextremaindicatetheamountandtimingofout-of-phasecoordinationoruncouplingbetween twosegments(Stergiou,2004).Conversely,thezerocrossingonaCRPDindicatesthesegments arein-phasewitheachother(Stergiou,2004).Aninectionpointdemarcatestheinstantwhenthe relationshipbetweenthetwosegmentshasreversedandthustheinstantwhenmusclesynergiesbegin changing(e.g.fromexiontoextension).FindingthePPandCRPDvaluescorrespondingtothe percentgaitcycleofothercommongaitevensbecomese ortlesswhenthesedynamicsystemstheory measureshavebeennormalizedtothegaitcycle.Thesmallcondenceintervalsoftherelativephase anglesfromeachCRPDforthefouressentialfootfallconditionsofanormalgaitcycleshowthereis greatpotentialforusingCRPDstoquantifycoordinationevents.Thisnormativereferencecanbe usedinfutureinvestigationstoelaborateuponndingsfromthisdatasetbyexploringrelationships betweenPPandCRPDcurvefeaturesandotherconventionalinstrumentedgaitanalysismeasures. CurvefeaturesfromCRPDsandPPscanalsobeusedtoquantifychangestotheneuromuscular system'sorganizationinresponsetoanintervention,identifywhichsegmentchangedthemostpostintervention,andrevealtheunderlyingmechanismsofchange.Intheexampleforasubjectwith asti kneegaitpattern,thestandardsurgicaltreatmentforthisgaitpatternisarectusfemoris transfer,whichremovesthebiomechanicalconstraintofanextensionsynergythatpromotesthe undesirableprolongedcouplingofthelowerextremityduringswinglimbadvancement(Gage,1987). Changesinthespatio-temporalorganizationofsegmentsfromthissurgicalinterventionmaya ord somepatientsanopportunitytoadoptchangesinmotorcontrolstrategiesthatresultinattenuation ofthisextensionsynergyandthusachievemoree cientswinglimbadvancement.Changesinthe thigh-footCRPDminimumquantieschangesinselectivemotorcontrolstrategiesbetweenpreand post-interventionandisameanstoidentifymechanismsofchangewithinagaitpattern.This additionalinformationmayaidintherehabilitationstrategiesemployedtohelpoptimizeapatient's benetsfromaninterventionortreatment. 160

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6.2.2Aim2 Sincethereispresentlynotastandardmethodforquantifyingcoordinationdynamicsduring thecyclicaltaskofgait,theproposedmeasuresofcoordinationdynamicswerecomparedtothree clinicalanalogues.ThepurposeofAim2wastothenexploretherelationshipbetweentheproposed measuresofcoordinationdynamicsandselectclinicalperformancemeasuresfromthreeclinical analoguesthatcharacterizeaspectsofcoordination.RecallfromthemethodsdiscussioninChapter 4,thattheresultsfromthesetestsonlypertaintotheprospectivesubjects. 6.2.2.1Hypothesis2A Itwashypothesizedthatimpairmentsinthespeedandaccuracyofvoluntaryreciprocalmovements,astestedbyatimed,spatiallyconstrainedlowerextremitytappingtask,wouldbesignicantlycorrelatedwithtaskspeciccoordinationdecitscharacterizingselectivemotorcontrol. ResultspresentedinChapter4andAppendixGsupportthishypothesisfortheprospectivesubjects withcerebralpalsy.Aspredicted,theaccuracyoftargettapsincreasedwithtargetsizeforallofthe prospectivesubjectswithcerebralpalsy.Alsoasexpected,theforwardswinglegspeedincreased astargetsizeincreasedforbothsubjectgroupsandwassignicantlyslowerforthesubjectswith cerebralpalsythanthelegswingspeedoftheunimpairedsubjects.Therewasalsoasignicantdifferenceinthetargetaccuracyandforwardswinglegspeedbetweentheunimpairedsubjectsandthe subjectswithcerebralpalsy.Thisindicatestherewasasdi erenceinboththespeedandaccuracy ofthesetwocohortsforthisvoluntaryreciprocaltappingmotorcontroltask. Thetimingandmagnitudeofthemaximuminstantaneousslopeduringinitialswingofthe thigh-shankCRPDwasfoundtobesignicantlydi erentbetweenthetwoprospectivesubject groups.Comparedtotheunimpairedcohort,themeanensemblethigh-shankCRPDforsubjects withcerebralpalsywasattenuatedandtheoccurrenceofthiscoordinationeventwassignicantly delayedandshallower.TheCRPD'smaximuminstantaneousslopeisameasureoftheratethetwo segmentschangedominance.Individualswithasti kneeorcrouchgaitpatternareknowntohave di cultdissociatingthethighandshanksegmentsduringinitialswingasaresultoftheimpaired motorcontrolduetocerebralpalsy.Thehighcorrelationsbetweenthisthigh-shankCRPDmaximum instantaneousslopeandtheforwardswinglegvelocityforsubjectswithcerebralpalsyindicatesthis coordinationeventiscapturingthesesubjects'di cultywithdissociatingthesetwosegmentsat thiscriticaltimeinswinglimbadvancement.Thelowcorrelationbetweenthiscoordinationevent andforwardswinglimbspeedfortheunimpairedsubjectsisconsistentwiththisinterpretationand 161

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isexpectedsincethissubjectgroupdoesnothaveanydi cultywiththiscriticalmotortaskin initialswing.TheseexcitingndingsdemonstratecertaincurvefeaturesfromCRPDsarecapableof characterizingmotorcontrolandcandetecthowvaryingdegreesofmotorcontrolimpairmenta ect anindividual'sgaitpattern.Sincetheseproposedmeasuresofcoordinationdynamicsareconstructed frommarkertrajectories,whichisthefundamentalmeasurementcollectedduringinstrumentedgait analysis,theycanbeusedtoquantifymotorcontrolduringgaitanddonotrequireadditionaldata collection.Usingthesemeasurestoquantifyanindividual'scoordinationdynamicsduringgaitalso alleviatestheneedtoperformadditionaldiscretemotorcontroltasks,noneofwhicharedirectly analogoustowalking,inane orttoindirectlycharacterizethisfundamentalelementofgait. Itisalsointerestingtonotethatthethigh-shankandthigh-footCRPDminimumnearfooto arebothhighlycorrelatedwiththesubsequentmaximuminstantaneousslopeandinectionpointin theinitialtomidswingperiodsofthegaitcycle.Thesecorrelationsemphasizetheimportanceofthe magnitudeandtimingofthisprecursorcoordinationevent(e.g.dissociateofthigh-footextension synergy)anditsinuenceonthecoordinationdynamicsandcoordinationeventsfortheremainder ofswinglimbadvancement.Althoughthishypothesisdidnotexhaustivelyexploretherelationship betweenthespeed-accuracytrade-o duringareciprocaltappingtaskandtheproposedmeasures ofcoordinationdynamics,thesendingssupportfurtherinvestigationsofthesemeasuresandtheir clinicalandresearchapplications. 6.2.2.2Hypothesis2B Itwashypothesizedthatthedegreeofselectivemotorcontrolimpairments,astestedbythe SelectiveControlAssessmentoftheLowerExtremity(SCALE),wouldbesignicantlycorrelated withtaskspeciccoordinationdecits.AspresentedinChapter5,therewasasignicantdi erence betweentheSCALEscoresfortheunimpairedsubjects'andthesubjectswithcerebralpalsy.This indicatestherewasadi erenceinthesetwocohort'sabilitytoperformtheselectivevoluntarymotor controltasks. SincethevoluntaryselectivemotorcontrolSCALEtasksofthelowerextremityjointsaresimilar totheabilitytovoluntarilydissociatevarioussynergiesduringinitialswing,itisperhapsofnogreat surprisethatthreeCRPDcoordinationeventswerefoundtobesignicantlydi erentbetweenthetwo subjectgroups.Thesethreecoordinationeventsalsoquantitativelyrevealhowtheinter-segmental interactionsarecontributingtoadelayedoccurrenceofcriticalswingperiodgaiteventsando era mechanisticexplanationastowhyindividualswhostrugglewithinitialswingcoordinationevents arethenplayingcatchupfortheremainderofthegaitcycle.First,thetimingandmagnitude 162

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ofthethigh-shankCPRDminimumnearfooto wassignicantlydelayedandattenuatedforthe subjectswithcerebralpalsy.Thisndingindicatesthatthesubjectswithcerebralpalsywere unabletodissociatethethigh-footextensionsynergyatfooto tothesamedegreeandasquickly astheunimpairedsubjectsandasaresultthesegmentpositionswererestrictedandlimited.This ndingisconsistentwiththedescriptionsofsti kneeandcrouchgaitpatternsinChapter2and demonstratestheseproposedmeasuresofcoordinationdynamicsareabletoquantifythisaberrant motorbehaviorduringthetaskofgait.Thesecondsignicantcoordinationdynamicsndingwas therateatwhichthethighandshankchangeddominancewassignicantlyslowerforthesubjects withcerebralpalsy.Themaximuminstantaneousslopeonthethigh-shankCRPDcapturesthis inter-segmentalrelationship.Theshallowerslopeforsubjectswithcerebralpalsycapturesthe di cultythesesubjectshavewithchangingsegmentrelationshipsattheidealspeed.Considering thatspasticityisvelocitydependent,thenitisproposedthatthesubjects'spasticityistriggered andpreventsthemfromchangingsegmentrelationshipsatafasterspeed.Thethirdsignicant coordinationdynamicsndingwasthetimingofthethigh-footCRPDinectionpointintheinitial swingperiodofthegaitcycle.ThisCRPDeventcorrespondstotheinstantwhentwosegmentsbegin tochangebehaviorandisagainproposedtoreecthowthesubjects'spasticitydelaysthetiming ofwhenasubjectcanchangesegmentalrelationships.Whiletherelationshipbetweenvoluntary motorcontrolduringgaitandtheproposedmeasuresofcoordinationdynamicsarenotexhaustively discovered,theseexcitingndingssupportfurtherinvestigationsofthesemeasuresandtheirclinical andresearchapplications. 6.2.2.3Hypothesis2C Itwashypothesizedthatcerebellarbasedimpairmentsinspatialaccuracyofmovementand dynamicbalance,testedbylowerextremitytasksfromtheInternationalCooperativeAtaxiaRating Scale(ICARS)andScalefortheAssessmentandRatingofAtaxia(SARA),wouldbesignicantly correlatedwithtaskspeciccoordinationdecits.Therewasnotasignicantdi erencebetweenthe ICARS/SARAscorefortheunimpairedsubjectsandthesubjectswithcerebralpalsy.However,the smallsamplesizeofprospectivesubjectswithcerebralpalsymayhavecontributedtothisstatistical result.Itisalsoimportanttonotethatthesetwoperformancetestswereoriginallydesignedfor andvalidatedwithindividualsdiagnosedwithcerebellarataxia,whichisacompletelydi erent etiologyofmotorcontrolimpairmentthanthatofindividualswithcerebralpalsy.Twomeasures werecalculatedfromtwoofthewalkingtasksperformedbysubjectsaspartoftheICARS/SARA experimentaltasks. 163

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Therstofthesemeasureswasthebaseofsupportwidthduringtandemandover-ground walking.Baseduponotherresearchstudiesreportedintheliterature,itwaspostulatedthata largerbaseofsupportwouldindicateanincreaseddi cultywithdynamicbalanceduringthesetwo walkingconditions.Therewasnotasignicantdi erencebetweenthebaseofsupportwidthfor theunimpairedprospectivesubjectsandtheprospectivesubjectswithcerebralpalsyduringovergroundwalking.Again,thisstatisticalresultcouldbeinuencedbythefactthatonlyoneofthe prospectivesubjectswithcerebralpalsywhowasabletoperformthetandemwalkingtask.This onesubjectwasclassiedatleveloneoftheGrossMotorFunctionClassicationSystem,indicating littletonoimpairmentwithover-groundwalking.Thebaseofsupportwidthduringover-ground walkingforallprospectiveandretrospectivesubjectswasthencalculatedandrevealedstatistically signicantdi erencesbetweenthetwoclinicalcohortsandtheunimpairedcohort.Thisnding conrmstheproposalthatthesubjectgroupswithimpairedoralteredmotorcontroladoptalarger baseofsupportinordertoeasethedynamicbalancerequirementsofmaintainingabipedalgait patternandpreventfalling. ThesecondmeasurederivedfromtheseICARS/SARAtaskswasthecurvatureofthecenter ofmass'trajectorywhileturningleftandrightwhilewalking.Baseduponotherresearchstudies reportedintheliterature,itwasproposedthatwiderturnradius(e.g.asmallercurvature)during aturnwouldindicatedi cultyinperformingtheturnandthusimpairedcoordinationanddynamic balance.However,asreportedinChapter5,therewasnotasignicantdi erenceinthecurvature betweenthetwoprospectivesubjectcohorts.Afterreviewingthevideoandmotioncapturedata ofthesubjectswhiletheyperformedthiswalkingtask,itwasdiscoveredthatthesubjectswith cerebralpalsywouldslowtheirwalkingspeedconsiderablypriortoandduringtheturnandthen pivotontheinsidelegtochangedirections.Thispivotingtechniquecausedatighterturn(larger curvature)thatwassimilartoorlargerthantheturningcurvatureoftheunimpairedsubjects. Whenconsideringtheturncurvatureinthecontextoftheadoptedmovementstrategy,theaxiom thatasmallercurvatureisindicativeofpathologyistoosimplisticofageneralizationandmaybe misleadingwhenviewedinisolation.Thisconclusionaboutthismeasureisfurthersupportedby thelowcorrelationsbetweentheICARS/SARAscoreandthemaximumcurvatureforsubjectswith cerebralpalsy. Inregardstothedi erencesincurvaturevaluesfortheleftandrightturnsofsubjectswith cerebralpalsy,itisproposedthatthedi erenceincurvaturevaluesisrelatedtothesubjects' topographicalcategory.Ofthefourprospectivesubjectswithcerebralpalsy,twowereclassiedas diplegicandtwowereclassiedashemiplegic.Sinceallfoursubjectswerea ectedontheright 164

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sideandonlytwowerea ectedontheleftside,thecurvatureoftherightturnswaslargerthan thecurvatureoftheleftturnsbecauseofthenumberofa ectedlimbswasgreaterfortheright turningtasks.Whiletherelationshipbetweenvariousfunctionalelementsofgait(e.g.postural control,dynamicbalance)andtheproposedmeasuresofcoordinationdynamicsarenotexhaustively exploredinthishypothesis'tests,thesendingssupporttheabilityofthesemeasurestocharacterize varyingdegreesofcoordinationabilityduringgaitandwarrantfurtherinvestigation. 6.2.3Aim3 ThehypothesesofAim3weredesignedtotesttheconstructvalidityofthelongheldanalogythat themotionofthelegsduringswingperiodislikeapassivecompoundpendulum.Severalsoftware simulationsusingthemathematicalpendularmodelandsubjectmotioncapturedatawererunto comparethemotionofatheoreticaldoublependulumtothesagittalplanemotionofthethighand shankduringtheswingperiodofgaitforvariousclinicalcohorts. Whenexaminingeachcohort'ssummedresiduals(e.g.rankings)forthefourdi erentdamping conditions,severalinsightsintotheirunderlyingcoordinationdynamicsarerevealed.Theangular displacementsofthethighandshankforthesubjectswithoutneurologicalpathology(e.g.unimpairedsubjects,subjectswithlowerlimbamputation)di eredmorefromthetheoreticalmodelthan theangularvelocitiesofthesesegments.However,theangulardisplacementandangularvelocityof thethighandshanksegmentsforthesubjectswithcerebralpalsydi erednearlythesameamount fromthetheoreticalmodel.Whenconsideringthevelocitydependentnatureofspasticityincerebral palsy,whichresultsinlimitedrange(e.g.angularposition)ofmotionforsegments,itmakessense thatthegaitpatternsa ectedbyspasticitywoulddeviatefromthetheoreticalmodelindescriptors ofbothpositionandvelocity. Exceptfortheun-dampedcondition,thesubjectswithanabovekneeamputationwerethe closesttothetheoreticalpendulummodel.Sinceindividualswithatransfemoralamputationdo nothaveanyneurologicalcontrolatandbelowthekneejoint,theyrelyupontheinertialproperties oftheirprosthesistoadvancetheprostheticlimbforwardduringtheswingperiodofgait.The othersubjectgroups(e.g.unimpaired,sti kneegait,crouchgait)havesomeneurologicalcontrolat theknee,evenifitisundesirable,whichcreatesvariabledampingduringswinglimbadvancement. Consideringthesedi erencesinthekneejointpropertiesforthesedi erentsubjectcategories,it makessensethatthosewithalowerlimbamputationaretheclosesttothetheoreticalpendulum model.AsmentionedinChapter5,futureinvestigationswithlargersubjectsizescouldbeconducted todetermineifthesummedresidualsforthedi erentdampingconditionsareclinicallymeaningful, 165

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whatisaclinicallytrivialinterval,andwhatthresholdsareclinicallysignicant. 6.2.3.1Hypothesis3A Itwashypothesizedthatsubjectswithalowerlimbamputationwouldhavecoordinationdynamicsmeasureswiththesmallestresidualwhencomparedtoapassivedoublependulum.This wasfoundtobetruewhensubjectswereorganizedbygaitpattern.Thesubjectswithabelowknee amputationweretheclosesttothetheoreticalpendulum.Theresultsfromthisanalysissupport thehypothesisthatwhensubjectswereorganizedbygeneralpathology(e.g.unimpaired,cerebral palsy,lowerlimbamputation)theindividualswithabelowkneeamputationwereclosesttothetheoreticalpendulum.Thesubjectswithalowerlimbamputationweretheclosesttotheun-damped theoreticalpendulum.Baseduponthesendings,itisproposedthatthesagittalplanemotionof thethighandshankduringswingforindividualswithalowerlimbamputation,especiallyfora transfemoralamputation,isthesubjectgaitpatternthatmostcloselyresemblesthemotionofa passivecompoundpendulum. 6.2.3.2Hypothesis3B Itwashypothesizedthatsubjectswithcerebralpalsywouldhavecoordinationdynamicsmeasures withthesmallestresidualwhencomparedtoanover-dampeddoublependulum.Resultsfromthis analysisdidnotsupportthishypothesiswhensubjectswereorganizedgenerallybygaitpathology (e.g.unimpaired,cerebralpalsy,lowerlimbamputation)andmorespecicallybygaitpattern(e.g. sti kneegait,crouchgait,amputationlevel).Ofthefourdampingconditionsconsidered,the subjectswithcerebralpalsydi eredthemostfromthetheoreticalpendulum.Whenthesubjects wereorganizedbygaitpattern,thesubjectswithcerebralpalsyalsodi eredthemostfromall dampingconditionsofthetheoreticalpendulum.Therefore,itisproposedthatbaseduponthese ndings,thesagittalplanemotionofthethighandshankduringswingforindividualswithcerebral palsyisnotthatofapassivecompoundpendulumbutinsteadvariablydampedcompoundpendulum thatisinuencedbysegmentvelocity(e.g.spasticity). 6.2.3.3Hypothesis3C Itwashypothesizedthatsubjectsfreeofgaitpathologywouldhavecoordinationdynamicsmeasureswiththesmallestresidualwhencomparedtoacriticallydampeddoublependulum.Results fromthismodelsimulationsupportedthishypothesiswhenthesubjectswereorganizedgenerally 166

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bygaitpathology.Infact,whenorganizedbygaitpathology,themotionoftheunimpairedsubjects'thighandshankwastheclosestofthethreesubjectgroupstothetheoreticalmodelforthe under-damped,criticallydamped,andover-dampedconditions.However,whensubjectswereorganizedbygaitpatterntheresultsfromthemodelsimulationdidnotsupportthishypothesis.For theunder-dampedandcriticallydampedconditions,theunimpairedsubjectswererankedsecond whenorganizedbygaitpattern.Althoughitisdi culttodrawconclusionsabouttherankings, thesendingsforthesedampingconditionsmayindicatetheamountofvariabledampingemployed inunimpairedswinglimbadvancementliessomewherebetweenthesetwodampingconditions.Futureworkusingmoreadvancedmodelingtechniquesorvariabledampingfunctionsmightrevealthe dampingproleofthehipandkneejointsforunimpairedsubjectsduringswinglimbadvancement. Itisproposedthatbaseduponthesendings,thesagittalplanemotionofthethighandshank duringswingforindividualsfreeofgaitpathologyisnotthatofapassivecompoundpendulumbut insteadanelegantlycontrolled,variablydampedcompoundpendulum. 6.2.4Aim4 Afterestablishinganormativereference,comparingthesemeasuresofcoordinationtoclinical analogues,andcontrastingthependularmotionofthelegduringswingtoatheoreticalpendulum model,thenextlogicalstepindevelopingthesecoordinationmeasureswastodemonstratethey areabletodistinguishbetweendi erentgaitpatternsofpopulationswithdi erentphysiological reasonsforimpairedswinglimbadvancement.Whilethisfourthaimisbynomeansthenalstep neededbeforeclinicaladoptionofthesemeasuresitisanessentialprecursortothedissemination andhopefullyadoptionofthesemeasuresofcoordinationdynamicsbyresearchersandcliniciansin theinstrumentedgaitanalysiscommunity. AsdiscussedinChapter1,thereiscurrentlynotagoldstandardformeasuringthecoordination dynamicsofthelegsegmentsduringgait.Whiletheproposedmodelofcoordinationdynamics usestwolowdimensionaldescriptors(e.g.phaseportraits,continuousrelativephasediagrams), comparingthesemeasuresforlargesubjectcohortsandforeachgaitcycletimeepochstillresultsin largecumbersomedatasets.Thereforeinane orttoconsolidatethesedescriptorsofcoordination intoasimplescalarvalue,twoindicesofcoordinationdynamicswerecreatedfromphaseportraits andcontinuousrelativephasediagrams.Therstcoordinationdeviationindex(CDI)isbasedupon featurecomponentanalysisandwasconstructedusingtheentiregaitcycle.Thesecondmetric, thecoordinationperformancescore(CPS),wasconstructedfromsignicantcoordinationevents occurringduringtheswingperiodofgait.Afterdevelopingthesetwonovelmetrics,additional 167

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analyseswereperformedtoexploretheapplicabilityofthesenewcoordinationindicesindescribing gaitpathologyforsubjectswithcerebralpalsyoralowerlimbamputation.Asdiscussedbelow, theresultsfromtheseadditionalanalysesjustifytheuseoftheseindicestoquantifydi erences incoordinationdynamicsbetweenvarioussubjectgroups.Thesenovelindiceswerethenusedto quantitativelytestthisaim'shypothesisanddeterminewhethertheproposedmodelofcoordination dynamicsiscapableofdistinguishingbetweenthevariouspathologicalgaitpatternsconsideredin thisbodyofwork. 6.2.4.1TheCoordinationDeviationIndex Instrumentedgaitanalysishasbecomethemostcommonlyusedmethodforquantifyingcertain aspectsofanindividual'sgaitpattern,informingclinicaldecisions,andassessingtreatmentoutcomes [1,2]inindividualswithvariousmotordecitsincludingcerebralpalsy[1,2,3],lowerlimbamputation [4,5].Inane orttoconsolidatethelargeamountofcomplexinformationcapturedduringIGA, severalindiceshavebeenproposedtoquantifygaitdeviationsfromanormativereference[6,7,8]. Inparticular,thegaitdeviationindex(GDI)quantieschangesinanoverallkinematic(e.g.joint angle)patternanditsgrowingpopularityinclinicalandresearchapplicationsisatestamenttothe valueandusefulnessofsuchanindex.WhiletheGDIhasbeenshowntodetectdeviationsingait pathologya ectingjointangles[7,8,9],thisdissertationproposesanindexofcoordinationbased ontheunderlyingcoordinationdynamicsasameaningfulandappropriatecomplementtotheGDI whenstudyingthegaitpatternofindividualswithaberrantcoordination.Therefore,acoordination deviationindex(CDI)wasconstructedfromsagittalplanePPsandCRPDs.Thisnewcoordination indexwasthencomparedtotheGDIandGrossMotorFunctionClassicationSystem(GMFCS) levelofindividualswithvaryingdegreesofmotorimpairment. Whilethemanifestationofmotordisordersinindividualswithcerebralpalsy(CP)iscomplex anduniquelyexpressed,therearecommongaitpatterns[14]usedtodescribethisgroup'sinability toachievevariousspatialandtemporalaspectsofgait(e.g.gaiteventsandtasks[15,16],decreased steplengthandwalkingspeed[15,16,17]).Individualswithalowerlimbamputation,whilefroma di erentetiologythanCP,haveunderlyingcoordinationimpairmentslinkedtotheirgaitpatterns thatlimittheirabilitytoperformcriticalgaitevents(e.g.decreasedwalkingspeed[18],delayedand insu cientpeakkneeexion[5],excessivehipexion[4,5]). Molloyetal.,2010evaluatedtherelationshipoftheGDIandgrossmotorfunctionbyusing theGrossMotorFunctionClassicationSystem(GMFCS)anddemonstratedtheGDIdistinguishes betweendi erentGMFCSlevelsinindividualswithCP.ToevaluatetheCDI'sabilitytostratifygait 168

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pathologyrelatedtocoordination,wealsoanalyzedtherelationshipbetweentheGMFCSlevelsfor individualswithCP.SinceincreasingamputationlevelforindividualswithaLLAhasbeenshown todecreasefunctionalgaitabilities[4],theCDI'sabilitytodetectdi erencesincoordinationdueto amputationlevelwasalsoexamined. AnindexconstructedfromPPsandCRPDs,whichdescribemovementatthelevelofcoordination,providescliniciansandresearcherswithametricthatmaybemoremeaningfulandappropriate indescribingtheunderlyingmechanismsofgaitpathology.Forexample,theCRPDmeasureof inter-segmentalcoordinationdescribesselectivemotorcontrolimpairmentsinindividualswithCP. Likewise,theCRPDdescribescoordinationstrategiesandreorganizationofsegmentsbyindividuals withaLLAthatresultfrominertialconsequencesofamputationandwearingaprosthetic.Inconjunctionwiththenormativereferencedatasetfromalargecohortofsubjectsfreeofgaitpathology constructedinAim1,theconsolidatedmetricforindexingtheseverityordegreeofdeviationfrom typicalcoordinationpresentedinthispaperprovidesanadditionalapplicationofthesecoordination measuresandhopefullyhelpseasetheincorporationofthesetechniquesintoclinicalandresearch applications. Theoverallobjectiveofthissub-investigationwastoexploretheapplicabilityoftheCDIindescribinggaitpathologyfortwocohortswithdi erentreasonsforcoordinationdecits.Thespecic aimsofthissub-investigationwereto1)generateacoordinationdeviationindexusingtheGDI methodologyforthesegroups,2)compareCDIscoresofthegroupsusingtheGDIasabenchmark todescribevaryingdegreesofgaitperformanceinthesedistinctgroups,and3)demonstratethat themagnitudeofcoordinationimpairment(CDI)correspondstothemagnitudeofkinematicimpairment(GDI).TheresultspresentedinChapter5fromtheseanalysesshowtheCDIiscapable ofdistinguishingbetweenvaryinglevelsofgaitimpairment,theCDIfollowedsimilartrendsasthe GDIforthevariousclinicalgroups,andtheCDIdetectedvaryinglevelsofmotorimpairment(e.g. ascharacterizedbyGMFCSlevels)forindividualswithcerebralpalsy. AsindicatedinFigure5.3.8A,subjectswithgaitpathology(e.g.CP,LLA)hadsignicantly reducedCDIsthanthosefreeofgaitpathology,whichisaconsistentwithtrendsfromotherstudies usingkinematicbasedindices[6,7,8,9].Althoughthepatternsofthevariouscohorts'CDIscores followthesametrendastheGDIscores,theGDIvaluesweresignicantlydi erent(p 0.05)from theCDIvaluesinallsubjectgroupsexceptforthosewithanabovekneeamputation.However,if thesamplesizeofthissubjectgroup(n=6legs)wasincreasedtheremaybeastatisticallysignicant di erencebetweenthegroup'sGDIandCDIvalues.SimilartotheGDI,decreasesintheCDI reectedincreasesinthediagnosisseverity(e.g.topographically,levelofamputation).Thescatter 169

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plot(Figure5.3.9A ) oftheGDIversusCDIshowsthereisamoderaterelationshipbetweenthetwo indices.Thesignicantspreadofpointssuggestthesetwoindicesmeasuredi erentaspectsofgait, whichfurthersupportstherationalefordevelopinganindexbaseduponcoordinationdynamicsto complementconventionalgaitanalysismeasures. TheGMFCShasbecomethebenchmarkmeasureforclassifyingthefunctionalgaitabilityofindividualswithcerebralpalsy[20].Itwashypothesizedthatasindividual'sGMFCSlevelsincreased, theCDIwoulddecreaseandthusreecttheindex'sabilitytocharacterizevaryinglevelsofcoordinationimpairmenta ectinggait.AsillustratedinFigure5.3.8B,theCDIvalueindeeddecreasedwith diminishinggrossmotorfunction,ascharacterizedbytheGMFCS.Signicantdi erencesbetween themeanCDIandeachGMFCSlevelaswellasbetweenGMFCSlevelsIandIIIindicatetheCDI distinguishesbetweendi erentlevelsofcoordinationimpairment.Whenconsideringthefunctional di erencesbetweenGMFCSlevelsIandIII,itmakessensethatthecoordinationmeasuredinthe motioncaptureenvironmentwouldmoreeasilydi erentiatebetweenthesetwolevelsthanlevelsI andII.Theseresultsfurthersupportthetheoreticalconstructofthesedynamicssystemstheory measuresandobservationsfromotherstudiesshowingthatPPsandCRPDsquantifythebehavior ofcoordination[21,22].Furthermore,theCDIdemonstratesthesenonlinearmeasurescanbeused todistinguishbetweenvaryinglevelsofmotorfunctioninrelationtoone'sabilitytoperformthe cyclicaltaskofgait. Sixcoordinationfeaturesaccountedfor98%ofthetotalvarianceandwereusedtoreconstructa subject'scoordinationdynamicscurves(PPs,CRPDs).Onedisadvantageofusingfeatureanalysis isthatitrequireslargenormativereferencedatasets,whichmanylabsmaynothave.Thenormative referencedatasetusedtocreatetheCDIisapproximatelyonethirdthesizeoftheGDI'sreference datasetandisalimitationofthisstudyandthistypeoffeatureanalysis.Itisexpectedthat increasingthenumberofsamplesinthenormativereferencewouldresultinreconstructedsubject curvesthatareclosertotheoriginalcoordinationcurvesandsmooththereconstructedcurves, whichpresentlyhavesharperextremaduetothesamplesizeandsamplingofthegaitcycle(2% increments).ItisexpectedthatincreasingthenormativedatasetfortheCDIwouldnotinvalidate thestudy'sndingssincetheminimumrequirednumberofsamples(612samples)forsinglevalue decompositionisexceededwiththecurrentnormativedataset.Ratheritisexpectedthatusinga largernormativedatasettocreatethecontrolfeaturesandincreasingthenumberofclinicalsubjects ineachcategorywouldresultingreaterdistinctionbetweenthecohorts'CDIvalues,likethesubjects' GDIvalues.Intheaccompanyingelectronicaddendum,thecontrolfeaturesusedinthispaperare providedalongwithaclearlydenedprocessforcalculatingasubject'sCDI. 170

