Citation
A model of the structure/function relationship of the pulmonary artery in recovery from hypoxic pulmonary hypertension

Material Information

Title:
A model of the structure/function relationship of the pulmonary artery in recovery from hypoxic pulmonary hypertension
Creator:
Dufva, Melaine J. ( author )
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
1 electronic file (100 pages). : ;

Subjects

Subjects / Keywords:
Pulmonary hypertension ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Review:
Pulmonary hypertension (PH) is a condition characterized by vascular remodeling and chronic inflammation, resulting in right ventricular failure. Vascular remodeling associated with fibrosis die to deposition of extracellular matrix (ECM) has been proposed as a mechanism of vascular stiffening, resulting in right ventricle afterload increases beyond those indicated by pulmonary vascular resistance. This stiffening as characterized by medial and adventitial hypertrophy and accumulation of ECM proteins. Acute hypoxia exposure induces pulmonary hypertension with mild vascular remodeling that is thought to be reversible. However, chronic hypoxia exposure has shown to result in poor prognosis and morbidity. Little is understood about the transition to chronic, irreversible PH, the role of permanent vascular stiffening, and its contribution to reduced cardiac function. Therefore, the chronically hypoxic represents a robust, and physiologically relevant model to study the disease. It is important to understand the structure and function of vessels and their ability to mechanically adapt to disease and injury. A simple model of stress/strain relationships can be used to determine the materials response when forces are applied. A strain energy function was fit to characterize the mechanical behavior of the pulmonary artery between healthy, hypoxic, and hypoxic recovery rates. Vascular stiffening in hypoxic PH did not resolve upon recovery, as indicated by histology. Increased circumferential wall stress was observed in the hypoxic and recovery cohorts. Modulus of the elastin dominated region (Ee) was not significantly different between cohorts. But the modulus of the collagen dominated region (Ee) was significantly increased in the hypoxic and recovery cohorts. These differences in modulus wee correlated to increases in collagen content alone, described in a mathematical relationship. Stiffness at zero pressure was then calculated and correlated with material constants and percentages of collagen and elastin. An increase in stiffness was observed that was concomitant with an increase in percentage of collagen from control to hypoxic and recovery. Percentage of collagen and elastin was correlated with collagen engagement strain and produced a linear relationship. This relationship was characterized by a correlation of decreasing collagen strain with increasing collagen and elastin percentage. These results suggest that the increase in stiffness and wall tension that remains during recovery from hypoxia results from a combination of increased collagen and lower fiber engagement strains, providing evidence that residual stress is due to changes in structure during mechanical adaptation.
Thesis:
Thesis (M.S.)--University of Colorado Denver. Bioengineering
Bibliography:
Includes bibliographic references.
System Details:
System requirements: Adobe Reader.
General Note:
Department of Bioengineering
Statement of Responsibility:
by melanie J. Dufva.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
910852390 ( OCLC )
ocn910852390

Downloads

This item is only available as the following downloads:


Full Text

PAGE 1

AMODELOFTHESTRUCTURE/FUNCTIONRELATIONSHIPOFTHE PULMONARYARTERYINRECOVERYFROMHYPOXICPULMONARY HYPERTENSION by MELANIEJDUFVA BS,UniversityofFlorida,2013 Athesissubmittedtothe FacultyoftheGraduateSchoolofthe UniversityofColoradoinpartialfulllment oftherequirementsforthedegreeof MasterofScience Bioengineering 2015

PAGE 2

ThisthesisfortheMasterofSciencedegreeby MelanieJDufva hasbeenapprovedforthe BioengineeringProgram by KendallHunter,Chair JohnWalker,Advisor VitalyKheyfets BlairDodson April25,2015 ii

PAGE 3

Dufva,MelanieJM.S.,Bioengineering AModeloftheStructure/FunctionRelationshipofthePulmonaryArteryinRecovery fromHypoxicPulmonaryHypertension ThesisdirectedbyProfessorKendallHunter ABSTRACT PulmonaryhypertensionPHisaconditioncharacterizedbyvascularremodeling andchronicinammation,resultinginrightventricularfailure.Vascularremodeling associatedwithbrosisduetodepositionofextracellularmatrixECMhasbeen proposedasamechanismofvascularstiening,resultinginrightventricleafterload increasesbeyondthoseindicatedbypulmonaryvascularresistance.Thisstieningis characterizedbymedialandadventitialhypertrophyandaccumulationofECMproteins.Acutehypoxiaexposureinducespulmonaryhypertensionwithmildvascular remodelingthatisthoughttobereversible.However,chronichypoxiaexposurehas showntoresultinpoorprognosisandmorbidity.Littleisunderstoodaboutthetransitiontochronic,irreversiblePH,theroleofpermanentvascularstiening,andits contributiontoreducedcardiacfunction.Therefore,thechronicallyhypoxicrepresentsarobust,andphysiologicallyrelevantmodeltostudythedisease.Itisimportant tounderstandthestructureandfunctionofvesselsandtheirabilitytomechanically adapttodiseaseandinjury.Asimplemodelofstress/strainrelationshipscanbeused todeterminethematerialsresponsewhenforcesareapplied.Astrainenergyfunctionwasttocharacterizethemechanicalbehaviorofthepulmonaryarterybetween healthy,hypoxic,andhypoxicrecoveryrats.VascularstieninginhypoxicPHdid notresolveuponrecovery,asindicatedbyhistology.Increasedcircumferentialwall stresswasobservedinthehypoxicandrecoverycohorts.Modulusoftheelastindominatedregion E e wasnotsignicantlydierentbetweencohorts,Butthemodulus ofthecollagendominatedregion E c wassignicantlyincreasedinthehypoxicand iii

PAGE 4

recoverycohorts.Thesedierencesinmoduluswerecorrelatedtoincreasesincollagencontentalone,describedinamathematicalrelationship.Stinessatzeropressure wasthencalculatedandcorrelatedwithmaterialconstantsandpercentagesofcollagenandelastin.Anincreaseinstinesswasobservedthatwasconcomitantwithan increaseinpercentageofcollagenfromcontroltohypoxicandrecovery.Percentageof collagenandelastinwascorrelatedwithcollagenengagementstrainandproduceda linearrelationship.Thisrelationshipwascharacterizedbyacorrelationofdecreasing collagenengagementstrainwithincreasingcollagenandelastinpercentage.These resultssuggestthattheincreaseinstinessandwalltensionthatremainsduring recoveryfromhypoxiaresultsfromacombinationofincreasedcollagenandlower berengagementstrains,providingevidencethatresidualstressisduetochangesin structureduringmechanicaladaptation. Theformandcontentofthisabstractareapproved.Irecommenditspublication. Approved:KendallHunter iv

PAGE 5

DEDICATION Thisthesisisdedicatedtomyparents,whoinspiredmetopursuemycareerin engineeringandscience.AndtomyColoradofriends,whohelpedmealongmy path. v

PAGE 6

ACKNOWLEDGMENT Iwouldliketothank: MyAdvisers:Dr.KendallHunter,Dr.VitalyKheyfets,Dr.BlairDodson,andDr. JohnWalker ShawnaBurgett,forbeingsowonderfultoworkwith RyanDelaney,forsupportingmethrougheverything Dr.MichaelYeager,forhismentorshipinmyrstyear MyfellowBioengineeringStudents vi

PAGE 7

TABLEOFCONTENTS Tables........................................x Figures.......................................xii Chapter 1.Introduction...................................1 1.1Purpose..................................1 1.2PulmonaryHypertension........................1 1.3WallStressCharacterization......................4 1.3.1ResidualStressesandStrains..................9 1.4ConstitutiveModelingwithaStrainEnergyFunction........9 1.5Justication...............................12 1.6Goals...................................13 2.Methods.....................................14 2.1AnimalModel..............................14 2.2MyographyTesting...........................15 2.3Hemodynamics..............................17 2.4Histology.................................17 2.5WallStressCharacterization......................17 2.6ConstitutiveModelingofExperimentalMechanicsMeasurements..19 2.6.1LinearModuliofElastinandCollagenRegions........19 2.6.2CollagenFiberEngagementStrains...............21 2.6.3DeterminationofStiness....................21 2.6.4DeterminationofMaterialConstants..............22 2.7StatisticalMethods...........................23 2.7.1CorrelationstoDetermineMathematicalRelationships....23 3.Results......................................24 3.1Hemodynamics..............................24 vii

PAGE 8

3.2Histology.................................24 3.3CircumferentialWallStressCalculations................26 3.4ResidualStresses.............................26 3.5FTestforVariance...........................27 3.6StrainEnergyFunctions.........................29 3.7CollagenandElastinFitting......................32 3.8Structure/FunctionRelationships...................35 3.8.1ComparingMaterialConstantstoModulusandStiness...35 3.8.2ComparingPercentageofCollagenandElastintoModulusand Stiness..............................38 3.9Relationshipof C 1 andCollagenandElastinPercentagewithCollagen StrainIntercepts.............................41 4.Discussion....................................46 4.1HistologicalAnalysis...........................46 4.2Hemodynamics..............................46 4.3ArterialWallStresses..........................47 4.3.1ResidualStresses.........................48 4.4VarianceTestingforCircumferentialWallStressBetweenGroups..49 4.5StrainEnergyFunctions.........................50 4.6CollagenandElastinFitting......................50 4.6.1CollagenandElastinModulusinParallel...........51 4.7Structure-FunctionRelationships....................52 4.7.1ComparingMaterialConstantstoModulusandStiness...52 4.7.2ComparingCollagenandElastinPercentagetoModulusand Stiness..............................52 4.8StrengthsandLimitations.......................53 4.9FutureWork...............................55 viii

PAGE 9

4.9.1HalfLifeofCollagen.......................55 5.Conclusion....................................57 References ......................................59 Appendix A.FiguresandTables...............................66 B.MatlabCode..................................78 B.1ImageThresholdingforCollagenQuantication............78 B.2WallStressCalculations.........................79 B.3Constitutivemodeling..........................83 ix

PAGE 10

TABLES Table 2.1ComponentsoftheKrebs-HenseleitSolutiondissolvedin1literofdeionizedwater.Thissolutionwascarbonatedusingaerosolizedcarbogen % O 2 :5% CO 2 ..............................15 3.1Thicknessescalculatedforeachcohort....................26 3.2PercentageofcollagenandelastincalculatedforeachcohortusingMatlab thresholding..................................28 3.3Residualstressescalculatedforeachcohort.................28 3.4Materialconstantsdeterminedforeachcohortwithleastsquares.....35 3.5Thelineartsfortheelastinandcollagenregions,denedasbeforeand afterthetransitionpoint,respectively....................35 3.6Relationshipsbetween C 1 andcollagenandelastinmodulusforallcohorts, asgraphedingure3.11...........................40 3.7Relationshipsbetween C 1 andcollagenandelastinstinessforallcohorts, asgraphedingure3.11...........................40 3.8Relationshipsbetweencollagenandelastinpercentageandtheirmoduli forallcohorts,asgraphedingure3.14...................41 3.9Relationshipsbetweencollagenandelastinpercentageandtheirstiness forallcohorts,asgraphedingure3.15...................41 3.10Relationshipsbetween C 1 andstrainintercepts,asshowningure3.16..43 3.11Relationshipsbetweencollagenandelastinpercentageandthecollagen strainintercepts,asgraphedingure3.17..................44 A.1ComponentsofAvertin.Take0.25mlofthissolutionanddissolvein10 ml1XPhosphatebueredsalinePBS...................66 A.2Modulusofcollagenandelastindominatedregionsofthestress-strain curveforeachrat...............................67 x

PAGE 11

A.3MaterialconstantsdeterminedforeachratintheCTRLcohort......67 A.4MaterialconstantsdeterminedforeachratintheHXcohort.......68 A.5MaterialconstantsdeterminedforeachratintheRTNcohort.......68 A.6Modulusofcollagenandelastindominatedregionsofthestress-strain curveforeachrat...............................68 xi

PAGE 12

FIGURES Figure 1.1Thethreelayersofthepulmonaryartery,shownhereinVerhoe'sVan Giesonelastinstain..............................3 1.2Schematicofhypothesistobetested.Threeweekexposuretohypoxia inducesvascularremodeling,aprocessconsistingofadventitialhypertrophy,smoothmusclehyperplasia,andchronicinammation.Returnto normoxiaatsixweeksresultsinbroticregression,butwithirreversible alterationsinthematerialpropertiesofthetissue.............5 1.3Left:Circumferentialsliceofathick-walledpressurevessel.Right:Elementalcutfromthevessel[12].Circumferentialstress ,andradial stress rr areshownhereinrelationtogeometry.............5 1.4Anexampleofthegeneratedcircumferentialwallstress overcircumferentialstrain usingthickandthinwalledequationsforapulmonary artery.Bluedatapointsarestressescalculatedforeachpressure-diameter pointwithequation.1.Greendatapointsarestressescalculatedwith equation.3.Redandmagentalinesarethethickandthinttedequations,respectively...............................7 1.5Left:AdiagramofthetestingrigthatFungusedtoperformpressure/diametermeasurementsofbloodvessels[15].Right:therawpressurediameterthatismeasuredwiththerig....................8 1.6Left,thegeometryofthevesselatanunloadedstatewithresidualstress conguration;Right,thegeometryofthevesselwithastress/strainfree conguration.Angle 0 istheopeningangle................10 xii

PAGE 13

2.1OurmodelconsistedoffourcohortsofadultmaleSpragueDawleyrats. Theratsweretestedattheendofeachtreatmentofcontrol,3weeksin thehypobaricchamber,6weeksinthehypobaricchamberand3weeksin thehypobaricchamberwith6weeksrecoveryatDenver,CO pO 2 .....14 2.2VesselChamberPressure-DiameterApparatus.Thepulmonaryartery segmentissecuredoncannulasbysilkligaturesatbothends.Physiologic solutionisaeratedandpumpedthroughthewaterbathaswellasthe cannulas.Transducersmeasureoninputandoutputsides.Thevideo dimensionanalyzerdisplaysthetissueandmeasurestheouterdiameter fromthemicroscopeandcameraoutput...................16 2.3Imagethresholdingforcollagenandelastincontentquantication.The imageonthefarleftistheuneditedcross-sectionofaPA.Themiddle imageistheconversionoftheoriginalimagetoblackandwhitebinarization.Theimageontherightiswithathresholdof > 150pixelsto isolateelastinstainedelements........................18 2.4ACross-sectionofaPAstainedwithMassontrichrome.Thicknesswas measuredusingtheMATLABpixelmeasuringtool,averagedover6regions,andconvertedtomicrometers,shownhere.Measuringbarsarein unitsofpixels.................................19 2.5Aschematicoftheisovolumetricdeformationwhenforceisincreased. Whenpressureisincreased,diameterandthicknesschange,butthecrosssectionalareaofthetissue,A,isconserved.................20 2.6Theproposedrelationshipfor E e and E c asparallelspringsasamechanical model......................................21 2.7Estimationoftheelastinandcollagenmodulusthroughlineartting.The strainatwhichcollagenbersareengagedisshownastheintercepton thex-axisofthecollagenmodulusline....................22 xiii

PAGE 14

3.1Hemodynamicdataforeachcohort.Heartratebpm,mPAPmmHg, andstokevolume lareshownhere.Bluebarsrepresentstandarddeviation.....................................24 3.2ThicknessesofPAforacontrolbhypoxicandcrecoverycohorts.Imagesare10xmagnication..........................25 3.3CollagenstainingblueforcontrolCTRL,hypoxicHPX,andrecovery RTNcohorts.Imagesareat10xmagnication..............27 3.4ElastinstainingblackforcontrolCTRL,hypoxicHPX,andrecovery RTNcohorts.Imagesareat10xmagnication..............29 3.5Therawpressure-diameterdataobtainedfrommyographinationtesting.30 3.6Thecircumferentialwallstress plottedovercircumferentialstrain..31 3.7Thegeneralelasticmoduliforeachcohortthatisovertheentirerangeof strains,asdeterminedbythederivativeofthestress-straincurve.....32 3.8Thestrainenergyfunctionsforeachcohort. ? isexperimentalcontrol data,redperforatedlineisthettedstrainenergyfunctionforCTRL, isexperimentalhypoxicdata,blueperforatedlineisthettedstrain energyfunctionforHX, isexperimentalrecoverydata,andtheblack solidlineisthettedstrainenergyfunctionforRTN............33 3.9Theresidualsofthestrainenergyfunctiont plottedoverthepredictedvalues.acontrols,bhypoxic,andcrecoverycohort.......34 3.10Theelastinandcollagenregionaltsforeachcohort............36 3.11 C 1 correlatedwithelasticmodulus E e andcollagenmodulus E c .Blue ? is E e versus C 1 ,blueperforatedlineisthettedlinearregression,red is E c versus C 1 ,andtheredperforatedlineisthettedexponential. 2 = 492.1p < 0.05,forthecollagent,and R 2 =0.014fortheelasticlinear regression....................................37 xiv

PAGE 15

3.12Percentageofcollageandelastinwascorrelatedwithelastinmodulus E e andcollagenmodulus E c .Blue ? is E e versus%elastin,blueperforated lineisthettedlinearregression,red is E c versus%collagen,andthe redperforatedlineisthettedexponential. 2 =1255.8p < 0.05,for thecollagent,and R 2 =0.0002fortheelasticlinearregression.....38 3.13Theelastinandcollagenparalleltsforeachcohort. 2 valuesare6102.8, 7519.0,and7538.7,forcontrols,hypoxics,andrecovery,respectively...39 3.14 C 1 wascorrelatedwithcollagenstiness S c andelastinstiness S e Blue is C 1 versuselastinstiness S e ,blueperforatedlineisthetted linearregression,red is C 1 versuscollagenstiness S c ,andthered perforatedlineisthettedlinearregression. R 2 =0.108,forthetted elastinstiness,and R 2 =0.512forthettedcollagenstiness......42 3.15%Collagenandelastinwascorrelatedwithcollagen S c andelastinstiness S e .Red is%collagenversuscollagenstiness S c ,andthered perforatedlineisthettedlinearregression.Blue is%elastinversuselastinstiness S e ,andtheblueperforatedlineisthettedlinear regression. R 2 =0.55for S c ,and R 2 =0.432for S e .............43 3.16 C 1 wascorrelatedwithstraininterceptsfromthecollagenmodulusline. Red is C 1 versusinterceptmm/mmcollagen,andtheredperforated lineisthettedexponential. 2 =1.55p > 0.05,forthettedline....44 3.17Percentageofcollageandelastinwascorrelatedwiththeinterceptsfrom thecollagenmodulusline.Blue is%elastinversusinterceptmm/mm, blueperforatedlineisthettedlinearregression,red is%collagen versusinterceptmm/mm,andtheredperforatedlineisthettedlinear regression. R 2 =0.38forthe%collagent,and R 2 =0.70forthe% elastint....................................45 xv

PAGE 16

4.1AnAttemptatattingofarecoveryrattoKao'sfunction,shownin equation.1.................................56 A.1Theheartblockisextractedandthepre-hilarleftpulmonaryarteryis disectedandlungsareisolatedforsubsequentanalysis.Timepointsof3 weekhypoxia,3weekhypoxia+6weekreturn,andagematchedcontrols aretobeperformed..............................66 A.2ANOVAcomparisonofthethicknessesofeachcohort...........69 A.3ANOVAcomparisonofpercentagesofcollagenbetweeneachcohort...70 A.4ANOVAcomparisonofpercentagesofelastinbetweeneachcohort....71 A.5ANOVAcomparisonofpercentagesofthecircumferentialwallstresses foreachcohort..............................72 A.6ANOVAcomparisonof E e betweencohorts.................73 A.7ANOVAcomparisonof E c betweencohorts.................74 A.8ANOVAcomparisonofresidualstressesbetweencohorts..........75 A.9ANOVAcomparisonofelastindominatedregionstiness.........76 A.10ANOVAcomparisonofelastindominatedregionstiness.........77 xvi

PAGE 17

1.Introduction 1.1Purpose PulmonaryhypertensionPHisaconditioncharacterizedbyincreasedblood pressureandresistanceinthearterialvasculatureofthelungastheresultofnumerous pathologicalmechanisms,eventuallyculminatinginrightventricularRVfailure. Currently,thereexistsnodenitivecureforPH.Hypoxiaisthoughttoinducea mild,reversibleformofPH,yetstudieshaveshownincreasedmorbidityandmortality withhypoxicexposure.Understandingthebiomechanicsofthedisease,especially theprocessofresolutioninhypoxicPH,bydevelopingamodelforarterialwall stress,isimportantforfuturedesignofengineeredtissue,andengineeringtherapies toattenuateandultimatelyreversediseaseprogression. 1.2PulmonaryHypertension PulmonaryhypertensionPHinhumansisdenedbythespeciedparametersof ameanpulmonaryarterypressuregreaterthan25mmHg,anormalcapillarywedge pressurelessthan15mmHg,andincreasedpulmonaryvascularresistancePVR [38].Whenleftuntreated,PHrepresentsanincreasedventricularafterloadcausing decreasedcardiacoutput,eventuallyleadingtocardiacfailure.Thedevelopmentof PHmayalsobelinkedtootherdiseasesasaderivedsecondarydisease,ormaydevelopwithknownetiology,oritmaybeidiopathic.Furthermore,PHmaydevelop inbothchildrenandadults,regardlessofage.AsdictatedbytheWorldHealth Organization,therearevecategoriesofpulmonaryhypertension,withthemost commonformamountingtoapproximately90percentofcasesoccurringinGroupI [59].GroupI,denotedaspulmonaryarterialhypertensionPAH,includesidiopathic IPAH,familialFPAH,PAHassociatedwithvenousand/orcapillarydisorders,or associatedwithotherdiseasesAPAH,includingHIVinfection,drugs,toxins,congenitalshuntsbetweenpulmonaryandsystemiccirculation,collagenvasculardisease, andothers.GroupsII-VarecategorizedasPHassociatedleftheartdiseaseII, 1

PAGE 18

PHassociatedwithlungdiseases/hypoxiaIII,PHduetoembolicand/orchronic thromboticdiseaseIV,andPHassociatedwithmiscellaneousconditionsV.The animalmodelusedforthisstudyfallsunderthecategoryofWHOgroupIII.Currenttherapiestargetvasoreactivesignalingpathwaysthroughtheuseofendothelin, prostacyclin,andnitricoxide[8].Thesedrugcategoriesareendothelinreceptorantagonists,phosphodiesterasetype-5inhibitorsPDE-5iorsolubleguanylatecyclase stimulatorsandprostanoids,andserveasvasodilators.WhilethesedrugstargetloweringPVRthroughvasodilation,manypatientsstillexperiencehighRVafterload. Earlydiagnosisimprovespatientprognosisandmortality,yetnodenitivecureexists forthisdebilitatingdisease.Pathologically,PHpresentsasthickeningandstiening orarterialvessels.Thepulmonaryarteryiscomposedofthreelayers,asshownin gure1.1.Theinnermostlayer,theintima,iscomposedofasinglelayerofendothelialcellsanchoredonabasementmembraneofcollagenIV.Themiddlelayer, themedia,iscomposedamatrixofcollagenIwith3elasticlaminaesurroundedby smoothmusclecells.Theoutermostlayer,theadventitia,iscomposedofadiverse cellpopulationwithbroblaststhroughoutabrousnetworkofvariousECMproteins.DuringPH,hypertrophyofthemedialandadventitiallayeroccurs,causing arterialstiening,aprocesscalledremodeling[49],asdepictedingure1.2.Changes inthefunctionalphenotypeofeachvascularcelltypeoccurs,mostnotablytheexpressionofsmoothmuscle -actinbysmoothmusclecellsSMCsandbybroblasts resultinginmyobroblastpresence[62].Chronicinammationisalsocharacteristic ofthismicro-environmentthatcontributestothebroticstate[41,37],however,this characteristicwillnotbeanalyzedforthepurposesofthisstudy.Areductionin thetotalcross-sectionalareaofthevascularcompartmenthasalsobeenreported, aphenomenacalledvascularpruning[19,20,42].Thebrosisisduetodeposition ofECMproteinssuchascollagenandelastin,whichisbroughtonbytheincreased numberofmyobroblasts[28,43,61].Thestieningofthevesselresultsinincreased 2

PAGE 19

Figure1.1:Thethreelayersofthepulmonaryartery,shownhereinVerhoe'sVan Giesonelastinstain. pulmonarypressure,thusincreasingafterloadontherightventricle.ThemeasurementofPVRisusedasastandarddiagnosisforPH,yetthismeasurementofthe meanpressureandowdoesnotaccountforbloodowpulsatilityandisthuslimited [17,70].PulmonaryvascularimpedancePVIisamorerobustmeasurementthat accountsforbloodowandpressurepulsatility.Thisisimportantbecausechangesin PVRareinuencedprimarilybydistalvascularremodeling,yetchangesinchangesin PVIareinuencedbybothdistalandproximalremodeling[17].Therefore,proximal PAvascularremodelingismorephysiologicallyrelevanttounderstandingchangesin PVI,aschangesinPAstinesshaveproventobeapredictorinpatientmortality [63,16,39,40,54]. 3

PAGE 20

Hypoxia,denedasoxygendeprivationbyadecreaseinthepartialpressure ofoxygen,isknowntoinducepulmonaryhypertensionPH.Severalstudieshave demonstratedvascularremodelingandelevatedpulmonaryarterialpressureinhigh altitudepopulations[2,73,36].However,acutePHinducedbymildhypoxiais thoughttoberesolvable,asindicatedinhypoxicrecovery[11].Hypoxicexposure resultsinhypoxicpulmonaryvasoconstriction,aprocessinwhichthepulmonary arteriesredirectbloodowfromaveolithatarepoorlyventilatedtoareasthatarewell ventilated,maximizingtheperfusion-ventilationprocess[71].Thisvasoconstrictionis duetoachangeinthepartialpressureofoxygen,causingdepolarizationoftheoxygen sensitivepotassiumionchannelsinsmoothmusclecells,accumulationofintracellular calcium,andsubsequentcontraction[68].Theextendeddurationofcontractionthat occursinchronichypoxiathenleadstopulmonaryhypertensionandrightheart failure,andthetransitionfromacutetoirreversiblePHremainsunclear.Smooth musclecellsarewidelyacceptedastheprimarycellsresponsibleforregulationof vasculartone[71,48].Severalstudieshaveseparatelytestedthedeformationresponse oftheintactPA,theendothelial,medial,andadventitiallayers,andhaveshowna minimaldierenceintheYoungsmodulusoftheintactPAandthemediallayer [69,27].Therefore,themediallayerprovidesthebestinsighttomodelchangesin arterialmechanicsandvasculartone. 1.3WallStressCharacterization Inordertounderstandhowvesselcompliancecontributestoprogressionofright heartdysfunction,thewallstressofthepulmonaryarterymustbecalculated.This canbedonetoarstapproximationbymodelingthemediallayerofthepulmonary arteryasanincompressiblecylindricalvesselwithisovolumetricdeformation[12],as showningure1.3.Thesymmetryofvesselsallowsforcircumferential ,radial rr ,andlongitudinal r stressesastheprinciplestressesofthesystem.With thismodel,solvingforcircumferentialstressbecomesatwo-dimensionalproblem. 4

PAGE 21

Figure1.2:Schematicofhypothesistobetested.Threeweekexposuretohypoxia inducesvascularremodeling,aprocessconsistingofadventitialhypertrophy,smooth musclehyperplasia,andchronicinammation.Returntonormoxiaatsixweeks resultsinbroticregression,butwithirreversiblealterationsinthematerialproperties ofthetissue. Figure1.3:Left:Circumferentialsliceofathick-walledpressurevessel.Right:Elementalcutfromthevessel[12].Circumferentialstress ,andradialstress rr areshownhereinrelationtogeometry. Byapplyinganinternalpressureandmeasuringtheincreaseindiameterofavessel, thecircumferential andradialstress rr canbeestimatedusingthethick 5