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WhiletheCDIwasgeneratedfromsagittalplanecoordinationcurves,whichhasbeenshowntobe theplanewithsignicantdeviationsespeciallyforindividualswithCP[14],thisindexcouldeasilybe expandedtoincorporatecoordinationcurvesfromtheothertwoplanesofmotion.Resultsfromthis study'sanalysessupportsfurtherdevelopmentoftheCDIasacomplementarymeasuretotheGDI anddemonstratetheCDIcapturespathologynotrepresentedinkinematicbasedanalyses.These ndingsprovideevidencesupportingthesecoordinationmeasures(e.g.PP,CRPD)describevarying degreesofgaitperformanceinsubjectswithbothmusculoskeletalandneurologicalimpairmentsand theuseofthesemeasurestocharacterizesubjectswithatypicalcoordinationthatcontributestoan overallaberrantgaitpattern.AstheGDIisoftenusedtoquantifychangesinkinematicsfroman interventionorovertime,theCDImayalsobeavaluableresearchtoolbecauseitprovidesadeeper levelofunderstandingaboutthemechanismsassociatedwithchangesinjointanglesbyreecting theunderlyingorganizationofsegmentoscillationsduringgait. FeatureanalysiswasusedtocreateanindexofcoordinationdynamicsfromPPsandCRPDs andprovidesaconcisemetricoftheamountanindividual'scoordinationdeviatesfromanormative reference.Thisinvestigationdemonstratedthisnewcoordinationindexcandistinguishbetween di erentgaitpatternsintwoclinicalcohortswithdi erentetiologiesa ectingtheircoordination andthusabilitytoproduceatypicalgaitpattern.ComparisonsbetweentheGDIandCDIfound thatwhilethesetwoindicesfollowsimilartrendsinvariousclinicalgroups,theymeasuredi erent aspectsofgait.Therefore,theCDImayprovetobeavaluableresearchtoolforstudyingpopulations withimpairedmotorcontrolbecauseitprovidesadeeperlevelofunderstandingaboutthemechanismsassociatedwithchangesinjointanglesbyreectingtheunderlyingorganizationofsegment oscillationsduringgait. 6.2.4.2TheCoordinationPerformanceScore Althoughavarietyofgaitindiceshavebeenpresentedintheliterature(e.g.GilletteGaitIndex [1],GaitDeviationIndex[2],GaitPerformanceScore[3])andarewidelyacceptedmeasuresof gaitpathology,alloftheseindicesareconstructedexclusivelyfromjointanglesandtheindices usingfeatureanalysisrequirealargenumberofnormativereferencesubjects,whichmaynotbe availableformanylabs.Sincephaseportraitsandcontinuousrelativephasediagramsaredynamic systemstheoryderivednonlinearmethodsthatquantifythetimingandpositionofanindividual segmentandpairsofsegments,thesenonlineartechniqueswereusedtoquantifythebehaviorof coordinationduringtheswingperiodofgait[4,5,6].Anindexcreatedfrommeasuresmoresuitable forcharacterizingmotorcontrolmechanismsthatcontributetowalking,maybemoremeaningfuland 171

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appropriateforstudyingthegaitofindividualswithaberrantcoordination.Therefore,employing asimilarmethodologytothegaitperformancescorepresentedbyBakeretal,2008,statistically signicantcurvefeaturesfromPPsandCRPDswereidentiedandusedtocreateacoordination performancescore(CPS).Additionally,thesesignicantcoordinationeventswereusedtocreatetwo nominalregressionmodelscapableofdistinguishingbetweenunimpairedandimpairedgaitpatterns forindividualswithcerebralpalsy. InChapter3,coordinationwasdenedastheorganizationofthetimingandpositionofindividual segmentsandsegmentpairsduringthecyclicaltaskofgait.Successfulcompletionofswinglimb advancementisacriticalgaitachievementbecauseitadvancesandclearsthefootandinanticipation ofinitialcontact,coordinatesthetimingandsequencingofsegmentswithfeed-forwardmotorcontrol mechanisms.Itwasassumedthatthecoordinationoflimbsegmentsisindividualtothemoverand inuencedbysignicantcoordinationeventsthatarerequiredtoachievenormalfootcontactand constrainthecoordinationsolution.Whilethemethodsemployedherecanbeappliedtotheentire gaitcycle,thissub-investigationfocusedonthecriticaltaskofswinglimbadvancementbecauseit advancestheleg,a ectsfootfallforthenextcycle,andrequirestheappropriatecoordinationand controlofbodysegments[9].Elucidatingthecoordinationdynamicsofthiscomplextaskrequires amethodologycapableofisolatinganindividualsegment'scontributiontothesystem'sbehavior andidentifyingthetimingandsequencingofadjacentandnon-adjacentsegmentpairs.Asdiscussed inChapter3,PPsandCRPDsarelow-dimensionalmeasuresthatsatisfythisneedbecausethey quantifythependularlikemotionofthelegsandrespectivesegmentsduringthecontinuous,cyclical taskofgait[4,5,6]. Identifyingsignicantcoordinationeventsduringtheswingperiodofgaitforacohortofunimpairedsubjectsprovidesameanstoenhancetheunderstandingoffeed-forwardmotorcontrolstrategiesemployedinswingperiodgaitando ersareferenceforsubjectswithatypicalcoordination resultinginimpairedswinglimbadvancement.ExtractingspeciccurvefeaturesfromPPsand CRPDstoidentifycoordinationeventsdemonstratestheclinicalutilityofthesenonlinearmeasures asacomplementtotraditionalinstrumentedgaitanalysismeasures.Usingsignicantcoordination eventsfromPPsandCPRDstodescribemovementatthelevelofcoordinationprovidesclinicians andresearcherswithametricthatmaybemoremeaningfulandappropriatewhenstudyingagait pattern'sintrinsiccoordinationdynamics.Additionally,usingtechniquesderivedfromthesecoordinationmeasurestodistinguishbetweendi erentgaitpatternsdemonstratesthevalueofthese measuresandtheirabilitytoprovideadi erent,yetcomplementaryperspectiveofinstrumented gaitanalysisdatabyelucidatingunderlyingindividualsegmentpositionsandtimingthatcontributes 172

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toagaitpattern.InadditiontothemethodologyandlargenormativereferenceprovidedinAim 1,theCPSandregressionmodelspresentedinthisbodyofworkprovidetwoadditionalmeansto helpfacilitatetheincorporationofthesecoordinationdynamicsmeasuresintoclinicalandresearch instrumentedgaitanalysisapplications. Theoverallobjectiveofthissub-investigationwastoexploretheapplicabilityofcurvefeatures fromPPsandCRPDstodescribegaitpatternswithvariousdegreesofcoordinationimpairment. Usingstepwiseregressionmodelstoidentifysignicantswingperiodcoordinationevents,theCPS wasconstructedfromcurvefeaturesfromsagittalplanePPsforthepelvis,thigh,shank,andfoot andCPRDsforthepelvis-thigh,thigh-shank,shank-foot,andthigh-footsegmentpairings.The specicaimsofthissub-investigationasto1)determineifsignicantcoordinationeventsexisted duringtheswingperiodofgait,2)generateacoordinationindexfromthesesignicanteventsfor threedi erentgaitpatterns,and3)determineifthesesignicanteventscouldbeusedtocreate regressionmodelscapableofdistinguishingdi erentgaitpatterns. Deciphering the Signicant Coordination Events. AspresentedinChapter5,abackward stepwiseregressionmodelwasusedtoidentifysixsignicantcoordinationeventsduringtheswing periodofgait.WhilemoredetailisprovidedinChapter3aboutvariouscurvefeaturesofPPs andCRPDs,abriefreviewofthesecurvefeaturesisprovidedhereforconvenience.Extremaof aPP'sabscissaandordinatemeasuresassistinidentifyinganindividualsegment'spositionand velocityatanyinstantinthegaitcycleandprovideinsightsintohowonesegment'soscillationsare contributingtotheorientationoftheentirelimb.ACRPDzerocrossingindicatesthetwosegments aremovingin-phasewitheachother[7],whereasanextremumindicatestheinstantwhenthetwo segmentsaremostout-of-phasewitheachother[7].ACPRDinectionpointcorrespondstowhen therelationshipbetweenthetwosegmentshasreversedandthusistheinstantwhenmusclesynergies arechanging(e.g.exiontoextension).Bycomparingthetimingandpotentialabsenceofthese signicantcoordinationeventsfromatypicalgaitpatternstoanunimpairedreference,thesecurve featureso erameansforidentifyingtheexacttimingduringthegaitcyclewhensegment(s)are contributingtoanaberrantcoordinationbehaviorandspecifyingwhichsegmentsarecontributing toanimpairedgaitpattern. Usingtheaforementionedcurvefeaturedenitions,thefollowingparagraphso eraninterpretationofthesixsignicantcoordinationeventswithrespecttoanunimpairedgaitpattern.The thigh-footCRPD'sabsoluteminimumcorrespondstothedissociationoftheextensionsynergyat footo andtheabilitytocorrectlytimethisessentialmotorcontroleventisimperativeforthe initiationofswingperiodandsuccessfulswinglimbadvancement[16].Theabilitytoprovidesuf173

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cientforwardmomentumofthelegsegmentsatfooto andforwardpendularmotionoftheleg iscapturedinpartbythetimingofthemaximumangularvelocityofthethigh'sPP.ThemagnitudesofthemaximumandminimumangulardisplacementsofthepelvisPPcorrespondtothe anterior/posteriorpelvicrangeofmotionnecessaryforuninhibitedforwardrotationofthethigh. Thefoot'smaximumangulardisplacement,withrespecttotheglobalhorizontal,indicatesthefoot's maximumverticalorientation,whichcorrespondstothetimingoffootclearanceinswingbyactive dorsiexion.Thelastinectionpointofthethigh-footCRPDcorrespondstotheinstantwhenthe thighandfootrelationshipreversesinpreparationforfootstrikeandanticipationofloadingresponse.Thesesignicantcoordinationeventsalsosuggestswingperiodcoordinationisconstrained bythefoot'soscillationtowarddorsiexionasitbeginstoleadthethigh'soscillation.Thetimingof thesixcoordinationeventswascomparedtotheunimpairedcohort'smeantimingofPerry'scritical gaitevents[9]andfoundtonotcoincidewiththeseothergaitevents. Theimportanceofthetimingandmagnitudeofthesesignicantcoordinationeventsisdemonstratedbytheunimpairedcohort'snarrowstandarddeviationandtheconvergenceofeventsfor bothindividualsegmentsandalsononadjacentsegments.Byidentifyingcoordinationeventsinthe swingperiodofgaitforacohortoftypicalsubjects,thesendingsprovideameanstoenhancethe understandingoffeed-forwardmotorcontrolstrategiesemployedinatypicalgaitpatternandthus o erareferenceforsubjectswithatypicalcoordinationresultinginimpairedswinglimbadvancement.Thesmallstandarddeviationsandnarrowcondenceintervalsoftheunimpairedcohort's coordinationeventsalsosuggestthatalthougheachunimpairedindividualhasuniqueswingperiod coordination,anindividual'sspatio-temporalsolutionoftheavailabledegreesoffreedomconverges uponsharedcoordinationrequirements[1,4,5,17].Althoughtheexistenceofthesesixcoordination eventsindicatethereareinstancesinanormalgaitpatternthatsharecommonpointsinthesolutionofswinglimbadvancement,anindividual'sdesiredvariabilityispreservedasillustratedbythe variouscurvepatternsandtrajectoriesbetweenthesecoordinationevents.Weproposethatthese underlying,fundamentalcoordinationeventsdescribeinstancesofapreferredstateofthemotor controlsystemandasareference,havethepotentialtoilluminatewhenandhowimpairedswing limbadvancementismanifestinginagaitpattern. SinceindividualswithCPareknowntohavereducedwalkingspeeds[16,26,29,69]anddelayed orabsentcriticalgaiteventsduringswingperiod[16,26,29,69],thenitisperhapsofnogreatsurprise thatthetimingandmagnitudeofthesesignicantcoordinationeventswasdelayedandattenuated forthesesubjects(Figure5.3.10 ) .However,priortothisinvestigationtheunderlyingmechanisms contributingtotheinabilitytoachievecertainswingperiodgaitevents,asoftencharacterizedby 174

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reducedrangeofmotioninjointanglesanddecreasedtemporal-spatialvariables,hadnotbeen identiedatthesegmentlevelornon-adjacentinter-segmentalperspective. Assessment of the Coordination Performance Score. AsshowninFigure5.3.12,relative totheunimpairedsubjectgroup,theCPSvaluesarereducedinthegeneralcohortwithCPand therespectivesubdivisions(sti kneegait,crouch).Therewerestatisticallysignicantdi erences betweenallCPgroupmeanCPSvaluescomparedtotheunimpairedsubjects'meanCPS.These ndingssupportthattheCPSiscapableofdistinguishingbetweenthecoordinationdynamicsof subjectswithandwithoutagaitimpairmentassociatedwithaberrantcoordination. AsshownindatapresentedinChapter5,relativetotheunimpairedsubjectgroup,theCPS valuesarereducedinthegeneralcohortwithCPandtherespectivesubdivisions(sti kneegait, crouch).Therewerestatisticallysignicantdi erencesbetweenallCPgroupmeanCPSvalues comparedtotheunimpairedsubjects'meanCPS.ThesendingssupportthattheCPSiscapableof distinguishingbetweenthecoordinationdynamicsofsubjectswithandwithoutagaitimpairment associatedwithaberrantcoordination.BoththeCDIandCPSwerecreatedfrommeasuresmore suitableforcharacterizingmotorcontrolmechanismsthatcontributetowalkingandthereforemay bemoremeaningfulandappropriatemetricsforstudyingthegaitpatternsofindividualswith aberrantcoordination.OneadvantageoftheCPSovertheCDIisthetechniquesusedtocreatethis index.Bycreatinganindexfromsignicantcoordinationcurvefeatures,therequirementforalarge numberofnormativereferencesubjectsbyfeatureanalysismethodsisremoved.Additionally,this approachtocreatingacoordinationindexallowsfortheeasyexpansionofsignicantcoordination eventsduringstanceandotherplanesofmotionwithoutcreatingacumbersomeincreaseindata necessaryforcalculatingtheindexorgeneratingitsnormativereference. Regression Models for Distinguishing Coordination of Di erent Gait Patterns. While bothqualitative[10,15]andquantitative[16,17]classicationsforvariousgaitpatternsexistusing conventionalinstrumentedgaitanalysismeasures,analgorithmcreatedfrommeasuresofcoordinationwouldprovideclinicallymeaningfulinformationthatmayassistcliniciansandresearchers studyingthegaitofthosewithimpairedmotorcontrol.Anindexandgaitclassicationmodel constructedfromtheselow-dimensionalmeasuresofcoordinationarefreeoflinearassumptions foundinotherquantitativegaitclassicationtechniques(e.g.principalcomponentanalysis,supportvectormechanics,clusteranalysis),whennormalizedtothegaitcycleareeasilyrelatedtoother gaitevents,donotrequirealargereferencenormativedatasetlikeothertechniques,consolidatea segment'sspatio-temporaloscillatorybehavior,andrepresenttheprogressionofthelimitcycle's trajectorythroughoutthegaitcycle.Thehighareaunderthecurve(AUC)valuefortheunim175

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pairedvs.impairedregressionmodel'sreceiveroperatorcharacteristic(ROC)curveindicatesthe model'soutstandingabilitytodistinguishbetweenthesetwogeneralgaitpatterncategories.The moderateAUCvalueforthesti kneegaitvs.crouchgaitmodel'sROCcurveindicatesthismodel hasmoderateabilitytodistinguishbetweenthesetwogaitpatternsusingonlytwoswingperiod coordinationevents.Sincethegaitpatternofthosewithcerebralpalsyisoftenamixofseveral patterns(e.g.sti kneegait,crouch),theincorporationofothercoordinationeventsoccurringin stanceperiodandotherplanesofmotionmayincreasetheAUCvalueforthisregressionmodeland improveitsabilitytodistinguishbetweenthesetwopathologicalgaitpatterns.Anotherbenetof usingregressionmodelstodistinguishbetweengaitpatternsisthattheregressionequationandlogit canberearrangedtosolvefortheprobabilityanindividualhasoneofthegaitpatternsconsidered. Example Applications of the CPS. TheCPSmaybeavaluableresearchtoolbecauseit providesadeeperlevelofunderstandingabouttheunderlyingmechanismsassociatedwiththe organizationofsegmentoscillationsduringswinglimbadvancementinaconcisescalarvalue.These ndingsfurtherdemonstratethatPPsandCRPDsarecapableofcharacterizingthebehaviorof coordinationingait,describevaryingdegreesofgaitperformanceinsubjectswithneurological impairments,andsupporttheuseofthesemeasuresforsubjectswithatypicalcoordinationthat contributestoanoverallaberrantgaitpattern.Whileexaminationofasubject'sPPsandCPRDs providerichinsightsintoanindividuals'coordinationdynamics,calculationofasubject'sCPS throughoutaninterventionmayalsoprovideanindexforquantitativelytrackingtheprogressionof coordinationchangesresultingfromtheintervention,astheGDIisoftenusedfordescribingchanges injointangles. Sincemostgaitdeviationsforsubjectswithcerebralpalsy,presentinthesagittalplane[10,14], wefeltthiswasanappropriateplaneofmotiontoinvestigaterst.Thesixcoordinationevents presentedarebynomeansanexhaustivelistofsignicantcoordinationeventsandwepostulate thatdi erentpathologicalgaitpatternsmaybelinkedtocoordinationeventsinotherplanesof motionandothersegmentpairings.Identicationofothersignicantcoordinationeventscould thenbeusedtogeneratenewregressionmodelsfordistinguishingbetweenothergaitpatternsof interest.Forexample,pelvis-footCRPDcoordinationeventsinthetransverseplanemayproveto bemoreimportantfordistinguishingwhetherasubjecthasatrueorapparentequinusgaitpattern. Furtherworkisneededtodetermineclinicallymeaningfulthresholdsfortheprobabilityasubject's gaitpatternisoneofthoseconsideredinthenominalregressionmodel.Hopefully,theversatility ofthesenonlinearmeasuresandthemethodspresentedhereinspireotherinvestigationsofdi erent gaitpatterns,whichwouldsimplyrequiredi erentcombinationsofPPsandCRPDs,portionsof 176

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thegaitcycle,andplanesofmotion. 6.2.4.3MissingCoordinationEventsbyGaitPattern Theidenticationofmissingcoordinationeventsbygaitpatternwasconductedtodemonstrate theutilityoftheproposedmeasuresofcoordinationdynamics,theirabilitytoanalyzemotioncapture dataatadi erentlevel,andidentifythespecicposition,speed,andinter-segmentalcoordination dynamicsthatunderlieagaitpattern.InadditiontoaddressingAim4,byrelatingthesendingsto knowcharacteristicsofaparticulargaitpatternthefollowingsectionsprovideclinicallymeaningful examplesofhowthesemeasuresofcoordinationdynamicsandtheircurvefeatureselucidatethe underlyingmechanismscontributingtoanoverallpatternofgait.RecallTable5.3.8providesalist ofthemissingcoordinationevents,indicationofwhichgeneralsubjectgroupsaremissingeachof thesecoordinationevents,andadescriptionofthecurvefeature.Aswillberevealedinthediscussion below,onecoordinationeventwasconsistentlymissinginthetwoclinicalpopulationsconsidered: rstzero-crossingaftertheswingperiodmaximumonthethigh-shankCRPD.Theimplicationsof notachievingthiscoordinationeventarediscussedbelowinthecontextofeachsubjectsub-category. Giventheprevalenceofthismissingcoordinationevent,furtherinvestigationintoitsimportance andperhapsweightinrelationtootherSLAcoordinationeventsiswarrantedandwouldperhaps revealanorderinwhichcoordinationeventsareremovedfromagaitpatternastheseverityof impairmentincreases. Unimpaired Gait Pattern. Ofthe140unimpairedsubjects,only9ofthemweremissing threecoordinationeventsduringtheswingperiodofgait.AsdetailedinChapter5,twoofthese coordinationeventswerezero-crossings.Whilethesefewsubjectsweremissingthesecoordination events,theirCRPDcurveswerethesameshapeastheothersinthiscohort.Thereasontheydid nothavethesetwocoordinationeventswasbecausetheirCRPDswereshiftedupwardabovethe zerodegreephaseangleline;noticethestandarddeviationbandsinFigure5.2.1.Additionally,the timingoftheinectionpointonthepelvis-thighCRPDforthesesubjectsoccurredbeforeopposite footstrike.So,whilethiscurvefeaturedoesexist,thecoordinationeventoccurredearlierinthe gaitcyclethanthedenitionofthisevent.ByreferringtoFigure5.2.1,thestandarddeviationband onpelvis-thighCRPDinpre-swing,wherethisinectionpointoccurs,isoneofthemorevariable instancesinthegaitcycleforthisCRPD.Eventhoughthesecurvefeaturesmaynothaveoccurred (zero-crossing)oroccurredoutsidethedeningtemporallimits(inectionpoint),thisvariabilityis stillwithinonestandarddeviation,thecurveshapesarethesameastheotherunimpairedsubjects, andthisshowsthatthegeneralinter-segmentalrelationshipsexistforalltheunimpairedsubjects 177

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whilemaintainingtheuniquevariabilityofnormalgait. Subjects with Cerebral Palsy. Overseventy-sixpercentofthesubjectswithCPweremissing atleastonecoordinationeventduringtheswingperiodofgait.Thisndingfurthersupportsthat theproposedmeasuresofcoordinationingaitareabletodistinguishbetweenvariousgaitpatterns (Aim4).Uponacloserlookatthesemissingcoordinationevents,severaltrendswereidentiedfor thisgeneralcohort.Whenorganizingthesubjectswithcerebralpalsybygaitpattern(SKG,C)and topographically,over70%ofthesubjectsweremissingatleastonecoordinationevent(Figure5.3.15). Thisndingprovidesanotherexampledemonstratinghowtheseproposedmeasuresofcoordination areabletodetectvaryingdegreesofcoordinationimpairmentinsubjectsknowntohaveaberrant coordinationasaresultoftheirpathology(Aim4).Perhapsmostinterestingofallforthisgeneral cohort,isthatover60%ofsubjectswithCPweremissingthelastzero-crossingonthethigh-shank CRPD.RecallingthedescriptionofCRPDcurvefeaturesandthesegmentalbehaviortheycapture (Chapter3),thiscoordinationeventcapturestheinstantinthegaitcyclewhenthethighandshank aremovingin-phasewitheachother(e.g.phaseangleschangeatthesamerate),correspondstothe zero-crossingafterthemaximuminswing,andoccurswithinthelastfewpercentagesofthegait cycleforunimpairedsubjects.Itisproposedthatthiscoordinationeventcapturestheorientation ofthesegmentsinanticipationoffootstrikeandloadingresponse.AsdiscussedinChapter2, subjectswithCPareoften"playingcatchup"duringswingbecausespasticityinhibitstheideal segmentorientationsanddelays(orprevents)theoccurrenceofcriticalgaitandtemporalevents. Thedelayedtimingofprecursorgaiteventsleadinguptoswingcontinuetobecomecompounded asthesesubjectsprogressthroughswinglimbadvancementandintoterminalswing,whenthis coordinationeventshouldoccur.Whenrecallingtheseswinglimbadvancementcharacteristicsfor thesesubjects,itmakessensethatthiscoordinationeventdoesnotoccurinmostofthesubjects becausethiscohortisstrugglingwithpositioningthethighandshankinanorientationoptimalfor footstrikeandinthetighttemporalconstraintsattheendofterminalswing. Hemiplegia. ReferringtoFigure5.3.16,itisinterestingthatnoneofthesubjectswitha hemiplegiaclassication(onesidea ected)struggledwithachievingtherstzero-crossinginswing onthepelvis-thighCRPD,therstzero-crossingaftertheabsolutemaximuminswingonthe pelvis-thighCPRD,ortherstzero-crossingafterfooto onthethigh-shankCRPD.However,a considerablepercentageofthesubjectswithadiplegiaclassication(bothlimbsarea ected)were unabletoachievethiscoordinationevent.Whilethegaitpatternofsubjectswithahemiplegia classicationmaybelessimpairedthansomesubjectswithadiplegiaclassication,perhapsthis patternisrevealingthecoordinationimplicationsonbothlimbswhenbilaterallya ectedandis 178

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characterizingthea ectsonacontralaterallimb'sabilitytoachievecertaincoordinationevents whenbothlimbsarea ectedbyimpairedmotorcontrol.Itisalsoworthnotingthatofthesubjects withhemiplegicgaitwhoweremissingacoordinationevent,nearly80%ofthemwereunableto achievetherstzero-crossingafterthemaximuminswingonthethigh-shankCRPD.Asdiscussed above,thisterminalswingcoordinationeventiscrucialforproperlimborientationintimefor footstrikeandloadingresponse.Theidenticationofthistrendandspeciccoordinationevent demonstratesthevaluableinsightsintotheunderlyingmechanismsthatarecontributingtoand inhibitingsubjectswithahemiplegicgaitpatternfromachievinganormalgaitpatternandits compoundinga ectsonthebeginningofthenextgaitcycle. Diplegia. Ofthemissingcoordinationeventsfortheindividualswithadiplegicgaitpattern, thesesubjectswereabletoachievethelastzero-crossinginswingontheshank-footCRPD.It proposedthatthisterminalswingzero-crossingcapturesthepositioning(slightdorsiexion)ofthe footwithrespecttotheshankinanticipationoforinanattempttoachieveaheelrstinitialcontact. Byachievingthiscoordinationevent,thesesubjectswereabletocoupletheshankandfootandthen potentiallydorsiexion,dependingupontheirnalCRPDvalues(e.g.positiverelativephase)after thiscurvefeature.Thisndingmayatrstbemisleadingandseemtoindicatethatthissub-group hadlessimpairedmotorcontrola ectingtheanklejoint.However,whilethissub-groupwasable toachievethiscoordinationevent,sowheretheindividualswithacrouchgaitpattern.Recalling thedescriptionofcrouchgaitinChapter2,thesesubjectsoftenhaveincreasedankledorsiexion interminalswingasaresultofexcessivehipandkneeexion.Uponfurtherexaminationofthis sub-groupitwasfoundthat92%ofthesubjectswithadiplegicgaitpatternalsohadacrouchgait pattern.Therefore,itisproposedthattheachievementofthiscoordinationeventisratheraresult ofthesegmentsorientationduetocrouchgaitandfortheremaining3subjectswithdiplegiaitis proposedthattheseindividualsmayhaveacombinationofcrouchandsti kneegaitand/ortheir shankandfootarecoupled(in-phase)asaresultofcompensatorymechanisms(e.g.hiphikeor circumductionwithxed/excessivedorsiexion)forlimbadvancementandfootclearance.Sincethe segmentPPsarecreatedwithrespecttotheglobalhorizontal,suchacompensatorygaitmechanism couldresultinaphaseanglethatcapturesthefoot'sglobalorientationasitiscoupledwiththe shankandcausetherelativephaseanglefromthesetwosegmentstobezero.Furtherexaminationof thistrendforthosewithadiplegicgaitpattern,againdemonstratestheabilityofthesemeasuresto capturethecomplexandoftensubtleinter-segmentalcoordinationdynamicsandtheinherentease atwhichthesemeasuresquantifysuchgaitbehaviorsthataremoretypicallyclinicallyqualied. Sti Knee Gait Pattern. Aspreviouslymentioned,thesubjectswithcerebralpalsywere 179

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organizedintofoursub-categories:hemiplegia,diplegia,sti kneegait,andcrouchgait.Thesubjects withasti kneegaitpatternweretheonlysub-categoryofsubjectswithCPthatwasmissingall tencoordinationevents(Table5.3.8).Itisproposedthatthecompensatorymechanismsthese subjectsusedforlimbadvancementandfootclearancecontributestotheinabilitytoachievethese coordinationevents.Itisalsoimportanttorestatethatindividualswithasti kneegaitpattern mayalsohaveelementsofacrouchgaitpatternandthereforestrugglewithcoordinationevents thatfallintobothgaitpatterns.Asmentionedabove,thea ectsoftheimpairedmotorcontrol inindividualswithasti kneegaitpatterniscompoundedthroughoutthegaitcycle,whichis especiallyevidentinthissub-groupandtheirinabilitytoachievethethreecoordinationeventsof thethigh-footCRPDinterminalswing.AsdiscussedinAppendixF,theremainingcriticalgait eventinterminalswingistocontinuethependularkneeextensionfrommid-swinginorderto preparethelimbforfootcontactandweightacceptanceduringtheupcominginitialdoublesupport. Thisidealterminalswingbehavioriscapturedonthethigh-shankCRPDasthelastmaximumin swing,followedbyaninectionpointandzero-crossingandonthethigh-footCRPDbytwolocal extremaandazero-crossing.Theinabilitytouncoupleandcouplethethigh,shank,andfoot(often duetocompensatorymeasures)segmentsattheidealtimesthroughoutswinglimbadvancementis thehallmarkcharacteristicofasti kneegaitpattern.ThesemissingCRPDcurvefeaturesnotonly quantifythesesti kneegaitcharacteristicsinalowdimensionaldescriptorbutalsoquantifythe inter-segmentalcoordinationstrategiesofadjacentandnon-adjacentsegmentpairingsandallowone toexaminehowindividualsegmentpositionsandvelocitiescontributestotheoverallgaitpattern. Crouch Gait Pattern. Thesubjectswithacrouchgaitpatternwereunabletoachievenineof thetencoordinationeventsthatweremissinginsubjectswithcerebralpalsy.Asdiscussedabove, thissub-groupofsubjectswereabletoachievelastzero-crossinginterminalswingontheshankfootCRPD.Itwasproposedthatthesesubjects'CRPDscontainedthiscurvefeatureasaresultof theorientationoftheirsegments(e.g.hipexion,kneeexion,ankledorsiexion),compensatory limbadvancementmechanisms,andmethodsforcalculatingPPs(e.g.withrespecttotheglobal horizontal).Itisproposedthatinsteadofthisndingindicatingthesubjectshadsu cientdegrees offreedomavailableandtheabilitytoexecutethisnerdegreeofmotorcontrol,thiscoordination eventisactuallycapturingtheorientationoflimbsegmentsasaresultofcompensatorymechanisms. Thisndingisanexcellentexampleofunderstandinghowmeasuresofgaitareconstructedandthe elementofgaittheyaredesignedtoquantify.Aswithanymeasureofinstrumentedgaitanalysis,it isimportanttoconsiderthemethodforconstructingthemeasuresandthesubject'sgaitpattern, compensatorymechanismsthatmightprovidepotentiallymisleadingconclusions,andthesubject's 180

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abilitytoachievevariouscriticalelementsofgait. Subjects with a Lower Limb Amputation. Itisworthnotingthatunlikethesubjectswith CP,whooftenhadoverlappinggaitpatterns(e.g.SKGandC),noneofthesubjectswithalowerlimb amputationhadacombinationofbothamputationlevelsconsidered.Therefore,thefollowingtrends observedforthesetwolevelsofamputationapplyexclusivelytotherespectivegroupunlessotherwise indicated.Comparedtothesubjectswithcerebralpalsy,lessthan40%ofsubjectswithalowerlimb amputationthatweremissingatleastonecoordinationevent.Thisisconsistentwiththeexpectation thatbecausethesubjectswithalowerlimbamputationdidnothaveanyneurologicalpathology theyhavemoredegreesoffreedom,areabletoadapttotheinertialpropertiesoftheprosthesisand residuallimb'sremaininglevelsofneurologicalcontrol,andopportunitiestoexecuteamotorplan thatmorecloselyresemblesanunimpairedgaitpattern.Thisgeneralcohorttrendprovidesanother instancedemonstratingtheseproposedmeasuresofcoordinationareabletodistinguishbetween varyinglevelsofcoordination,asisthecaseforthetwoclinicalpopulationsstudiedinthisbodyof work.Ingeneral,thiscohortwasmissingthreecoordinationevents:1)therstzero-crossingafter theswingperiodabsolutemaximumonthepelvis-thighCRPD,2)therstzero-crossingafterthe swingperiodmaximumonthethigh-shankCRPD,and3)thelastzero-crossinginswingperiod ontheshank-footCRPD.Thesedi erencesintheabilitytoachievetheswingperiodcoordination eventsbetweenthesubjectswithaLLAandunimpairedsubjectsisconsistentwithndingsusing conventionalIGAmeasuresreportedintheliterature(Chapter2).Similartotheirconventional IGAcounterparts,theproposedmeasuresofcoordinationareabletodistinguishbetweenvarious gaitpatterns(Aim4). Subjects with Unilateral Lower Limb Amputation. AspreviouslymentionedinChapter 4,thesubjectswithalowerlimbamputationwereorganizedintofoursub-categories:belowknee amputation(a.k.a.transtibial),aboveknee(a.k.a.transfemoral)amputation,unilateralamputation, andbilateralamputations.OfthethreegeneralmissingcoordinationeventsforsubjectswithaLLL, allofthesubjectswithaunilateralLLAwereabletoachievethelastzero-crossinginswingperiodon theshank-footCRPD.Sincetheintactlimbprovidesbetterdynamicstabilityandbalanceforthese subjects,asopposedtothosewithabilateralLLA,itisproposedthattheyareabletorelyuponthis dynamicstabilitytoprovideabetterbaseofsupportandrequirelesstrunkandothercompensatory motions,whichallowsthemtooptimizetheswinglimbadvancementofprostheticandresiduallimb. WhilethesebehavioralcharacteristicsandmotionsofanindividualwithaLLAareknownclinical qualications,thisis,tothebestoftheinvestigator'sknowledge,therstinvestigationusingthese measuresofinter-segmentalcoordinationtoquantifythesebehaviorsandpin-pointthetimingand 181

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magnitudeoftheserelationshipsinthecontextofthegaitcycle. Subjects with Bilateral Lower Limb Amputations. OfthesubjectswithaLLAthatwere missingacoordinationevent,all(100%)ofthesubjectswithabilateralamputationweremissing atleastonecoordinationevent.Additionally,allofthesubjectsinthissub-categorywereunable toachievetherstzero-crossingaftertheswingperiodmaximumonthethigh-shankCRPD.The interpretationofthiscurvefeatureanditsrelationshipandimportancetothetaskofswinglimb advancementhasbeendiscussedintheprevioussectionsofthisinvestigation.Sincebothlimbsare a ectedbytheamputationinthissub-group,thesesubjectsmustrelyuponmorecompensatory motions(e.g.increasedtrunkinvolvement)towalkandachieveswinglimbadvancementcompared tothosesubjectswithaunilateralLLA.Onereasonallofthesubjectsthissub-groupwhowere missingthiscoordinationisthatinadditiontothealteredswinglimb,thecontralaterallimb's impairedstrength,dynamicstability,andposturalcontrolmaybeinuencingtheswinginglimb. Thisndingwarrantsfurtherinvestigationintothepotentialcoordinationa ectsofcontralateral limbsandproximalsegments(e.g.trunk,armswing).Also,thepassiveordynamic(e.g.CLeg ¨ )propertiesofaprosthesisthatdictatethemotionbetweentheprostheticthighandprosthetic shanksectionsmaypreventsubjectsfromachievingtheinter-segmentalrelationship.Thisnding illustrateshowthesemeasurescanbecombinewithconventionalIGAmeasuresando erinsights intothecoordinationdynamicsofagaitpatternthatcouldbeusedtoenhanceorreneaprosthetic's parametersandjointpropertiesandthusimprovethewearer'soverallgait. Transtibial Amputation Gait Pattern. Allofthesubjectswithatranstibialamputation whoweremissingacoordinationevent(53.85%)wereunabletoachievethreecoordinationevents: 1)therstzero-crossingaftertheswingperiodabsolutemaximumonthepelvis-thighCRPD,2) therstzero-crossingaftertheswingperiodmaximumonthethigh-shankCRPD,and3)thelast zero-crossinginswingperiodontheshank-footCRPD.Inanunimpairedgaitpattern,therst zero-crossingaftertheswingperiod'sabsolutemaximumonthepelvis-thighCRPDindicatesthe phaseanglesforthepelvisandthigharechangingatthesamerateandarethusin-phasewitheach other.Sincesubjectswithatranstibialamputationnolongerhavetheuseofthegastrocnemiussoleusmuscles,theyrelyheavilyuponthehipexorstoprovidesu cientpowergenerationforSLA (Chapter2).Itisproposedthattheinabilityoftoachievethispelvis-thighCRPDcoordinationevent reectsthealteredhipcoordinationstrategiesadoptedbytheseindividualsinordertoadvancethe swinginglimb.Thisndingdemonstrateshowtheseproposedmeasuresofcoordinationdynamics identifyspeciccompensatorycoordinationstrategiesadoptedbythesesubjectsinordertoadvance theswinginglimb.Providingclinicianswiththisspecicandmoredetailedinformationabout 182

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segment-prosthesisbehaviorsandinteractionshasthepotentialtoinformclinicaldecisions,dynamic prostheticalignment,andinterventionsthatmaycorrectsuboptimalcompensatorycoordination strategies(refertotranstibialamputationcasestudy).Theinabilityofsubjectswithatranstibial amputationtoachievetherstzero-crossingaftertheswingperiodmaximumonthethigh-shank CRPDidentiesoneinstanceinthegaitcyclewhenthethighandprosthetic'sinter-segmental behaviordeviatesfromanunimpairedgaitpattern.Infact,ensuringaprosthesishasanappropriate amountofkneeexionforindividualswithatranstibialamputationisoneofthemostdi cultand challengingaspectsofthedynamicalignmentprocess.ByusingtheseCRPDcurvefeaturesto identifythespatialandtemporalpatternsoftheresiduallimbandprosthetic,thereisthepotential toimproveasubject'sdynamicalignmentprocessandreduceundesirablecompensatorymotions andthepainthatoftenaccompaniessuchmotions. Transfemoral Amputation Gait Pattern. Thesubjectswithanamputationatorabovethe kneejointwereabletoachievetwoofthethreecoordinationeventsinthisgeneralcohort(LLA).A littlemorethan30%ofthesesubjectswerehowever,unabletoachievetherstzero-crossingafter theswingperiodmaximumonthethigh-shankCRPD.Whileonemightbeinclinedtoexpectthat thesubjectswithatransfemoralamputationmaynotbeabletoachievemorecoordinationevents thanthesubjectswithatranstibialamputation,therearenumerousotherfactorsthatcontribute toanindividual'sfunctionallevelandoverallgaitpattern(e.g.prosthetictype,residuallimb proprioception,pain,prostheticalignment,overallhealth,strength,etc.).Inthecontextofand limitsofthisinitialsub-investigation,itisdi culttodeterminehowthepropertiesandparameters ofdi erentprosthetics(e.g.passive,dynamic,jointmechanisms)inuenceasubject'scoordination dynamicsandoverallgaitpattern.However,itisinterestingthatthisthigh-shankcoordination eventissodi cultforthesesubjectstoachieveandperhapsafterfutureinvestigations,thisinsight couldbeusedinformtheprostheticalignment.Additionally,usingsuchcoordinationcurvefeatures toidentifyspecicinstancesandsegmentdynamicsthataremissingfromanindividual'sgaithasthe potentialtoinformprostheticdesign,whichmaybealteredinordertoreducethepotentialinuence oftheprostheticonnotachievingsuchcoordinationevents.Theinabilitytoachievethiscoordination eventmayalsobeacharacteristicofindividualswithatransfemoralamputation.Sinceonlysix retrospectivesubjectswereavailableforthiscohort,futureinvestigationswithalargersamplesize mayshedlightonthistrendandwhatinuencessubjectcharacteristics,prostheticparameters,and functionallevelmaybecorrelatedwiththeinabilitytoachievethiscoordinationevent. 183

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6.2.4.4Hypothesis4A UsingthemeanscaledCPSandmeanCDIforeachsubjectcohorttocharacterizethecoordinationdynamicsofsubjectswithanormal,sti knee,crouch,andmechanicallyalteredgaitpatterns, hypothesis4Awassupportedbytheseanalyses.Bothoftheseindicesquantitativelyshowedthere wasastatisticallysignicantdi erence(p 0.05)betweenthesevariousgaitpatterns.Thisisfurther supportedbythequalitativedi erencesthatarevisuallyevidentineachcohort'ssetofmeanPPs andCRPDs,providedinChapter4andAppendixG. 6.3AdditionalInvestigations 6.3.1ExploratoryInvestigationtoIdentifySignicantCoordinationEvents Itisworthnotingthatalthoughtwodi erentapproachesweretakentoidentifysignicantcoordinationeventsduringtheswingperiodofgait,therewasonecommoncoordinationeventdetected bybothapproaches:thelastinectionpointonthethigh-footCRPD.Itisproposedthatthis thigh-footCRPDinectionpointcapturesthehamstringringandresultingslightkneeexionthat positionsthelimbsegmentsinanticipationofheelrstinitialcontactandtheupcomingtaskof loadingresponse.Sincethisthigh-footCRPDcurvefeatureisasubtleyetcriticalaspectofswing limbadvancement,itisperhapsofnogreatsurprisethatthesemeasuresofcoordinationanddifferentinvestigationsaggedthiseventasanimportant,salientcoordinationevent.Asdiscussed previouslyinthischapterandinChapter2,thecriticalandtemporalgaiteventsduringswingare typicallydelayedforsubjectswithcerebralpalsyandthosewithalowerlimbamputation.Consideringthetemporaldelayinthiscoordinationeventforthesesubjectsitalsomakessensethatthis coordinationeventwasidentiedasaneventfordistinguishingbetweenthecoordinationdynamics ofsubjectsfreeofgaitpathologyandthosewithimpairedswinglimbadvancement.Findingsfrom thepre-doctoralinvestigationintochangesincoordinationandfunctionaloutcomesafterarectus femoristransferprocedureinchildrenwithspasticCPrevealedthatpreandpost-surgerychanges inthiscoordinationeventweresignicant.Whileelaborationuponthispre-doctoralinvestigation isnotwithinthescopeofthisdocument,itisworthnotingthecontinuedimportantofthiscoordinationeventfromnumerousinvestigations.Futureinvestigationsintothiscoordinationeventare warrantedandmayrevealthiscoordinationeventasausefulmarkerforchangesincertaingaitpatternsafteraparticularintervention.Coordinationeventsidentiedassignicantfromthevarious exploratoryinvestigationsconductedinthisbodyofwork,especiallythethigh-footCRPDinection 184

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point,arenotdenitive.However,itisproposedthatthesignicanceofcertaincoordinationevents willbedi erentfordi erentgaitimpairments,soitmaybemoreclinicallymeaningfultoorganize andanalyzecoordinationeventsbygaitimpairment,asdiscussedinsection6.2.4.3above. 6.3.2TranstibialAmputationCaseStudy Itwasproposedthatinane orttomaintainanormativegaitpattern,anindividualwitha lowerlimbamputationwhoisfreeofneurologicalimpairmentswouldadoptdistinctlydi erent coordinationpatterns,asquantiedbyPPsandCRPDs,dependingupontheprostheticlimb's alignment.Thiscasestudyshowedthatincorporatingmeasuresofcoordinationdynamicswith conventionalIGAmeasurestostudythegaitpatternofanindividualwithatranstibialamputation o ersclinicalinsightsintothepatient'sgaitpatternthatwereotherwiseundetectedbytraditional IGAmeasures. Althoughthereisnotastrikingdi erencebetweenthealignmentsusingconventionalinstrumentedgaitanalysismeasures,thereareconsiderabledi erencesdetectedbythenonlinearmeasures,especiallyfortheangularvelocityoftheshankandthethigh-shankrelativephasediagram. Thenormalreferencesubject'srootmeansquareerror(RMSE)valuesdemonstratethatthepatient'slargerRMSEsdetectedbythenonlinearmeasuresisnotdueanincreasedsensitivityofthese nonlinearmeasuresnorthenaturalstride-to-stridevariabilityinherentinnormalgait.Thepurposeofusingtheun-normalizedRMSEmeasurewastoexaminedi erencesbetweenthesubject's alignmentconditionsandnottoquantitativelycompareanydi erences.AsexplainedinChapter3, PPsandCRPDso eranalternativelevelofanalysisofmarkertrajectorydataandthesenonlinear methodsinherentlymeasuredi erentaspectsofgaitthansuchconventionalmethodsaskinematics andkinetics.TheapplicationofRMSEvaluesquantitativelysupporttheinvestigation'sproposal thatPPsandCRPDsmeasureadi erentelementofinstrumentedgaitanalysisdataandthuscan o eranalternativemeanstostudyingtheunderlyingcoordinationdynamicsthatcontributetoan individual'sgaitpattern,asmeasuredbykinematicsandkinetics. Traditionalinstrumentedgaitanalysismeasuresdidnotsupportchangingthealignmentofthe prosthesis.X-raymeasurementssupporttherecommendationtomovetheprostheticfootmedially toachieveamoreoptimalmechanicalaxisintheleftleg.Physicaltherapywasalsorecommended tohelpthepatientmeettheincreasedstrengthandendurancedemandsoftheproposedprosthesis alignmentchange. Unliketheconventionalinstrumentedgaitanalysismeasures,theRMSEsofnonlinearmeasures revealedconsiderabledi erencesbetweenthethreeprostheticalignmentconditionsstudied.Itis 185

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proposedthatthesenonlinearmeasuresaredetectingthepatient'sabilitytoemulateatypicalgait pattern,fromtheperspectiveoftraditionalinstrumentedgaitanalysismeasures,byadoptingdi erentcoordinationstrategiesforeachalignmentcondition.Specically,thesubjectadoptedadi erent coordinationstrategybymodifyingthea ectedthigh'sangulardisplacementandvelocitythroughoutthegaitcycle.Thisclinicalexampledemonstrateshowexaminingthebehaviorofanindividual segmentusingPPsprovidesameanstoidentifythelociofimpairment(s)inagaitpatternand o ersinsightsintotheorganizationofindividualsegmentsthatmayotherwisebeundetectablewith conventionalinstrumentedgaitanalysismeasures.Furtherinvestigationisneededtodetermineif thesecoordinationstrategiesmaycontributetounderlyingmechanismsassociatedwiththepatient's painanddecreasedmobility. Describingmovementatthelevelofcoordinationinthispopulationhasthepotentialtoenhance thee cacyofapatient'srehabilitationandprostheticalignmentbyprovidinginsightsintohowthe nervoussystemisadaptingtoandcontrollingthealteredbiomechanicalpropertiesoftheresidual limbandprosthetic.Limbamputationleadstomajorchangesinbiomechanicalandneurophysiologicalrelationshipsthatalsoinuencethephysiologicalqualityoftheresiduallimbandcontribute totheindividual'soverallwalkingability.Severalresearchstudieshavefoundthatamajorreorganizationofbotha erentande erentprojectionsoccursinsuchpatientsandthatthisneurological reorganizationcontributestothechangesinmotorpatternsseeninpersonswithlowerlimbamputations[8].Thisreorganizationoftheneuromuscularsystem'smanyelementsdemonstratessuch individualsareabletoconsolidatethedynamicalsystem'sredundantdegreesoffreedomwhileaccountingfortaskandenvironmentalconstraintsandlimb-prostheticinteractions(Bernstein,1967). Thesetheoreticalmodelssuggestthemotorcontrolsystemcanre-organizeafterthereductionor removalofbiomechanicalconstraintsandresultincoordinationchanges.Forexample,compensation forlossofproprioceptivecues,whichnormallyhelpsignaltheinitiationandterminalofcertaingait events,andalteredinertialpropertiescanbeachievedinindividualswithanamputationthatare freeofneuromuscularpathology. Determiningtheoptimalprosthesisalignmentcanbeadi culttask,especiallyinpatientswho havewornaprostheticforyearsandhavetheabilitytoadoptarelativelytypicalgaitpatterneven withvariousprostheticalignments.Thealternativeperspectiveofgaitprovidedbythesemethods providesameanstoidentifythelocusofimpairmentando ervaluableclinicalinsightsforinforming rehabilitationprogramsandprostheticalignment. 186

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7SummaryandConclusions 7.1SummaryoftheProposedCoordinationDynamicsModel Althoughcoordinationhasbeenidentiedasafundamentalelementnecessaryforthesuccessful achievementofwalking,thisaspectofgaithasyettobeembracedintoinstrumentedgaitanalysis, perhapsinpartduetoanunfamiliarityorinconsistencyofthemathematicalmethodsforgenerating thesecoordinationcurves,thelackofanormativereference,examplesoftheuniqueclinicalinsights o eredbythesemeasures,andinterpretationofcurvefeatures.Therefore,theprospectiveexperimentsandfouraimsofthisbodyworkaddressedtheseissuesusingretrospectiveandprospectivethe motioncapturedatafromsubjectswithanunimpairedgaitpattern,subjectswithcerebralpalsy, andsubjectswithalowerlimbamputation.Specically,coordinationdynamicsduringthecritical gaittaskofswinglimbadvancementinthesagittalplanewasexaminedforthesesubjectswiththe dynamicsystemstheorybasedphaseportraitsandcontinuousrelativephasediagrams. Aim1createdanormativereferencedatasetforthesemeasuresofcoordinationdynamicsfrom thelargestreportedcohortofindividualsfreeofgaitpathology.Thisnormativedatasetprovideda contextfortheutilityofthesemeasuresasacomplementtoconventionalinstrumentedgaitanalysis measures,wasareferencefortheotherthreeaimsandtheirrespectivehypotheses,andcontinued theadvancementoftheapplicationofdynamicsystemstheorytechniquesinlocomotion.The detailedexplanationandrationaleofthetechniquesusedtogeneratethesemeasureswillhopefully provideamoreuniedmethodologyandthoroughdescriptionforconstructingthesecurvesforfuture investigationsandresearchers. Currently,thereisnotagoldstandardmethodormeasureforthebehaviorofcoordinationthat characterizesthetimingandpositionofindividualsegmentsandpairsofsegments,bothadjacent andnon-adjacentthroughoutthecyclicaltaskofgait.Furthermore,onlyafewotherinvestigations byotherresearchershavebeenconductedtoexplorethesemeasuresforindividualswithanaberrant gaitpattern,demonstratethatthesemeasurescharacterizecoordination,andprovideexamplesof howthesetechniquescanbeusedtoidentifythelociofimpairmentorchangesincoordination asresultofanintervention.Therefore,theprospectiveexperimentsinAim2weredesignedto expandcontributetothisareaofgaitresearchbyexploringtherelationshipbetweentheproposed measuresofcoordinationdynamicsandselectclinicalperformancemeasuresthatcharacterizeaspect ofcoordination. Althoughthetheoretical,mathematicalpendulummodelcreateinAim3ismoresimplisticthan 187

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otherreportedmodels,thismodelretainedtheinitialconditionsandinertialpropertiesofmotion capturedatafromhumansubjectsinsteadoftheapproachofothermodelswhichunrealistically manipulateparameters(e.g.limblength,centerofmasslocation)toachieveanobservedhuman gaitpattern.Originatingfromalimitcycle,thecomponentsofaphaseportrait(e.g.angular displacement,angularvelocity)wereideallysuitedtoassessthesimilarityofatheoreticalcompound pendulumtothemotionofthethighandshankduringtheswingperiodofgait.Thispendulum modelwasusedtoassessthelongheldconstructvaliditythatthesagittalplanemotionofthethigh andshankduringswingperiodofgaitisanalogoustothemotionofapassivecompoundpendulum. Whilethevastmajorityofpatientswithneurologicalmovementdisordersprimarilystrugglewith advancingthelimbinswing,thiscriticalportionofthegaitcycleisrarelyaddressedinclinical interventions,inpartduetothelackofmathematicalmodelsandclinicallyusefultechniquesfor identifyingthelocusofdeviationfromtheoptimalmotion. Lastly,thefourthaimofthisbodyofworkexaminedthecoordinationdynamicsoftheunimpaired cohortandthetwoclinicalcohorts,whohavedi erentreasonsforstrugglingwiththecriticalgait taskofswinglimbadvancement.Varioustechniqueswereusedtoidentifyandquantifythedi erent motorcontrolstrategiesofthesesubjectsandtwonovelindicesofcoordinationdynamicswere createdtoprovideaconcisemetricforcomparingthecoordinationdynamicsbetweendi erentgait patterns.Usingthecoordinationcurvesforthecohorts'variousgaitpatterns,numerousexamples wereprovidedtoillustratehowcurvefeaturesofPPsandCRPDsprovideinsightsintothemotor controlstrategiesofasubjectgroup.Importantcoordinationeventsandinter-segmentalspatiotemporalrelationshipsduringswinglimbadvancementwereidentiedanddiscussedtodemonstrate theuniqueclinicalinsightsofthisalternativelevelofanalysisoftri-planarmarkertrajectorybased data. Thefollowingsectionprovidesspecicconclusionsforeachaimanditscorrespondinghypotheses.Hopefully,thisbodyofworkhasprovidedsu cientlycompellingevidencetoconvincethe instrumentedgaitanalysiscommunitythatthesemeasureso eruniquelyvaluableclinicalinsights intotheunderlyingcoordinationdynamicsofagaitpatternandsharingofthisworkwillprovidea foundationfortheproposedmeasuresofcoordinationdynamicstobemorereadilyconsideredand embracedbyfellowresearchersandclinicians. 7.1.1GeneralConclusionsforAim1 Phaseportraitsforthepelvis,thigh,shank,andfootandcontinuousrelativephasediagramsfor thesegmentpairsofpelvis-thigh,thigh-shank,shank-foot,andthigh-footwerecalculatedforthe 188

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completegaitcycle.Thestraightforwarddescriptionandrationalepresentedforgeneratingthese descriptorsofcoordinationdynamicsprovidesaclearlydenedandcohortprocessforcalculating thesemeasures.Thisnormativedatasetisthelargestreporteddatasetofsagittalplanecoordinationmeasures,includingadjacentandnon-adjacentsegmentpairings,forindividualsfreeofgait pathology.Thendingsfromthevariousanalysisofthisdatasupporttheuseofthisnormative datasetasareferenceforcoordinationdynamics.Inadditiontoprovidinganormativereference forthisbodyofwork,thisdatasetandmethodscanbeusedtoimprovethegeneralunderstandingofgaitstrategiesfromthelevelofcoordination.Furthermore,bycharacterizingthenatural variabilityingaitpatternsthisdeliverableo ersameanstoenhancethegeneralunderstandingof atypicalgaitpatterns.Variouscurvefeatures(e.g.coordinationevents)fromthesecoordination curvesforthisunimpairedcohortwereidentiedasbeingsignicanttothesuccessfulcompletionof swinglimbadvancementinChapter5.Additionally,combinationofthesecoordinationeventswere foundtocomprisefourmotorcontrolmechanismsessentialtotheelegantande cientachievement ofswinglimbadvancement.Hopefully,disseminatingthisnormativereferenceandmethodologyfor calculatingthesecoordinationmeasuresinapeerreviewedjournalwillenableotherresearchersto identifyimportantcoordinationdynamicsinclinicalandresearchpopulationswithmusculoskeletal andneurologicallybasedgaitpathologyandlinkthemtoshortcomingsinperformingcriticalgait events. 7.1.2GeneralConclusionsforAim2 Whilethereispresentlynotagoldstandardmethodforquantifyingcoordinationdynamics duringthetaskofgaitintheinstrumentedgaitanalysiscommunity,theexcitingcorrelationsbetweencurvefeaturesfromcoordinationcurvesandselectclinicalperformancetasksfromthisaim demonstratedthatphaseportraitsandcontinuousrelativephasediagramsquantifyessentialintersegmentalcoordinationdynamics(e.g.dissociationofsynergies)duringswinglimbadvancement. Usingthesenonlinearmeasurestoquantifycoordinationfromcommonlycollectedinstrumentedgait analysisdataissupportedbythisaim'sndings.Thecomparisonofthevariousprospectivelycapturedclinicalperformancemeasurestodiscretecoordinationeventsfromcontinuousrelativephase diagramsfromAim2demonstratedtheproposedmeasuresofcoordinationdynamicscanbeused tocharacterizethecoordinationofsegmentsduringthetaskofgait,detectaberrantcoordination, andidentifythelociofimpairment(s).Findingsfromthisaimsupportthevalidityofthetheoreticalconstructthatthesephaseportraitsandcontinuousrelativephasediagramscanbeusedto characterizethebehaviorofcoordinationanddetectvaryingdegreesofimpairedcoordination.The 189

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incorporationofthesecoordinationmeasuresintoIGAmay,incertaincases,alleviatetheneedfor multipleoradditionalclinicalperformancemeasuresusedtocharacterizeaspectsofvoluntarymotor controlinane orttomakecorrelationsbetweenthesetasksandtheactualcoordinationdynamics duringgait. 7.1.3GeneralConclusionsforAim3 Asshownwiththetheoretical,mathematicalpendularsoftwaremodel,swinglimbadvancement isnotapurelypassivemotion,evenforsubjectswearingalowerlimbprosthetic.Whilethethigh andshankmotionofsubjectswithaprosthesiswasfoundtodi ertheleastfromvariousconstantdampingconditionsofatheoreticalcompoundpendulum,thesagittalplanemotionofthesubject's legsegments/prostheticstilldeviatedfromthetheoreticalmodel.Theresultsforthisaim'shypothesesfurthersupportthegeneralproposalthatthetaskofswinglimbadvancementisacomplexmotor controltaskrequiringtheeleganttimingandorganizationofsegmentstosuccessfullyande ciently achieve.Sincethelegsegmentsduringswinglimbadvancementareactivelycontrolled(e.g.variable damping),theuseofmeasures(e.g.phaseportrait,continuousrelativephasediagram)designedto quantifythebehaviorofcoordinationisfurthersupported. 7.1.4GeneralConclusionsforAim4 Theresultsfromthenumerousanalysesofthisaimdemonstratedthattheproposedmeasures ofcoordinationdynamicsareabletodistinguishbetweendi erentgaitpathologiesandpatterns associatedwithalteredlimbadvancementduringtheswingperiodofgait.AsevidentbythePPs andCPRDsgeneratedforthisinvestigation'svarioussubjectgroups,therearedistinctqualitative di erencesforthedi erentsubjectcohortsandgaitpatternsstudied.Furthermore,itwasfound thatthesevisualdi erencescanbequantiedbythepresenceorabsenceofcertaincurvefeatures andeachoftheatypicalgaitpatternsexamined(e.g.sti knee,crouchhemiplegia,diplegia,below kneeamputation,abovekneeamputation)hadauniquecombinationofmissingcoordinationevents thatcorrespondedtothecohort'sdi cultyinsuccessfullyachievingswinglimbadvancement. Quanticationofthesedi erentcoordinationstrategieswasfurtherexploredandcharacterized bythecreationoftwonovelcoordinationindices.Theseindicesuseddi erenttechniques,eachwith di erentadvantages,toconsolidatethelargeamountofdataassociatedwithasubject'scoordination curvesintoasinglescalarvalue.Bothindicesfoundstatisticallysignicantdi erencesbetweenthe di erentgaitpatternsandgeneralsubjectcohorts(e.g.unimpaired,cerebralpalsy,andlower limbamputation).Findingsfromanalysesoftheseindicesdemonstratedtheseindiceswereableto 190

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di erentiatebetweentheclinicalcohortsandtheunimpairedgroupanddecreasedsignicantlyas theGMFCSleveldecreasedinsubjectswithcerebralpalsy.Additionally,thesecoordinationindices weresignicantlydi erentfromthesubjects'gaitdeviationindexbutfollowedsimilartrendsto theGDIthusreectingincreasesinthediagnosisseverityofsubjectswhentheywereorganized topographicallyandbylevelofamputation. Overall,theuseofphaseportraitsandcontinuousrelativephasediagramstoexamineandcomparedi erentgaitpatternsforthisaim,furtherdemonstratedtheadditionallevelofanalysisand alternativeperspectiveofmarkerbasedtrajectorydataprovidedbythesemeasures.Theanalysesof thisaimanditshypothesisfurtherdemonstratetheabilityofthesemeasurestoenhanceandexpand insightsintogaitpathologybyquantifyingtheorganizationofindividualsegments,identifymechanismsofchange,andlociofimpairment.Sincethefundamentalorganizationofthelegsegments duringgaitislinkedtogaitpathologyandguidestherationaleforinterventions,incorporatingPPs andCRPDsintoinstrumentedgaitanalysiswillopennewavenuesforunderstandingthecomplexity ofcoordinationandallowcliniciansthemeanstomoree ectivelyande cientlytreatpatientswith neuromusculargaitimpairments. 7.1.4.1CoordinationDeviationIndex Featureanalysiswasusedtocreateanindexofcoordinationdynamicsfromtheproposedmeasuresofcoordination(e.g.phaseportrait,continuousrelativephasediagram).Thisnovelindex providesaconcisemetricoftheamountanindividual'scoordinationdeviatesfromanormative reference.InvestigationsintothisnewindexdemonstratedtheCDIiscapableofdistinguishing betweendi erentgaitpatternsintwoclinicalcohorts(e.g.cerebralpalsy,lowerlimbamputation) withdi erentetiologiesa ectingtheircoordinationandtheabilitytoproduceatypicalgaitpattern. ComparisonsbetweentheGDIandCDIfoundthatwhilethesetwoindicesfollowsimilartrendsin variousclinicalgroups,theymeasuredi erentaspectsofgait.Therefore,theCDImayprovetobe avaluableresearchtoolforstudyingpopulationswithimpairedmotorcontrolbecauseitprovides adeeperlevelofunderstandingaboutthemechanismsassociatedwithchangesinjointanglesby reectingtheunderlyingorganizationofsegmentoscillationsduringgait. 7.1.4.2CoordinationPerformanceScore Phaseportraitsandcontinuousrelativephasediagramscharacterizetheessentialbehaviorof coordinationingaitando eraquantitativemeanstoelucidatetheunderlyingmechanismscontributingtoagaitpatternbyanalyzingmarkertrajectorydatafromadi erentperspective.Thesix 191