PAGE 22

approximationequationasshowningure1.3,shownbelow: = p i r 2 i )]TJ/F19 11.9552 Tf 11.955 0 Td [(p o r 2 o r 2 o )]TJ/F19 11.9552 Tf 11.955 0 Td [(r 2 i )]TJ/F19 11.9552 Tf 13.151 8.087 Td [(r 2 i r 2 o p o )]TJ/F19 11.9552 Tf 11.955 0 Td [(p i r 2 r 2 o )]TJ/F19 11.9552 Tf 11.955 0 Td [(r 2 i .1 rr = p i r 2 i )]TJ/F19 11.9552 Tf 11.956 0 Td [(p o r 2 o r 2 o )]TJ/F19 11.9552 Tf 11.956 0 Td [(r 2 i + r 2 i r 2 o p o )]TJ/F19 11.9552 Tf 11.955 0 Td [(p i r 2 r 2 o )]TJ/F19 11.9552 Tf 11.955 0 Td [(r 2 i .2 Where p o isexternalpressure, p i isinternalpressure, r o isexternalradius,and r i is internalradius.Withtheseequations,zeroexternalpressure p o =0isassumed. Thin-walledcalculationscanalsobedoneforinitialmodelsimplicity,andthisis showninequation.3: = p i r t .3 where t isthickness.Forthisequationtohold,thethicknesstoradiusratiot:r mustbelessthan0.10.Thisallowsforshearstresstobeneglected.Sincethethickness toradiusratiosfordatainthisstudywere > .10,equations.1and.2wereused foranalysis,andcalculationsusing.3wereusedduringpreliminaryanalyses. Fung,etal[15]werethersttodevelopatestingrigforbloodvesselsthatapplied pressureforsubsequentmeasurementofdeformation,asshowningure1.5a.Inthis setup,zerolongitudinaldeformationoccursduetotheclampingofvessels,andthus onlycircumferentialandradialstrainoccur.Circumferentialandradialstresscan thenbedeterminedusingthegeometrydescribedingure1.3.Inthisstudy,we utilizedamodiedversionofthissetup,asoutlinedinthemethodssectionofthis paper.Oncecalculated,aplotofthechangeincircumferentialstressoverarangeof circumferentialstrains r )]TJ/F20 7.9701 Tf 6.586 0 Td [(r 0 r 0 canbemade.Takingthederivativeslopeofthiscurve yieldstheelasticmodulusEforthelinearportionofthecurve.Alternatively,the dynamicelasticmoduluscanbeestimatedfromthestrain,showninequations.4 and.5. = 1 E rr )]TJ/F19 11.9552 Tf 11.955 0 Td [( .4 rr = 1 E )]TJ/F19 11.9552 Tf 11.956 0 Td [( rr .5 6

PAGE 23

Figure1.4:Anexampleofthegeneratedcircumferentialwallstress overcircumferentialstrain usingthickandthinwalledequationsforapulmonaryartery. Bluedatapointsarestressescalculatedforeachpressure-diameterpointwithequation.1.Greendatapointsarestressescalculatedwithequation.3.Redand magentalinesarethethickandthinttedequations,respectively. WhichcanbesolvedasasystemoftwoequationsforPoisson'sratio and elasticmodulusE.BothPoisson'sratioandelasticmodulusarematerialproperties thatdescribethemechanicalbehaviorofthevessel.Withtheseparametersknown, circumferentialandradialstresscanthenberewrittenas: = E 1 )]TJ/F19 11.9552 Tf 11.955 0 Td [( 2 [ C 1 + + C 2 1 )]TJ/F19 11.9552 Tf 11.955 0 Td [( r 2 ].6 rr = E 1 )]TJ/F19 11.9552 Tf 11.955 0 Td [( 2 [ C 1 + )]TJ/F19 11.9552 Tf 11.955 0 Td [(C 2 1 )]TJ/F19 11.9552 Tf 11.955 0 Td [( r 2 ].7 7

PAGE 24

aTestingrig bPressure-DiameterData Figure1.5:Left:AdiagramofthetestingrigthatFungusedtoperformpressure/diametermeasurementsofbloodvessels[15].Right:therawpressure-diameterthat ismeasuredwiththerig. withconstants C 1 = 1 )]TJ/F19 11.9552 Tf 11.955 0 Td [( E [ r 2 i p i )]TJ/F19 11.9552 Tf 11.955 0 Td [(r 2 o p o r 2 o )]TJ/F19 11.9552 Tf 11.956 0 Td [(r 2 i ].8 C 2 = 1 )]TJ/F19 11.9552 Tf 11.955 0 Td [( E [ r 2 i r 2 o p i )]TJ/F19 11.9552 Tf 11.955 0 Td [(p o r 2 o )]TJ/F19 11.9552 Tf 11.956 0 Td [(r 2 i ].9 Anexampleofcalculatedexperimentalwallstressusingequation.1withabestt modelusingequation.6isplottedbelowoverstrain.Itisimportanttonotethe dierencebetweenamechanicalpropertylikestiness,anextrinsicproperty,anda materialpropertylikemodulus,anintrinsicproperty.Stinessisameasurementdependentuponmaterialgeometry,whileelasticmodulusisindependent.Forexample, twoidenticaltissuesofdierentdimensionswillexhibitthesameelasticmodulus,yet thetissuewiththehigherthicknesswillexhibithigherstiness.Theequationfor stinessisshownbelow: S = AE l .10 Where A isthetotalcross-sectionalareaofthetissue, E istheelasticmodulus, and l isthecircumferentiallength.Inthisdocument,Iwillrefertoeachonesep8

PAGE 25

aratelyfortheirrespectivemeasurements.Bothareimportantwhendiscussingthe deformationbehaviorofmaterials. 1.3.1ResidualStressesandStrains Residualstressisdenedasthesmallamountofstressremaininginthestructurewhenitisintheunloadedstate.Thisstressisalsoassociatedwithresidual strain.Residualstressesandstrainsrepresentthetensionalintegritytensegrityof thestructureofthePA,thatdenethestabilityandsecurityofthesystem.The highertheresidualstress,thegreatertheabilitytosustainlargerloads.Inthissense, residualstressesandstrainsareknowntogreatlyaectthestraindistributionacross thewallatelevatedpressures[52,26,21,7,13],andthusisimportanttostudyfor alteredvesselmechanics.Itiscommontogeometricallydescribetheseparameters usingthegeometryingure1.6.Theresidualstressandstraincongurationisthe gureontheleft.Ifaradialcutisusedtoopenthecircle,theresultingconguration isontheright.Theopeningangle 0 istheanglebetweenthetwolinesbisecting thecenterofthetissuefromtheedgesofthecut.Thiscongurationhasaslightly dierentinnerandoutercircumferences.Thedierenceincircumferencesisdened asthecircumferentialresidualstrain.Recentstudieshavecorrelatedchangesinthe openingangletochangesinmechanicalpropertiesduringdisease[67].Inparticular, theresidualstressesforeachlayerofthePAaredierent,andthusmustbecalculated individuallyforaccuratemodeling.Forthisstudy,theresidualstresswasestimated fromthestress-straincurvesasanextrapolationoftheelastintoe-inline,asutilized inpreviousstudies[55,7,60]. 1.4ConstitutiveModelingwithaStrainEnergyFunction Itisimportanttounderstandthestructureandfunctionofvesselsandtheir abilitytomechanicallyadapttodiseaseandinjury.Asimplemodelofstress/strain relationshipscanbeusedtodeterminethevesselandcomposingmaterialsresponse 9

PAGE 26

Figure1.6:Left,thegeometryofthevesselatanunloadedstatewithresidualstress conguration;Right,thegeometryofthevesselwithastress/strainfreeconguration. Angle 0 istheopeningangle. whenforcesareapplied,suchasindiseaseandinjury[23].Constitutivemodels presentsawaytoachievethisbyapplyingasystemoflinearcombinationsofdashpots andsprings.Gasser,etalrstdevelopedastructuralcontinuummodelofarterial layerstointegratetissuestructureandfunctiontomechanicalloading[22].Inthis workIemployaneo-hookeanmodelofhyperelasticstrainenergybasedontheadapted frameworkofFung,etal[14].Inthisstress-strainmodel,weassumethatthetissue hasbeencyclicallyloadedwith2distinctlinearareas,whicharetreatedastwo separatematerials.Thisisbasedophysiologicalconditions,whichiscyclicalloading bythecardiaccycleofsystoleanddiastole.Therstlinearregionofthecurveatlow strainsmodelsthedeformationofelastin,wherethesecondlinearregionathigher strainsmodelscollagendeformation[53].Inthissense,themodelisaconstitutive combinationofhyperelastictissues.FinitestrainisemployedusingtheCauchy-Green tensortodetermineastrainenergyfunctionwithconstantsthatarecharacterisitic ofthematerial,andthuscantellusuniquepropertiesaboutthetissue'sbehaviorin responsetostress.TheCauchy-Greentensorisamathematicaldescriptionofmaterial 10

PAGE 27

deformationthatislargeenoughtoaltermechanicalpropertiessuchasstiness.Fung, etalwerethersttoproposeageneralformofthestrainenergyfunctionforanytype ofsofttissue[15].Thisequation,shownbelow,containsameasurefordeformation andformaterialconstantsthatcanbeestimatedfromexperimentaldata: W = 1 2 ijk ij jk + 0 + ijk ik ij e ij ij + ijk ij ik + ::: .11 whereWistheworkdonebythematerial, , ,and arethematerialconstants tobeexperimentallydetermined,and istheGreen-Lagrangestraintensor,asdenedbyequations.4and.5.UsingtheGreen-Lagrangestraintensorassumes nitestraintheoryinwhichthestrainsinthecircumferentialandradialdirection arelargeincomparisontotherelativedimensionsofthematerial.Inthegeneral functiondenedby.11,certainconstantsmaybeignoreddependingonthetissue. ThePiola-Kirchostresstensor,whichisanexpressionoftherelativestresstothe referenceconguration,canbedeterminedbydierentiatingequation.11: ij = @W @" ij .12 Usingthegeometryoutlinedingure1.3,wecanthensolveforthecircumferential andradialstressforthick-walledbloodvessels: = C a 1 + a 4 rr e a 1 2 + a 2 2 rr +2 a 4 E rr .13 rr = C a 2 rr + a 4 e a 2 2 + a 2 2 rr +2 a 4 " rr .14 Where C a 1 a 2 ,and a 4 arethematerialconstants.Thesematerialproperties canthenberelatedtostructuralparameterssuchaspercentageofcollagenand elastin,whichgiveinsighttotissuemechanicaladaption.Withthisinformation, thestructure-functionrelationshipofthepulmonaryarterycanbeanalyzedfrom diseaseandhealthy,andinparticular,recoveryfromdisease. 11

PAGE 28

1.5Justication Hypoxicpulmonaryhypertensionisthoughttobemildandreversible[62],althoughchronichypoxiahasproventodirectlyinduceirreversiblepulmonaryhypertension[57,62,58,64].Littleresearchhasfocusedonproximalarterialremodeling, asPHhasbeenlongthoughttobeadiseaseofthedistalvasculature.Recently,studieshaveshownthatremodelingofthePAsdirectlycontributestocompromisedright heartfunctionleadingtoremodelinginthedistalcirculation[9,24,25,4].Vascular remodelingisahallmarkofPH,yethowPAstinessaloneaectsRVdysfunction remainsunclear.ThreeweekhypoxicexposureinducesvascularremodelingandelevatesmeanpulmonaryarterialpressuremPAP[31,25,51].Whenremovedto normalatmosphericpressure,cardiacoutputreturnstonormalvalues[18,20].This reversaltohealthystateisnotfullyunderstood,andourpreliminaryevidenceshows thatresidualbrosisstillremains.Therefore,ananalysisofthestructure/functionrelationshipofthePAiswarrantedtodeterminethemechanicaladaptationofthemain PAanditsreverseremodelingofbrosisduringrecoveryfromhypoxia.Themedial layerisknowntobetheprimaryregulatorofvasculartone,andisthustheprimary layerforactuationofstiness.Therefore,themediallayeristhemostpertinentinthe studyofvascularmechanics.Constitutivemodelingwithstrainenergyfunctionshas beenusedasameanstodeterminethefunctionalresponseoftissuesduringaltered statesofdiseaseandinjury[1,44,22,45,34].Thematerialconstantsdetermined experimentallyfromthistypeofmodelcanthenbecorrelatedwithtissuestructure togivevaluableinsighttohowchangessuchasECMcontent,berorientiation,and bermorphologycontributetomechanicaladaptationindiseaseandinjury.Thisinsightcanthenbeusedtoengineersolutionstodevelopingacuretothediseaseorfor tissueengineeringdesign.N.C.Chesler[65]hasshownthatexcessaccumulationof collagenintheadventitiainhibitsanormalrecoveryfromhypoxicPH,andthatthis hasimportantimplicationsforrightheartfunction.Thus,itiscriticaltodiscernthe 12

PAGE 29

relationshipthatcollagenandelastinhavewithincreasingstinessandwallstress, andinparticular,howthisinhibitshypoxicrecovery. 1.6Goals Here,weproposethatvascularremodelingassociatedwithbrosisduetodepositionofextracellularmatrixisamechanismofvascularstieninganddecreased circumferentialwallstress,resultinginafterloadincreasesbeyondthoseindicated bypulmonaryvascularresistance.Vascularstieninganddecreasedwallstressin hypoxicPHdoesnotresolveuponrecovery,andwehypothesizethatitisdueto increasesincollagenandelastincontent.Inthisstudy,weinvestigatedthestructure/functionrelationshipofthemediallayerofthemainPAinhypoxia-exposed, andhypoxiarecoveryrats.Intact,mainPAswerehistologicallyanalyzedforcollagen andelastincontent,andcomplianceofthePAswereevaluated.Aconstitutivemodel ofhyperelasticstrainenergywasdevelopedforPAmediawallstress,andthiswas correlatedtostructuraldierencesseenbetweendiseaseandhealthystates.These goalsareoutlinedbelow. SpecicAim1:EvaluatethewallstressinthePAincontrols,3weekhypoxia, andrecoveryfromhypoxiautilizingpressure-diameterPDmeasurements. SpecicAim2:Determinetherelativeamountsofcollagenandelastinthrough histologyutilizingimageprocessing. SpecicAim3:Determinemathematicalrelationshipbetweenmaterialconstants, stiness,andamountsofcollagenandelastin,ofthePAincontrol,hypoxic,andposthypoxicanimals. 13