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signicant,sagittalplanecoordinationeventsinswingidentiedbythecoordinationperformance scoreinvestigationdemonstratesthediverseutilityofthesemeasuresandtheeaseofusingthese measurestodeconstructessentialmechanismsofagaitpattern.Theproposedcoordinationperformancescoreforcharacterizingthedeviationofsubject'sswingperiodcoordinationdynamicsfrom alargenormativereferenceprovidesaclinicallyusefulandconcisealternativetoexaminingthePPs andCPRDs.Sincecoordinationmeasuresdescribemovementatadi erentlevelthanconventional instrumentedgaitanalysismeasuresandbynaturearelowdimensionaldescriptors,thesenonlinear techniquesmayholdthekeytoenhancinggaitclassicationalgorithmsforindividualswithimpaired coordination(e.g.cerebralpalsy). 7.2RecommendationsforFutureWork Eventhoughthisbodyofworkprovidedaninitialframeworkforthemethodologicalgeneration, clinicalinterpretation,andapplicationsofsagittalplanecoordinationdynamics,itisbynomeans exhaustive.Thesemethodscouldeasilybeexpandedfortheentiregaitcycle,incorporateupperbody segments,andincorporatecoronalandtransverseplanesofmotion.Itwouldbeexcitingtoalsoapply thesemethodsandmeasurestootherclinicalpopulationswhostrugglewithimpairedcoordination andotherpathologicalgaitpatterns.Itisproposedthatincorporatingthesemeasuresofcoordination tocharacterizechangesinthebehaviorofsegmentsduringotherwalkingtaskswhileusingassistive devices,di erentprostheticsprostheticsettings/alignments,orafterclinicalinterventionswould enhanceinsightsfrominstrumentedgaitanalysisdata.Theinclusionofthesenonlinearmeasures intoinstrumentedgaitanalysisforvariouswalkingtasksthataredesignedtoalterorinhibitvarious aspectsofmotorcontrol(e.g.obstacleavoidance,treadmillwalkingwithvirtualreality)mayprovide amoremeaningfulandappropriatemeasuresofanindividual'smotorcontrolstrategiesduringsuch tasks.Theutilityofthesemeasuresinclinicalandresearchdomainswillcontinuetounfoldas themethodologyisappliedtoinstrumentedgaitanalysis.Whilethepossibilitiesforclinicaland researchapplicationsofthesemeasuresarelimitless,thefollowingsectionsprovidesomeadditional recommendationsforfutureworktofurtherdevelopthesecoordinationmeasures. 7.2.1ContinuousEquationsofCoordinationDynamics Thisbodyofworkhasprovidedaninitialframeworkwithdiscretecurvevaluesusingpercentagesofthegaitcycleasthetemporalunitofmeasure.Whileinstrumentedgaitanalysisdatais traditionallyvieweddiscretely,itisproposedthatdeningthesecoordinationmeasureswithcontin192

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uousequationswouldprovideadditionalbenetstoanalyzinggaitdataandopenthedoortonew analyticaltechniques.Onemeansofgeneratingequationsforcontinuouscoordinationmeasuresis functionaldataanalysis(FDA). Theperiodicnatureofgaitdata(e.g.kinematics,phaseportraits,continuousrelativephase diagrams)impliesthesecyclical,oscillatorygaitcurvesformaclosedcurve.Theoverallshapeof thesecyclicalcurvesisdi erentforvariousgaitpatterns,asaddressedinAim4,andisoftendi erent fortheindividualwhencomparedtoamean,normativereference.FDAo ersatechniquethat exploresthevariabilityinthesefunctiondataandfocusesonthedi erentfeaturesofthesecurves. AsdetailedbyRamsay(1997),applyingFDAtothesecoordinationcurveswould1)representthe datainnewwaystoaidindeeperandadditionalanalysis,2)highlightsvariouscurvecharacteristics, 3)provideameanstostudyimportantsourcesofpatternandvariationsamongdi erentsubjects andcohorts,4)provideameanstoexplainthevariationinanoutcomeordependentvariables, and5)comparetwoormoresetsofdatawithrespecttocertaintypesofvariation.Bycreating functionsforthesecoordinationcurves,FDAwouldprovideameanstoquantitativelydetermine howtwofunctionsdependuponeachotherandcovarywithoneanother.FDAwouldalsoprovide ameanstoexpanduponthesignicantcoordinationevents(e.g.curvefeatures)identiedinAims 1and4.Inparticular,FDAcouldbeusedtostudywhichmodesofvariabilityintwocoordination curvesaremostassociatedwitheachother.Forexample,thismethodologycoulddeterminehow variabilityinthepelvis-thighCRPDisrelatedtothevariabilityinthethigh-footCRPD.This additionalperspectiveintocoordinationcurvesmightrevealhowaphysicalpropagationoferrors causedbytheinabilitytoachieveonecoordinationevent(e.g.curvefeature)atanearliertimein thegaitcyclea ectscoordinationdynamicsinalaterportionofthegaitcycle. Tofurtherillustratethebenetsofusingcontinuousmeasuresofcoordination,considerthe coordinationdeviationindexcreatedinAim4.Thecoordinationdeviationindex(CDI)wascreated tosolvetheproblemofcomparingthemagnitudeateachdiscretetimeepochofasubject'sthephase portraitsandcontinuousrelativephasediagramstoanothersubject.Aswithanyconventionalgait measureorgaitindex,thismetricusesthetimingandmagnitudeofcurvesbutisunabletoaccount forslope.Generatinganindexthatusescontinuousequationforeachcoordinationcurvewould incorporatethethreefundamentalelementsofanycurve:timing,magnitude,andslope.Froma methodologicalperspective,thiswouldalsoalleviatetheneedforresamplingofgaitdata,removethe e ectsoftemporalnormalizationonthecurves,anddrasticallyreducetheamountofdataanalyzed andrequiredfornormativereferencedatasets.Latash(2008)stated,"...parametersofequations usedwithinthedynamicsystemsapproachhavebeenselectedratherarbitrarilyinordertomake 193

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surethatthemodelproducesdesiredcoordinationpatterns."Deningequationsforcoordination dynamicswithamethodologysuchasfunctionaldataanalysiso ersanelegantsolutiontothis problem. 7.2.2IncorporationofElectromyographicData Inchapter3,currentusesofelectromyographicdatatocharacterizecoordinationwerediscussed. Whilethisapproachtoquantifyingmotorcontrolusesamorelocalperspective,thecombinationof muscleactivationpatternswiththemoreglobalbehavioralperspectivea ordedbyphaseportraits andcontinuousrelativephasediagramshasexcitingpotential.Creatingamodelofcoordination thatincorporatestheactivationofselectmusclesandtheresultingbehavioroftheentirelimbhas thepotentialtoprovidemorespecicinsightsintowhichmusclesarecontributingtothemotor behaviorofanindividual'sgaitpattern.Theadditionofelectromyographicdatawiththeproposed measuresofcoordinationmayalsoprovideadditionalclinicalinsightsthatmightinformtreatment decisionsforindividualsundergoinganinterventiondesignedtoreduceaberrantcoordination.The balancebetweenpotentialandkineticenergyoflegsegmentscanbemodeledusingphaseportraits constructedfromasegment'sangulardisplacementandangularacceleration.Includingmuscle activationpatternswithsuchphaseportraitswouldbeanotherexcellentinitialinvestigationinto thependularenergeticsofagaitpattern. 7.2.3IncorporationofForwardModelingSimulations Creatingamultifacetedmodelofcoordinationhasthepotentialtosignicantlyexpandgeneral knowledgeofchangesinmotorcontrolassociatedwithanintervention,unifydi erentgaitanalysis methodsanddescriptorsofgait,andprovidenew,clinicallymeaningfulinsightsintothisconstitutive elementofgait.Aspreviouslymentioned,theincorporationofelectromyographydataisoneway tocreateanexpandedmodelofcoordinationdynamics.Anotheroptionwouldbetoincludethese measuresofcoordinationdynamicsintosomeoftheadvancedforwardmodelingsimulationsoftware programscurrentlyavailable(e.g.OpenSim),whichwouldalsogreatlyenhancethesimpletheoretical pendulummodelcreatedtoaddressAim3.Theuseofsuchadvancedmusculoskeletalmodels couldbeusedtosimulatevariousclinicalinterventionsandpredictdi erentpermutationsofthe resultinggaitpatternandthusunderlyingcoordinationdynamics.Forexample,individualswith sti kneegaitoftenundergoarectusfemoristransfertosurgicallyremovethemuscle'sspasticity basedinhibitorye ectsonkneeexionduringswinglimbadvancement.Usingapatient'spreoperativeinstrumentedgaitanalysisdata,variousforwardsimulationscouldbecreatedtoassess 194

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howdi erentsurgicaltechniquesforthisproceduremighta ectthepost-operativegaitpatternand potentialre-organizationofsegments(e.g.changesincoordination)aboutthekneejointinresponse tothisintervention.Additionally,futureworkusingsuchadvancedforwardmodelingtechniquesand softwareprogramscouldexpandupontheinvestigationinAim3intovariabledampingconditions andpotentiallygeneratedampingfunctionsfordi erentclinicalcohorts. 195

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60.Haak,BS2009,Cerebralpalsyandaging'.DevelopmentalMedicineandChildNeurology, vol.51,no.4,pp.16-23. 61.BradleyWC,Daro RB,FenichelGM,MarsdenCD.NeurologyinClinicalPractice:The NeurologicalDisorders.VolumeII,3rdEdition,Butterworth-Heinemann,WoburnMA,2000. Chapter67. 62.StanleyF,BlairE,AlbermanE.Cerebralpalsies:epidemiologyandcausalpathways. LondonUnitedKingdom:MacKeithPress;2000. 63.SangerTD,ChenD,DelgadoMR,Gaebler-SpiraD,HalletM,MinkJW,andtheTaskforce onChildhoodMotorDisorders.DenitionandClassicationofNegativeMotorSignsin Childhood.Pediatrics2006;118;2159. 64.StaudtM,PavlovaM,BohmS,GroddW,Krageloh-MannI.Pyramidaltractdamage correlateswithmotordysfunctioninbilateralperiventricularleukomalacia(PVL). Neuropediatrics2003;34:18288. 65.BaxM,TydemannC,FlodmarkO.ClinicalandMRIcorrelatesofcerebralpalsy:the EuropeanCerebralPalsyStudy.JAMA2006;296:1602-1608. 66.LanceJW.1980.Symposiumsynopsis.In:FeldmanRG,YoungRR,KoellaWP,editors. Spasticity:Disorderedcontrol.Chicago:YearbookMedical.p485-494. 67.OlssonMC,KrugerM,MeyerLH,AhnlundL,GransbergL,LinkeWA,LarssonL.2006. Fibretype-specicincreaseinpassivemuscletensioninspinal-cordinjuredsubjectswith spasticity.JournalofPhysiology577:339-52. 68.LeonardCT,HirschfeldH,FossbergH.(1991).Thedevelopmentofindependentwalkingin childrenwithcerebralpalsy.DevMedChildNeurol33:567-577. 69.SutherlandDH,DavidsJR.(1993)Commongaitabnormalitiesofthekneeincerebralpalsy. ClinicalOrthopaedicsandRelatedResearch.288:139-147. 70.GoldbergSR,OunpuuS,DelpSL.Theimportanceofswing-phaseinitialconditionsin sti -kneegait.JBiomech2003;36(8):1111-6. 71.GageWH,WinterDA,FrankJS,etal.Kinematicandkineticvalidityoftheinverted pendulummodelinquietstanding.Gait&Posture2004;19(2):124-32. 72.NovacheckTF,GageJR.Orthopedicmanagementofspasticityincerebralpalsy.ChildsNerv Syst2007;23(9):1015-31. 73.Ziegler-GrahamK,MacKenziE,EphraimP,TravisonG,BrookmeyerR.(2008)Estimating theprevalenceoflimblossintheUnitedStates:2005to2050.ArchPhysMedRehabilvol 89:422-429. 74.DillinghamTR,PezzinLE,ShoreAD.Reamputation,mortality,andhealthcarecostsamong personswithdysvascularlower-limbamputations.ArchPhysMedRehab,2005;vol86: 480-486. 75.BurkeMJ,RomanV,WrightV.Boneandjointchangesinlowerlimbamputees.AnnRheum Dis1978;37(3):252-4. 76.KulkarniJ,AdamsJ,ThomasE,SilmanA.Associationbetweenamputation,arthritisand osteopeniainBritishmalewarveteranswithmajorlowerlimbamputations.ClinRehabil 1998;12(4):348-53. 77.DeansS,McFadyenAK,RowePJ.Physicalactivityandqualityoflife:astudyofa lower-limbamputeepopulation.ProstheticsandOrthoticsInternational2008;32:186-195. 199

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78.SmithD,MichaelJW,BowkerJH.AtlasofAmputationsandLimbDeciencies:Surgical, Prosthetic,andRehabilitationPrinciples.3rded.Illinois;2004.Chapters29-32. 79.DayHJB(1991).TheISO/ISPOclassicationofcongenitallimbdeciency.Prostheticsand OrthoticsInternational,15:67-69. 80.Eberhart,H.D,ElftmanH,InmanVT.(1954).Thelocomotormechanismoftheamputee. HumanLimbsandtheirSubstitutes.McGraw-Hill,NewYork. 81.Radcli eCW.Functionalconsiderationsinthettingofabove-kneeprostheses.Selected ArticlesFromArticialLimbs,Huntington,NY,KreigerPublishingCo,Inc,1970,pp.5-30. 82.PrinsenEC,NederhandMJ,RietmanJS.Adaptationstrategiesofthelowerextremitiesof patientswithatranstibialortransfemoralamputationduringlevelwalking:asystematic review.ArchPhysMedRehabil2011;92:1311-1325. 83.BreakeyJ.Gaitofunilateraltrans-tibialamputees.OrthotProsthet1976;30:17-24. 84.MurrayM,MollingerL,SepicSB,GardnerGM.Gaitpatternsintrans-femoralamputee patients:hydraulicswingcontrolversusconstant-frictionkneecomponents.ArchPhysMed Rehabil1983;64:339-45. 85.EngsbergJR,LeeAG,TedfordKG,HarderJA.Normativegroundreactionforcedatafor able-bodiedandtranstibialamputeechildrenduringwalking.JPediatrOrthop 1993;13:169-73. 86.SuzukiK.Forceplatestudyonthearticiallimbgait.JJpnOrthopAssoc1972;46:43-55. 87.EngsbergJR,LeeAG,PattersonJL,HarderJA.Externalloadingcomparisonsbetween able-bodiedandtranstibialamputeechildrenduringwalking.ArchPhysMedRehabil 1991;72:657-61. 88.NolanL,WitA,DudzinskiK,LeesA,LakeM,WychowanskiM.Adjustmentsingait symmetrywithwalkingspeedintrans-femoralandtrans-tibialamputees.Gait&Posutre17 (2003):142-151. 89.HurwitzDE,SumnerDR,BlockJA.Bonedensity,dynamicjointloadingandjoint degeneration.CellsTissuesOrgans2001;169(3):201-9. 90.WatersRL,PerryJ,AntonelliD,HisplopH.Energycostofwalkingofamputees:the inuenceofamputationlevel.JBoneJtSurg1976;58-A:42-46. 91.WatersRL,YakuraJS.Theenergyexpenditureofnormalandpathologicalgait.CritRev PhysRehabilMed1989;1:183-209. 92.TraballesiM,PorcacchiaP,AvernaT,BrunelliS.Energycostofwalkingmeasurementsin subjectswithlowerlimbamputations:Acomparisonstudybetweenoorandtreadmilltest. Gait&Posture27(2008):70-75. 93.TorburnL,PowersCM,GuiterrezR,PerryJ.Energyexpenditureduringambulationin dysvascualarandtraumaticbelow-kneeamputees:acomparisonofveprostheticfeet.J RehabilResDev1995;32:1119. 94.DonkerSF,BeekPJ.Interlimbcoordinationinprostheticwalking:e ectsofasymmetryand walkingvelocity.ActaPsychologica,2002;110:265-288. 95.SchmalzT,BlumentrittS,JaraschR.Energyexpenditureandbiomechanicalcharacteristics oflowerlimbamputeegait:Theinuenceofprostheticalignmentanddi erentprosthetic components.Gait&Posture2002,16:255-263. 96.Latash,M.NeurophysiologicalBasisofMovement.2ndedition,Chapter21,33-35. 200

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97.SandersCT.Lower-LimbAmputations:AGuidetoRehabilitation.Philadelphia,Pa:FA DavisCo;1986:13-33. 98.MuninMC,Espejo-DeGuzmanMC,BoningerML,FitzgeraldSG,PenrodLE,SignhJ. Predictivefactorsforsuccessfulearlyprostheticambulationamonglower-limbamputees.J RehabilResDev2001;38:379-384. 99.TorburnL,PerryJ,AyyappaE,ShaneldSL.Below-kneeamputeegaitwithdynamicelastic responseprostheticfeet:Apilotstudy.JournalofRehabilitationRes.Dev.1990;27:369-384. 100.PowersCM,BoydLA,FontaineCA,PerryJ:Theinuenceoflower-extremitymuscleforce ongaitcharacteristicsinindividualswithbelow-kneeamputationssecondarytovascular disease.PhysTher1996,76:369-385. 101.PowersCM,RaoS,PerryJ.Kneekineticsintranstibialamputeegait.Gait&Posture8 (1998):1-7. 102.DziubaAK,Tylkowska,JaroszczukS.Indexofmechanicalworkingaitofchildrenwith cerebralpalsy.ActaofBioengineringandBiomechanics,2014;vol16,no.3,77-87. 103.SchwartzM,RozumalskiA.Thegaitdeviationindex:anewcomprehensiveindexofgait pathology.Gait&Posture2008;28:351-357. 104.FowlerEG,StaudtLA,GreenbergMB,OppenheimWL.Selectivecontrolassessmentoflower extremity(SCALE):development,validation,andinterraterreliabilityofaclinicaltoolfor patientswithcerebralpalsy.DevelopmentalMedicineandChildNeurology.2009;51:607-614. 105.FowlerEG,GoldbergEJ.Thee ectoflowerextremityselectivevoluntarymotorcontrolon interjointcoordinationduringgaitinchildrenwithspasticdiplegiccerebralpalsy.Gait& Posture2009;29:102-107. 106.WeyerA,AbeleM,Schmitz-HubschT,SchochB,FringsM,TimmannD,KlockgetherT. ReliabilityandValidityoftheScalefortheAssessmentandRatingofAtaxia:Astudyin64 ataxiapatients.MovementDisorders,vol22,no.11,2007;p.1633-1637. 107.TrouillasP,TakayanagiT,HalletM,CurrierRD,SubramonySH,WesselK,BryerA,Diener HC,MassaquiS,GomezCM,CoutinhoP,HamidaMB,CampanellaG,FillaA,SchutL, TimannD,HonnoratJ,NighoghossianN,ManyamB.InternationalCooperativeAtaxia RatingScaleforpharmacologicalassessmentofthecerebellarsyndrome.Journalofthe NeurologicalSciences.1997;145:205-211. 108.TisonF,YekhelF,BalestreE,ChrysostomeV,QuinnN,WenningG,PoeweW.Application oftheinternationalcooperativeataxiascaleratinginmultiplesystematrophy.Movement Disorders,2002;vol17,no.6,pp.1248-1254. 109.Newell,K.M.(1986).Constraintsonthedevelopmentofcoordination.InM.G.Wade& H.T.A.Whiting(Eds.),Motordevelopmentinchildren:Aspectsofcoordinationandcontrol (pp.341-360).Dordrecht,Netherlands:MartinusNijho 110.SchmidtRA,LeeTD.MotorControlandLearning:ABehavioralEmphasis.4thEd., HumanKinetics,2005,Champaign,IL. 111.FittsPM.Theinformationcapacityofthehumanmotorsystemincontrollingtheamplitude ofmovement.JournalofExperimentalPsychology.1954;47:381-391. 112.WrenTA,RethlefsenS,KayRM.Prevalenceofspecicgaitabnormalitiesinchildrenwith cerebralpalsy:inuenceofcerebralpalsysubtype,age,andprevioussurgery.JPediatr Othrop2005;25(1):79-83. 201

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113.SutherlandDH,SantiM,AbelMF.Treatmentofsti -kneegaitincerebralpalsy:a comparisonbygaitanalysisofdistalrectusfemoristransferversesproximalrectusrelease. JournalofPediatricOrthop.1990;10:433-441. 114.AlexanderMA,MatthewsDJ.PediatricRehabilitation:PrinciplesandPractice.4thEd. 2010,DemosMedicalPublishing,NewYorkNY.Chapter16. 115.DeBruin,H.,Russell,D.J.,Latter,J.E.,Sadler,JT.,1982.Angle-anglediagramsin monitoringandquanticationofgaitpatternsforchildrenwithcerebralpalsy.American JournalofPhysicalMedicine;vol.61,no.4,pp.17692. 116.Clark,J.,Phillips,S.,1993.Alongitudinalstudyofintralimbcoordinationinrstyearof independentwalking:adynamicalsystemsanalysis.ChildDevelopment,64,1143-1157. 117.Winstein,C.,Garnkel,A.,1989.Qualitativedynamicsofdisorderedhumanlocomotion:a preliminaryinvestigation.JournalofMotorBehavior,vol21,no4,373-391. 118.Farmer,S.,Pearce,G.,Stewart,C.,2006.Developingatechniquetomeasureintra-limb coordinationingait:applicabletochildrenwithcerebralpalsy.Gait&Posture,28,217-221. 119.Barela,J.,Whitall,J.,Black,P.,Clark,J.,2000.Anexaminationofconstraintsa ectingthe intralimbcoordinationofhemipareticgait.HumanMovementScience,19,251-273. 120.ScholzJP,KelsoJAS.1989.Aquantitativeapproachtounderstandingtheformationand changesofcoordinationmovementpatterns.JournalofMotorBehavior,21(2):122-144. 121.SchmidtRC,Tre nerPJ,TuryeyMT.1992.Dynamicalaspectsoflearninganinterlimb rhythmicmovementpattern.JournalofMotorBehavior24:67-83. 122.ByrneJE,StergiouN,BlankeD,HouserJJ,KurzM.2002,Comparisonofgaitpatterns betweenyoungandelderlywomen:Anexaminationofcoordination.PerceptualandMotor Skills94:265-280. 123.StrogatzSH.NonlinearDynamicsandChaos:WithApplicationstoPhysics,Biology, Chemistry,andEngineering.1994.PerseusBooksPublishing,CambridgeMA. 124.KabadaMP,RamakrishnanK,WootenME.Measurementoflowerextremitykinematics duringlevelwalking.JOrthopRes.1990;8:338-392. 125.HagioS,KouzakiM.Theexiblerecruitmentofmusclesynergiesdependsontherequired force-generatingcapability.JNeurophysiol112:316327,2014. 126.ClarkDJ,TingLH,ZajacFE,NeptuneRR,KautzSA.Mergingofhealthymotormodules predictsreducedlocomotorperformanceandmusclecoordinationcomplexitypost-stroke.J Neurophysiol103:844857,2010. 127.SteeleKM,TreschMC,PerreaultEJ.Thenumberandchoiceofmusclesimpacttheresultsof musclesynergyanalyses.FrontiersinComputationalNeuroscience.2013;7,article105:1-9. 128.Zajac,FE.Muscleandtendon:properties,models,scaling,andapplicationtobiomechanics andmotorcontrol.CritRevBiomedEng14:359411,1989. 129.Kurz,M,2002.E ectofnormalizationandphaseanglecalculationsoncontinuousrelative phase.JournalofBiomechanics,35,pp.369-374. 130.StergiouN,JensenJL,BatesBT,ScholtenSD,Tzetzis,G.,2001."Adynamicalsystems investigationoflowerextremitycoordinationduringrunningoverobstacles".Clinical biomechanics,16(3),p.213. 202

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150.LeeSJ,HidlerJ.Biomechanicsofovergroundvs.treadmillwalkinginhealthyindividuals. JournalofAppliedPhysiology2007:104:747-755. 151.RegnauxJP,RobertsonJ,SmailDB,DanielO,BusselB.Humantreadmillwalkingneeds attention.JournalofNeuroengineeringRehabilitation2006,3:19. 152.FinleyJ,StattonM,BastianA.Anovelopticowpatternspeedssplit-beltlocomotoradaptation.JournalofNeurophysiology2014:111:969-976. 153.Strathy,G.M.,E.Y.Chao,andR.K.Laughman.Changesinkneefunctionassociatedwith treadmillambulation.JournalofBiomechanics16:517-522,1983. 154.Begnoche,D.,Pitettie,K.E ectsoftraditionaltreatmentandpartialbodyweighttreadmill trainingonthemotorskillsofchildrenwithspasticcerebralpalsy:apilotstudy.Pediatric PhysicalTherapy,2007,19(1):11-19. 155.Thelen,E.Motordevelopment:anewsynthesis.AmPsychol.1995;50:7995. 156.Kamm,K.,Thelen,E.,Jensen,J.L.Adynamicsystemsapproachtomotordevelopment.Phys Ther.1990;70:763775. 157.Scholz,JP.Dynamicpatterntheory:someimplicationsfortherapeutics.PhysTher.1990;70:827 843. 158.Kelso,J.A.S.Anticipatorydynamicsystems,intrinsicpatterndynamicsandskilllearning. HumanMovementSci.1991;10:93111. 204

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AppendixAInternalReviewBoardDocuments A.1ProspectiveSubjectPre-screeningScriptandForm PI:"Hello,mynameisKateWorsterandIamadoctoralstudentattheUniversityofColorado inDenver.Thankyouforyourinterestinmyresearchproject.Canyoutellmetowhichyeryou arerespondingorinwhichgroupofsubjectsyoumightparticipate? MyresearchprojectwillusemotioncapturetechnologyattheCenterforGaitandMovement AnalysisLabattheChildren'sHospitalColoradotolearnmoreaboutthecoordinationofwalking.A studysubjectwillwalkover-groundandonatreadmillwhileIcollectvideoandmotioncapturedata. Thetotaldatacollectionsessionatthelabwouldlast1to2hoursatmost,withtheopportunities forrestingbreaksinbetweenwalking.Asubjectwhoparticipatesinthisstudywillwearclothing he/sheownssuchasatanktopandshortsorabathingsuit,whicheverfeelsmostcomfortable, duringthedatacollection.Areyoustillinterestedinparticipating?" Interestedsubject/parent:"No."PI:"ThankyouforyourtimeandIhopeyouhaveawonderful day." Interestedsubject/parent:"Yes."PI:Thankyouforyourinterestinthisstudy.Beforeyoucome totheCenterforGaitandMovementAnalysisLaboratorytolearnmoreaboutthestudy,itwould behelpfultoseeifyouarelikelytoqualifytobeinthestudy.Inordertodothis,Iwouldliketoask youacoupleofeligibilityquestions.Itshouldtakeabout5minutestogothroughthesequestions. Youdonothavetoansweranyquestionthatmightmakeyouuncomfortableoryousimplywould notliketoanswer,butwithoutanswerstothesequestionsyouwillnotbeeligibletoparticipatein thisstudy.Iwillnotrecordyournameoranyotherinformationthatwouldidentifyyouontheform IusetorecordyouranswersuntilIknowyouhavequaliedforthisstudy.Ifyoudonotqualifyfor thisstudy,IwillimmediatelydestroyanyinformationIhavecollected.BeforeIbeginaskingyou questions,IamrequiredtogiveyouthenumberofCOMIRB,theEthicsBoardthatoverseesour research.Thenumberis(303)724-1055.Ifyouhaveanyquestionsorconcernspleasecontactthem atthisnumber. Doyouhaveanyquestionsaboutthepre-screeningquestionsIwillaskyouoraboutthestudy? DoIhaveyourpermissiontobeginthequestions? 1.)DoyouspeakandunderstandEnglish? _Yes_No_Noanswer 2.)Areyoubetweentheagesof7-100? _Yes_No_Noanswer 3.)Canyouwalkcontinuouslyunassisted,withoutadevicesuchasawalkerorcane,for3 minutes? _Yes_No_Noanswer 4.)Doyouhaveadiagnosisofoneofthefollowing:spasticcerebralpalsyorhavealowerlimb amputation? _Yes_No_Noanswer a.Ifyestospasticcerebralpalsy: i.Doyoutakeanymedicationsorusemedicaldevicesthata ecthowyouwalk? _Yes_No_Noanswer ii.Haveyoubeendiagnosedwithanyadditionalneuromuscularorcardiovascularconditions? _Yes_No_Noanswer b.Ifyestolowerlimbamputation: i.Haveyoubeenusingtheprostheticlimbforatleast6monthsforindependentwalking? _Yes_No_Noanswer ii.Doyouhaveabelowkneeorabovekneeamputation? _Yes_No_Noanswer iii.Haveyoubeendiagnosedwithanyneuromuscularorcardiovascularconditions? _Yes_No_Noanswer 5.)Haveyouhadsurgeryatyourhip,knee,oranklewithinthelast2years? _Yes_No_Noanswer 205

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6.)Haveyoubeendiagnosedorareawareofhavingaleglengthdiscrepancyofgreaterthan2 cmor1? _Yes_No_Noanswer 7.)Doyouhavepaininahip,knee,and/oranklejoint? _Yes_No_Noanswer 8.)DoyouhavereliabletransportationtoChildren'sHospitalColorado? _Yes_No_Noanswer 9.)Wouldyoubewillingtoconsenttomotioncapturetrialsandvideoofyouwalking? _Yes_No_Noanswer Ifinterestedsubjectmeetsallinclusioncriteriaandnoneoftheexclusioncriteria: PI:"Baseduponyouranswers,youarelikelytoqualifytobeinthisstudy.Wouldyouliketo scheduleatimetovisittheCenterforGaitandMovementAnalysis?" StudyCodeforInterestedParticipant:______________________________ 206

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A.2ProspectiveSubjectCombinedConsentandHIPPAAuthorizationForm Youarebeingaskedtobeinaresearchstudy.Thisformprovidesyouwithinformationabout thestudy.Amemberoftheresearchteamwilldescribethisstudytoyouandanswerallofyour questions.Pleasereadtheinformationbelowandaskquestionsaboutanythingyoudon'tunderstand beforedecidingwhetherornottotakepart. Whyisthisstudybeingdone? Adults or children ages 13-18 without gait pathology & typically developing children. Thisstudyplanstolearnmoreabouthowindividualswithoutpathologicalgaitwalkinresponse tovaryingconditions.Wewillstudyhowyouwalkinthevariousconditions: Atyourpreferredspeedovergroundandonatreadmill Overgroundatfasterandslowerspeeds Onatreadmillatyourpreferredspeedwithsmallweightsaddedtoyourlegs Whenyouaresupportedbyaharnessthatpartiallyliftsyourweight(lowergravity)andwill preventfallingonthetreadmillifneeded Walkingonatreadmillatyourpreferredspeedwithresistanceandassistancetoyourlegsby usingcablesattachedtoyourankles Turningacorner Withonefootinfrontoftheother(tandem) Youarebeingaskedtobeinthisresearchstudybecauseyouareeitheranadultorchildbetweenthe agesof13-18yearswithoutgaitpathologyoratypicallydevelopingchild.Datafromhowyouwalk willbeusedtohelpusunderstandindividualswhohavedi cultywalkingandpotentiallydevelop newwaystohelpthoseindividualswalkmorelikeyou. Subjects with a diagnosis of lower limb amputation, cerebellar ataxia, or spastic cerebral palsy. Thisstudyplanstolearnmoreabouthowanindividualwithyourdiagnosiswalksinresponse tovaryingconditions.Wewillstudyhowyouwalkinthevariousconditions: Atyourpreferredspeedovergroundandonatreadmill Whenyouaresupportedbyaharnessthatpartiallyliftsyourweight(lowergravity)andwill preventfallingonthetreadmillifneeded Turningacorner Withonefootinfrontoftheother(tandem) Youarebeingaskedtobeinthisresearchstudybecauseyouhaveadiagnosisofeitheralowerlimb amputation,cerebellarataxia,orspasticcerebralpalsy.Datafromhowyouwalkwillbeusedto helpusunderstandotherindividualswithasimilardiagnosis. Otherpeopleinthisstudy Upto80peoplefromyourarea(Colorado)willparticipateinthestudyassubjectswhose motioncapturedatawillbecapturedprospectively.Additionally,motioncapturedatapreviously collectedattheCenterforGaitandMovementAnalysisLaboratorywillbereviewedandincluded inthisstudy.Ofthispreviouslyrecordeddata,therewillbeamaximumof280typicallydeveloping subjects,amaximumof280subjectswithcerebralpalsy,andamaximumof10subjectswithalower limbamputation.Combiningthenumberofallsubjectsinthisstudy,therewillbeamaximumtotal of650subjects,consistingofatmost300typicallydevelopingsubjects,300subjectswithcerebral palsy,20subjectswithcerebellarataxia,and20subjectswithalowerlimbamputation. WhathappensifIjointhisstudy? Ifyoujointhestudy,youwillwearcomfortableathleticclothing(e.g.shorts,t-shirt,tennis shoes)whilewalkinginourtwomotioncaptureenvironments.Beforeyouwalkinthemotion 207

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captureenvironments,measurementsofyourlegs,arms,weight,andheightwillbetakenforthe computermodels.Aspartofanoninvasivemovementevaluation,youwillalsobeaskedtomove yourlegsthroughvariousmotions(e.g.extendyourknee,exyourhip,etc.).35passiveretroreectivemarkerswillbeplacedonyourlegs,torso,arms,andheadtocaptureyourmovement. Twovideocameraswillrecordvideoofyou(fromtheshouldersdown)walkingandperformingthe study'smotioncapturetasks.Allofthestudy'stasksareforresearchpurposesonly.Afteryou've completedyourstudyandifyou'dlike,wewillgiveyouacompactdiskwithyourmotioncapture dataandcomputermodelforyourownuse/record.Themotioncapturesessionforatypically developingsubjectwilllast2-3hours.Themotioncapturesessionforanatypicalsubjectwilllast 1-2hours. Whatarethepossiblediscomfortsorrisks? Discomfortsyoumayexperiencewhileinthisstudyincludeslightdiscomfortwhileinthebody weightsupportharnesswornduringthetreadmillwalkingtasks.Foryoursafety,alltreadmill walkingtaskswillbeperformedwhilewearingaharnesstopreventinjury.Otherpossiblerisks includethepossibilityoffallingduringtheover-groundwalkingtasks.Thereisariskthatpeople outsideoftheresearchteamwillseeyourresearchinformation.Wewilldoallthatwecantoprotect yourinformation,butitcannotbeguaranteed. Whatarethepossiblebenetsofthestudy? Thisstudyisdesignedfortheresearchertolearnmoreabouthownormaladultsortypically developingchildrenwalkinresponsetovariousconditionsandhowanindividualwiththediagnosis ofalowerlimbamputation,cerebellarataxia,orspasticcerebralpalsywalk.Thereisnodirect benetforyourparticipationinthestudy.Thisstudyisnotdesignedtotreatanyillnessorto improveyourhealth.Also,theremayberisks,asdiscussedinthesectiondescribingthediscomforts orrisks. WillIbepaidforbeinginthestudy? Youwillnotbepaidtobeinthestudy. WillIhavetopayforanything? Itwillnotcostyouanythingtobeinthestudy. Ismyparticipationvoluntary? Takingpartinthisstudyisvoluntary.Youhavetherighttochoosenottotakepartinthis study.Ifyouchoosetotakepart,youhavetherighttostopatanytime.Ifyourefuseordecideto withdrawlater,youwillnotloseanybenetsorrightstowhichyouareentitled. CanIberemovedfromthisstudy? Thestudyinvestigatormaydecidetostopyourparticipationwithoutyourpermissionifthe studyinvestigatorthinksthatbeinginthestudymaycauseyouharm,orforanyotherreason. WhodoIcallifIhavequestions? TheresearchercarryingoutthisstudyisKateWorster.Youmayaskanyquestionsyouhave now.Ifyouhavequestions,concerns,orcomplaintslater,youmaycallKateWorsterat720-777-8216 oremailatkate.worster@childrenscolorado.org.Youwillbegivenacopyofthisformtokeep. Youmayhavequestionsaboutyourrightsassomeoneinthisstudy.YoucancallKateWorster withquestions.YoucanalsocalltheresponsibleInstitutionalReviewBoard(COMIRB).Youcan callthemat303-724-1055. Whowillseemyresearchinformation? TheUniversityofColoradoDenverandthehospital(s)itworkswithhaverulestoprotectinformationaboutyou.FederalandstatelawsincludingtheHealthInsurancePortabilityandAccountabilityAct(HIPAA)alsoprotectyourprivacy.Thispartoftheconsentformtellsyouwhat informationaboutyoumaybecollectedinthisstudyandwhomightseeoruseit.Theinstitutions involvedinthisstudyinclude: UniversityofColoradoDenver Children'sHospitalColorado Wecannotdothisstudywithoutyourpermissiontosee,useandgiveoutyourinformation.You donothavetogiveusthispermission.Ifyoudonot,thenyoumaynotjointhisstudy.Wewill 208

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see,useanddiscloseyourinformationonlyasdescribedinthisformandinourNoticeofPrivacy Practices;however,peopleoutsidetheUniversityofColoradoDenveranditsa liatehospitalsmay notbecoveredbythispromise.Wewilldoeverythingwecantokeepyourrecordsasecret.It cannotbeguaranteed. Theuseanddisclosureofyourinformationhasnotimelimit.Youcancancelyourpermission touseanddiscloseyourinformationatanytimebywritingtothestudy'sPrimaryInvestigator, atthenameandaddresslistedbelow.Ifyoudocancelyourpermissiontouseanddiscloseyour information,yourpartinthisstudywillendandnofurtherinformationaboutyouwillbecollected. Yourcancellationwouldnota ectinformationalreadycollectedinthisstudy. KateWorster Children'sHospitalColorado CenterforGaitandMovementAnalysis 13123East16thAvenueB476AuroraCO80045 Boththeresearchrecordsthatidentifyyouandtheconsentformsignedbyyoumaybelooked atbyotherswhohavealegalrighttoseethatinformation. Federalo cessuchastheFoodandDrugAdministration(FDA)thatprotectresearchsubjects likeyou. PeopleattheColoradoMultipleInstitutionalReviewBoard(COMIRB). Thestudyinvestigatorandtherestofthestudyteam. O cialsattheinstitutionwheretheresearchisbeingconductedando cialsatotherinstitutionsinvolvedinthisstudywhoareinchargeofmakingsurethatwefollowalloftherules forresearch. Wemighttalkaboutthisresearchstudyatmeetings.Wemightalsoprinttheresultsofthis researchstudyinrelevantjournals.Butwewillalwayskeepthenamesoftheresearchsubjects, likeyou,private.Youhavetherighttorequestaccesstoyourpersonalhealthinformationfromthe Investigator. Informationaboutyouthatwillbeseen,collected,usedanddisclosedinthisstudy: DemographicInformation(age,sex) PortionsofmypreviousandcurrentMedicalRecordsthatarerelevanttothisstudy:Diagnosis(es) Allmotioncapturedata(markersandde-identiedvideo) WhathappenstoDatathatarecollectedinthisstudy? ScientistsattheUniversityofColoradoDenverandthehospitalsinvolvedinthisstudyworkto ndthecausesandcuresofdisease.Thedatacollectedfromyouduringthisstudyareimportant tothisstudyandtofutureresearch.Ifyoujointhisstudy: Thedataaregivenbyyoutotheinvestigatorsforthisresearchandsonolongerbelongto you. Boththeinvestigatorsandanysponsorofthisresearchmaystudyyourdatacollectedfrom you. Ifdataareinaformthatidentiesyou,UCDorthehospitalsinvolvedinthisstudymayuse themforfutureresearchonlywithyourconsentorIRBapproval. Anyproductorideacreatedbytheresearchersworkingonthisstudywillnotbelongtoyou. Thereisnoplanforyoutoreceiveanynancialbenetfromthecreation,useorsaleofsuch aproductoridea. 209

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AgreementtobeinthisstudyandusemydataIhavereadthispaperaboutthestudyoritwas readtome.Iunderstandthepossiblerisksandbenetsofthisstudy.Iunderstandandauthorize theaccess,useanddisclosureofmyinformationasstatedinthisform.Iknowthatbeinginthis studyisvoluntary.Ichoosetobeinthisstudy.Iwillgetasignedanddatedcopyofthisconsent form. Signature:_______________________________ Date:_________ PrintName:_______________________________ Consentformexplainedby:_______________________________ Date:_________ PrintName:_______________________________ Investigator:_______________________________ Date:_________Investigatormustsignwithin30days Date:_________ WitnessofSignature:_______________________________ Witnessofconsentprocess:_______________________________ Date:_________ Child Consentformexplainedby:_______________________________ PrintName:_______________________________ Date:_________ Investigator:_______________________________ Date:_________ 210

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A.3InformedAssentForm InformedAssentforages:7-12 Whatisthisstudyabout? IambeingaskedifIwanttobeinthisstudy.Thegoalofthisstudyistolearnmoreabouthow peoplewalk. Whyareyouaskingme? (Forsubjectwithcerebralpalsyonly)IambeingaskedtobeinthestudybecauseIhavewhat doctorscallcerebralpalsyandthischangeshowIwalk. (Forsubjectwithalowerlimbamputationonly)IambeingaskedtobeinthestudybecauseI havewhatdoctorscallalowerlimbamputationandthischangeshowIwalk. (Forsubjectwithoutgaitimpairmentonly)IambeingaskedtobeinthestudybecauseIwalk normally. WhatDoIHavetoDoorWhatWillHappentoMe? IfIaminthestudy,Iwill: TheResearcherwilldoashortphysicalexam. Walkonthegroundandonatreadmill. Spend1to2hoursatthemotioncapturelab. WillthisHurt? WhenIwalkonthetreadmill,Iwillwearaharnessformysafetythatmayfeeluncomfortable butitwillnothurtme.Iwillwearmarkersonmylegs,arms,head,andtrunkthatarelikestickers andwillnothurtme. DoIgetanythingforbeinginthestudy? IfIaminthestudy,Iwillgetacompactdisccontainingallmydataandthecomputermodelof meifIwouldlikeone. CanIaskQuestions? IaskedanyquestionsIhavenowaboutthestudy.Allmyquestionswereanswered.Iknowthat ifIhaveaquestionlater,Icanaskandgetananswer.IfIwantto,IcancallKateWorsterat 720-777-8216. DoIHavetoDoThis? IknowthatIdonothavetobeinthisstudy.NoonewillbemadatmeifIsayno. Iwanttobeinthestudyatthistime._Yes_No Iwillgetacopyofthisformtokeep. Child'sPrintedName:______________________________________ Child'sSignature:_________________________________________ Date:________ WitnessorMediator:___________________________________________________ Date:__________________________________ Ihaveexplainedtheresearchatalevelthatisunderstandablebythechildandbelievethatthe childunderstandswhatisexpectedduringthisstudy. SignatureofPersonObtainingAssent:______________________Date:__________ Initials:________ 211

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A.4ProspectiveSubjectDataCollectionForm DATA COLLECTION SHEET FOR PROSPECTIVE SUBJECTS SubjectStudyID:___________Age:___________ Height(cm):___________Weight(kg):___________ DominantLeg(L/R):___________ ANTHROPOMETRICS(cm):LR LegLength:______________ KneeWidth:______________ AnkleWidth:______________ ElbowWidth:______________ WristThickness:______________ HandThickness:______________ MODIFIEDICARSTASK S Knee-TibiaTest:L_______R_______ TandemWalking:_______ Turning&Walking:_______ 212

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FigureA.4.1:SCALEdatacaptureandscoringsheet. 213

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AppendixBProceduralFidelityofPerformanceMeasures B.1SCALETasks Thefollowingsectionsprovidethemethodology,instructions,proceduresandscoringcriteria fortheSelectiveControlAssessmentoftheLowerExtremity(SCALE)examadministeredtoeach prosectivesubject. Beforeaskingthesubjecttoperformeachjointtest,theexaminerpassivelymovedthejointto assessthesubject'srangeofmotion.Toassurethesubjectunderstoodthetask,theexaminerrst demonstratedthemovementsequencewhilesupportingthelimb.Thelanguageusedtoinstruct subjectisprovidedforeachjoint'stask.Toguidesubjectsatthedesiredspeedofmovement,the examinerprovidedaverbalthree-secondcountduringeachtask.Multipleattemptswereallowed andfeedbacktoimproveperformancewasusedwhennecessary.Thefollowinggeneralinstructions weregiventoeachsubjectpriortothebeginningoftheexam:"Iamgoingtoaskyoutomoveina certainway.MovethewayIaskyoutomove.Trynottomoveanyotherpartofyourbody.Ifyou haveanyquestionsoryoudon'tunderstandwhatIamaskingyoutodo,pleasetellme." Thevefactorsusedasgradingcriteriaforeachsubjectwere:1)abilitytoselectivelymoveeach joint;2)involuntarymovementatotherjointsincludingthecontralaterallimb;3)abilitytoreciprocatemovement;4)speedeachmovementwasperformed;and5)generationofforceasdemonstrated byexcursionwithinthesubject'savailablerangeofmotion.Inadditiontothespecicjointtask scoringdescriptionsprovidedabove,thefollowinggeneralcriteriafordesignatingamovementtask asnormal',impaired',orunable'isconsistentwiththeoriginaldenitionsoftheSCALEperformancetasks.Thedesignationofanormal'performanceisdenedaswhenthesubjectcompletes thedesiredmovementsequenceintimewiththeexaminer'sthree-secondverbalcountandwithout movementofuntestedipsilateralorcontralaterallegjoints.Thedesignationofimpaired'isdened aswhenthesubjectisabletoisolatejointmotionduringpartofthetask,butalsoisonlyableto movethejointinonedirection,subject'smovementislessthan50%oftheapproximateavailable passiverangeofmotionfoundduringthepassivedemonstration,movementoccursatanon-tested joint(e.g.mirrormovements),orthesubjectperformsthetaskslowerthantheexaminer'sthreesecondverbalcadence.Thetaskisdesignatedunable'ifthesubjectdoesnotinitiatethemovement orperformsthemotionusingasynergisticmassexororextensorpattern(e.g.simultaneous,obligatoryexororextensorpatternattwoormorejoints).ASCALEscoreforeachlimb(left,right)is obtainedbysummingthepointsassignedtoeachjoint.Sinceonlythehip,knee,andankle,joints arebeingmeasuredforthisresearchproject,amaximumlimbscoreof6pointsispossible. B.1.1HipFlexion/Extension Purpose: Testsubject'svoluntaryabilitytouseselectivelycontrolhipexion/extension. SubjectPosition: Subjectliesononesidewithbottomlegexedforstabilityandtopleg extended.Thetaskisperformedforeachhip. InstructiontoSubject: Subjectwasaskedtoex,extendthenexthehipwhilekeeping thekneeextended.Forexample:"Moveyourlegforward,back,thenforwardagainwhile keepingyourkneestraight.Iwilltakeyouthroughthemotionrst,andthenI'dlikeyouto doityourself." PassivelyGuidedMotion: Whilesupportingweightoflimb,theexaminermoveseachleg throughexion,extension,andexionintimewithaverbalthree-secondcount.Examiner alsostabilizespelvisand/orhassubjectusehandstokeeppelviserectandtrunkinneutral alignment. ActiveMotionbySubject: Subjectexes,extends,andexeshipwhilemaintainingknee inextensionandwithexaminersupportingweightoflimb. Scoring: Thelistbelowprovidesthecriteriaandcorrespondingscoreforthisaspectofthe SCALEprocedure. 214

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% 2=Normalperformanceoftask.Completesisolatedmovementwithin3secondverbal count. % 1=Impairedperformanceoftask.Lessthan50%ofavailablemotion;slowerthan3 secondcount;mirrormovementsofcontralaterallimb;motionatotherjoints;and/or movementoccursonlyinonedirection. % 0=Unabletoperformtask.Cannotexorexeswithsimultaneouskneeexion. B.1.2KneeExtension/Flexion Purpose: Testsubject'svoluntaryabilitytouseselectivelycontrolkneeexion/extension. SubjectPosition: Subjectsitsontheedgeoftheexamtablewithhipandkneeexed.If needed,canusearmsfortrunksupport,tomaintainanuprightsittingposture,andvertical pelvisposition.Thetaskisperformedforeachknee. InstructiontoSubject: Subjectwasaskedtoex,extendthenextheknee.Forexample: "Bendyourknee,extendyourknee,andthenbendyourknee.Trytodothiswithoutleaning furtherbackormovingyourotherleg.Iwilltakeyouthroughthemotionrst,andthenI'd likeyoutodoityourself." PassivelyGuidedMotion: Examinerstabilizesthethighwhilemovingthesubject'sshank throughthekneeexion,extension,andexionmotionintimewithathree-secondverbal count. ActiveMotionbySubject: Subjectexes,extends,andexeskneewhilemaintaining trunksupportandwithexaminerprovidingaverbalcadenceforthespeedofmovement. Scoring: Thelistbelowprovidesthecriteriaandcorrespondingscoreforthisaspectofthe SCALEprocedure. % 2=Normalperformanceoftask.Completesisolatedmovementwithin3secondverbal count. % 1=Impairedperformanceoftask.Lessthan50%ofavailablemotion;slowerthan3 secondcount;mirrormovementsofcontralaterallimb;motionatotherjoints;and/or movementoccursonlyinonedirection. % 0=Unabletoperformtask.Cannotextendorextendskneeonlywithsimultaneouship extension(extensorsynergy). B.1.3AnkleDorsiexion/Plantarexion Purpose: Testsubject'svoluntaryabilitytouseselectivelycontrolankledorsi/plantarexion. SubjectPosition: Subjectsitsonexamtablewithhipandkneeexed.Ifneeded,canuse armsfortrunksupport,tomaintainanuprightsittingposture,andverticalpelvisposition. Thetaskisperformedforeachankle. InstructiontoSubject: Subjectwasaskedtoex,extend,andthenextheanklewhile theexaminersupportsthelegwiththekneeextended.Forexample:"Keepyourkneestraight andwhileIsupporttheweightofyourleg,moveyourfootup,thendown,thenupagain.I willtakeyouthroughthemotionrst,andthenI'dlikeyoutodoityourself." PassivelyGuidedMotion: Examinersupportslimbunderdistalportionofshankandwith caretotouchonlythelateralsidesofthefoot,examinermovestheanklethroughplantarexion, dorsiexion,andplantarexionintimewithaverbalthree-secondcount. ActiveMotionbySubject: Subjectplantarexes,dorsiexes,andplantarexesanklewhile examinersupportsweightoflimbaskneeisextendedandintimewithexaminer'sverbal cadence. 215

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Scoring: Thelistbelowprovidesthecriteriaandcorrespondingscoreforthisaspectofthe SCALEprocedure. % 2=Normalperformanceoftask.Completesisolatedmovementwithin3secondverbal count.Mustobserveatleast15 ¡ arcofdorsiexionmotion. % 1=Impairedperformanceoftask.Lessthan50%ofavailablemotion;slowerthan3 secondcount;mirrormovementsofcontralaterallimb;motionatotherjoints;movement occursonlyinonedirection;simultaneousinversionorprimarilymovestoes. % 0=Unabletoperformtask.Cannotdorsiexordorsiexeswithsimultaneoushipand kneeexion(exorsynergy). B.1.4SCALEResistedSynergies B.1.4.1KneeExtensionwithResistedLimbExtension Purpose: Testforpresenceofextensionsynergy. SubjectPosition: Subjectsitsattheedgeoftheexamtablehipandkneeexed.Ifneeded, canusearmsfortrunksupport,tomaintainanuprightsittingposture,andverticalpelvis position.Thetaskisperformedforeachleg. InstructionstoSubject: Subjectisaskedtopushhis/herthighupwardagainsttheexaminer'shand,whichisplacedatthedistalendofthesubject'sthigh,andresisttheexaminer frompushingthethighdownward. ActiveMotionbySubject: Examinerprovidesresistancetohipexionatthedistalthigh assubjectexeship.Examinerwatchesforsimultaneousdorsiexionoftheankle. Score: ThetablebelowprovidesthescorecriteriaforthisaspectoftheSCALEprocedure. TableB.1.1:SCALEscoringforkneeextensionwithrestedlimbextensiontask. ScoreCriteria AbsentNoperceptibledorsiexion. PresentPerceptibledorsiexionatanklewithresistancetohipexion. B.1.4.2PlantarexionContractureTest Purpose: Thistasktestsforthepresenceofacontractureattheankleduringplantarexion. SubjectPosition: Subjectsitsattheedgeoftheexamtablehipandkneeexed.Ifneeded, canusearmsfortrunksupport,tomaintainanuprightsittingposture,andverticalpelvis position.Thetaskisperformedforeachleg. InstructionstoSubject: Subjectisaskedtopushhis/herfootdownwardagainsttheexaminer'shand,whichgripsthesubject'sfootatthemedialsideoftherstmetatarsaland lateralsideofthefthmetatarsal,andresisttheexaminerfrompushingthefootupward.The subjectisinstructedtotrytomaintainaneutralpositionoftheankle. ActiveMotionbySubject: Examinerprovidesresistancetohipexionatthedistalthigh assubjectexeship.Examinerwatchesforsimultaneousdorsiexionoftheankle. Score: ThetablebelowprovidesthescorecriteriaforthisaspectoftheSCALEprocedure. TableB.1.2:SCALEscoringforplantarexioncontracturetask. ScoreCriteria 2Rangeofmotionbeyond 90 ¡ 1Passiverangeofmotionat 90 ¡ 0Passiverangeofmotiondoesnotachieve( 90 ¡ ). 216

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B.1.4.3HipFlexionSynergyTest Purpose: Thistasktestsforthepresenceofasynergyduringhipexion. SubjectPosition: Subjectsitsattheedgeoftheexamtablehipandkneeexed.Ifneeded, canusearmsfortrunksupport,tomaintainanuprightsittingposture,andverticalpelvis position.Thetaskisperformedforeachleg. InstructionstoSubject: Subjectisaskedtopushhis/herthighupwardagainsttheexaminer'shand,whichisplacedatthedistalendofthesubject'sthigh,andresisttheexaminer frompushingthethighdownward. ActiveMotionbySubject: Examinerprovidesresistancetohipexionatthedistalthigh assubjectexeship.Examinerwatchesforsimultaneousdorsiexionoftheankle. Score: ThetablebelowprovidesthescorecriteriaforthisaspectoftheSCALEprocedure. TableB.1.3:SCALEscoringforhipexionsynergytask. ScoreCriteria 2Noperceptibledorsiexion. 1Mildtoinvariantdorsiexionatanklewithresistancetohipexion. 0Perceptibledorsiexionatanklewithresistancetohipexion. B.1.5SCALEDesriptors ThefollowingSCALEdescriptorswereperformedandserveasgeneraldescriptorsforthesubject. ThescoresfortheseSCALEdescriptorswerenotincludedintheSCALElimbscore. B.1.5.1HipAdductionContracture Purpose: Thistaskistotestforthepresenceofacontractureatthehipduringadduction. SubjectPosition: Subjectliesonsidewithbottomlegexedforstability.Thetaskis performedforeachleg. InstructionstoSubject: Subjectwasaskedtorelaxhis/herlegasexaminersupportsthe weightofthelegandmovesitawayfromhis/hersideuntilresistancefromjoint'srangeof motionismet. PassivelyGuidedMotion: Whilesupportingweightoflimb,theexaminermoveslegto maxabductionincoronalplane. Score: ThetablebelowprovidesthescorecriteriaforthisaspectoftheSCALEprocedure. TableB.1.4:SCALEscoringforhipadductioncontracturetask. ScoreCriteria 2 Normalperformanceoftask. Hipabductsbeyondhorizontal. 1 Impairedperformanceoftask. Hipabductstohorizontal. 0 Unabletoperformtask. Hipdoesnotabducttohorizontal. 217

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B.1.5.2HamstringTightness Purpose: Thistaskisperformedtoassesstheamount,ifany,ofhamstringtightness. SubjectPosition: Subjectliesinasupinepositionontheexamtable.Thetaskisperformed foreachleg. PassivelyGuidedMotion: Subjectisaskedtorelaxhis/herlegasexaminersupportsthe weightofthelegattheankleandmovesitawayfromthetableasfarascomfortablypossible oruntilmotionisfeltattheoppositeanteriorsuperioriliacspine.Theexaminer'sotherhand isplacedonthesubject'soppositeanteriorsuperioriliacspinetoprovidepelvicstability.If hamstringmusclesprovideresistanceorthereisacatch,thelegisloweredslightlyandthen raisedagainataslowerratetodeterminerangeofmotion. Score: ThetablebelowprovidesthescorecriteriaforthisaspectoftheSCALEprocedure. TableB.1.5:SCALEscoringforhamstringtightnesstask. ScoreCriteria 2 Normalperformanceoftask. Legexesfromstartingpositionto 90 ¡ 1 Impairedperformanceoftask. Legisexedbetween 45 ¡ -90 ¡ 0 Unabletoperformtask. Hamstringtightnesslimitshipexionto 45 ¡ B.1.5.3ThomasTest Purpose: Forsubjectswithareducedhipexion/extensionrangeofmotion,thistestwas usedtoassessthetightnessofthemusclesinvolvedinore ectinghipexion(e.g.rectus femoris,illiopsoas). SubjectPosition: Subjectliesinasupinepositionontheexamtableandbringsoneknee intowardthechest,thusexingthehip,whiletheotherlegremainsextendedonthetable. PassivelyGuidedMotion: Examinerassist'ssubjectifunabletoperformthismotionindependently.Examinerwatchesforextendedleg'sorientation,hipmotion,andpelvisorientation. Apositivetestindicatesthesubjecthasdecreasedhipexibilityduetotightnessoftherectus femorisand/oriliopsoasmuscles. Score: ThetablebelowprovidesthescorecriteriafortheThomastest[141]. TableB.1.6:SCALEscoringforThomastest. ScoreCriteria 2 Testisnegative. Contralateralhipdoesnotex, legremainsextendedhorizontally, andnorotationofpelvisoccurs. 1 Testispositive. Legisexedupto 45 ¡ fromhorizontal. 0 Testispositive. Legisexed 45 ¡ fromhorizontal. 218

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B.1.5.4DuncanElyTest Purpose: Forsubjectswithcerebralpalsy,thistestwasusedtoassessspasticityoftherectus femorismuscle. SubjectPosition: Subjectliesinapronepositionontheexamtablewithonelegextended. PassivelyGuidedMotion: Examinerexesthesubject'skneerapidlywhilethepatient liesproneinarelaxedstatewiththeotherlegextended.Ifresistanceoracatchisfeltby theexaminerand/orsimultaneoushipexionoccurs,thenspasticityispresentintherectus femorismuscle. Score: ThetablebelowprovidesthescorecriteriafortheDuncanElytest[139,141]. TableB.1.7:SCALEscoringforDuncanElytest. ScoreCriteria 2 Normalperformanceoftask. Kneeexesfromextendedpositionto 90 ¡ 1 Impairedperformanceoftask. Kneeisexedgreaterthan 45 ¡ but<90 ¡ 0 Unabletoperformtask. Kneeisexedtolessthan 45 ¡ B.2SelectICARSandSARATasks Thefollowingsectionsprovidethescoringcriteriafortheprospectivesubjectswhoperformed selectwalkingtasksfromtheInternationalCooperativeAtaxiaRatingScale(ICARS)andScale fortheAssessmentandRatingofAtaxia(SARA)exams.Priortoperformingthetasks,subjects weregivenaverbaldescriptionofthetaskandtheexaminerdemonstratedeachtask.Subjects werethenaskedtoperformthetaskataself-selectedspeed.Eachtaskforasubjectwasscored usingthefollowingcriteria.ThescoreforeachICARS/SARAtaskwasthensummedandusedas thesubject'snalICARS/SARAscore.Ascoreof40pointsisthemaximumpossiblescoreand indicatesnoimpairmentordi cultperformingthetasks.Asubjectscorethatislessthan40points indicatesvaryinglevelsofdi cultyinperformingthetasks. B.2.1ForwardWalkingCapacities Thefollowingdescriptionswereusedtoscoreeachprospectivesubject'sforwardwalkingability. 8=Normal,nodi cultiesinwalking % 7=Almostnormalnaturally % 6=Walkingwithoutsupport,butclearlyabnormalandirregular % 5=Walkingwithoutsupportbutwithconsiderablestaggering % 4=Walkingwithautonomoussupportnolongerpossible;patientrequiresintermittent supportofthewall % 3=Walkingonlypossiblewithlightsupportbyonearmrequired(e.g.onestick/person), severestaggering % 2=Walking>10monlypossiblewithstrongsupport(e.g.twospecialsticks,stroller,or accompanyingperson) % 1=Walking<10monlypossiblewithstrongsupport(e.g.twospecialsticks,stroller,or accompanyingperson)0=Unabletowalk,evenwithsupport 219

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B.2.290 ¡ TurningTask Thefollowingdescriptionswereusedtoscoreeachprospectivesubject'sabilitytoexecuteleft andright90degreeturns. 8=Normal,nodi cultiesinturning 7=Almostnormalnaturally 6=Walkingwithoutsupport,butclearlyabnormalandirregular 5=Walkingwithoutsupportbutwithconsiderablestaggering;di cultiesinhalfturnbut withoutsupport 4=Walkingwithautonomoussupportnolongerpossible;patientrequiresintermittentsupport 3=Walkingonlypossiblewithlightsupportbyonearmrequired(e.g.onestick/person), severestaggering 2=Walking>10monlypossiblewithstrongsupport(e.g.twospecialsticks,stroller,or accompanyingperson) 1=Walking<10monlypossiblewithstrongsupport(e.g.twospecialsticks,stroller,or accompanyingperson) 0=Unabletowalk,evenwithsupport B.2.3TandemWalkingTask Thefollowingdescriptionswereusedtoscoreeachprospectivesubject'sabilitytoexecutetandem walking. 8=Normal,nodi cultiesintandemwalking 7=Almostnormalnaturally,butunabletowalkwithfeetintandemposition 6=Walkingclearlyabnormalandirregular,tandemwalking>10stepsnotpossible 5=Walkingwithoutsupportbutwithconsiderablestaggering 4=Walkingwithautonomoussupportnolongerpossible;patientrequiresintermittentsupport 3=Walkingonlypossiblewithlightsupportbyonearmrequired(e.g.onestick/person), severestaggering 2=Walking>10monlypossiblewithstrongsupport(e.g.twospecialsticks,stroller,or accompanyingperson) 1=Walking<10monlypossiblewithstrongsupport(e.g.twospecialsticks,stroller,or accompanyingperson) 0=Unabletowalk,evenwithsupport 220

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B.2.4Knee-TibiaSlideTask Thefollowingdescriptionswereusedtoscoreeachprospectivesubject'sabilitytotouchtheheel ontheopposinglimb'skneeandslidetheheeldownthetibialcrest,pickuptheheel,andrepeat thismotionforatotalofthreetimesperlimb. 4=Normal 3=Loweringofheelincontinuousaxis,butmovementisdecomposedinseveralphases,without realjerks,orabnormallyslow.Slightlyabnormal,contacttoshinmaintained 2=Loweringjerkilyintheaxis,clearlyabnormal,goeso shinupto3timesduring3cycles 1=Loweringjerkilywithlateralmovements,severelyabnormal,goeso shin4ormoretimes during3cycles 0=Loweringjerkilywithextremelystronglateralmovementsorunabletoperformtask B.2.5ActionTremorinHeel-to-Kneetest Thefollowingdescriptionswereusedtoscoretheamountofactiontremorpresentforeach prospectivesubject'sduringtheknee-tibiaslidetask. 4=Notrouble 3=Tremorstoppingimmediatelywhenheelreachesknee 2=Tremorstoppinginlessthan10secondsafterreachingtheknee 1=Tremorcontinuingformorethan10secondsafterreachingtheknee 0=Uninterruptedtremororunabletoperformtask 221