PAGE 30

2.Methods 2.1AnimalModel Thirty-sixSpragueDawleyrats,10weeksoldatinitiationofstudy,wereused. Figure2.1outlinestheexperimentaldesign.Atthepointofeuthanasia,eachrat washarvestedforheart,rightpulmonaryartery,leftlung,andanteriorsegmentof therightlungforsubsequenttissueanalysis.SixteenratswerekeptatDenver, COaltitude,280ftabovesealevel,630mmHg,p O 2 =128mmHg.Atthreeweeks, eightofthosecontrolCTRLratswereeuthanized.Afternineweeks,theother eightCTRLratsweresacriced.Theothersixteenratswerehousedinahypobaric chambersimulating18,000feetaboveseallevelmmHg;p O 2 =82mmHgfor21 daysbeforebeingremovedtoDenveraltitude.Eightoftheseratswereimmediately sacricedHPX,whiletheothereightwerehousedatDenveraltitudeforsixmore weeksRTN. Figure2.1:OurmodelconsistedoffourcohortsofadultmaleSpragueDawleyrats. Theratsweretestedattheendofeachtreatmentofcontrol,3weeksinthehypobaric chamber,6weeksinthehypobaricchamberand3weeksinthehypobaricchamber with6weeksrecoveryatDenver,CO pO 2 Animalswereeuthanizedwithathoracotomysecondarytooverdoseofisopentobarbitolviafemoralveininjectionconcentrationdeterminedbyweight.TheheartblockwasexcisedgureA.1,andasegmentofpre-hilarpulmonaryarterywasiso14

PAGE 31

Table2.1:ComponentsoftheKrebs-HenseleitSolutiondissolvedin1literofdeionizedwater.Thissolutionwascarbonatedusingaerosolizedcarbogen% O 2 :5% CO 2 ComponentAmount NaCl 6.9g KCl 0.35g MgSO : 4 7 H 2 O 0.259g KH 2 PO 4 0.16g CaCl : 2 2 H 2 O 0.373g NaHCO 3 2.085g L-NameHCl0.005g Glucose1.8g latedusingmicrodissection,denudedofendothelium,cannulatedwithmetalpipettes, securedwithsilkligaturesandperfusedwithcalcium-freeKrebs-Henseleit Cin aperfusedvesselapparatus.ThecomponentsfortheKrebs-Henseleitsolutionare outlinedintable2.1.Theleftlungwasexcisedandpreppedforparanembedding, whilearightlobewaspreppedforfrozensectioning.Theheartwasashfrozenin liquidnitrogentobemeasuredlaterforRV/LVweightratio. 2.2MyographyTesting AschematicofthemyographapparatusLivingSystemsInstrumentation,St. Albans,VTisdepictedingure2.2.SegmentsofPAweresecuredoncannulasby silkligaturesatbothends.Physiologicsolutionisaeratedandpumpedthroughthe waterbathaswellasthecannulas.Transducersmeasureoninputandoutputsides. Thevideodimensionanalyzerdisplaysthetissueandmeasurestheouterdiameter fromthemicroscopeandcameraoutput.Forallmeasurements,longitudinalstrain 15

PAGE 32

z wassetat0.01mm/mm.Pressurewascontrolledandsteadilyincreased,starting at5mmHg,andheldforveminutesat5mmHgincrements,until55mmHgwas achieved.55mmHgwaschosenasthemaximumpressureforrelevancewithinthe physiologicalrangeofPApressures.Diametersweremeasuredateachincrement.The pressurewasbroughtbackdownat5mmHgincrementsanddiametermeasurements wererepeated. Figure2.2:VesselChamberPressure-DiameterApparatus.Thepulmonaryartery segmentissecuredoncannulasbysilkligaturesatbothends.Physiologicsolution isaeratedandpumpedthroughthewaterbathaswellasthecannulas.Transducers measureoninputandoutputsides.Thevideodimensionanalyzerdisplaysthetissue andmeasurestheouterdiameterfromthemicroscopeandcameraoutput. 16

PAGE 33

2.3Hemodynamics Fourratsfromeachcohortunderwentrightheartcatheterizationformeasurementsofhemodynamics.Ratswereweighed,thenanesthetizedwithAvertinsee tableA.1,andplacedsupine.Oncesedated,theratschestwereshaved,andanincisionismadeontherightfemoralcalfforthefemoralveincatheter.Thefemoral veinisdissectedoutthroughmuscle,andapunctureholeismadeandthecatheter isinserted.Asecondincisionismadeonthechestinbetweenthe5thand6thrib arms,muscleisteasedapart,andtherightventricleisexposedandpuncturedfor thecardiaccatheter.Meanpulmonaryarterialpressure,heartrate,pulsepressure, andstrokevolumearerecordedovera5minuteperiod.Oncerecorded,ratswere subsequentlyeuthanizedviathoracotomy,asdescribedabove. 2.4Histology Tissuesectionswerexedinfourpercentparaformaldehydefor48hoursand thenparanembeddedandsectionedfortransversecross-sections.Eachtissuewas stainedwithMassonTrichromeandVerhoe'sVanGiesonforcollagenandelastin content,respectively. Percentageofcollagenandelastincontentwerequantiedviaimageanalysis usingMatLab.Thiswasacheivedthroughpixelthresholding,asdepictedingure 2.3.Imageswererstbinarized,thenathresholdwasappliedtoisolateareasinthe imagethatstainedeitherblackelastinorbluecollagen.ThicknessofeachPAwas measuredinMatlab.Foreachcross-section,thethicknesswasmeasured6timesand averagedforeachrat,asdemonstratedingure2.4. 2.5WallStressCharacterization Circumferentialandradialwallstresswerecalculatedfromtherawpressurediameterdatausingequations.1,.2,and.3.Thechangeinthicknesswasmodeled basedonisovolumetricdeformationoftissue,asconceptuallyshowningure2.5.The 17

PAGE 34

Figure2.3:Imagethresholdingforcollagenandelastincontentquantication.The imageonthefarleftistheuneditedcross-sectionofaPA.Themiddleimageisthe conversionoftheoriginalimagetoblackandwhitebinarization.Theimageonthe rightiswithathresholdof > 150pixelstoisolateelastinstainedelements. determinationofinnerdiameterwascalculatedasfollows: t = d o )]TJ/F19 11.9552 Tf 11.956 0 Td [(d i .1 where d o istheouterdiameterdeterminedbyPDmeasurements,and d i iscalculated usingtheareasdeterminedbythePDmeasurementsandareasdeterminedbyimage thresholding,asshownbelow: d i =2 r A small .2 A small = d o 2 2 )]TJ/F19 11.9552 Tf 11.955 0 Td [(A total .3 where A total isthetotalcross-sectionalareaofthePA.Thistissueareawasquantied usingimageprocessinginMatlab.Innerdiameterwerethencalculatedastheouter diameterincreasedduetopressure.Thickandthinwallequationsweredetermined. 18

PAGE 35

Figure2.4:ACross-sectionofaPAstainedwithMassontrichrome.Thicknesswas measuredusingtheMATLABpixelmeasuringtool,averagedover6regions,and convertedtomicrometers,shownhere.Measuringbarsareinunitsofpixels. Thederivativewastakenofthesecurvesusingpolynomialinterpolationandelastic moduluswasobtainedforthelinearregion.DynamicmodulusandPoisson'sratio werecalculatedusingequations.4and.5asasystem.Oncetheseparameters weredetermined,equations.6and.7werettothedata.Thecodeforthese calculationsareoutlinedinappendixB. 2.6ConstitutiveModelingofExperimentalMechanicsMeasurements Oncecircumferentialandradialwallstresseswerecharacterized,attingwith astrainenergyfunctionwasapplied.Thiswasdoneconvertingequation.6to equation.13.Themethodologyforthisisoutlinedbelow. 2.6.1LinearModuliofElastinandCollagenRegions Atheoreticalthick-walled,cylindricaltube,composedofcollagenandelastin, wasmodeledasthepulmonaryartery,withtherelationshipof E e and E c inparallel, 19

PAGE 36

Figure2.5:Aschematicoftheisovolumetricdeformationwhenforceisincreased. Whenpressureisincreased,diameterandthicknesschange,butthecross-sectional areaofthetissue,A,isconserved. asshowningure2.6.ThiswasdoneinMatLabandPythonwithalineartof theempiricaldataforeachratusingthefunctionpolyt,withadegreeof1.Low strainslopeswereestimatedasthemodulusofelastinandhighstrainslopeswere estimatedasthemodulusofcollagen,asseeningure2.7.Theseweredetermined bymaximizingthe R 2 valuesofthelineart,andcomparedtothepublishedvalues oftheYoungsmodulusforcollagenIandarterialelastin.075MPaand3MPa, respectively[32,3]toensuretheirphysiologicalrelevance.Thevaluesestimated bythelineartswereinputintoequation.6overanevenlydistributedrangeof circumferentialstretch.Astipulationinthemodelwasappliedatachangeinthe slopeoftheexperimentaldatareferredtoasthetransitionpointT.BeforeT,the modulusofelastin E e wasusedinequation.6
PAGE 37

transitionfromlowtohighstrainwasnotskewingthelineart.Thismodeldata wasthenoverlayedontotheexperimentaldataandanalyzedforqualityoft.The codeisoutlinedinappendixB. Figure2.6:Theproposedrelationshipfor E e and E c asparallelspringsasamechanical model. 2.6.2CollagenFiberEngagementStrains Thestrainsatwhichcollagenbersbegintobeactivelyengagedwereestimated usingthex-interceptofthecollagenmodulusline,asshowningure2.7.Theregion totheleftofthislinerepresentsthestress-strainrelationshipofthematerialthatis purelydescriptiveofthemechanicsofelastinbers,whicharedominantatlowstrain. Theregiontotherightoftheinterceptrepresentsthepresenceofcollagenbersthat arebeingstretched,andthuscauseashiftinthecurvetoasteeperslopethatis paralleltothemodulusofcollagen,dominatingthemechanicsathigherstrains. 2.6.3DeterminationofStiness StinessforeachratPAwascalculatedusingtheestimatedvaluesofthelowand highstrainmodulus,usingtheequationshownbelow: S = AE l .4 21

PAGE 38

Figure2.7:Estimationoftheelastinandcollagenmodulusthroughlineartting.The strainatwhichcollagenbersareengagedisshownastheinterceptonthex-axisof thecollagenmodulusline. Wherethearea A isthecross-sectionalareaasdeterminedbytheimageprocessing methodsdescribedearlier,and l isthecircumferentiallengthatzerostress. 2.6.4DeterminationofMaterialConstants Theexperimentaldatawastwiththefunctionoutlinedinequation.13.The determinationofconstantswasdoneusinganon-linearleastsquaresmethodutilizing theblankfunctioninMatLab,whichminimizestheerrorbetweentheexperimental dataandtheestimatedequation.Afunctionwasmadeutilizingtheequationforthe t,asfollows: 2 = n X j =1 mod )]TJ/F19 11.9552 Tf 11.956 0 Td [( exp 2 j .5 Where j isthejthofndatapoints, exp isthecircumferentialstresscalculated directlyfromtheexperimentaldataand mod isthemodel.Thestress-straindatawas calledtotheexternalfunctionusingtheMatLabcommand 'lsqnonlin' andaninitial 22

PAGE 39

guessfortheconstantsseeAppendixBforcode.Constantsandresidualsofthet werereturnedfromthefunction.Oncetheconstantsweredetermined,theequation wasplottedoverthecircumferentialstrain,andthegoodnessoftwasassessedusing .5withap-valueof0.05. 2.7StatisticalMethods Severalstatisticalmethodswereutilizedtocomparecohortsanddeterminetheir signicance.Forhemodynamicdata,analysisofvarianceANOVAtestsweredone todetermineifvariancesbetweeneachgroupwerethesame.Tukey-HSDtestswere alsodonetodetermineiftheirwassignicantdierencepairwisebetweeneachcohort. Forthestrainenergyfunctionts,thegoodnessoftwasdeterminedusingbotha 2 testand R 2 test.The 2 valueisdeterminedasfollows: 2 = n X j =1 [ mod )]TJ/F19 11.9552 Tf 11.956 0 Td [( exp j exp ] 2 .6 Thesignicanceofthe 2 isthendeterminedbythedegreesoffreedomofthedata set.Forcomparisonofcollagenandelastinmoduliasdeterminedbylineartting, ANOVAandTukey-HSDtestsweredone.Forcomparisonofcollagenengagement strains,ANOVAandTukey-HSDtestsweredone. 2.7.1CorrelationstoDetermineMathematicalRelationships Oncethevaluesformodulus,materialconstants,engagementstrains,andpercentagesofcollagenandelastinweredonewereeachrat,thesevalueswerecorrelated againsteachothertodetermineifasignicantmathematicalrelationshipexisted betweenthem.Ascatterplotofvalueswasgeneratedformodulusversusmaterialconstants,modulusversusengagementstrains,andmodulusversuscollagenand elastinpercentage.Thesecorrelationswererepeatedforstiness.Graphsofthese plotswerevisuallyanalyzedtodecipheraspecicrelationship,andtsoflinear,exponential,logarithmic,andpolynomialsofdegree2and3wereapplied,usingan R 2 todetermineagoodnessoft.Inthisdocument,onlythebesttsarereported. 23

PAGE 40

3.Results Figure3.1:Hemodynamicdataforeachcohort.Heartratebpm,mPAPmmHg, andstokevolume lareshownhere.Bluebarsrepresentstandarddeviation. 3.1Hemodynamics Hemodynamicsareshowningure3.1.Forthecontrolcohort,averageheart ratewasobservedtobe340 16.8beatsperminutebpm,meanpulmonaryarterial pressuremPAP,wasobservedtobe14.75 1.87mmHg,andaveragestrokevolume wasobservedtobe346 64.8 l.Forthethreeweekhypoxiccohort,287 26.3bpm and24 5.9mmHgwereobservedforaverageheartrateandmPAP,respectively, withaveragestrokevolumeat205 15.0 l.Forthethreeweekhypoxic,6week recoverycohort,310 14.4bpmand17 4.6mmHgwereobservedforaverage heartrateandmPAP,respectively,withaveragestrokevolumeat256 67.4 l.The dataofeachmeasurementforeachratisshowninappendixA. 3.2Histology ThemassontrichromeandVerhoeVanGiesonstainsareshowningures3.3 and3.4,respectively.Theentirewallthicknessvaluesforeachratdepictedingure 3.2andtable3.1. AnANOVAtestwasperformedagainsteachcohort.ThethicknessofCTRL versusHPXandRTNissignicant,asindicatedbythep-valuesp=0.003,p=0.0018, 24