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AppendixCPendulumEquationsofMotion C.1EquationsofMotion TheLagrangianapproachwasusedtosolvefortheequationsofmotionofasimple,twodimensionalcompoundpendulum.First,theequationsofmotionweresolvedwithoutdampingorinertia terms.Second,theequationsweresolvedtoaccountforthesetwoterms.Thissecondsetofequationswasthenre-organizedtoeaseitsformattingandtranslationintothecustomMatlabfunction thatwasusedtocomparethemotionofthetheoreticalpendulumtothesagittalplanemotionof thethighandshankfromsubjectmotioncapturedataduringthetaskofswinglimbadvancement (Aim3).Thefollowingguresprovidethederivationandnalequationsofmotionfortwodi erent compoundpendulummodels. FigureC.1.1:Part1ofLagrangianapproachtosolvingtheequationsofmotionforadoublependulumwithoutdampingorinertiaterms. 222

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FigureC.1.2:Part2ofLagrangianapproachtosolvingtheequationsofmotionforadoublependulumwithoutdampingorinertiaterms. 223

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FigureC.1.3:Part1ofLagrangianapproachtosolvingtheequationsofmotionforadoublependulumwithdampingandinertiaterms.Thissetofequationswereusedforthesoftwaremodeland allanalyses. 224

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FigureC.1.4:Part2ofLagrangianapproachtosolvingtheequationsofmotionforadoublependulumwithdampingandinertiaterms.Thissetofequationswereusedforthesoftwaremodeland allanalyses. 225

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FigureC.1.5:Part3ofLagrangianapproachtosolvingtheequationsofmotionforadoublependulumwithdampingandinertiaterms.Thissetofequationswereusedforthesoftwaremodeland allanalyses. 226

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C.2MatlabCode ThefollowingcodewascalledbyMatlab'sbuilt-infunctionode45tosolvethedoublependulum's equationsofmotion.Allanglesareinradians.Charactersorlineswith%atthebeginningare commentedout. %Parameters(derivedfromasubject/cohort)passedthroughMatlabfunctionstatement %linkagemass(kg) m1=params(1);m2=params(2); %linkagelength(m) L1=params(3);L2=params(4); %proximal(1)&distal(2)pivots'dampingcoe cients z1=params(5);z2=params(6); %Setupvariables %y(1)=angulardisplacementofproximallinkage %y(2)=angularvelocityofproximallinkage %y(3)=angulardisplacementofdistallinkage %y(4)=angularvelocityofdistallinkage g=-9.81;%constant,accelerationduetogravity(m/s2) I1=m1*(L1^2)*y(2);%Inertiaofproximallinkagekg*(m/s2)*(radians/sec) I2=m2*(L2^2)*y(4); %Inertiaofdistallinkagekg*(m/s2)*(radians/sec) %Simplifyandgroupdi erentialequations'terms A=(m2*L2+0.5*z2+I2); B=m1+m2; C=g*sin(y(1)); D=-m2*L1*(y(2)^2)*sin(y(1)-y(3)); E=m2*L2*(y(4)^2)*sin(y(1)-y(3)); F=L1*(y(2)^2)*sin(y(1)-y(3)); G=(m2^2)*L1*L2*(cos(y(1)-y(3))*cos(y(1)-y(3))); H=0.5*z2*m2*L1*cos(y(1)-y(3)); J=(B*L1+z1+I1); K=m2*L1*cos(y(1)-y(3)); N=(y(4)^2)*sin(y(1)-y(3)); %Di erentialEquations dy(1)=y(2);%Angularvelocityofproximallinkage %Angularaccelerationofproximallinkage %dy(2)=(e*d-b*f)/(a*d-c*b);%equationwithoutdampingorinertia dy(2)=(D-m2*C-(E-B*g*sin(y(1)))*A+0.5*z2*m2*(F-C))/((J*A)-G+H);%proximal linkage'sequationwithdampingandinertialterms dy(3)=y(4);%Angularvelocityofdistallinkage %Angularaccelerationofdistallinkage %dy(4)=(a*f-c*e)/(a*d-c*b);%equationwithoutdampingorinertia dy(4)=(G*N+K*B*g*sin(y(1))+(-D-C)*J)/((J*A)+G+H);%distallinkage's equationwithdampingandinertiaterms 227

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AppendixDPhaseAngleInvestigation Thisappendixprovidesthemethodsandresultsfortheinvestigationintonormalizationofphase anglecalculation.Thephaseangle( % )iscalculatedbytakingtheinversetangent(a.k.a.arctangent) ofthexandyvalues. AlgorithmD.1 Phaseangleequations. tan ( % )= sin ( y ) / cos ( x ) Alternativelystated,thephaseangleistheinverseoftheslopeofthelinewithendpointsof (0,0)and(x,y). AlgorithmD.2 Alternativephaseangleequations. % = atan ( sin ( y ) / cos ( x ) )= tan 1 ( sin ( y ) / cos ( x ) ) Inthisparticularapplication,thephaseportraitplaneisa2Dplaneformedbythexaxis, consistingofangulardisplacementangles,andtheyaxis,consistingofangularvelocityangles.The tangentfunctionisatrigonometricratioandisundenedwhencos(x)=0.Thereforethetangent functionhasaverticalasymptotewhenevercos(x)=0.Similarly,thetangentandsinefunctions havezerosatintegermultiplesof ) becausetan( % )=0whensin(y)=0.Thearctangentissimplythe inverseofthetangentfunction.Theoneargumentarctangentfunction(atan)cannotdistinguish betweendiametricallyoppositedirections.Forexample,theanglebetweenthex-axisandthevector (1,1)iscalculatedwiththefollowingequation. AlgorithmD.3 Equationtocalculatetheanglebetweenthex-axisandphaseanglevector. atan ( % )=( sin (1) / cos (1) )=45 ¡ However,theanglebetweenthex-axisandthevector(-1,-1),yieldsthesameanswerasabove eventhoughtheactualangleis-135 ¡ .Theatan2functiontakesintoaccountthesignsofbothvector componentsandplacestheangleineitherquadrantI,II,III,orIVdependinguponthesignofx andy. FigureD.0.1:Quadrantsforatan(left)andatan2(right)functions 228

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TableD.0.1:Propertiesofthetangentandarctangentfunctions. Property Tangent atan atan2 Domain &
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FigureD.0.5:Calculationofthigh-footrelativephaseanglesusingMatlab'satanfunction(blue) andatan2function(red). 230

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AppendixEAdditionalMethods E.1RepresentativeTrialSelection ThefollowingalgorithmwasimplementedintoacustomMatlabprogramandusedtoidentifythe representativemotioncapturetrialforeachsubjectandeachmotioncapturecondition. FigureE.1.1:AlgorithmusedbycustomMatlabfunctiontoselectasubject'srepresentativemotion capturetrial. E.2CoordinationDeviationIndexCalculation Thefollowingsectioncontainstheequationsandmethodologyforcalculatingthecoordination deviationindex(CDI).SagittalplanePPs(pelvis,thigh,shank,foot)andCRPD(pelvis-thigh, thigh-shank,shank-foot,thigh-foot)werecalculatedin2%incrementsthroughouttheentiregait cycleandformthecoordinationdynamicsvector(cd)foreachsubject. cd =[ Pelvis ang.displ. ,Pelvis ang.velocity ... ,ThighFoot CRPD ] T cd =[ cd 1 51 ,cd 52 102 ... ,cd 561 612 ] T Inordertocreateanormativereferenceforeachsubject'snalCDIscore,controlfeaturesfor singlevaluedecompositionanalysismustbegenerated.Thesizeofthecontrolfeaturesmusthave thesamelengthasacoordinationvectorandbegreaterthanorequaltothatsamelength.The topvegaittrialsfromeachretrospectivesubjectwereconcatenatedtogethertoformonelongtrial foreachsubject.Thenthecoordinationvectorswerecalculatedfor120unimpairedretrospective subject'sconcatenatedgaittrialandcombinedtogethertoformacoordinationdynamicsmatrixCD withdimensionsof612x1941,where1941isthetotalnumberofgaitcycles. 231

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ThesingularvaluedecompositionofCDwasthencalculatedusingMatlab'sbuildinfunctionsvd. Theunitlengthsingularvectors { f 1 f 2 f 3 ,..., f 612 } andsingularvalues { $ 1 $ 2 $ 3 ,..., $ 612 } were storedasseparatevariablesintheMatlabcode.Thesingularvectorsorcoordinationfeatureswere thenusedtoformanoptimalorthonormalbasis(f-basis)forreconstructionofthecoordination curves.Thisbasisisconsideredoptimalbecauseitmaximizesvarianceaccountedfor(VAF)by usingtheminimumnumberoffeaturesnecessarytoreconstructtheoriginalcoordinationcurves. Usingthef-basis,anm th orderapproximationofanycoordinationdynamicsvectoriscalculated usingthefollowingequation,wherethefeaturecomponentscd k aredenedas cd k = g f k cd m = m k =1 ( cd k f k ) Thesefeaturecomponentscanbearrangedasavector cd =( cd 1 ,cd 2 ,cd 3 ,...,cd m } andthoughtof asthecoordinationdynamicsvectorprojectedintothek th featuredirections. Twodi erentcriteriawereusedtodeterminetheappropriateorderofreconstruction(m=m crit ) thatwillproduceareconstructedcd m vectorthatis"su ciently"closeto cd .Therstcriterionis anevaluationoftheportionofoverallvariationaccountedforbytherstmfeatures(VAF m ), whichwascalculatedwiththefollowingequation. VAF m = m i =1 2 i 612 j =1 2 j Thedelityofthereconstructedcoordinationdynamicsvector cd m comparedtotheoriginal coordinationdynamicsvector cd wasmeasuredandusedasthesecondcriterion.Thisdelityof reconstruction( )wascalculatedastheprojectionofthereconstructedcoordinationdynamics vectorontotheoriginalcoordinationdynamicsvectorandnormalizedbythemagnitudeofthe originalcoordinationdynamicsvector. % = cd cd m || cd || 2 Aperfectreconstructionofthecoordinationdynamicsvector( cd = cd m ) correspondsto =1and decreasestowardzeroas cd m deviatesfrom( cd ) Nowthatacontrolfeaturebasishasbeenconstructed,aCDIcanbecalculatedforanysubject. Let cd N betheaverageofthefeaturecomponentsfortheallthesubjectsintheunimpairedcontrol group.Thefeaturecomponents cd N thendescribetheaveragenormativecoordinationdynamics. TheEuclideandistancebetweenthecoordinationdynamicsvectorofanysubject(c s )and cd N can becalculatedusingthefollowingequation. d s,N = || c s c N || ThisdistanceisthenusedtocalculatearawCDIscoreforthesubjectusingthefollowingequation. CDI s raw = ln ( d s,N ) WhiletherawCDIcanbeusedinitcurrentformasameasureofgaitpathologyrelatedto coordination,thefollowingscalingstepsareimplementedtohelpimproveitsinterpretability.The samplemeanandstandarddeviationof CDI s raw areusedtocalculatethesubject'sz-scorewith respecttotheaveragenormativefeaturecomponents.ThisscalingresultsinaCDIvaluethatis measured(scaled)adistanceawayfromtheaveragefeaturecomponentsfromtheunimpaired cohort. 232

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zCDI s raw = CDI s raw mean ( CDI N raw ) stdev ( CDI N raw ) Lastly,bymultiplyingthez-scoresby10andsubtractingthemfrom100thenalCDIforthe subjectiscomputed. CDI s =100 10( zCDI s raw ) Theoretically,anindividualwithoutanydeviationsfromthenormativereferencewouldhavea perfectCDIscoreof100.Every10-pointincrementbelowthetheoreticalperfectscorecorresponds toanincreasingnumberstandarddeviationsawayfromthenormativereference.Therefore,a subject'sCDIvaluecanbeinterpretedasfollows.ACDIscoregreaterthanorequalto100 indicatesthesubject's(sagittalplane)coordinationdynamicsisatleastasclosetotheunimpaired averageasthatofarandomlyselectedunimpairedsubject.ACDIgreaterthanorequalto100 indicatestheabsenceof(sagittal)coordinationpathology.Every10pointstheCDIfallsbelow100 correspondstoonestandarddeviationawayfromtheunimpairedmean.Forexample,asubject withaCDIof75indicatesthecoordinationdynamicsofthatsubject(s)is2.5standarddeviations awayfromtheunimpairedmean. E.3LegendofSwingPeriodCoordinationEvents Thefollowingtableprovidesalistofthethirty-sevencoordinationevents,identiedfromthree curvefeatures(e.g.zero-crossing,inectionpoint,extremum),intheswingperiodofgait. 233

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TableE.3.1:Legendofswingperiodcoordinationevents. CRPDCEDescriptionPPCEDescription PelvThi1AbsoluteMaxinSwingPelv1MinAngDisplacement PelvThi21stzero-crossinginSwingPelv2MaxAngDisplacement PelvThi31stzero-crossingafterAbsMaxinSwingPelv3MinAngVelocity PelvThi4InectionpointbetweenOFOnandMaxinSwingPelv4MaxAngVelocity PelvThi51stInectionpointafterMaxinSwingThi1MinAngDisplacement ThiSha1AbsoluteMininSwingThi2MaxAngDisplacement ThiSha2AbsoluteMaxinSwingThi3MinAngVelocity ThiSha31stzero-crossingafterFOThi4MaxAngVelocity Thisha41stzero-crossingafterSwingMaxSha1MinAngDisplacement ThiSha5InectionpointafterFOSha2MaxAngDisplacement ShaFoot11stMaxafterFOSha3MinAngVelocity ShaFoot2AbsoluteMininSwingSha4MaxAngVelocity ShaFoot3InectionpointafterSwingAbsMinFoot1MinAngDisplacement ShaFoot4Lastzero-crossinginSwingFoot2MaxAngDisplacement ThiFoot1AbsoluteMininSwingFoot3MinAngVelocity ThiFoot21stzero-crossingbefore1stmaxafterFO/AbsMinFoot4MaxAngVelocity ThiFoot32ndzero-crossingafterFO(MidSw) ThiFoot4AbsMaxbetween1st&2ndzero-crossingafterFO ThiFoot5LastmininSwing(occursafter2ndzero-crossing,afterFO) ThiFoot6Lastzero-crossinginSwing ThiFoot7LastinectionpointinSwing E.4TranstibialAmputationCaseStudyMethods Themotioncapturedatafromoneoftheretrospectivesubjectswithalowerlimbamputationwas investigatedwiththemeasuresofcoordinationdynamicstodetermineifclinicallymeaningful insightscouldbegainedfromthesemeasuresthatwereotherwiseundetectedwithconventional instrumentedgaitanalysismeasures.This35-yearoldfemalewithalefttranstibialamputation underwentaninstrumentedgaitanalysistodetermineifherrecent,diminishingabilitytowalkwas duetogeneralizedpaininherrightkneeandrightankleorifitwasduethecurrentprosthetic 234

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tting.Inspiteofarelativelysuccessfulrecovery,inthelastfewyearsthepatient'sindependent ambulationhasreducedto30-60minutesofwalkingandshenowusesamanualwheelchairasher primarymeansofmobility. ConventionalIGAmeasuresweregeneratedfromthree-dimensionalmotiontrackingandanarray oftenforceplatestocomparetherightlegandthreedi erentprosthesisalignmentswhilethe subjectwalkedataself-selectedspeedonlevelground.Therstalignmentconditionwasthe standardprosthesissetting(0.1875inchesout,lateralside),thefootwasmoved0.125inches mediallyforthesecondalignment,andthefootwasmoved0.25incheslaterallyforthethird alignment.Thesedi erentalignmentsaredemonstratedinthefollowinggure. FigureE.4.1:Diagramofthethreeprostheticalignmentstested,whereblackindicatesstandard prosthesisalignment,blueindicateslateralalignment,andgreenindicatesmedialalignment.Transverseviewofprosthetic(A)andisometricviewofprosthetic(B). Footoorcontacteventsweremanuallyidentied,aWoltringlterwithmeansquareerrorof17 wasappliedtoallmarkertrajectories,andtheViconPlug-in-Gaitmodelwasappliedtoeverytrial intheViconNexussoftware.TheGAMScustomMatlabprogramcalculatedthevarianceratiofor eachtrial'skinematicsandtemporal-spatialmeasures.Therepresentativetrial,fromeach alignmentcondition'ssetof5trials,wasidentied,usingtheGAMSMatlabprogram,asthetrial withthelowestvariancerationandusedfortheremainderoftheanalyses.Thekinematic,kinetic, andtemporal-spatialmeasuresforthethreettingsandthepatient'srightlegwerecalculated. Additionally,sagittalandcoronalphaseportraitsandcontinuousrelativephasediagramsforthe pelvis,thigh,andshankweregenerated.Toquantifyanddi erencesbetweeneachttingandthe rightleg,therootmeansquareerror(RMSE)wascalculatedforthetraditionalinstrumentedgait analysisandnonlinearmeasures.AsareferencetotheseRMSEvaluesforconventionaland nonlinearmeasures,thecorrespondingvariableswerecalculatedfrommotioncapturedataofa 32-yearoldunimpairedfemalesubject'srepresentativeover-groundwalkingtrial. 235

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AppendixFNormalCoordinationDynamics F.1CoordinationMechanismsofUnimpairedSwingLimbAdvancement Thissectionoftheappendixdemonstratestheproposedmeasuresofcoordinationdynamics(e.g. sagittalplanePPsandCRPDs)explaintheinherentmechanismsunderlyingtheswingperiodgait patternsof20healthysubjectsduringOGandTMwalking.Changesinthesubjects'gaitpatterns describedbyconventionalIGAmeasuresareproposedtobeaccomplishedbyalteringthetiming andorganizationofthefollowingfourmechanisms,elucidatedbycoordinationdynamics,thatare essentialforsuccessfulcompletionofswinglimbadvancement.Thefollowinggureisthemean PPsandCRPDsfortheover-groundandtreadmillwalkingconditionsofthetwentyunimpaired propsectivesubjects.Severalcoordinationevents(e.g.curvefeatures)werestudiesandwiththe useofpendularmodelsofthesubjects'legmotionandthesenonlinearmeasures,fouressential mechanismsofthecoordinationdynamicsduringswinglimbadvancementareproposed.The followinggureidentiesthecoordinationeventsassociatedwitheachofthefourmechanismsand thetablebelowprovidesthemean,standarddeviation,andassociatedmechanismforeach coordinationevent. FigureF.1.1:Coordinationeventsassociatedwiththeproposedswinglimbadvancementmechanism areshowonthemeansagittalPPs(readclockwise)andensembleCRPDsfortherightthigh,shank, andfootfromtheunimpairedprospectivecohort'sOGandTMwalkingtrials. 236

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TableF.1.1:Themeanandstandarddeviationforthemagnitudeand/ortiming(percentgaitcycle= %GC)ofswingperiodcoordinationevents(CE)fortheunimpairedprospectivecohort'sover-ground andtreadmillwalkingconditions.EachCEisalsoassociatedwithamechanismcategory. CoordinationEventOGTMMechanism 1.ThighminAD(%GC)64(1.65)65(1.45)A 2.ShankminAV( ¡ /%GC)-155.97(23.10)-138.29(20.72)A 3.Thigh-Shankabs.swingmin( ¡ )-141.28(4.44)-137.74(7.02)A 4.ShankminAD( ¡ )34.73(2.57)37.27(3.92)B 5.Thigh-Shankzero-crossingpostFO(%GC)71(1.57)72(1.61)B 6.Shank-FootlocalmaxpostFO( ¡ )74.81(25.39)50.91(25.17)B 7.ShankmaxAV( ¡ /%GC)399.89(37.47)373.68(35.46)C 8.FootmaxAD( ¡ )178.45(0.54)175.15(1.44)C 9.FootminAV(%GC)88(1.79)91(1.10)C FootminAV( ¡ /%GC)-444.18(58.93)-375.59(61.26)C 10.Thigh-Footlocalmax( ¡ )58.58(9.68)48.85(7.09)C 11.Shank-Footabs.swingmin(%GC)88(1.77)91(1.17)C Shank-Footabs.swingmin( ¡ )-146.94(5.15)-136.74(5.91)C 12.Thigh-Footminterminalswing(%GC)89(2.86)91(1.32)C Thigh-Footminterminalswing( ¡ )-67.65(9.57)-57.46(11.57)C 13.ThighmaxAD( ¡ )112.35(3.27)109.62(3.47)D 14.ShankmaxAD(%GC)98(0.97)99(0.88)D ShankmaxAD( ¡ )116.10(2.53)112.71(3.84)D 15.Shank-Footlastzero-crossing(%GC)98(1.06)99(0.83)D Byidentifyingcoordinationeventsintheswingperiodofgaitforacohortoftypicalsubjects,these ndingsprovideameanstoenhancetheunderstandingoffeed-forwardmotorcontrolstrategies employedinatypicalgaitpatternandthuso erareferenceforsubjectswithatypicalcoordination resultingimpairedswinglimbadvancement.Itissuggestedthatalthougheachtypically developingindividualhasuniqueswingperiodcoordination,anindividual'ssolutionconverges uponsharedcriticalcoordinationrequirements.Althoughtheexistenceofthesefundamental coordinationeventsindicatethereareinstancesinanormalgaitpatternthatsharecommonpoints inthesolutionofswinglimbadvancement,anindividual'sdesiredvariabilityispreservedas illustratedbythevariouscurvepatternsandtrajectoriesbetweenthesecoordinationevents.These underlying,fundamentalcoordinationevents(CE)describeinstancesofapreferredstateofthe motorcontrolsystemandasareference,havethepotentialtoilluminatewhenandhowimpaired swinglimbadvancementismanifestinginagaitpattern. F.1.1UncouplingofThigh-FootTrajectories MechanismAistheuncouplingofthethigh-foottrajectoriesatfooto .ThreeCEs,occurringat footo ,quantifythesimultaneousuncouplingofankleplantarexionandhipextension.First,the delayedtimingofthethigh'sminimumangulardisplacementduringTMwalkingoccurredwhile thethighwasinatrailinglimbposture.Second,themagnitudeoftheminimumangularvelocity oftheshankwassignicantlylessnegativeduringTMwalkinganddirectlya ectstheshankphase angle,whichinturninuencesthethigh-shankrelativephaseangle'smagnitude.Third,the absoluteminimumofthethigh-shankCRPDduringTMwalkingwassignicantlylessnegative. ThisCRPDminimumcorrespondstoareversalintherelationshipbetweenthethighandshank andindicateswhenthesetwosegmentsaremostout-of-phasewitheachother.Anegativerelative phaseangleindicatesthethighsegment'scontributiontothisvalueisdominantandthepositive slopeafterthisminimummeanstheshankisbecomingtheleadingsegmentintherelativephase 237

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anglecalculation.Thedelayedtimingofkneeexionto40 ¡ andreducedhiprangeofmotion duringTMwalkingisfurtherexpandeduponbytheseCEs,whichrevealthereducedrangeisdue toadelayedtimingoffooto thatcausesthethighPPtrajectorytoadvanceclosertovertical (e.g.decreasing,divergentTMPPtrajectory).ThesethreeCEsrevealthespeedatwhich segmentsaredissociatingfromthisextensionsynergyisbeingreducedandcontributingtothe overallgaitpatternatfooto .Asaresultofthereducedshankangularvelocityandbecausethe thighisclosertoverticalatfooto duringTMwalking,theabsoluteminimumofthethigh-shank CPRDisattenuated. F.1.2Knee-AnkleFunctionalParadox MechanismBcapturesthecoordinationdynamicsofthethigh,shank,andfootduringinitial swing.Thefollowingdiagramhighlightsthesegmentsorientationandcorrespondingthigh,shank, andfootphaseportraitfeatures. FigureF.1.2:Diagramofknee-anklefunctionalparadoxandcorrespondingthigh,shank,andfoot phaseportraits. Achievingsu cientkneeexionforuninhibitedfootclearanceandlegswingisanimportant functionofthelegduringswinglimbadvancement.Adequatekneeexion,su cientforwardlimb momentumfromrapidhipexion,andactivationofthebicepsfemorismuscletoreachmaximum kneeexionarethreemechanisms,whoseprecisetimingandmagnitudemustbeaccomplishedin ordertoliftthefootenoughforunobstructedgroundclearanceandlimbadvancement[17].In additiontoidentifyingthesecriticalfunctionsininitialswing,Perrypresentedtheparadoxical relationshipbetweenthekneeandanklejointswhileliftingthefoot.ThreeCEscapturethis paradoxicalknee-anklerelationship:thigh-shankCRPDzero-crossingafterfooto ,shank-foot CRPDlocalmaximum,andshankminimumangulardisplacement.DuringTMwalking, attenuationoftheshankminimumangulardisplacementandresultingreductioninangular velocitynotonlyexpoundsuponhowthepeakkneeexionandstridelengtharereducedbutalso 238

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correspondstoashankPPphaseanglenearzero.Thereforetherelativephaseanglemagnitudeof theshank-footCRPD'sreectschangesinthefootPPtrajectory,resultinginalocalmaximum thatcaptureswhenthefootisatitsmostverticalorientationwithrespecttotheoor.The thigh-shankCRPDzero-crossingindicatesthesetwosegmentsarein-phasewitheachotherbecause thePPtrajectoriesforthesetwosegmentsarechangingatthesamerate,thethighPPphaseangle isdecreasing,andtheincreasingshankPPphaseanglebeginsdominatingtherelativephaseangle asitswingsforwardabouttheknee.ThesethreeCEselucidatetheprecisetemporalandspatial organizationofthesesegmentsnecessaryfortheoptimalsegmentorganizationcriticalforsu cient footclearanceandrevealtheparadoxicalknee-anklerelationshipbetweenduringlimbclearance. F.1.3PassiveKneeExtension Thisthirdmechanism(C)describesthependularsegmentalrelationshipsduringpassiveextension oftheknee.AsthethighPPtrajectoryrateofchangedecreasesandapproachesanabscissa zero-crossing(e.g.maximumangulardisplacement),thefootPPtrajectoryisacceleratingasthe footapproachesahorizontalorientationwithrespecttotheoorandtransitionsfrom plantarexiontodorsiexion(e.g.nearanklekinematiczero-crossing).Thischangeinrelationship betweenthesetwosegmentsmanifestsasalocalmaximumonthethigh-footCRPD,whichis predominantlyinuencedbythefootPPphaseanglebecausethethighPPphaseangleis approximatelyzero.TheattenuationofthisextremumduringTMwalkingmeansthesubjects increasedtherateofchangeinthefootPPtrajectory(e.g.positionandvelocity)inorderto su cientlyadvancethefootintimefortheup-comingfootstrikeandcompensateforanoverall reducedswingperiodduration. Oncethefootislocatedaheadofthehipjointcenter,thependularmotionofthelegsegmentsand momentumfromhipexioncontributestocompletionofswinglimbadvancement(e.g.passive kneeextension).Asignicantreductioninthemagnitudeoftheshank'smaximumangularvelocity duringTMwalkingcoincideswiththePPtrajectorybeginningtonoticeablydivergetoasmaller orbitfromtheOGtrajectorycausingareducedpendularvelocityanddisplacementoftheshank fortheremainderofswingperiod.Otherstudiesreportingshorterswingperioddurationhavealso observedincreasedcadenceandshortersteplength,allofwhichcanbeattributedtodecreasedhip andkneeextension,inpartasaresultofthealteredpendularmotionofthecontralateralsupport limbasmovesbackwardbythetreadandrotatesaboutthehipinsteadoftheinvertedpendular motionabouttheankleduringOGwalking.Consideringthesealteredpendularmechanicsofthe legs,thetemporal-spatialandkinematicsofthelegsegmentsduringterminalswingcanbefurther expoundeduponbytheabatedshankPPtrajectoryduringTMwalking.ThediminishedPP trajectoryrevealedtheshankphaseanglecausedanattenuationoftheshank-footCRPDabsolute maximum,thigh-footCRPDlocalminimum,andfootPPmaximumangulardisplacementand minimumangularvelocity.Thesignicantlydelayedandreducedfootminimumangularvelocity andmaximumangulardisplacement,occurringjustafterthefootisorientedhorizontally,is predominantlyduetotheshank'spendularmotionbecausethereisasmallamountofchangein theanklejointangleduringterminalswing.Sincetherewasageneraltrendofdelayedand attenuatedswingeventsduringTMwalking,therewaslesstimetoswingthetibiaforwardfrom verticalandthesubjectscompensatedbyincreasingthephaseanglerateofchange(e.g.spatial adjustmentoftheshanktomeettemporalconstraintofimpendingfootstrike). F.1.4AnticipationofHeelFirstInitialContact Thefourthmechanism(D),capturestheelegantorganizationofthelowerlimbsegmentsin anticipationofaheelrstinitialcontactandtheimpendingtaskofloadingresponse.Inorderto positionthelegsegmentsintheideallocationsunderthetemporalconstraintofareducedswing periodandspatialconstraintofashorterstridelengthduringTMwalking,thesegmentsmustbe coupledanduncoupledattheappropriateinstancesinthegaitcycle.Preparationofthelimb segmentsforaheelrstinitialcontactandweightacceptanceduringloadingresponseisassociated withthethighPPmaximumangulardisplacement,shankPPmaximumangulardisplacement,and 239

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shank-footCRPDzero-crossing,afterwhichantagonisticactionofthehamstringsdeceleratethe hipandpreventexcessivekneeextension.Aspreviouslymentioned,duringTMwalkingthethigh andshankPPtrajectoriesnoticeablydivergefromtheOGtrajectoriesasacompensationforthe decreasedswingperioddurationandshorterstridelength.Thedelayedoccurrenceofthenal zero-crossingontheshank-footCRPDrevealsthesubjectspostponedwhentherelationship betweenthesetwosegmentsswitchedfromkneeextensiontoslightexion.Themaximumangular displacementoftheshankcorrespondstothepreparatorypositioningofthelowerlegandthe abilitytoachievefullkneeextensionwithslightkneeexioninanticipationofheelstrikeand weightacceptance.Thesubjects'intactnervoussystemswerecapableofmaintaininganormal kinematicpatternbyusingsmalladjustmentsincoordinationdynamicstoreorganizeand appropriatelypositionthesegmentsforheelrstinitialcontactandloadingresponsewithinthe lastfewpercentagesofthegaitcycle. F.2SagittalThigh-ShankCoordinationDynamics Theremainingsectionsofthisappendixprovideadditionalobservationsaboutsagittalphase portraitandcontinuousrelativephasediagramcurvefeaturesduringthetaskofswinglimb advancement.Thecontentsinthefollowingsectionsoftheappendixaremeanttoserveasa generalprimerthatrelatesthesecurvefeaturestothesegmentalandinter-segmentalbehaviorin Euclideanspace.Whiletheobservationsandinterpretationsweremadefromalargecohortof unimpairedsubjects,themeanphaseportraitsandmeanensemblecontinuousrelativephase diagramswereconstructedfromanexemplarunimpairedretrospectivesubjectwhilewalking over-groundataself-selectedspeed.Allplotmagnitudesandtimingsreportedareapproximate valuesandareusedasageneralguide. F.2.1Pre-Swing50-60% FigureF.2.1:Thighandshankphaseportraits&continuousrelativephasediagramfrom50-60%of gaitcycle. Similartotheterminalstancephase,thepre-swingphasehasthreeimportantmechanismsthat mustoccurinordertogainsu cientkneeexionandpreparethelimbforswing.First,thecenter ofpressure(CoP)musttransitiontothedistalsideofthe(MP)jointssoastoremoveany stabilizingforcesonthefootandshank(seeprevioussectionabouttheseforces).Secondly,the gastrocnemiusmusclemustresoastocauseadirectexoractiononthekneejoint,which preparesthefootforsu cientgroundclearance.Thirdly,inorderforthestancelimbtosu ciently unload,thebodyweightmustberapidlytransferredfromthestancelimbtotheoppositelimb. F.2.1.1ThighPhasePortrait Asthestancelimbisunloadedandstabilizingforcesthatwerepresentinterminalstanceare removed,thethighbeginstoincreaseitsangularvelocitytowardexion.Allthreeofthe 240

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previouslymentionedcriticalpre-swingmechanismsresultinapproximately40 ¡ ofpassiveknee exion.Thisisdisplayedonthethighphaseportraitasanincreaseinangulardisplacementandon theshankphaseportraitasadecreaseinangulardisplacement,thereforecausingbothphase portraittrajectoriestocontinueinaclockwisecirculardirection. FigureF.2.2:Thighandshankangulardisplacementchangesatthestartandendofpre-swing. Duringthebeginningofthisphase,thethighphaseportraithastheabsoluteminimumangular displacementbetweenapproximately70 ¡ and75 ¡ fortheentiregaitcycle.Thiscorrespondstothe zerocrossingdiscussedintheterminalstancesectionandtrailinglimbposture. F.2.1.2ShankPhasePortrait Inconjunctionwiththeresidualtensionintheplantarexionmuscles,theremovaloftibial stabilityallowsforaccelerationofheelriseandtibialadvancement.Thismechanismmanifestsin phasespaceasadecreaseintherateofchangeoftheshank'sangulardisplacementandalocal minimum.Thissecondlocalminimumofstancecorrespondstoanapproximateangular displacementof50 ¡ andanangularvelocityof-200 ¡ /s.Afterthislocalminimum,theshank's phasetrajectorybeginstoprepareforfooto bymovingtowardexion(decreasingextension angularvelocityanddecreasingangulardisplacement),asaresultofthekneeexioncausedbythe ringofthegastrocnemiusmuscleandpreviouslymentionedcriticalpre-swingmechanisms.Foot o willoccuratorwithinafewpercentsofthegaitcycleofthislocalminimum;variationsinthis gaiteventareattributedtotheindividualvariationsofeachperson'sgait. F.2.1.3ContinuousRelativePhaseDiagram Therelativephasediagram'snegativeslopeincreasesinmagnitude,whichcorrespondstothe increasedangularvelocityofthethigh,indicatingthethighismovingfasterthantheshankin phasespace.Ifthee cientbiomechanicsofgaitaretooccurthistrendcannotcontinuepastfoot o ,thereforeatapproximatelyfooto thecurvereachestheabsoluteminimumrelativephase anglefortheentiregaitcycle. 241

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F.2.2InitialSwing60-75% FigureF.2.3:Thighandshankphaseportraits&continuousrelativephasediagramfrom60-75%of gaitcycle. Themostimportantfunctionofthelegduringthisgaitcycleistoachievesu cientkneeexion (60 ¡ )foruninhibitedfootclearanceandswing.Again,therearethreemechanisms,whoseprecise timingandmagnitude,mustbeaccomplishedinordertoliftthefootenoughforunobstructed groundclearanceandlimbadvancement.Therstofthesecriticalmechanisms,adequateknee exionof(40 ¡ )occursattheendofthepre-swingphase.Secondly,rapidexionofthehipis requiredtoinstigateamplelimbmomentum.Lastly,activeexionofthekneebythebiceps femorismuscleensuresthekneereachestherequired60 ¡ ofexion. Inadditiontoidentifyingthecriticaleventsofthekneeininitialswing,Perryalsopresentsthe paradoxicalrelationshipbetweenthekneeandanklejointsduringthisphasewhileliftingthefoot. Kneeexionasopposedtoankledorsiexionallowsforsu cientfootclearance.However,inorder toobtainthisessentialkneeexion,otherdistalmechanismsaremoreinuentialinachievingthis exionvaluethanthekneejointitself.Thisparadoxicalrelationshipisanexemplarcaseingait thatshowshowindividualsegmentmovementbehaviorandinter-segmentalcoordination,derived fromnonlineartechniques,providesclinicalinsightsintothecomplexanddynamicrelationshipsof segmentsduringgait. F.2.2.1ThighPhasePortrait Duringthisphaseofgait,thethighismovingatitshighestexionangularvelocities(200 ¡ /s)and isthereforeadvancingthethightowardthecycle'smaximumangulardisplacement.When consideringtheanalogyofapendulum,itislogicalthatatthethigh'smaximumangularvelocity ormaximumkineticenergy,thethighisapproximatelyvertical.Physiologically,thismaximum (exion)angularvelocityandthesegment'smomentumcanbeattributedtotherapidcontraction oftheiliacusmuscleandisoneofthethreecriticalinitialswingmechanismspreviouslymentioned. Oncethethighhasreacheditspeakangularvelocityandverticalorientation,atapproximately 65%ofthegaitcycle,itstaystruetoitspendularmotionandbeginstodeceleratewhile continuingtoadvanceforwardinswing. F.2.2.2ShankPhasePortrait Whenthethighisverticalandatitsmaximumangularvelocity,theshankisatitssmallest angulardisplacementfortheentiregaitcycle(35 ¡ ).Thisminimumangulardisplacementofthe shankcorrespondstoazerocrossingoftheangularvelocityaxis.Fortheshank,thiszerocrossing representsthetransitionfromextensiontoexionoftheshank.Additionally,thesmallestangular displacementangleoftheshankcorrespondstoexionofthekneeandtheankle'sabilityto transitionfrompassiveplantarexiontoactivedorsiexion(refertoshank-footinitialswing 242

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sectionformoredetails).Whenthethighisverticalandthekneeisapproachingitspeakknee exion,theanklebeginstoactivelydorsiextoassistinfootclearance.Thesethreecrucial mechanicaleventsareeasilyidentiedonthephaseportraitsbelow,aslocalextremaandillustrate theparadoxbetweenthekneeandankleduringlimbclearance. FigureF.2.4:Dynamicconnectionbetweenkneeandanklemovementcriticalforfootclearance. Deviationoftheoccurrenceofanyoftheseeventswillimpairthelimb'sabilitytoe ectively continueitsswingmomentum,achievetherequiredswingkneeexion,andclearthefoot. F.2.2.3ContinuousRelativePhaseDiagram Theparadoxoffootclearanceandinter-dependenceofcriticaleventsatthekneeandankleare alsoclearlyillustratedwiththethigh-shankandshank-footrelativephasediagrams.Whenthe shank'sangularvelocityisapproximatelyzero,itsphaseangleisalsozero.Atthissametimein 243

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thegaitcyclethethighisverticallyorientedsoitsphaseangleisapproximately45 ¡ ,asshownin thegurebelow. FigureF.2.5:Momentofoptimalfootclearancedemonstratedonthethigh-shank&shank-foot continuousrelativephasediagrams. Thereforethethigh-shankrelativephaseangleisapproximately-45 ¡ andcorrespondstothe previouslymentionedcriticaleventsatthekneeandanklethatarenecessaryforfootclearance. Thisinectionpointonthethigh-shankrelativephasecurvealsocorrespondstothemaximum instantaneousslopeduringswingandisalsoacriticalvaluetoachieveduringtheswingphasein ordertosu cientlypreparethelimbforterminalstanceandtheimpendingfootcontactofthe nextgaitcycle.Similarly,theshank-footrelativephasecurveillustratesthedynamicandcomplex relationshipsbetweenthelowerlimbsegments.Oncetheanklebeginstoactivelydorsiex,the correspondingfootphaseangleisapproximately35 ¡ .Atthissametimeinthegaitcycle,the shank'sphaseangleiszero;thereforealocalmaximumofapproximately35 ¡ canbeseenonthe shank-footrelativephasediagram.Thelowdimensionalityoftherelativephasediagramallowsfor e ortlessidenticationofthesecriticalandcomplexgaitmechanismsandrequirestheexamination ofonlytwocurves,comparedtousingmultiplekinematiccurves. 244

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F.2.3Mid-Swing75-87% FigureF.2.6:Thighandshankphaseportraits&continuousrelativephasediagramfrom75-87%of gaitcycle. Oncethefoothasclearedtheground,kneeextensionisanecessarymotioninordertocontinue limbadvancementsoastopreparetheswinglimbfortheup-comingheelstrikeandbeginningofa newstancephase.Thetransitionfromkneeexiontoextensionispassivelyachievedbyhipexion andthecompoundpendularmotionofthethighandshank. F.2.3.1ThighPhasePortrait Thethighsegmentiscontinuingtoadvancetowarditsabsolutemaximumangulardisplacement valuefortheentiregaitcycle.Duringthisportionofthighadvancement,theangularvelocity beginstodecreaseinanticipationofreachingthemaximumnecessaryhipexionandsoasnotto overshootandcausehyper-exionofthehiporhyper-extensionoftheknee. F.2.3.2ShankPhasePortrait Oncethefoothassu cientlyclearedthegroundandbecomesanteriortothehipjointcenter,the kneebeginstoextend.Atthisphaseinthegaitcycletheshank'spositioninEuclideanspaceis trailingthethigh'sposition.Passivekneeexionisachievedasaresultofthecombinedinuence ofhipexionandtheforceofgravityactingontheshank.Returningtotheanalogyofa compoundpendulum,themomentumcausedbyhipexionpullstheshankforwardinconjunction withgravity'spullontheshank,asillustratedinthefollowinggure.Whentheshankreachesa verticalorientation,thesetwoforcesbalanceeachotherout. FigureF.2.7:Compoundthigh-shankpendulumfreebodydiagram,withforceofhipexionon shank(greenarrow)andforceofgravityonshank(bluearrow). 245

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Theshankphaseportraitcontinuesadvancingtowarditsmaximumangulardisplacementduring theswingphase,whichistraditionallyknownastheachievementoftibiavertical.Whentheshank reachesaverticalorientation,thecorrespondingangularvelocity(400 ¡ /s)isthemaximumforthe entiregaitcycle. F.2.3.3ContinuousRelativePhaseDiagram Thethigh-shankrelativephasediagramcontinuestoapproachitsabsolutemaximum(60 ¡ )atthe endofthisgaitcyclephase.Additionally,thereisanoticeablechangeintheslope'ssteepness duringthisphasewhencomparedtotheslopeduringinitialswing.Thisdecreaseinthesteepness oftheslopecanbeattributedtothedecreasingangularvelocityofthethigh.Dependinguponthe individual'sparticulargaitpattern,theremaybeadistinguishabledoublebumpatthisphasein thegaitcycle. F.2.4TerminalSwing87-100% FigureF.2.8:Thighandshankphaseportraits&continuousrelativephasediagramfrom87-100% ofgaitcycle. Atthisnalphaseinthegaitcycle,theremainingcriticaleventistocontinuethekneeextension frommidswinginordertopreparethelimbforfootcontactandweightacceptanceduringinitial doublesupport. F.2.4.1ThighPhasePortrait Thethighcontinuestodeceleratenowthatoptimalhipexionhasbeenachieved(30 ¡ ).Inphase spacethisoptimalhipexioncanbecorrelatedwithanangulardisplacementbetween110 ¡ and 115 ¡ andanangularvelocityofzero,asshowninthegurebelow. 246

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FigureF.2.9:Angleofthethighwithrespecttoglobalhorizontalandglobalverticalatmaximum hipextensioninterminalstancephase. Additionally,attheendofterminalswing,thehamstringsmuscleresinordertoprevent excessivekneeextensionandcontributetothedecelerationofthehip.Thefollowingguredepicts thissubtlemuscleactivation,whichiseasilydistinguishableonthethighphaseportraitasa suddendecreaseintheangulardisplacementawayfromtheabsolutemaximum. FigureF.2.10:Hamstringsactivationpreventingexcessivekneeextensiononthighphaseportrait. Atthecompletionofthisphase,thethigh'sphaseportraitvaluesshouldcorrespondtotheinitial contactangulardisplacementof110 ¡ andanangularvelocityof-20 ¡ /s. F.2.4.2ShankPhasePortrait Theshankcontinuestoincreaseitsangulardisplacementasthekneeisextendedinpreparationfor stance.Theshankreachesitsabsolutemaximumangulardisplacementfortheentiregaitcycleat approximately97%ofthegaitcycle.Thismaximumangulardisplacement(108 ¡ )correspondsto zeroangularvelocity.Thequadricepsmusclesareactivatedtoliftthecombinedweightofthe shankandfootduringthisphase.Astheshankandfootareliftedbythequadriceps,theforceof gravitypullsontheshankandcausesaslightdecreaseinthesegment'sangulardisplacement.This actionshouldresultinanalangulardisplacementof106 ¡ andanangularvelocityof-120 ¡ /s. 247

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F.2.4.3ContinuousRelativePhaseDiagram Duringthebeginningofthisphase,theabsolutemaximumrelativephaseangle(60 ¡ )demarcatesa changeinthecoordinationrelationshipbetweenthethighandshank.Afterthismaximum,the slopebecomesnegativeandindicatesthethighisnowmovingfasterinphasespacethanthe shank.Thisnegativeslopewillcontinuefortheremainderofthegaitcycleandresultinazero crossing.Atapproximately97%ofthegaitcycle,correspondingtotheshankphaseportrait'szero crossing;therelativephaseanglewillbezero.Thiszerocrossingontherelativephasediagram indicatesthetransitionfromtheshankleadingthethightothethighnowleadingtheshankin phasespace.Atthecompletionofthisphase,therelativephasediagramwillhaveavalueof approximately-25 ¡ whichisideallyequivalenttothestartinginitialcontactvalue. F.3SagittalShank-FootCoordinationDynamics F.3.1Pre-Swing50-60% FigureF.3.1:Shankandfootphaseportraits&continuousrelativephasediagramfrom50-60%of gaitcycle. Pre-swingbeginswithoppositefootcontactonthewalkingsurfaceandendswithfooto .Priorto footo ,theanklerapidlyplantarexessoastocreatetheballisticforwardforcesnecessaryto su cientlypropelthelowerlegintotheinitialphasesofswing. F.3.1.1ShankPhasePortrait Thetrajectoryoftheshank's(andfoot)phaseportraitbeginstoapproachalocalminimumthat correspondsapproximatelytothemaximumplantarexionofthegaitcycle,asshownbythe verticallineinthesagittalplaneanklekinematiccurvebelow. FigureF.3.2:Minimumsagittalankle(kinematic)plantarexioncorrespondingtolocalminimum onshank&footphaseportraits. 248

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Thislocalminimum( ( 50 ¡ )ontheshankphaseportraitcorrespondstothelargestnegative angularvelocity(-200 ¡ /s)fortheentiregaitcycle.Afterthisminimumandinanticipationoffoot o ,theshankphaseportraitbeginstoapproachexion(positiveangularvelocity)anditssmallest angulardisplacementasaprecursortotrailinglimbposture. F.3.1.2FootPhasePortrait Attheendofterminalstance,thereisnostabilizingforcewithinthefoot,sotheunrestrictedfoot plantarexesasaresultoftheringofthegastrocnemiusmuscle.Thefootphaseportrait continuestowardthelargestnegativeangularvelocityorlocalminimum,whichcorrespondstothe maximumplantarexionintheentiregaitcycle.Afterthislocalminimum(135 ¡ ),thetrajectoryof thefootphaseportrait'sangularvelocitybeginstoapproachzero. F.3.1.3ContinuousRelativePhaseDiagram Thelocalminimaofthephaseportraitsdescribedabovealsocorrespondtoalocalminimuminthe relativephasediagram,whichhasarelativephaseangleofapproximatelyzero.Thislocalextrema indicatesachangeinthecoordinationpatternbetweentheshankandfoot,whichcanbe physiologicallyattributedtothelackofastabilizingforceonthefootcausingunrestricted plantarexion.Furthermore,thisprecursoreventiscrucialforpreparationoffooto ande cient biomechanicsforunimpairedswinglimbadvancement.Footo willoccurwithinafewpercentages ofthegaitcycleofthislocalminimumandmightbeslightlybeforefooto asaresultofthe individual'strailinglimbposture.Thislocalminimumisfollowedbyapositiverelativephase slope,whichcorrespondstotheexpectedincreasingandpassiveplantarexionmovementofthe footandisnotthepredominantlycontributingsegmentoftherelativephaseangle. F.3.2InitialSwing60-75% FigureF.3.3:Shankandfootphaseportraits&continuousrelativephasediagramfrom60-75%of gaitcycle. Thisphasebeginswithfooto andendswithfeetbeingadjacent,whichinordertooccurrequires theabilitytotransitionfrompassiveplantarexiontoactivedorsiexionforsu cientlimb clearance.Othercriticalinter-segmentalcoordinationstrategiesmustoccurforsu cientlimb clearancebutthosearecreatedbyothermoreproximalsegments. F.3.2.1ShankPhasePortrait Slightlyafterthefoot'stransitionfrompassiveplantarexiontoactivedorsiexion,theshank phaseportraitcrossestheangularvelocityaxis'zeropointdenotingatransitionfromextensionto exion.Additionally,thiszerocrossingiscorrelatedwiththesmallestangulardisplacement( ( 35 ¡ ) oftheshankfortheentiregaitcycle. 249

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F.3.2.2FootPhasePortrait Theabsoluteminimumangulardisplacementofthefootfortheentiregaitcycleoccursinthis phaseandcorrespondstoazerocrossingattheangularvelocityaxis.Thezeroangularvelocity andtheminimumangulardisplacement( ( 115 ¡ )distinguishthetransitionfrompassive plantarexiontothebeginningofactivedorsiexion.Thisisacriticaleventinthegaitcycle becauseitsigniestheability(attheankle)tosu cientlyprepareforlimbclearanceduringswing. Attheendofthegaitphase,thefootbeginstoplateauandmaintainsaconstantrateofangular velocitywhileitcontinuestodorsiex.Additionally,thisclearanceofthetoesattheendofinitial swingresultsinthefootbeinginanearneutralpositionatapproximatelythesametimetheswing footisoppositethestancelimb. F.3.2.3ContinuousRelativePhaseDiagram Thelocalminimum( ( 50 ¡ )atorjustpriortofooto isfollowedbyapositiverelativephaseslope andaspreviouslymentionedcorrespondstotheexpectedincreasingandpassiveplantarexion movementofthefoot(whichisnotthepredominantlycontributingsegment).However,ife ective anklefunctionistobeachievedinswing(i.e.limbclearance)thefootcannotremainpassivelyin plantarexionandthereforeitmustbegintoactivelydorsiex( ( 35 ¡ ).Thismotorcontrolschema changeisindicatedontherelativephasediagramasalocalmaximumthatisapproximatelyhalfof themaximumintheloadingresponsephase.Thischangeinmotorschemaisacriticalmechanism thatnotonlyallowsforsu cientlimbclearanceattheanklebutalsoattheknee. F.3.3Mid-Swing75-87% FigureF.3.4:Shankandfootphaseportraits&continuousrelativephasediagramfrom75-87%of gaitcycle. Mid-stanceisinitiatedwhentheswingfootisadjacenttothestancefoot.Astheswingleg continuestoadvance,thetibiawillbecomeverticalandinpreparationforterminalstancethe anklemustcontinuedorsiexionuntilitreachesaneutralposition. F.3.3.1ShankPhasePortrait Attheoccurrenceoffeetbeingadjacenttoeachother,theshankhasanangulardisplacementof approximately40 ¡ andcontinuesthroughoutthisphasetoextowardavertical(90 ¡ )angular displacement.Whenthetibiareachesvertical,thiscorrespondstotheabsolutemaximumangular velocity(400 ¡ /s)fortheentiregaitcycle.Additionally,whentheangulardisplacementisequalto 90 ¡ ,theanklehasreachedaneutralposition.Throughoutthisgaitphasetheshankcontinuesto increaseitsrateofforwardswingadvancement,duetothepassivependularmomentumofthe segment,andbeginstoapproachitsfastestratesofmovementwhichoccurinterminalstance. 250

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F.3.3.2FootPhasePortrait Asthelowerlimbcontinuestoadvanceforwardduringthisphaseandthetibiabecomesvertical, thedownwardtorqueontheankleincreases.Thereforeinordertoachievesu cientfootclearance andpreparationforterminalstanceandinitialcontacttheanklemustincreasetheinternal dorsiexionmomenttoadequatelycounterthisexternalplantarexionmoment.Fortypically developinganklesthiswillresultinanearneutralfootposition,asshownonthephasediagram's downwardturn(160 ¡ ,350 ¡ /s)towardanegativeangularvelocityanddeviationfromthepreceding nearlyhorizontalslopeandapproximateangularvelocityof380 ¡ /s. FigureF.3.5:Initiationofincreasedinternaldorsiexionmomentandankleapproachesneutral position. Whenthefootisneutral,theangulardisplacementshouldbenearly180 ¡ andcoincideswiththe tibiabeingvertical. F.3.3.3ContinuousRelativePhaseDiagram Theshankisnowtheleadingsegmentinphasespaceandthereforetherelativephaseangleis negative.Sincethetwosegmentsaremovingatapproximatelythesamespeedinphasespacethe slopeoftherelativephasediagramisnearlyhorizontal( & ( -20 ¡ ),withperhapsaslightnegative trendastheshankbeginstoapproachitsfastestratesofforwardadvancement.Asthetibia reachesaverticalpositionandtheankleachievesaneutralposition,therelativephasecurvemakes asignicantandrapiddirectionchangedownwardtothemaximumnegativephaseangleforthe entiregaitcycle(FigureF3.6). 251

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FigureF.3.6:Therstarrowindicatesnearlyhorizontalslopeandthesecondarrowdemarcatesthe rapidchangetowardthelocalmaximumatankleneutral/tibiavertical. F.3.4TerminalSwing87-100% FigureF.3.7:Shankandfootphaseportraits&continuousrelativephasediagramfrom87-100%of gaitcycle. Uponachievingatibiaverticalpositiontheswinglimbisinitsnalstagesandmakessignicant changesinthemotorcontrolschemasoastoadequatelyprepareforinitialcontactandloading response.Thequadricepsmusclescontracttosupporttheshankandfootasthethighisextended inpreparationforheelrstinitialcontact. F.3.4.1ShankPhasePortrait Attheinitiationofthisphase,theshankisverticalbutasaresultofthepassivependular momentumcreatedatfooto continuestopropeltheshankforwardbeyondverticalbutata decreasingangularvelocity.Atthelastfewpercentsofgaitcycle,thehamstringseccentrically contractjustenoughtoreducetheangularvelocitytozero.Thiszerocrossingalsocorrespondsto themaximumangulardisplacement( ( 110 ¡ )oftheshankfortheentiregaitcycle.Atthissecond zerocrossingoftheshankphaseportrait,theringofthehamstringscausestheshanktomove eversosubtlyintoextension.Thisanticipatoryringofthehamstringsandresultingextensionof theshankoptimallypositionsthesegmentforinitialcontactandtheupcomingdemandofweight 252

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acceptance.Thereforetheshank'sangulardisplacementwillbeslightlylessthanthemaximum valueatzeroangularvelocity. F.3.4.2FootPhasePortrait Inpreparationforinitialcontact,thepretibialmusclescontinuetocontractandensuretheankle maintainsaneutralorslightlydorsiexedposition.Duringtherstportionsofthisphaseinthe gaitcyclethefoot'sangulardisplacementchangesarepredominatelyaresultoftheshank's continuedforwardadvancementbeyondverticalandnottheresultofindependentfootmovement. However,atthistimeinthegaitcyclethefootisnowleadingtheshankinEuclideanspaceand hasanangulardisplacementrangingfrom160 ¡ to170 ¡ .Ane ectivelyfunctioninganklewillbe slightlydorsiexedandhaveanangulardisplacementintherangelistedabovesoastoachieve heelcontact.Duringthelastportionsofthisphase,theankleactivelydorsiexesthefootin anticipationofoptimalheelcontact.Thefollowinggureillustratesthisdynamicmovementofthe foot,whichisshownasaloopthatisnowmovingtowardapositiveangularvelocityandnal dorsiexedposition.Inthelastpercentagesofthisphasethefootphaseportraitshouldreturnto theinitialphasevaluesofanangulardisplacementof ( 165 ¡ andanangularvelocityof ( 210 ¡ /s. FigureF.3.8:Ankleneutralandtibiavertical(circled).Dorsiexiontrendinpreparationforheel contact(arrow). F.3.4.3ContinuousRelativePhaseDiagram Whentheshankreachesaverticalpositionandtheankleachievesaneutralposition,therelative phasecurveequalsthemaximumnegativephaseanglefortheentiregaitcycle.Thismaximumwill occuratarelativephaseangleofapproximately110 ¡ andsigniesachangeinthecoordination strategiesoftheshankandfoot.Afterthismaximumthefootmustmaintainit'snearneutral positionastheshankcontinuesswingingforwardtowardmaximumexion.Astheshankcontinues toincreaseitsangulardisplacement,therelativephasecurvewillrapidlychangeitsslopetoa positivetrend.Atapproximately,97%ofthegaitcycletheringofthehamstringmusclesis correlatedwithazerocrossingoftherelativephasediagram,foratthispointinthegaitcyclethe 253

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shankwillberetractedslightlyfromitsmaximumexionpositiontowardextensioninpreparation forinitialcontact.Fortheremainingpercentagesofthegaitcycle,thefootassumestheroleofthe leadingsegmentinphasespace(indicatedbyapositiverelativephasevalue).Terminalswingon therelativephasediagramshouldcorrespondtothesamerelativephasevalueatinitialcontactof thisgaitcycle,whichisapproximately65 ¡ 254

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AppendixGAdditionalResults G.1AdditionalResultsforProspectiveExperiments Thefollowingtableprovidesthevariouscohorts'meanvaluesforthetimingofcriticaland temporalgaitevents. TableG.1.1:Meanvaluesforthetimingofcriticalandtemporalgaitevents. Cohort FOFATV (%GC)(%GC)(%GC) NPro(n=20)65(1.65)79(1.35)87(1.50) NRetro(n=120)60(2.14)77(1.08)85(1.49) CPPro(n=4)68(4.93)83(3.15)94(2.74) CPRetro(n=55)62(5.44)79(3.12)93(3.78) LLARetro(n=15)62(3.16)79(1.85)87(1.22) Cohort Knee0 ¡ MaxKneeFlexMaxHipFlexKnee40 ¡ (%GC)(%GC)(%GC)(%GC) NPro(n=20)96(2.24)74(1.43)93(5.66)65.9(1.33) NRetro(n=120)93(1.43)73(1.47)94(4.95)64(2.19) CPPro(n=4)67(20.79)85(8.28)98(3.27)65(1.41) CPRetro(n=55)98(8.39)80(6.05)96(3.56)62(7.00) LLARetro(n=15)92(19.28)75(4.67)96(4.78)59(19.81) Mean(standarddeviation)timing(%GC)ofeachcohort'stemporalandcriticalgaiteventsofgait forover-groundwalking,whereFO=footo ,FA=feetadjacent,andTV=tibiavertical. Thefollowingtableprovidesthevariouscohorts'meanvaluesforcommontemporal-spatial descriptorsofgaitandthetimingofcriticalandtemporalgaiteventsduringover-groundwalking. TableG.1.2:Cohorts'commontemporal-spatialdescriptorsofgait. Cohort RapidAnkle Ankle0 ¡ Walking Cadence DorsiexionSpeed ( ¡ /%GC)(%GC)(m/min)(steps/min) NPro(n=20)-2.10(0.39)85(5.81)81.18(11.42)110.60(7.19) NRetro(n=120)-2.24(0.58)74(7.40)77.00(9.60)118.93(13.48) CPPro(n=4)-1.01(0.46)84(11.17)62.00(7.93)113.63(9.65) CPRetro(n=55)-1.19(0.58)77(12.63)55.53(15.48)128.29(21.66) LLARetro(n=15)-0.62(0.46)79(17.60)66.66(10.76)108.62(11.16) Cohort StrideStrideStep LengthTimeTime (m)(sec)(sec) NPro(n=20)1.47(0.17)1.09(0.07)0.54(0.04) NRetro(n=120)1.30(0.15)1.02(0.11)0.51(0.06) CPPro(n=4)1.12(0.18)1.07(0.09)0.54(0.04) CPRetro(n=55)0.87(0.19)0.96(0.16)0.49(0.09) LLARetro(n=15)1.23(0.18)1.11(0.11)0.57(0.06) Mean(standarddeviation)ofeachcohort'scriticalgaiteventsandcommontemporal-spatial measuresofgait. 255

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Thefollowingtablewasgeneratedfromtheunimpairedprospectivecohort'sover-groundwalking task. TableG.1.3:Relativephaseanglesforcommontemporalgaiteventsforunimpairedprospective subjects. CRPDFootStrike0%( 0.00%)OppositeFootO 13%( 1.40%) Pelvis-Thigh2.49( 11.99)-2.96to0.96-38.93( 5.84)-35.16to-32.84 Thigh-Shank-41.88( 18.27)-52.30to-45.70-12.31( 8.43)-22.54to-19.46 Shank-Foot90.57( 18.54)96.93to103.0757.20( 6.70)51.06to54.94 Thigh-Foot48.69( 13.04)49.12to52.8844.89( 6.35)29.89to34.11 CRPDOppositeFootOn50%( 0.80%)FootO 65%( 1.70%) Pelvis-Thigh-25.46( 12.36)-28.50to-23.5067.22( 2.87)58.65to61.35 Thigh-Shank-40.04( 14.95)-46.06to-39.94-136.87( 7.37)-137.54to-134.46 Shank-Foot22.52( 7.92)15.83to18.1727.31( 30.54)1.87to4.13 Thigh-Foot-17.53( 19.59-29.82to-22.18-109.55( 36.20)-137.30to-128.70 Mean,1standarddeviation,and95%condenceintervalsfortherelativephaseangles(degrees)at commontemporalgaiteventsforunimpairedprospectivesubjects.Theprospectivecohort'smean and1standarddeviationforthepercentgaitcycleforeachtemporalgaiteventisalsoreported. Thefollowingtableindicatesifthecontinuousrelativephaseanglevaluesfortheunimpaired prospectivesubjectsarewithinthe95%condenceintervalsofthecontinuousrelativephaseangle valuesforunimpairedretrospectivesubjects. TableG.1.4:Comparisonoftheunimpairedprospectiveandretrospectivesubjects'relativephase angles. CRPDFootOnOppositeFootO OppositeFootOnFootO Pelvis-ThighYNYN Thigh-ShankYNYY Shank-FootNNNN Thigh-FootNNNN Comparisonoftheunimpairedprospectiveandretrospectivesubject'sgroups.Yindicatesthe unimpairedprospectivegroups'CRPDvaluesfallwithinthe95%condenceintervalsofthe unimpairedprospectivesubjectsandNindicatestheprospectivegroupsCRPDvaluesareoutside oftheretrospectivegroup's95%condenceintervals. Thefollowinggureprovidesacloserviewofthecontinuousrelativephasediagramsduringswing periodfortheprospectiveunimpairedsubjects'varioustreadmillspeedswalkingtask. 256