PAGE 41

Figure3.2:ThicknessesofPAforacontrolbhypoxicandcrecoverycohorts. Imagesare10xmagnication. respectivelyandinsignicantforHPXversusRTNp=0.5795,asshowningure A.2.Percentageofcollagenandelastinforeachratisshownintable3.2.Percentage ofcollagenremainedsignicantlyhighfortherecoverycohort,yettheamountof elastinwasdecreasedcomparedtothecontrols,asindicatedbytheANOVAtestin 25

PAGE 42

Table3.1:Thicknessescalculatedforeachcohort. CTRLHPXRTN ThicknessThicknessThickness Rat m Rat m Rat m 1100.31148.21138.8 279.82226.62177.9 389.93156.73176.4 488.04181.04157.7 5138.85205.45171.0 Mean:99.4 23.2Mean:183.6 32.8Mean:168.2 9.8 guresA.3andA.4.Thecodeforcalculatingthesepercentagesaregiveninappendix B. 3.3CircumferentialWallStressCalculations Therawpressure-diametergraphsareplottedingure3.5.Thisdatawasconvertedtocircumferentialwallstressusingequations.1and.3.Thewallstresses foreachratineachcohortareshowningure3.6,withthickandthinwallstress approximationsshowninredandmagenta,respectively.AnANOVAcomparison wasdonebetweeneachcohort,showningureA.5. Thederivativeofthegraphsingure3.6weretakenforeachcohorttodetermine theirelasticmodulusovertheentirestrain.Thegraphsofthesemodulusareshown ingure3.7. 3.4ResidualStresses Theresidualstresseswereestimatedfromthestrainenergyfunctionsastheyinterceptfor .Theseweredoneforeachrat,shownintable3.3.AnANOVA 26

PAGE 43

Figure3.3:CollagenstainingblueforcontrolCTRL,hypoxicHPX,andrecovery RTNcohorts.Imagesareat10xmagnication. analysiswasdonetocomparethevaluesbetweencohortsshowningureA.8.The residualstressesbetweeneachcohortweresignicantlydierentfromeachother. 3.5FTestforVariance Atwo-sampletestforequalvariancewasdonetodetermineifthespreadofthe dataweresignicantlydierentbetweencohorts.Thiswasdoneusingthefunction 'vartest2'inMatLab.Valuesforcircumferentialwallstress werecompared. Controlversushypoxia,controlversusreturn,andreturnversushypoxiaallrejected thenullhypothesisthatvarianceswerethesame,withp-valuesof < 0.0001foreach comparison. Atwo-sampletestforequalvariancewasalsodoneforthethicknessesofeach rat,inordertodeterminethesourceofhighvariance.Thiswasalsodoneusing 27

PAGE 44

Table3.2:PercentageofcollagenandelastincalculatedforeachcohortusingMatlab thresholding. CTRLHPXRTN %%%%%% RatCollagenElastinRatCollagenElastinRatCollagenElastin 125.317.6128.610.4125.911.9 214.617.3228.612.6224.09.7 320.320.8327.511.0323.811.9 411.815.0426.89.5427.112.4 58.923.0529.512.9525.812.1 Mean:16.218.7Mean:28.211.3Mean:25.411.6 6.6 3.2 1.1 1.4 1.4 1.1 Table3.3:Residualstressescalculatedforeachcohort. CTRLHPXRTN ResidualResidualResidual RatStresskPaRatStresskPaRatStresskPa 15.2516.7616.53 23.8523.3825.37 312.9733.2735.54 410.8744.9345.79 57.6152.6155.12 Mean:8.11 3.8Mean:4.19 1.67Mean:5.67 0.54 28

PAGE 45

Figure3.4:ElastinstainingblackforcontrolCTRL,hypoxicHPX,andrecovery RTNcohorts.Imagesareat10xmagnication. thefunction'vartest2'inMatLab.Controlversushypoxiareturnedanacceptednull hypothesisthatthevarianceofthethicknesseswerethesame,withap-valueof0.207. Controlversusreturn,andreturnversushypoxiabothrejectedthenullhypothesis thatvarianceswerethesame,withp-valuesof < 0.0001foreachcomparison. 3.6StrainEnergyFunctions TheStrainEnergyFunctionsweredeterminedforeachratineachcohort.For convenience,thedataforentirecohortsaredisplayedhereingure3.8,butthe constantsforeachratcanbefoundinappendixAintablesA.3,A.4,andA.5.Table 3.4givesthevaluesforeachconstantthatwasestimatedusingequation.13and .5.Chi-squared 2 aregivenforthegoodnessofts.Thegoodnessoftforthe controlandrecoverycohortshad 2 lessthantheircriticalvalue,andarethusnot signicantlydierent.However,thetforthehypoxiccohorthada 2 greater 29

PAGE 46

aCTRL bHX cRTN Figure3.5:Therawpressure-diameterdataobtainedfrommyographinationtesting. 30

PAGE 47

aCTRL bHX cRTN Figure3.6:Thecircumferentialwallstress plottedovercircumferentialstrain. 31

PAGE 48

Figure3.7:Thegeneralelasticmoduliforeachcohortthatisovertheentirerangeof strains,asdeterminedbythederivativeofthestress-straincurve. thanthecriticalvalue,andthusissignicantlydierentthantheexperimentaldata. Thismaybeduetoincreasedvarianceseeninthehypoxiccohort,asindicatedby thetestforvariancedescribedpreviously.Poortsatlowstrainmayalsobedueto skewingofthetduetooutlierdatapoints,ormaybeduetotheneedtoinclude moreparametersforatightert.Analysisoftheresidualsofthetsrevealsdenitive trends.Ineachcohort,ageneraltrendcanbeobservedforlowpredictionsatlow strains,andhighpredictionvaluesathighstrains,withhighererrorathigherstrains. Foreachcohort,thehighesterrorresidualvalueisobservedathigherwallstress. 3.7CollagenandElastinFitting 32

PAGE 49

Figure3.8:Thestrainenergyfunctionsforeachcohort. ? isexperimentalcontrol data,redperforatedlineisthettedstrainenergyfunctionforCTRL, isexperimentalhypoxicdata,blueperforatedlineisthettedstrainenergyfunctionforHX, isexperimentalrecoverydata,andtheblacksolidlineisthettedstrainenergy functionforRTN. Theestimatedequationsforthecollagenandelastinregionsareshowningure 3.10.Theequationsfortheelastinandcollagendominatedregionsforeachcohort areshownintable3.5. TheindividualslopesforthecollagenandelastindominatedportionsofthestressstraincurvesforeachrataregivenintableA.2inappendixA.AnANOVAcomparisonwasdonetodetermineiftheModulusweresignicantlydierentthaneachother. ThisisdepictedingureA.6andA.7.Fromtheanalysis,wecanseethat E e between 33

PAGE 50

aCTRL bHX cRTN Figure3.9:Theresidualsofthestrainenergyfunctiont plottedoverthe predictedvalues.acontrols,bhypoxic,andcrecoverycohort. 34

PAGE 51

Table3.4:Materialconstantsdeterminedforeachcohortwithleastsquares. Cohort C 1 kPa a 1 a 2 a 4 2 p-valueDOF CTRL2.511.631.632.55670 : 2p < 0.0584 HX12.4412.21.01.47164 : 4p < 0.05102 RTN12.3112.441.01.7534 : 1p < 0.0582 Table3.5:Thelineartsfortheelastinandcollagenregions,denedasbeforeand afterthetransitionpoint,respectively. CohortElastinFit R 2 CollagenFit R 2 CTRL =122 : 7 )]TJ/F15 11.9552 Tf 11.955 0 Td [(7 : 50.944 =248 :" )]TJ/F15 11.9552 Tf 11.955 0 Td [(179 : 20.997 HX =124 : 4 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 : 60.989 =619 : 7 )]TJ/F15 11.9552 Tf 11.955 0 Td [(142 : 70.977 RTN =125 : 9 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 : 890.986 =635 : 7 )]TJ/F15 11.9552 Tf 11.955 0 Td [(130 : 10.969 cohortsisnotsignicantlydierent,butthat E c issignicantwhencomparingCTRL versusHXandCTRLversusRTN. Inordertoassessiftherelationshipfor E c and E e wastrulyresistorsinparallel, theaveragevaluesfor E c and E e ineachcohortwereusedinequation.6fortheir respectiveregionsinaadditivemanner.Thetswerelayedovertheexperimental data,showningure3.13. 2 valuesforcontrols,hypoxic,andrecovery,are6102.8, 7519.0,and7538.7,respectively. 3.8Structure/FunctionRelationships 3.8.1ComparingMaterialConstantstoModulusandStiness Inordertoassesstherelationshipbetweenmaterialconstantsandstinessofthe vessel, C 1 wasplottedagainstcollagenmodulus E c andelastinmodulus E e .This graphisshowningure3.11.Theleftaxisis E e ,indicatingthebluestarpointsand t.Therightaxisis E c ,indicatingtheredcirclepointsandt.Severaltypesofts 35

PAGE 52

aCTRL bHX cRTN Figure3.10:Theelastinandcollagenregionaltsforeachcohort. 36

PAGE 53

Figure3.11: C 1 correlatedwithelasticmodulus E e andcollagenmodulus E c .Blue ? is E e versus C 1 ,blueperforatedlineisthettedlinearregression,red is E c versus C 1 ,andtheredperforatedlineisthettedexponential. 2 =492.1p < 0.05,forthe collagent,and R 2 =0.014fortheelasticlinearregression. wereapplied,includinglinear,exponential,andpolynomialsofdegree2-6.Itwas determinedthroughiterationthatthetwiththesmallest 2 valuewasalinearand exponentialt,for E e versus C 1 ,and E c versus C 1 ,respectively.Theequationsfor theserelationshipsareoutlinedintable3.6.Stiness,whichwascalculatedusingthe ModulusestimatedintableA.2andequation.10,wascalculatedforzerostress deformationPAatslacklength.Thediameteratzeropressurewasextrapolated usingalineartofthepressure-diametercurvefromgure3.5andusedtocalculate thecircumferentiallengthofthePAatzeropressure.Thesestinessesaregivenin 37

PAGE 54

Figure3.12:Percentageofcollageandelastinwascorrelatedwithelastinmodulus E e andcollagenmodulus E c .Blue ? is E e versus%elastin,blueperforatedlineis thettedlinearregression,red is E c versus%collagen,andtheredperforatedline isthettedexponential. 2 =1255.8p < 0.05,forthecollagent,and R 2 =0.0002 fortheelasticlinearregression. theappendix,tableA.6. 3.8.2ComparingPercentageofCollagenandElastintoModulusand Stiness Toassesstherelationshipbetweenthepercentageofcollagenandelastinand vesselstiness,percentcollagenandelastinwasplottedagainstcollagenmodulus E c andelastinmodulus E e .Thisgraphisshowningure3.12.Againtheleftaxis is E e ,indicatingthebluestarpointsandt.Therightaxisis E c ,indicatingthered 38

PAGE 55

aCTRL bHX cRTN Figure3.13:Theelastinandcollagenparalleltsforeachcohort. 2 valuesare 6102.8,7519.0,and7538.7,forcontrols,hypoxics,andrecovery,respectively. 39

PAGE 56

Table3.6:Relationshipsbetween C 1 andcollagenandelastinmodulusforallcohorts, asgraphedingure3.11. Goodness AnalysisRelationshipoftp-value C 1 versus E e E e =-0.638 C 1 +142.81 R 2 =0.0138p < 0.05 C 1 versus E c E c =-3569.0exp-1.16 C 1 +557 2 =541.4p < 0.05 Table3.7:Relationshipsbetween C 1 andcollagenandelastinstinessforallcohorts, asgraphedingure3.11. Goodness AnalysisRelationshipoftp-value C 1 versus S e S e =-0.031 C 1 +1.54 R 2 =0.108p < 0.05 C 1 versus S c S c =0.010 C 1 +1.19 R 2 =0.512p < 0.05 40

PAGE 57

Table3.8:Relationshipsbetweencollagenandelastinpercentageandtheirmoduli forallcohorts,asgraphedingure3.14. Goodness AnalysisRelationshipoftp-value %Elastinversus E e E e =-0.015*% e +138.88 R 2 =0.0002p < 0.05 %Collagenversus E c E c =22.62*% c +42.27 R 2 =0.79p > 0.05 Table3.9:Relationshipsbetweencollagenandelastinpercentageandtheirstiness forallcohorts,asgraphedingure3.15. Goodness AnalysisRelationshipoftp-value %Elastinversus S e S e =0.0845*% e +0.114 R 2 =0.432p < 0.05 %Collagenversus S c S c =0.085*% c +0.165 R 2 =0.55p > 0.05 circlepointsandt.Severaltypesoftswereapplied,includinglinear,exponential, andpolynomialsofdegree2-6.Itwasdeterminedthroughiterationthatthetwith thesmallest 2 valuewasalinearandexponentialt,for E e versus C 1 ,and E c versus C 1 ,respectively.Theequationsfortheserelationshipsareoutlinedintable3.8. 3.9Relationshipof C 1 andCollagenandElastinPercentagewith CollagenStrainIntercepts Thestraininterceptsforeachcollagendominatedregionallinecollagenmodulus wereestimated.Theseinterceptswerethenplottedagainstmaterialconstant C 1 and collagenandelastinpercentagestodetermineifasignicantrelationshipexisted.The collagenengagementinterceptsrepresentthestrainatwhichcollagenbersarebeing activelyenagedinthetissue. C 1 versusinterceptisshowningure3.16,andpercent 41