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FigureG.1.1:Continuousrelativephasediagramsfortreadmillwalkingconditionsofunimpaired prospectivesubjects. Zoomedinviewofswingperiod,ensemblecontinuousrelativephasediagramsfortreadmill walkingconditionsofunimpairedprospectivesubjects(green=80%Vss,purple=90%Vss, blue=100%Vss,orange=110%Vss,red=120%Vss). Thegurebelowcontainsthemeanensemblesagittalplanekinematiccurvesfortheprospective subjects'over-groundandtreadmillwalkingtasks. 257

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FigureG.1.2:Kinematiccurvesforunimpairedprospectivesubjects. Meanensemblesagittalplanekinematiccurvesfortheunimpairedprospectivesubjects' over-ground(blue)andtreadmill(red)walkingtasks. 258

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Thefollowingtablepresentstheresultsfortheinvestigationintotheinvarianceandindependence ofselectcoordinationeventsforthedi erentunimpairedsubjects. TableG.1.5:r 2 andPearson(P)valuesforfourcriticalcoordinationevents. Demographic Thigh-FootCRPDThigh-FootCRPD LocalMinInectionPoint r 2 Pr 2 P Age(n=140)0.0522%0.02280.6154%0.0784 Age(n=120)0.7573%0.08702.4363%0.1561 Age(n=20)4.4938%0.212015.4845%0.3935 LegLength(n=140)0.0093%0.00960.2711%0.0521 LegLength(n=120)0.4798%0.06930.6455%0.0803 LegLength(n=20)17.7090%0.42084.9186%0.2218 Weight(n=140)0.0435%0.02080.0004%0.0020 Weight(n=120)0.1616%0.04020.2766%0.0526 Weight(n=20)12.8970%0.35919.0148%0.3002 Demographic ShankPPFootPP MaxADMaxAV r 2 Pr 2 P Age(n=140)0.0580%0.02410.7480%0.0865 Age(n=120)1.6828%0.12972.6548%0.1629 Age(n=20)1.9005%0.13790.3544%0.0595 LegLength(n=140)0.2454%0.04951.1511%0.1073 LegLength(n=120)0.3060%0.05531.9602%0.1400 LegLength(n=20)9.5086%0.30840.4989%0.0706 Weight(n=140)0.0116%0.01080.3325%0.0577 Weight(n=120)0.1280%0.03581.7335%0.1317 Weight(n=20)3.4638%0.18610.7726%0.0879 r 2 andPearson(P)valuesforthefourcriticalcoordinationeventsidentiedwiththeindependent andinvariantmethodologyfortheunimpairedsubjects,whereADisangulardisplacement,and AVisangularvelocity. 259

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Descriptivestatisticsforthefourcriticalcoordinationeventsidentiedusingcriteriaof independenceandinvariancefortheunimpairedprospectivesubjects. TableG.1.6:Timingoffourcriticalcoordinationeventsforallsubjects. Thigh-FootCRPDLocalMinThigh-FootCRPDIP CoordinationEventMean(SD)95%CIMean(SD)95%CI All(n=140)89.91( 2.13)85.74to94.0897.74( 1.25)95.29to100.19 Retro(n=120)89.98( 2.16)85.75to94.2297.80( 1.24)95.38to100.22 Pro(n=20)89.95( 2.86)84.35to95.5598.50( 1.43)95.69to101.00 CoordinationEvent ShankPPMaxADFootPPMaxAV Mean(SD)95%CIMean(SD)95%CI All(n=140)98.35( 1.23)95.93to100.7782.94( 3.65)75.77to90.10 Retro(n=120)98.46( 1.15)96.20to100.7183.03( 3.61)75.96to90.10 Pro(n=20)99.1( 0.97)97.20to101.0084.35( 2.70)79.06to89.64 Mean,standarddeviation(SD),and95%condenceintervals(CI)ofthetimingofthefourcritical coordinationeventsidentiedwiththeindependentandinvariantmethodologyforunimpaired prospectivesubjects,whereIPisaninectionpoint,ADisangulardisplacement,andAVis angularvelocity.Thegaitcyclewasindexedfrom1to101%forthisanalysis. TableG.1.7:Timingoffourcriticalcoordinationeventsidentiedwiththeindependentandinvariant methodology. #Subjects AgeThigh-FootThigh-FootShankPPFootPP (yr)CRPDMin(%GC)CRPDIPMaxADMaxAV 757to1890(2.16)98(1.31)98(1.23)83(3.89) 4420to2890(2.00)98(1.18)99(1.04)83(3.37) 1030to3891(3.06)98(0.99)99(1.14)84(3.00) 640to4691(1.22)97(0.89)98(0.71)83(2.86) 550to6689(1.15)98(1.53)99(1.53)80(2.52) Meansandstandarddeviationsofthetimingofthefourcriticalcoordinationeventsidentiedwith theindependentandinvariantmethodologyforallunimpairedsubjectssortedbyage,whereIPis aninectionpoint,ADisangulardisplacement,andAVisangularvelocity.Thegaitcyclewas indexedfrom1to101%forthisanalysis. Thethirdsub-investigationintothefourcriticalcoordinationeventsidentiedbytheinvariance andindependencecriteriaexaminethetimingoftheseeventsinrelationtothetimingofother swingperiodgaiteventsandtasks.Thefollowingguredepictstheconventionalcriticaland temporalgaiteventsandthetimingofthecriticalcoordinationeventsfortheunimpaired retrospectivecohort. FigureG.1.3:Diagramofthetimingofthefourcriticalcoordinationeventsidentiedbytheinvariant andindependentcriteriawiththetimingoftemporalandcriticalgaiteventsduringtheswingperiod ofthegaitcycle.Themeanandstandarddeviationofeventtimingswerecalculatedfromthe unimpairedretrospectivesubjects(n=120)andthegaitcyclewasindexfrom0to100%. 260

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G.2AdditionalResultsforAim2 Thefollowingtableprovidestheprospectivesubjects'meanaccuracyoftargettaps,forthethree targetsizes,forthereciprocaltappingtask. TableG.2.1:Averageaccuracyoffoottapshittingthetargetforthethreetargetsizes(80%,100%, 120%)usedinHypothesis2Afortheprospective CohortAccuracyforTargetSizeCohortAccuracyforTargetSize SubjectID80%100%120%SubjectID80%100%120% N100045.9866.5766.1N101163.6169.2563.57 N100131.1242.3444.88N101289.0989.0385.58 N100247.0589.0394.86N101389.1389.2684.5 N100346.7950.946.53N101472.7279.0968.41 N100486.2381.9477.93N101594.4690.2476.54 N100587.9284.7584.35N101687.9284.7584.35 N100690.992.4573.22N101790.992.4573.22 N100779.9963.0349.62N101879.9963.0349.62 N100891.4785.0467.68N101991.4785.0467.68 N100985.1986.6991.21C100085.1986.6991.21 N101066.2681.590.82C100166.2681.579.93 N101163.6169.2563.57C100263.6169.2577.33 N101289.0989.0385.58C100389.0989.0335.29 N101389.1389.2684.5 Thefollowingtableprovidesthep-valuesfromt-testscomparingthetimingandmagnitudeof thigh-shankCRPDcoordinationeventsininitialswingthatweresignicantlydi erentbetween theprospectivesubjectswithcerebralpalsy(CP)andtheunimpairedprospectivesubjects(N). TableG.2.2:T-testresultsbetweenthemeantiming(%GC)andmagnitudeforinitialswingthighshankcontinuousrelativephasediagram(CRPD)coordinationeventsfortheprospectiveunimpaired subjectsandsubjectswithCP.Thecoordinationeventswereaminimum(min),maximuminstantaneousslope(MiS),inectionpoint(IP),andazerocrossing(0x). Comparison Thigh-ShankCRPDMin(%)Thigh-ShankCRPDMiS (%GC)( ¡ ) (%GC)( ¡ ) NvsCP0.2460.1730.3090.025 Comparison Thigh-ShankCRPDIPThigh-ShankCRPD0x (%GC)( ¡ ) (%GC)( ¡ ) NvsCP0.3350.6530.3140.201 Thefollowingtableprovidesthep-valuesfromt-testscomparingthetimingandmagnitudeof thigh-footCRPDcoordinationeventsininitialswingthatweresignicantlydi erentbetweenthe prospectivesubjectswithcerebralpalsy(CP)andtheunimpairedprospectivesubjects(N). 261

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TableG.2.3:T-testresultsbetweenthemeantiming(%GC)andmagnitudeforinitialswingthighfootcontinuousrelativephasediagram(CRPD)coordinationeventsfortheprospectiveunimpaired subjectsandsubjectswithCP.Thecoordinationeventswereaminimum(min),maximuminstantaneousslope(MiS),inectionpoint(IP),andazerocrossing(0x). Comparison Thigh-FootCRPDMinThigh-FootCRPDMiS (%GC)( ¡ ) (%GC)( ¡ ) NvsCP0.4150.3050.4760.837 Comparison Thigh-FootCRPDIPThigh-FootCRPD0x (%GC)( ¡ ) (%GC)( ¡ ) NvsCP0.1970.6920.6490.613 ThefollowingtableprovidestheSCALEandICARS/SARAtaskscoresfortheprospective subjectswithcerebralpalsy. TableG.2.4:SCALEandICARSvaluesforprospectivesubjectswithcerebralpalsy. ProspectiveSubject SCALEICARS/SARA LeftLimbRightLimbScore C10005434 C10016635 C10024424 C1003227 ScoresfortheSelectiveControlAssessmentoftheLowerExtremity(SCALE)andInternational CooperativeAtaxiaRatingScale(ICARS)/ScalefortheAssessmentandRatingofAtaxia(SARA) examsfortheprospectivesubjectswithcerebralpalsy. Thefollowingtableprovidesaconditionallyformattedcorrelationmatrixforforwardswinglimb velocity(FSLC)andtargetaccuracyforthethreetargetsizesoftheprospectivereciprocaltapping taskandover-ground(OG)walkingforthethigh-shankCRPD. 262

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TableG.2.5:Correlationmatrixforforwardswinglimbvelocityandtargetaccuracy. Correlationmatrix,withconditionalformatting,forforwardswinglimbvelocity(FSLC)and targetaccuracyforthethreetargetsizesofthereciprocaltappingtaskandover-ground(OG) walking,withthemagnitudeandtimingofthemaximuminstantaneousslope(MiS)ininitial swingforthethigh-shankCRPD. Thefollowingtableisthecorrelationmatrix,withconditionalformatting,forthemagnitudeand timingofcoordinationeventsduringinitialswingforthethigh-shankandthigh-footCRPDsofthe prospectivesubjectswithCP. 263

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TableG.2.6:Correlationmatrixforcoordinationeventsforsubjectswithcerebralpalsy. Correlationmatrix,withconditionalformatting,forthemagnitudeandtiming(%GC)of coordinationeventsduringinitialswingforthethigh-shankandthigh-footCRPDsofthe prospectivesubjectswithcerebralpalsy(CP),withthemaximuminstantaneousslope(MiS), inectionpoint(IP),andzero-crossing(0x). Thenexttableisacorrelationmatrix,withconditionalformatting,forthemagnitudeandtiming ofcoordinationeventsduringinitialswingforthethigh-shankandthigh-footCRPDsofthe unimpairedprospectivesubjects. 264

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TableG.2.7:Correlationmatrixforcoordinationeventsforunimpairedsubjects. Correlationmatrix,withconditionalformatting,forthemagnitudeandtiming(%GC)of coordinationeventsduringinitialswingforthethigh-shankandthigh-footCRPDsofthe unimpairedprospectivesubjects,withthemaximuminstantaneousslope(MiS),inectionpoint (IP),andzero-crossing(0x). ThetablebelowisaconditionallyformattedcorrelationmatrixfortheSCALEscoreand signicantthigh-shankCRPDinitialswingcoordinationeventsforallprospectivesubjectswith cerebralpalsy. 265

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TableG.2.8:Correlationmatrixforprospectivesubjectswithcerebralpalsy. Correlationmatrix,withconditionalformatting,forallprospectivesubjectswithcerebralpalsy, whereMiSisthemaximuminstantaneousslopeandIPistheinectionpoint. Thefollowingconditionallyformattedtableisacorrelationmatrixforallunimpairedprospective subjectsandthesignicantinitialswingcoordinationeventsfromthethigh-shankCRPD. TableG.2.9:Correlationmatrixforunimpairedprospectivesubjects. Correlationmatrix,withconditionalformatting,forallunimpairedprospectivesubjects,where MiSisthemaximuminstantaneousslopeandIPistheinectionpoint. Theconditionallyformattedcorrelationmatrixbelowexaminestherelationshipbetweenthe 90 ¡ turncurvature( & ) andcommontemporal-spatialgaitmeasuresforallunimpairedprospective subjects. 266

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TableG.2.10:Correlationmatrixforunimpairedprospectivesubjectsfor90 ¡ turningtask. Correlationmatrix,withconditionalformatting,forallunimpairedprospectivesubjects,where & istheturncurvatureandOGVssistheself-selectedover-groundwalkingspeed. Theconditionallyformattedcorrelationmatrixbelowexaminestherelationshipbetweenthe 90 ¡ turncurvature( & ) ,ICARS/SARAscores,andcommontemporal-spatialgaitmeasuresforall prospectivesubjectswithcerebralpalsy. TableG.2.11:Correlationmatrixforprospectivesubjectswithcerebralpalsyfor90 ¡ turningtask. Correlationmatrix,withconditionalformatting,forallprospectivesubjectswithcerebralpalsy (CP),whereKistheturncurvatureandOGVssistheself-selectedover-groundwalkingspeed. Thefollowingtableprovidesdescriptivestatisticsforthebaseofsupportwidthforthevarious subjectcohortsforover-groundwalking. TableG.2.12:Baseofsupportvaluesforsubjects. StatisticN(n=140)CP(n=59)LLA(n=15) Mean43.9488.4560.21 StandardDeviation30.3442.3849.04 Variance920.771795.652404.68 Mean,standarddeviation,andvarianceforbaseofsupportduringrepresentativeover-ground walkingtrialforunimpairedsubjects(N),subjectswithcerebralpalsy(CP),andsubjectswitha lowerlimbamputation(LLA). 267

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G.3AdditionalResultsforAim3 Thefollowingtablecontainsthenormalizedrootmeansquareerrorvaluesbetweentheunimpaired cohortandtheoreticalpendulummodelfortheproximalanddistallinkages/segmentsforthefour dampingconditions. TableG.3.1:Unimpairedcohort'srankingsfor4pendulummodeldampingconditions. UnimpairedSubjects(n=120legs) DampingRank NRMSENRMSENRMSENRMSE % NRMSE Prox Prox Dist Dist + =017.78893.59049.57612.362923.31834 + =0.527.79033.04559.56095.182825.57953 + =1.047.79152.45869.55536.497326.30241 + =1.537.79261.86099.55276.967426.17355 Unimpairedcohort'srankingsfor4di erentpendulummodeldampingconditionswiththe normalizedrootmeansquareerror(NRMSE)fortheangulardisplacement( )andangular velocity( )betweentheproximal(Prox)anddistal(Dist)linkages/legsegments. Thefollowingtablecontainsthenormalizedrootmeansquareerrorvaluesbetweenthecohortwith asti kneegaitandtheoreticalpendulummodelfortheproximalanddistallinkages/segmentsfor thefourdampingconditions. TableG.3.2:Rankingsofsubjectswithasti kneegaitpatternfor4pendulummodeldamping conditions. SubjectswithSti KneeGaitPattern(n=60legs) DampingRank NRMSENRMSENRMSENRMSE % NRMSE Prox Prox Dist Dist + =017.78893.59049.57612.362923.31834 + =0.527.79033.04559.56095.182825.57953 + =1.047.79152.45869.55536.497326.30241 + =1.537.79261.86099.55276.967426.17355 Rankingsofsubjectswithasti kneegaitpatternfor4di erentpendulummodeldamping conditionswiththenormalizedrootmeansquareerror(NRMSE)fortheangulardisplacement( ) andangularvelocity( )betweentheproximal(Prox)anddistal(Dist)linkages/legsegments. Thefollowingtablecontainsthenormalizedrootmeansquareerrorvaluesbetweenthecohortwith acrouchgaitpatternandtheoreticalpendulummodelfortheproximalanddistal linkages/segmentsforthefourdampingconditions. 268

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TableG.3.3:Rankingsofsubjectswithacrouchgaitpatternfor4pendulummodeldamping conditions. SubjectswithCrouchGaitPattern(n=46legs) DampingRank NRMSENRMSENRMSENRMSE % NRMSE Prox Prox Dist Dist + =017.78893.59049.57612.362923.31834 + =0.527.79033.04559.56095.182825.57953 + =1.047.79152.45869.55536.497326.30241 + =1.537.79261.86099.55276.967426.17355 Rankingsofsubjectswithacrouchgaitpatternfor4di erentpendulummodeldamping conditionswiththenormalizedrootmeansquareerror(NRMSE)fortheangulardisplacement( ) andangularvelocity( )betweentheproximal(Prox)anddistal(Dist)linkages/legsegments. Thetablebelowcontainsthenormalizedrootmeansquareerrorvaluesbetweenthecohortabelow kneeamputationandtheoreticalpendulummodelfortheproximalanddistallinkages/segments forthefourdampingconditions. TableG.3.4:Rankingsofsubjectswithabelowkneeamputationfor4pendulummodeldamping conditions. SubjectswithBelowKneeamputation(n=13legs) DampingRank NRMSENRMSENRMSENRMSE % NRMSE Prox Prox Dist Dist + =017.67081.93209.52981.316620.4492 + =0.547.67032.21219.51356.979726.3756 + =1.037.67121.62349.50947.537326.3413 + =1.527.67230.88869.50797.706125.7749 Rankingsofsubjectswithabelowkneeamputationfor4di erentpendulummodeldamping conditionswiththenormalizedrootmeansquareerror(NRMSE)fortheangulardisplacement( ) andangularvelocity( )betweentheproximal(Prox)anddistal(Dist)linkages/legsegments. Thetablebelowcontainsthenormalizedrootmeansquareerrorvaluesbetweenthecohortan abovekneeamputationandtheoreticalpendulummodelfortheproximalanddistal linkages/segmentsforthefourdampingconditions. TableG.3.5:Rankingsofsubjectswithanabovekneeamputationfor4pendulummodeldamping conditions. SubjectswithAboveKneeamputation(n=6legs) DampingRank NRMSENRMSENRMSENRMSE % NRMSE Prox Prox Dist Dist + =017.64343.10219.59822.096122.4398 + =0.527.64462.71319.58144.514224.4533 + =1.037.64552.26949.57485.850525.3401 + =1.547.64631.79879.57166.340825.3574 Rankingsofsubjectswithanabovekneeamputationfor4di erentpendulummodeldamping conditionswiththenormalizedrootmeansquareerror(NRMSE)fortheangulardisplacement( ) andangularvelocity( )betweentheproximal(Prox)anddistal(Dist)linkages/legsegments. 269

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G.4AdditionalResultsforAim4 G.4.1AdditionalResultsforCoordinationDeviationIndex(CDI) Thefollowinggureshowstheresultfordeterminingthenumberofcontrolfeaturesrequiredfora 98%reconstructionqualityofanindividual'ssagittalplanephaseportraitsandcontinuousrelative phasediagrams. FigureG.4.1:NumberofcontrolfeaturesforCDI. Numberofcontrolfeaturesrequiredfora98%reconstructionqualityofthecoordinationcurves usedtocalculateasubject'scoordinationdeviationindex(CDI). Thenextgureprovidestheoriginalandreconstructed(usingthe98%reconstructionqualityfrom above)coordinationcurvesforarandomlyselectedunimpairedsubject. 270

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FigureG.4.2:Reconstructionofcoordinationcurves. Theoriginal(blue)andreconstructed(red)phaseportraitsandcontinuousrelativephasediagrams foranunimpairedsubjectwiththemeanensemblecurves(black/grey)ofretrospectiveunimpaired subjects(n=120). Lastly,thetablebelowprovidesthedemographiccharacteristics,gaitdeviationindex,and coordinationdeviationindexfortheunimpairedsubjects,subjectswithcerebralpalsy(CP),and subjectswithalowerlimbamputation(LLA) 271

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TableG.4.1:Demographiccharacteristicsandindicesvaluesforsubjects. Group LegsAgeLegLengthWeight GDICDI (#)(yr)(mm)(kg) Unimpaired12019.3 11.5845.5 97.058.2 19.5101.9 8.498.2 8.5 CP10011.9 4.9716.3 96.333.2 12.770.4 8.684.8 8.6 Sti Knee5410.6 3.6700.0 96.532.2 14.172.1 9.085.0 6.0 Crouch4613.5 5.8735.4 93.434.4 11.068.5 7.784.5 7.3 Hemiplegia1011.2 4.1719.8 88.531.4 13.671.4 9.384.7 4.6 Diplegia9012.0 5.0715.9 97.533.4 12.770.3 8.584.8 6.8 GMFCSI3912.3 6.1721.2 112.133.3 13.971.1 8.185.8 6.2 GMFCSII5711.0 3.1707.0 84.932.0 11.570.9 8.484.7 6.4 GMFCSIII421.5 4.0801.3 20.650.1 4.357.0 3.675.5 6.9 LLA1517.0 7.6832.4 147.753.6 24.378.7 11.884.8 7.2 BelowKnee916.2 7.2821.2 171.849.1 23.576.3 13.185.2 7.8 AboveKnee618.8 9.0856.7 82.163.3 25.383.7 6.7883.9 6.1 Meanandstandarddeviation(SD)ofdemographiccharacteristics,GDI,andCDIforunimpaired subjects,subjectswithcerebralpalsy(CP),andsubjectswithalowerlimbamputation(LLA). SubjectswithCPweresortedbygaitpattern,a ectedside,andGrossMotorFunction ClassicationSystem(GMFCS)level.SubjectswithaLLAwerealsosortedbylevelof amputation. G.4.2AdditionalResultsforCoordinationPerformanceScoreStatisticalAnalysis AlogisticregressionanalysiswasusedtoexaminetherobustnessofamodelthatpredictsaCP typegaitpatternfromanormalgaitpatternbasedonselectswingperiodcoordinationevents. Cross-validationwasusedtocomparepredictedprobabilitiesbasedonthecompletedatasetversus thecross-validatedpredictedprobabilities.Ofthesixsignicantcoordinationeventsidentied, threeswingperiodcoordinationeventswereusedforthisregressionmodel.Themagnitudeofthe thigh-footCRPDminimumnearfooto (TF1),themagnitudeofthepelvisPP'sminimum angulardisplacement(P1),andthepercentgaitcycleofthefootPP'smaximumangular displacement(pF2). TableG.4.2:Responseprolefortheatypicalvs.typicalgaitpatternregressionmodel,where probabilitymodeledisCP=1. OrderedValueCPTotalFrequency 10140 21106 TableG.4.3:Modeltstatisticsfortheatypicalvs.typicalgaitpatternregressionmodel. CriterionInterceptOnlyInterceptandCovariates AIC338.31464.500 SC341.81978.522 -2LogL336.31456.500 272

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TableG.4.4:Resultsofmaximumlikelihoodestimatesanalysisfortheatypicalvs.typicalgait patternregressionmodel. ParameterDFEstimateStandardErrorWaldChi-SquarePr>ChiSq Intercept162.735213.746720.8270<.0001 P11-0.30920.068220.5490<.0001 TF110.21380.048919.1173<.0001 pF210.17070.06427.06490.0079 TableG.4.5:Oddsratioestimatesfortheatypicalvs.typicalgaitpatternregressionmodelcoordinationevents,whereP1isthemagnitudeoftheminimumangulardisplacementofthepelvisin swing,TF1isthemagnitudeofthethigh-footCRPDminimumnearfooto ,andpF2isthepercent gaitcycleofthefootPP'smaximumangulardisplacement. E ectPointEstimate95%WaldCondenceLimits P10.7340.6420.839 TF11.2381.1251.363 pF21.1861.0461.345 FigureG.4.3:Receiveroperatorcurve(ROC)comparisonbetweentheregressionmodelandROC1. 273

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TableG.4.6:Receiveroperatorcurveassociationstatisticsfortheatypicalvs.typicalgaitpattern regressionmodel. ROCModelAreaStandardError95%CondenceLimits Model0.98490.009380.96651.0000 ROC10.97670.01360.95011.0000 TableG.4.7:Receiveroperatorcurvecontrasttestresultsfortheatypicalvs.typicalgaitpattern regressionmodel,withdegreesoffreedom(DF),Chi-squarevalue,andcorrespondingprobability (Pr)oftheChi-square. ContrastDFChi-SquarePr>ChiSq Reference=Model12.02990.1542 TableG.4.8:Analysisofvariancefortheatypicalvs.typicalgaitpatternregressionmodel,with degreesoffreedom(DF),sumofsquares,meansquare,andFteststatisticandprobabilityfromthe Ftest. SourceDFSumofSquaresMeanSquareFvaluePr>F Model30.834640.2782172.12<0.0001 Error2420.933500.00386 CorrectedTotal2451.76814 TableG.4.9:Parameterestimatesforthecoordinationeventsoftheatypicalvs.typicalgaitpattern, withstandarderrorofeachestimate,tvalue,probabilityfromt-test,tolerance(TOL),andvariance inationfactor(VIF). VariableDFParameterEstimateStandardErrortValueTOLVIF Intercept18.742460.8537810.24.0 P11-0.045770.00424-10.800.829851.20504 TF110.032980.0030410.860.912491.09590 pF210.038150.003999.570.886541.12797 Thesecondlogisticregressionanalysiswasusedtoexaminetherobustnessofamodelthatpredicts asti kneegaitpatternfromacrouchtypegaitpatternbasedonselectswingperiodcoordination events.Cross-validationwasusedtocomparepredictedprobabilitiesbasedonthecomplete datasetversusthecross-validatedpredictedprobabilities.Ofthesixsignicantcoordinationevents identied,twoswingperiodcoordinationeventswereusedforthisregressionmodel.The magnitudeofthethigh-footCRPDminimumnearfooto (TF1),andthemagnitudeofthepelvis PP'sminimumangulardisplacement(P1). TableG.4.10:Responseproleforthesti kneevs.crouchgaitpatternregressionmodel,where probabilitymodeledissti kneegait=1. OrderedValueSKGTotalFrequency 1046 2160 274

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TableG.4.11:Modeltstatisticsforthesti kneevs.crouchgaitpatternregressionmodel. CriterionInterceptOnlyInterceptandCovariates AIC147.093141.931 SC149.756149.922 -2LogL145.093135.931 TableG.4.12:Testingglobalnullhypothesis( =0)forthesti kneevs.crouchgaitpatternregression model. TestChi-SquareDFPr>ChiSq LikelihoodRatio9.161520.0102 Score8.729120.0127 Wald7.815120.0201 TableG.4.13:Resultsofmaximumlikelihoodestimatesanalysisforthesti kneevs.crouchgait patternregressionmodel. ParameterDFEstimateStandardErrorWaldChi-SquarePr>ChiSq Intercept17.81644.06293.70130.0544 P11-0.05640.02584.76570.0290 TF11-0.01470.007174.17920.0409 275

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FigureG.4.4:Receiveroperatorcurve(ROC)comparisonbetweentheregressionmodelandROC1. TableG.4.14:Receiveroperatorcurveassociationstatisticsforthesti kneevs.crouchgaitpattern regressionmodel. ROCModelAreaStandardError95%CondenceLimits Model0.98490.009380.96651.0000 ROC10.97670.01360.95011.0000 TableG.4.15:Receiveroperatorcurvecontrasttestresultsforthesti kneevs.crouchgaitpattern regressionmodel,withdegreesoffreedom(DF),Chi-squarevalue,andcorrespondingprobability (Pr)oftheChi-square. ContrastDFChi-SquarePr>ChiSq Reference=Model128.7487<0.0001 276

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TableG.4.16:Analysisofvarianceforthesti kneevs.crouchgaitpatternregressionmodel,with degreesoffreedom(DF),sumofsquares,meansquare,andFteststatisticandprobabilityfromthe Ftest. SourceDFSumofSquaresMeanSquareFvaluePr>F Model20.492010.246014.670.0114 Error1035.425250.05267 CorrectedTotal1055.91727 TableG.4.17:Parameterestimatesforthecoordinationeventsofthesti kneevs.crouchgait pattern,withstandarderrorofeachestimate,tvalue,probabilityfromt-test,tolerance(TOL),and varianceinationfactor(VIF). VariableDFParameterEstimateStandardErrortValueTOLVIF Intercept12.239550.932452.40.0 TF11-0.003980.00165-2.420.978981.02147 P11-0.013050.00593-2.200.978981.02147 277

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G.4.3AdditionalResultsforHypothesis4A ThefollowinggurescontainthePPsandCRPDsforthevariousgaitpatterncomparisons conductedtoaddressHypothesis4AofAim4. FigureG.4.5:Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingfor allsubjectswithacrouchgaitpattern(orange),allsubjectswithasti kneegaitpattern(red),and allretrospectiveunimpairedsubjects(grey). 278

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FigureG.4.6:Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingforall subjectswithCPclassiedashemiplegic(red),allsubjectswithCPclassiedasdiplegic(orange), andallretrospectiveunimpairedsubjects(grey). 279

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FigureG.4.7:Phaseportraitsandcontinuousrelativephasediagramsforover-groundwalkingfor allsubjectswithabelowkneeLLA(darkgreen),allsubjectswithanabovekneeLLA(lightgreen), andallretrospectiveunimpairedsubjects(grey). 280

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FigureG.4.8:Phaseportraitsandcontinuousrelativephasediagramsforunimpairedprospective subjects(darkblue)forover-ground(OG)walkingataself-selectedspeed(Vss),unimpairedprospective(lightblue)fortreadmillwalking(TM)atthesameVss,andretrospectiveunimpairedcohort's meancoordinationcurves(grey)forover-groundwalkingatVss. 281

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G.5AdditionalResultsforTranstibialAmputationCaseStudy FigureG.5.1:Sagittalplanekinematicandkineticcurvesfortheleft(red)andright(green)legsfor thethreeprostheticalignmentconditions. 282

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FigureG.5.2:Sagittalandcoronalplanephaseportraitsandcontinuousrelativephasediagramsfor theleft(red)andright(green)legsforthethreeprostheticalignmentconditions. G.6AdditionalResultsforExploratoryInvestigationtoIdentifySignicantCoordinationEvents TableG.6.1:Comparisonofunimpairedprospective(shoes)subjects'criticalcoordinationeventsand unimpairedretrospective(barefoot)subjects'criticaleventsusingtheindependenceandinvariance criteria. Demographic FootThigh-FootCRPDThigh-FootCRPDShank PPLocalMinZero-crossingPP r 2 Pr 2 Pr 2 Pr 2 P Age(n=120)0.20%0.04470.10%0.03160.10%0.03160.10%0.0316 Age(n=20)0.75%0.08650.05%0.02280.62%0.07840.06%0.0241 LegLength(n=120)1.90%0.13780.30%0.05480.30%0.05480.60%0.0775 LegLength(n=20)1.15%0.10730.01%0.00960.27%0.05210.25%0.0495 Weight(n=120)0.90%0.09490.00%0.00000.20%0.04470.20%0.0447 Weight(n=20)0.33%0.05770.04%0.02080.00%0.00200.01%0.0108 283

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FigureG.6.1:Timingofcriticalcoordinationeventswithrespecttothecriticalandtemporalevents ofgaitduringswingperiod. 284