PAGE 58

Figure3.14: C 1 wascorrelatedwithcollagenstiness S c andelastinstiness S e Blue is C 1 versuselastinstiness S e ,blueperforatedlineisthettedlinearregression,red is C 1 versuscollagenstiness S c ,andtheredperforatedlineisthetted linearregression. R 2 =0.108,forthettedelastinstiness,and R 2 =0.512forthe ttedcollagenstiness. collagenandelastinversusinterceptsareshowningure3.17.Generally,itisevident thatthereisanincreasingrelationshipof C 1 withcollagenmodulusandstiness,with aexponentiallydecreasingrelationshipwithstrainintercept.Itisalsoevidentthat collagenpercentageascalculatedbyhistologyincreaseswithcollagenmodulusand stiness,anddecreaseswithstrainintercept. 42

PAGE 59

Figure3.15:%Collagenandelastinwascorrelatedwithcollagen S c andelastin stiness S e .Red is%collagenversuscollagenstiness S c ,andtheredperforated lineisthettedlinearregression.Blue is%elastinversuselastinstiness S e ,and theblueperforatedlineisthettedlinearregression. R 2 =0.55for S c ,and R 2 = 0.432for S e Table3.10:Relationshipsbetween C 1 andstrainintercepts,asshowningure3.16. Goodness AnalysisRelationshipoftp-value C 1 versusstraininterceptsstrain=0.52exp-0.07 C 1 2 =1.55p > 0.05 43

PAGE 60

Figure3.16: C 1 wascorrelatedwithstraininterceptsfromthecollagenmodulusline. Red is C 1 versusinterceptmm/mmcollagen,andtheredperforatedlineisthe ttedexponential. 2 =1.55p > 0.05,forthettedline. Table3.11:Relationshipsbetweencollagenandelastinpercentageandthecollagen strainintercepts,asgraphedingure3.17. Goodness AnalysisRelationshipoftp-value %Elastinversusstraininterceptstrain=0.035*% e -0.17 R 2 =0.70p > 0.05 %Collagenversusstraininterceptstrain=-0.015*% c +0.64 R 2 =0.38p < 0.05 44

PAGE 61

Figure3.17:Percentageofcollageandelastinwascorrelatedwiththeintercepts fromthecollagenmodulusline.Blue is%elastinversusinterceptmm/mm,blue perforatedlineisthettedlinearregression,red is%collagenversusintercept mm/mm,andtheredperforatedlineisthettedlinearregression. R 2 =0.38for the%collagent,and R 2 =0.70forthe%elastint. 45

PAGE 62

4.Discussion 4.1HistologicalAnalysis ChangesintheECM,andinparticularcollagenamount,structure,andmorphology,havelongbeenknowntobeassociatedwithdisease,brosis,inammation, andinjury.TheonsetofPHischaracterizedbyvascularremodelingintheformof hypertrophyandbrosisofthevascularlayers.Thus,inordertodemonstratetherobustnessofthehypoxicanimalmodeltoinducePH,weanalyzedtheextentofbrosis viachemicalstainingofcollagenandelastin.Asseeningures3.2,3.3,and3.4,and outlinedintables3.1and3.2,thethicknessremainedelevatedattheendofrecovery fromhypoxia,ascomparedtothecontrols.Thisisanindicationofhypertrophythat doesnotresolveduringsixweeksafterhypoxicexposure.Percentageofcollagenalso remainedelevatedattheendoftherecoveryperiod,indicatingunresolvedbrosis. Interestingly,thetotalamountofelastinasdeterminedbynumberofpixelsdidnot changefromcontroltohypoxictorecovery,butthepercentelastinbyareadecreased signicantlyduetotheincreasedcollagentoelastinratio.Thiscanbeinferredtobe duetoaninsignicantchangeintotalamountofelastin,relativetoanincreaseintotalcross-sectionalareafromhealthytodisease.Indeed,whencalculated,thepercent increaseinthicknessisroughlyproportionaltothedecreaseinelastincontent,and proportionaltotheincreaseofcollagencontent.Collectively,theseresultsindicate thatatsixweeksafterrecoveryfromchronichypoxia,vascularremodelingduetoPH doesnotreversetoanysignicantvalue,althoughmayuponfurtherrecoverytime. Thus,futurestudiesshouldconsistoflongerrecoverytimes 6weeksinorderto evaluatethesechangesovertime. 4.2Hemodynamics PHinhumansisdenedasmPAPabove25mmHg,diminishingcardiacoutput, andaPVRgreaterthan3mmHg : min/L.Hemodynamicmeasurementsweremade forratsineachcohorttoensurethatPHwasinducedduringthethreeweekhypoxic 46

PAGE 63

exposure.Atremovalfromhypoxia,heartratereturnstonormoxicvalues.Stroke volumealsoreturnstonormoxicvalues.mPAPinitiallydecreasestonormoxicvalues at3weeksrecovery,thenslightlyincreases3weeksfurther.ThesemeasurementsindicatethatPHwasinducedinthe3weekhypoxiacohort,andwashemodynamically resolvedintherecoverycohort.ThisdatasupportstheacceptedtheorythatrecoveryfromhypoxiaresultsinrecoveryofcardiacotputandresolutionofPH.Further recoverytimesshouldbecarriedout 6weekstoensurethatthehemodynamics donotsignicantlychangewithtime. 4.3ArterialWallStresses Arterialwallstressesforacylindricalvesselarterycanbebrokendowngeometricallytocircumferential,radial,andlongitudinalstresses.Circumferentialstress isconsideredthemostimportantstresswhenstudyinginationdeformationthat occursduringelevatedbloodpressuresinthepulmonaryartery.Figure3.5shows therawpressure-deformationdataobtainedthroughmyographtesting,andgure 3.6showstheconversionofthisdatatostress-strainusingequations.1and.3. Thisconversionallowsthedatatosimultaneouslybeanalyzedforintrinsicmaterial properties,aswellasnormalizesthedatatotighttrendlines.AsseenfromgureA.5, thewallstressissignicantlyhigherfromcontroltohypoxiaandrecoverycohorts. Thecircumferentialstrainforhypoxiaandrecoverycohortsmaxesoutathalfthatof thecontrols.Thisisaninitialindicationthathypoxicandrecoverycohortsexhibit stierPAsthanthecontrols.Thisisinterestingwhenconsideringthestrainatwhich collagenbersareengaged.Sincethecircumferentialwallstressesforhypoxicand recoverycohortsaresignicantlylessthanthecontrols,thisinitiallysuggeststhatthe hypoxicandrecoverycohortPAswerenotbeingstretchedtothesamestrainatwhich thecontrolswerebeingstrained.However,thiswasaloadcontrolledstudy,andthe hypoxicarterieswerethicker.Whenperformingpressure-diametermeasurements,we utilizedarangeofpressuresfrom5mmHgto55mmHg,andhigherpressuresthan 47

PAGE 64

60mmHgmaycausefailureandruptureofthetissue.Thus,atthistime,weare unabletorectifythelargediscrepancyofwallstressesbetweenthecohortsutilizing PDmeasurementsatthistime.Inordertoevaluatethewallstressbetweengroups onarelativescaletoachievesimilarwallstresses,experimentsshouldbeperformed byincreasingthepressureinthehypoxicandrecoverycohorts.Analysisofthecollagenlineinterceptsbetweencohortsshowsthatcollagenbersareengagedmuch earlierinthehypoxicsandrecoverysstrainsofapproximately0.30mm/mmthan thecontrolsstrainsofapproximately0.60mm/mm.Fromthis,wecaninferthat atlowerstrains,collagenisbeingengagedmoreofteninthehypoxicandrecovery cohortsthaninthecontrols,andthusisdominatingthemechanicsinthosecohorts. Theincreaseinstinessseeninthesecohortscanthusbeinferredtobeexplained bytheincreaseincollagenberengagementduetocollagensmuchhigherYoungs modulus.Thecircumferentialwallstressplotswerethenderivedwithrespectto straintoobtaintheElasticModulusE,gure3.7.Wecanseefromthegraphof theelasticmodulusthattheslopesofHXandRTNaredierentfromthatofCTRL. Furtheranalysisisdoneinthecollagenandelastinttingtodeterminetheslopesof thetwodistinctregionsinthestress-straincurves. 4.3.1ResidualStresses ResidualstressesaretheinherenttensegrityassociatedwiththeECMnetwork thatmakesupthestructureofthetissue.Residualstressesareimportantbecause theydenetheoverallintegrity,stability,andsecurityofthestructure.Thus,an analysisofthesestresseswasdonetodeterminethedierenceofthesebetweeneach cohort.TheANOVAtestshowsthatthereisnotenoughsignicantdierencefora probabilityoflessthan5%ofthetimebetweencohorts.Thissuggeststhatmoredata isneededtosmoothoutthedistributionwithineachcohort.However,andecrease inthemeanswasobservedfromcontrolstohypoxicsandrecoverys,suggestingthat thereisatrendtowardslowerresidualwallstressinthesecohorts.Thephysiological 48

PAGE 65

implicationsofthisisthatthelowerresidualstressinthehypoxicsandrecovery cohortswillgreatlyimpactthearteriesmechanicalbehaviorathigherpressuresi.e. physiologicpressurethatthencompromisesfunction.Basedontheseresults,anFtestwasperformedonthecircumferentialwallstressestodetermineifvarianceswere thesame.Furthermore,anF-testwasconductedtodetermineifPAthicknesseswere thesame.Thisisbecausethethicknessgreatlyaectsthevaluesfor ,asdepicted inequation.1. 4.4VarianceTestingforCircumferentialWallStressBetweenGroups Atestforequalvarianceswasdoneforcircumferentialwallstresses and forvesselthickness.Thiswasdonebecausethespreadofthedataseemeddierent byvisualinspection.For ,theF-testreturnedarejectionofthenullhypothesis, meaningthattherewasasignicantdierencebetweenthevariancesofeachcohort. Thishasimportantimplicationsforfurtherdownstreamanalysisofthedatainthat thevaluesfor 2 areconsequentlyastronomicallyhighforpopulationswithhigh variance.Thus,inessence,thesepopulationsarenotnecessarilycomparablefor statisticalanalyses.However,forthepurposeofthisstudyandthesis,thetrends hereprovidearstlookathypoxicrecoverymechanics,thoughtheymaynotbe statisticallysound.Infuturestudies,aMann-WhitneyUtestshouldbedonein ordertodetermineifthecohortsareofsimilarpopulations.AnF-testwasalso performedonthethicknessdatatodetermineifvarianceswereequalbetweencohorts. Thiswasdonebecausethicknessvaluesplayaheavyroleinthecalculationsfor seeequation.1.Theresultwasthatvariancesweresignicantlydierentfor controlversusreturnsandreturnsversushypoxic.Controlsversushypoxicwerenot signicantlydierentp=0.21.Theseresultsmayprovidetheexplanationforwhy variancesin areseen,andhencefurtherdownstreamanalysesthatarebasedo thesevalues.Futureworkforpublicationmayinvolveafurtherbreakdownofthe thicknessescalculatedbyimageprocessing,whichhasinherenterrorinthesizeofthe 49

PAGE 66

pixel.Usererrormayhavealsoplayedaroleforhighvariation,inthatthresholding forcross-sectionalareaquanticationwasdonemanually. 4.5StrainEnergyFunctions Atforastrainenergyfunctionintheformofequation.13wasmadefor eachratineachcohort.Thegoodnessofthetwasassessedusingchi-squared 2 calculations,equation.5.Thesevaluesweregivenintable3.4foreachcohort. Themodelsdevelopedforcontrolsandrecoverycohortsweredeterminedtonotbe signicantlydierentfromtheexperimentalvalues,butthehypoxiccohortwas.This meansthatthetsforthecontrolsandhypoxiccohortsweresignicantandhada highGOF,butthatthestrainenergytforthehypoxiccohortwasnotasgood. Theplotoftheresidualsgure3.9showsthatthereindeedisatrendinthetting forincreasingerrorasstrainincreases.Thiscouldbeduetoahighervarianceand distributionseeninthehypoxicdata.Nodatawasomittedfromanycalculations. Thiscouldalsobeduetothettingoftheequationitself,whichmayneedextra variablesthanwhatwaspostulatedbyFung,etal.Indeed,amoreaccuratemodelwas developedlateronthatisdiseasespecictothedeformationbehaviorseen.Future workmayincludedevelopingastrainenergyequationthatprovidesamoreaccurate descriptionofthemechanicalbehaviorofthehypoxicPA.Inordertodetermine ifthematerialconstantscalculatedhadacorrelationwithdisease,therelationship betweenconstant C 1 and E e and E c wasassessedforatrend.Thiswouldimplythat theconstantscalculatedcouldbepredictorsfordiseaseanddeformationbehavior relatedtothosediseasestates. 4.6CollagenandElastinFitting Theinectionpointinthestress-straingraphsrepresentthetransitionpointT thatdierentiatestheelastinandcollagendominatedregions.Analyzingthesecurves, wecanseethatthelinearelastinregionbetweeneachcohortisnotsignicantly 50

PAGE 67

dierentfromeachother.ThisisindicatedbytheANOVAcomparisoningures A.7andA.6,inwhichacomparisonbetween E e betweencohortswasdetermined tonotbesignicantlydierent.TheThisndinghasmajorimplicationsforthe structure-mechanicalrelationshipofthePA:thetotalamountofelastindoesnot changewiththeonsetofthedisease,andthusdoesnotaltertheinitialrateof deformationbeforethetransitionpoint.Wecanthusinferthatamountelastinand changeofelastinmechanicsisnotanindicatorfordisease.Conversely,analysisof thecollagendominatedregionshowsvastlydierentslopes.Thisisconrmedbythe ANOVAcomparisonof E c betweencohorts,showningureA.7,inwhichthe E c is signicantlydierentbetweenCTRLandHX,CTRLandRTN,butnotsignicantly dierentbetweenHXandRTN.Thisiscorroboratedbythesignicantincreasein percentcollagenfromcontrolstodisease,andmayprovideanexplanationforthe changein E c seenbetweencohorts.Previousstudieshaveshownthatthereisan increaseinexpressionofvarioustypesofcollageninvaryingratios[50,10,5],and thusmayprovideanexplanationtothesignicantdierencesinthecollagenmodulus calculated.Thisissupportedbymechanicalstrengthtestingofcollagenbersof typesI-VI,ofwhichrangefrom1kPato10mPa[72,6].Therefore,ananalysisofthe relationshipbetweencollagenandelastinpercentagewasdonetodetermineifthere wasasignicantcorrelationwith E e E c .Thisanalysisisoutlinedinthenextsection. 4.6.1CollagenandElastinModulusinParallel Thecircuitingure2.6wasproposedasasimpleschematicoftherelationship of E e and E c asaconstitutivemodel. E e and E c weremodeledasspringsinparallel, withtheoutput .Thisrelationshipwasconrmedbyutilizing.6withinputsof themodulusestimatesfromtheregionallineartting.Theequationsforcollagenand elastinwereaddedinparallelandoverlaidontothedata,asdepictedingure3.13. Thegoodnessofthesetswereevaluatedusing 2 values,giveningure3.13.Each 51

PAGE 68

tproducedap-valuegreaterthan0.05,meaningthatthetswerenotsignicantly dierentthantheexperimentaldata.Thisveriesthattherelationshipbetween E e and E c isindeedparallel,aspredictedbythemodel.Theconrmationofthis relationshipprovidesareasonableestimateandmodeltobasefuturestudiesonPA mechanicsthatpertaintostructure,composition,andfunction. 4.7Structure-FunctionRelationships 4.7.1ComparingMaterialConstantstoModulusandStiness Therelationshipbetweenmaterialconstantsandthemodulusoftheelasticand collagenlinearregionswasassessedtodetermineatrend.Thisisshowningure3.11. Fitsoflinear,exponential,andpolynomialwereappliedandgoodnessoftsGOF weredetermined,withthehighestGOFbeingalinearandexponential,for E e and E c respectively.Alas,thelineartwasnotsignicant,asexpected,sincetheoriginal dataisexponentialinnature.Thelineartthatwasappliedto E c hadan r 2 of 0.55,buttheexponentialtproducedahigherGOFasindicatedbythe @ value, althoughthiststillproducedsignicantdierencesthantheexpectedvalues.The datafor C 1 versus E c appearstohaveatrend,buttheredoesnotseemtobeenough datatodenitelymodelthistrend.Itseemsthathigher C 1 values > 6kPaexihibit similar E c .Thissuggeststhatthereisathresholdvaluefor C 1 thatencompassesa maximummodulus E c .Moredataisneededinordertodecipheramoreaccurate relationship. 4.7.2ComparingCollagenandElastinPercentagetoModulusand Stiness Therelationshipbetweencollagenandelastinperecntageandthemodulusofthe elasticandcollagenlinearregionswasassessedtodetermineatrend.Thisisshownin gure3.12.Fitsoflinear,exponential,andpolynomialwereappliedandgoodnessof tsGOFweredetermined,withthehighestGOFbeingalinearandexponential,for 52

PAGE 69

E e and E c respectively.Alas,thelineartfor%elastinwasnowherenearsignicant andcompletelyawful.Theexponentialtfor E c wassignicantlydierent,witha 2 valueastronomicallyhigh.Thedatafor%collagenversus E c appearstohavea trend,buttheredoesnotseemtobeenoughdatatodenitelymodelthistrend.At a E c valueofapproximately500kPa,thepercentageofcollagenrangesfrom20-30%. Again,thisdataseemstosuggestthatthereisathresholdvaluefor E c atwhich increasingconcentrationofcollagendoesnotcauseamaterialpropertychange/More dataisneededinordertodecipheramoreaccuraterelationship.Yet,acleartrend hasbeenestablishedforstructureandfunctionintheformofECMmakeupand circumferentialwallstress. 4.8StrengthsandLimitations Thereareseverallimitationsofthisstudy.Therstandmostapparent,istheextrapolationofthecharacterizationofmodulustothemechanicalpropertyofstiness. AlthoughYoung'smodulusandstinessareproportionalwithafactorofgeometry, thegeometricaldimensionschangebetweencohorts,andthischangeisnotdescribed intheinherentmaterialpropertiesofthetissue.Thus,furthercalculationsareneeded tobacktrackthegeometryoutofthemodulustoobtainstinessvalues.However, whatcanbeseenfromthedatahereisthatthechangeinstinesshasagreater increasethantheincrementalincreaseinthemodulusathighstraincollagenmodulus,andthisispotentiallymorereliantontheincreaseincollagenarea,whichis dimensional,ratherthanthechangeofamaterialproperty.Theadvantageofdescribingthemodulusofthetissue,ratherthanstiness,isthatmaterialproperties areintensive,anddonotchangethroughoutdeformation,andarethusamoreconsistentandrobustdescriptivevalue.Second,themodelofstrainenergythatwasused todescribethetissuedenesonlythemediallayerofthePA,wheninfactthePA iscomposedofthreecomplexlayersthatallcontribute,howeverminimally,tothe arterialmechanics.Theassumptionwasstatedinthestudydesignthatthemedial 53

PAGE 70

layerisresponsibleforthemajorityofthevasculartoneandstinessregulation.The advantagetothisapproachisthatthemediallayerwascharacterizedusingaunilayerequation,andthusisnotaninaccuratedescription.Tofullyaccountfortotal mechanicalcontribution,boththeintimaandadventitiashouldbecharacterizedseparatelyinasimilarmethodaswasdescribedinthiswork.Thisisfurthersupported bytheshiftincollagenandthehistologysuggestingthatthisislargelyanadventitial remodeling.Then,arelationshipbetweenthecontributionofeachlayerwouldneed tobedetermined,muchlikethecircuitingure2.6.Anotherlimitationthatarose afterdatacollectionwasthevalueofvariancebetweencohorts,whichwasunforeseen attheinitiationofthestudy.Thehighvariancevaluesofthecircumferentialwall stresscalculationsinhibitthestrainenergyfunctionfrombeingastatisticallysignicantmodel,andanysubsequentdownstreammanipulationofthisdatawouldalsonot bestatisticallysignicant.Thus,the 2 valuesreportedinthisthesisareextremely highduetothehighspreadofdata.Futureworkwillincludemoredatapointsto easeoutthevarianceforatightert.Anotherlimitationistheassumedgeometryof thePAasacylindricalvessel,whenitisinfactitismoreovalandoblong.Thus,the nitestraindeformationdescribedhereisnotexactlycylindricalinthephysiological setting,andonlyprovidesarstattemptatthecharacterizationofhypoxicrecovery PAmechanics.Therealsoexiststhelimitationofcollagenandelastincontentmeasurementusingimageprocessing.Theerrorofdetectionislimitedtothesizeofthe pixel,whichis0.67 m.Imagethresholdingbypixelintensityisfarlessaccuratethan proteinspecictechniques,suchaswesternblotting,andspectrophotometry.With westernblottechniques,theresiduesoftheproteinaretargetedspecically,andthus canbemeasuredwithhighersensitivitybyblotintensityorspectrophotometricintensity.Chemicalstainingisonlyspecicbybasophilicandeosinophilicbinding, meaningthatcellsandtissuewillbestainedaccordingtotheirionconcentrations, andisthusnotprotein/moleculespecic.Thus,forlessvarianceandincreasedaccu54

PAGE 71

racyinthemeasurementofcollagenandelastinconcentration,futureassaysshould includebothimageprocessingandproteinquanticationtechniques. 4.9FutureWork Futureworkshallincludeadevelopmentofastrainenergyfunctionthatincorporatesvolumefractionsofcollagenandelastin,muchlikethefunctiondevelopedby Kao,etal[33,30,29].Inhiswork,hedevelopedfunctionsthatincorporatedber orientation,volumefraction,andelasticmodulusofeachindividualconstituent.This functionisshownbelow: = f e e + c .1 Where f e isthevolumefractionofelastin, e isthestrainenergyofelastinbers,and c isthestrainenergyofcollagenbers.Ideally,thiswillbedonetoanalyzethese dierencesbetweencontrols,hypoxicPH,andhypoxicrecoveryrats.Anattemptwas madetotKao,etal'sstrainenergyfunctiontorecoveryratdataoutlinedinthis paper.Itisshowningure4.1.Theattemptdoesnottthedata,possiblyduetoan errorintheincreaseofunknownconstantsthroughleastsquarestting.Moreshould bedoneinordertodeterminevolumefractionsofeachprotein,andthuscorrelate thesendingswithhistologicaldata. 4.9.1HalfLifeofCollagen Aninterestingconcepttonoteisthehalf-lifeofcollagenanditsmetabolicturn over.Arterialcollagenhalf-lifehasbeenreportedtobe60-70daysinnormoxic ratsand17daysinhypertensiverats[47].Thus,collagendegradationoccursfaster inhypertensionthaninhealthytissue,andinrelationtoitslastingeectonECM mechanics,mayleaveanimpermanentimpactonthestinessandwallstressof thearterialwall.Withthisconsideration,alongerrecoverytimethanthreeweeks isneededtofullyidentifyhowcollagenmetabolismaectstheregressionofstiness andwallstress,asindicatedbythetrendofthedatainthisstudy.Forfuturestudies, 55

PAGE 72

Figure4.1:AnAttemptatattingofarecoveryrattoKao'sfunction,shownin equation.1. recoverytimefromhypoxicexposureshouldbeaperiodofabout10weeks,toaccount forthereportedcollagenhalf-life.Collagendegradationratescanalsobelookedat overeachcohortthroughanalysisofmatrixmetalloproteaseactivity. 56

PAGE 73

5.Conclusion Pulmonaryhypertensionisadiseasethathasnocurethatultimatelyendsinright heartfailure.Themainpulmonaryarteryisnowwidelyacceptedascontributingto theincreasedafterloadleadingtoincreasedmortality.Pulmonaryarterialstiness isjustrecentlybeginningtobemeasuredwith invivo techniques.Thesemethods includecardiacmagneticresonanceCMR,Dopplerwavetechniques,computedtomographyCT,andultrasoundtechniques.Withthesemeasurements,studieshave shownincreasesinarterialstinessassociatedwiththosediagnosedwithpulmonary hypertensionviarightheartcatheterization[56,66,46,35].Thus,itisimportantto beabletocharacterizearterialstinesswith invitro studiestounderstanditsphysiologicalimplicationsfordeformationmechanicsduringdisease.Inparticular,hypoxia inducedPHisthoughttobereversibleandmild.Yet,littleisunderstoodaboutthe transitionfromPHtohealthyduringtepost-hypoxicrecoveryperiod.Thus,understandingtheresolutionofPAmechanicstohealthyvaluesduringhypoxicrecovery mayprovidepivotalinsighttothereversalofthedisease.Inordertounderstandhow PAmechanicscontributetodiseaseprogression,aswellasforfuturetissueengineeringdesignofsyntheticarteries,thedeformationmechanicsandmaterialproperties needtobefullydened.Strainenergyfunctionshavebeenusedtocharacterizethe mechanicalbehavioroftissuessinceFung,etalrstdescribedhyperelastictissue deformationover60yearsago.Thesefunctionscanbettoempiricaldatainordertodeterminematerialconstantsthatdescribetheuniquematerialpropertiesof thetissue.Thisisimportantwhendescribingthechangeintissuefromhealthyto diseasedandunderstandinghowdierentfactorssuchasberorientation,structure, andmorphologycontributetodiseaseprogression.Thus,astrainenergyfunctionas aconstitutivemodelwasdevelopedforcontrol,hypoxic,andrecoveryratsforcircumferentialwallstressofthePA.Linearregressionswereappliedtothesestress-strain curvesinordertodeterminethemodulusbeforeandafterthetransitionpoint,re57

PAGE 74

ferredtoastheelastinandcollagenmodulus,respectively.Thesevalueswerethen correlatedtocollagenandelastinpercentageandmaterialconstantthatwascalculatedinthestrainenergyts.Thematerialconstantwasrelatedtothecollagen moduluswithanexponentialrelationship,whiletherewasnotdenitivetrendfor theelastinmodulus.Thiswascorrelatedwithanincreaseinthepercentageofcollagenandadecreaseinelastinwhiletotalelastincontentdidnotchange.Thiswas therstattempttocharacterizetherelationshipofstructureseenduringPHtothe changeinfunctionofPAmechanics.ThisthesisservesaspreliminarydatasupportingacharacterizedrelationshipbetweenthestructureandfunctionofthePAduring PH. 58

PAGE 75

REFERENCES [1]SHAdvani.Aconstitutiverelationshipforlargedeformationniteelementmodelingofbraintissue. JournalofBiomechanicalEngineering ,117:279,1995. [2]JavierArias-SteltandMarioSaldana.Theterminalportionofthepulmonaryarterialtreeinpeoplenativetohighaltitudes. TheAgingLung:NormalFunction page37,1974. [3]AlanJBank,HongyuWang,JamesEHolte,KathleenMullen,RogerShammas, andSpencerHKubo.Contributionofcollagen,elastin,andsmoothmuscle toinvivohumanbrachialarterywallstressandelasticmodulus. Circulation 94:3263{3270,1996. [4]HarmJBogaard,RameshNatarajan,ScottCHenderson,CarlinSLong,Donatas Kraskauskas,LisaSmithson,RamziOckaili,JoeMMcCord,andNorbertF Voelkel.Chronicpulmonaryarterypressureelevationisinsucienttoexplain rightheartfailure. Circulation ,120:1951{1960,2009. [5]EllenCBreen.Mechanicalstrainincreasestypeicollagenexpressioninpulmonarybroblastsinvitro. Journalofappliedphysiology ,88:203{209,2000. [6]MarkusJBuehler.Nanomechanicsofcollagenbrilsundervaryingcross-link densities:atomisticandcontinuumstudies. Journalofthemechanicalbehavior ofbiomedicalmaterials ,1:59{67,2008. [7]CJChuongandYCFung.Residualstressinarteries.In FrontiersinBiomechanics ,pages117{129.Springer,1986. [8]PaulCorrisandBrunoDegano.Severepulmonaryarterialhypertension:treatmentoptionsandthebridgetotransplantation. EuropeanRespiratoryReview 23:488{497,2014. [9]NeilJDavie,JosephTCrossno,MariaGFrid,StephenEHofmeister,JohnT Reeves,DallasMHyde,ToddCCarpenter,JacquelineABrunetti,IanKMcNiece,andKurtRStenmark.Hypoxia-inducedpulmonaryarteryadventitial remodelingandneovascularization:contributionofprogenitorcells. AmericanJournalofPhysiology-LungCellularandMolecularPhysiology ,286:L668{ L678,2004. [10]AnthonyGDurmowicz,WilliamCParks,DallasMHyde,RobertPMecham, andKurtRStenmark.Persistence,re-expression,andinductionofpulmonary arterialbronectin,tropoelastin,andtypeiprocollagenmrnaexpressionin neonatalhypoxicpulmonaryhypertension. TheAmericanjournalofpathology 145:1411,1994. 59

PAGE 76

[11]KarenAFagan,BrianWFouty,RobertCTyler,KennethGMorrisJr,LisaK Hepler,KoichiSato,TimothyDLeCras,StevenHAbman,HowardDWeinberger,PaulLHuang,etal.Thepulmonarycirculationofhomozygousorheterozygousenos-nullmiceishyperresponsivetomildhypoxia. JournalofClinical Investigation ,103:291,1999. [12]HisaoFukunagaandTsu-WeiChou.Simplieddesigntechniquesforlaminated cylindricalpressurevesselsunderstinessandstrengthconstraints. Journalof compositematerials ,22:1156{1169,1988. [13]YCFung.Whataretheresidualstressesdoinginourbloodvessels? Annalsof biomedicalengineering ,19:237{249,1991. [14]YCFung,SQLiu,andJBZhou.Remodelingoftheconstitutiveequationwhile abloodvesselremodelsitselfunderstress. Journalofbiomechanicalengineering 115B:453{459,1993. [15]Yuan-ChengFung. Biomechanics .Springer,1990. [16]CTji-JoongGan,Jan-WillemLankhaar,NicoWesterhof,JTimMarcus,AnnemarieBecker,JosWRTwisk,AncoBoonstra,PieterEPostmus,andAnton Vonk-Noordegraaf.Noninvasivelyassessedpulmonaryarterystinesspredicts mortalityinpulmonaryarterialhypertension. CHESTJournal ,132:1906{ 1912,2007. [17]BJBGrantandBBLieber.Clinicalsignicanceofpulmonaryarterialinput impedance. EuropeanRespiratoryJournal ,9:2196{2199,1996. [18]JHerget,AJSuggett,ENIDLeach,andGWENDARBarer.Resolutionof pulmonaryhypertensionandotherfeaturesinducedbychronichypoxiainrats duringcompleteandintermittentnormoxia. Thorax ,33:468{473,1978. [19]AHislopandLReid.Newndingsinpulmonaryarteriesofratswithhypoxiainducedpulmonaryhypertension. Britishjournalofexperimentalpathology 57:542,1976. [20]AHislopandLReid.Changesinthepulmonaryarteriesoftheratduring recoveryfromhypoxia-inducedpulmonaryhypertension. Britishjournalofexperimentalpathology ,58:653,1977. [21]GerhardAHolzapfel.Collageninarterialwalls:biomechanicalaspects.In Collagen ,pages285{324.Springer,2008. [22]GerhardAHolzapfel,ThomasCGasser,andRayWOgden.Anewconstitutiveframeworkforarterialwallmechanicsandacomparativestudyofmaterial models. Journalofelasticityandthephysicalscienceofsolids ,61-3:1{48, 2000. 60

PAGE 77

[23]GerhardAHolzapfel,JohnJMulvihill,EoghanMCunnane,andMichaelT Walsh.Computationalapproachesforanalyzingthemechanicsofatherosclerotic plaques:areview. Journalofbiomechanics ,47:859{869,2014. [24]YasushiHoshikawa,SadafumiOno,SatoshiSuzuki,TatsuoTanita,Masayuki Chida,ChunSong,MasafumiNoda,ToshiharuTabata,NorbertFVoelkel,and ShigefumiFujimura.Generationofoxidativestresscontributestothedevelopmentofpulmonaryhypertensioninducedbyhypoxia. JournalofAppliedPhysiology ,90:1299{1306,2001. [25]MarcHumbert,NicholasWMorrell,StephenLArcher,KurtRStenmark,MargaretRMacLean,IreneMLang,BrianWChristman,EKennethWeir,Oliver Eickelberg,NorbertFVoelkel,etal.Cellularandmolecularpathobiologyofpulmonaryarterialhypertension. JournaloftheAmericanCollegeofCardiology 43s1:S13{S24,2004. [26]KendallSHunter,StevenRLammers,andRobinShandas.Pulmonaryvascular stiness:measurement,modeling,andimplicationsinnormalandhypertensive pulmonarycirculations. ComprehensivePhysiology ,2011. [27]YunlongHuo,XuefengZhao,YanaCheng,XiaoLu,andGhassanSKassab. Two-layermodelofcoronaryarteryvasoactivity. JournalofAppliedPhysiology 114:1451{1459,2013. [28]RJonesandLynneReid.Vascularremodelinginclinicalandexperimental pulmonaryhypertensions.In PulmonaryVascularRemodelling ,pages47{115. PortlandPressLondon,1995. [29]PhilipHKao,StevenRLammers,KendallHunter,KurtRStenmark,Robin Shandas,andHJerryQi.Constitutivemodelingofanisotropicnite-deformation hyperelasticbehaviorsofsoftmaterialsreinforcedbytortuousbers. Theinternationaljournalofstructuralchangesinsolids:mechanicsandapplications 2:19,2010. [30]PhilipHKao,StevenRLammers,LianTian,KendallHunter,KurtRStenmark, RobinShandas,andHJerryQi.Amicrostructurallydrivenmodelforpulmonary arterytissue. Journalofbiomechanicalengineering ,133:051002,2011. [31]IMKeith,STjen-A-Looi,HKraiczi,andREkman.Three-weekneonatalhypoxiareducesbloodcgrpandcausespersistentpulmonaryhypertension inrats. AmericanJournalofPhysiology-HeartandCirculatoryPhysiology 279:H1571{H1578,2000. [32]TipaponKhamdaeng,JLuo,JVappou,PTerdtoon,andEEKonofagou.Arterialstinessidenticationofthehumancarotidarteryusingthestress{strain relationshipinvivo. Ultrasonics ,52:402{411,2012. 61

PAGE 78

[33]StevenRLammers,PhilHKao,HJerryQi,KendallHunter,CraigLanning,JosephAlbietz,StephenHofmeister,RobertMecham,KurtRStenmark, andRobinShandas.Changesinthestructure-functionrelationshipofelastin anditsimpactontheproximalpulmonaryarterialmechanicsofhypertensivecalves. AmericanJournalofPhysiology-HeartandCirculatoryPhysiology 295:H1451{H1459,2008. [34]YtLanir.Constitutiveequationsforbrousconnectivetissues. Journalofbiomechanics ,16:1{12,1983. [35]EdmundMTLau,NithinIyer,RahnIlsar,BrianPBailey,MarkRAdams, andDavidSCelermajer.Abnormalpulmonaryarterystinessinpulmonary arterialhypertension:invivostudywithintravascularultrasound. PloSone 7:e33331,2012. [36]FabiolaLeon-VelardeandFranciscoCVillafuerte.High-altitudepulmonary hypertension.In TextbookofPulmonaryVascularDisease ,pages1211{1221. Springer,2011. [37]MinLi,SuzetteRRiddle,MariaGFrid,KarimCElKasmi,TimothyAMcKinsey,RonaldJSokol,DerekStrassheim,BarbaraMeyrick,MichaelEYeager, AmandaRFlockton,etal.Emergenceofbroblastswithaproinammatory epigeneticallyalteredphenotypeinseverehypoxicpulmonaryhypertension. The JournalofImmunology ,187:2711{2722,2011. [38]YiLing,MartinKJohnson,DavidGKiely,RobinCondlie,CharlieAElliot, JSimonRGibbs,LukeSHoward,JoannaPepke-Zaba,KarenKKSheares, PaulACorris,etal.Changingdemographics,epidemiology,andsurvivalofincidentpulmonaryarterialhypertension:resultsfromthepulmonaryhypertension registryoftheunitedkingdomandireland. Americanjournalofrespiratoryand criticalcaremedicine ,186:790{796,2012. [39]SrijoyMahapatra,RickANishimura,JaeKOh,andMichaelDMcGoon. Theprognosticvalueofpulmonaryvascularcapacitancedeterminedbydoppler echocardiographyinpatientswithpulmonaryarterialhypertension. Journalof theAmericanSocietyofEchocardiography ,19:1045{1050,2006. [40]SrijoyMahapatra,RickANishimura,PaulSorajja,StephenCha,andMichaelD McGoon.Relationshipofpulmonaryarterialcapacitanceandmortalityinidiopathicpulmonaryarterialhypertension. JournaloftheAmericanCollegeof Cardiology ,47:799{803,2006. [41]RajammaMathew.Inammationandpulmonaryhypertension. Cardiologyin review ,18:67{72,2010. [42]BMeyrickandLReid.Pulmonaryhypertension.anatomicandphysiologiccorrelates. Clinicsinchestmedicine ,4:199{217,1983. 62

PAGE 79

[43]BarbaraMeyrickandLynneReid.Hypoxiaandincorporationof3h-thymidine bycellsoftheratpulmonaryarteriesandalveolarwall. TheAmericanjournal ofpathology ,96:51,1979. [44]KarolMiller.Constitutivemodelofbraintissuesuitableforniteelementanalysisofsurgicalprocedures. Journalofbiomechanics ,32:531{537,1999. [45]KarolMiller.Constitutivemodellingofabdominalorgans. JournalofBiomechanics ,33:367{373,2000. [46]EricEMorgan,AndrewBCasabianca,SamerJKhouri,andAndreaLNestor Kalinoski.Invivoassessmentofarterialstinessintheisouraneanesthetized spontaneouslyhypertensiverat.2014. [47]ReinhartNissen,GeorgeJCardinale,andSidneyUdenfriend.Increasedturnover ofarterialcollageninhypertensiverats. ProceedingsoftheNationalAcademyof Sciences ,75:451{453,1978. [48]GaryKOwens,MeenaSKumar,andBrianRWamho.Molecularregulation ofvascularsmoothmusclecelldierentiationindevelopmentanddisease. Physiologicalreviews ,84:767{801,2004. [49]GiuseppeGPietra,FrederiqueCapron,SusanStewart,OrnellaLeone,Marc Humbert,IvanMRobbins,LynneMReid,andRMTuder.Pathologicassessmentofvasculopathiesinpulmonaryhypertension. JournaloftheAmerican CollegeofCardiology ,43s1:S25{S32,2004. [50]IWProsser,KRStenmark,MANISHSuthar,ECCrouch,RPMecham,and WCParks.Regionalheterogeneityofelastinandcollagengeneexpressioninintralobararteriesinresponsetohypoxicpulmonaryhypertensionasdemonstrated byinsituhybridization. TheAmericanjournalofpathology ,135:1073,1989. [51]MARLENERabinovitch,WALTERJGamble,OLLISMiettinen,andLReid. Ageandsexinuenceonpulmonaryhypertensionofchronichypoxiaandon recovery. AmericanJournalofPhysiology-HeartandCirculatoryPhysiology 240:H62{H72,1981. [52]ARachevandSEGreenwald.Residualstrainsinconduitarteries. Journalof biomechanics ,36:661{670,2003. [53]MargotRRoachandAlanCBurton.Thereasonfortheshapeofthedistensibilitycurvesofarteries. Canadianjournalofbiochemistryandphysiology 35:681{690,1957. [54]JRodes-Cabau,EDomingo,ARoman,JMajo,BLara,FPadilla,IAnivarro, JAngel,JCTardif,andJSoler-Soler.Intravascularultrasoundoftheelastic pulmonaryarteries:anewapproachfortheevaluationofprimarypulmonary hypertension. Heart ,89:311{315,2003. 63

PAGE 80

[55]NASakharova,PAPrates,MCOliveira,JVFernandes,andJMAntunes.A simplemethodforestimationofresidualstressesbydepth-sensingindentation. Strain ,48:75{87,2012. [56]JavierSanz,MbabaziKariisa,SantoDellegrottaglie,SusannaPrat-Gonzalez, MarioJGarcia,ValentinFuster,andSanjayRajagopalan.Evaluationofpulmonaryarterystinessinpulmonaryhypertensionwithcardiacmagneticresonance. JACC:CardiovascularImaging ,2:286{295,2009. [57]ChristopherJSchoeldandPeterJRatclie.Oxygensensingbyhifhydroxylases. NatureReviewsMolecularCellBiology ,5:343{354,2004. [58]GreggLSemenza,LarissaAShimoda,andNanduriRPrabhakar.Regulation ofgeneexpressionbyhif-1.In NovartisFoundationSymposium ,volume272, page2.Chichester;NewYork;JohnWiley;1999,2006. [59]GeraldSimonneau,NazzarenoGalie,LewisJRubin,DavidLangleben,Werner Seeger,GuidoDomenighetti,SimonGibbs,DidierLebrec,RudolfSpeich,MauriceBeghetti,etal.Clinicalclassicationofpulmonaryhypertension. Journal oftheAmericanCollegeofCardiology ,43:S5{S12,2004. [60]ASTMStandardetal.Standardpracticeforestimatingtheapproximateresidual circumferentialstressinstraightthin-walledtubing. ASTMInternational,West Conshohocken,PA.doi ,10:1520,2007. [61]KurtRStenmark,NeilDavie,MariaFrid,EvgeniaGerasimovskaya,andMita Das.Roleoftheadventitiainpulmonaryvascularremodeling. Physiology 21:134{145,2006. [62]KurtRStenmark,KarenAFagan,andMariaGFrid.Hypoxia-inducedpulmonaryvascularremodelingcellularandmolecularmechanisms. Circulation research ,99:675{691,2006. [63]GerinRStevens,AnaGarcia-Alvarez,SheilaSahni,MarioJGarcia,Valentin Fuster,andJavierSanz.Rvdysfunctioninpulmonaryhypertensionisindependentlyrelatedtopulmonaryarterystiness. JACC:CardiovascularImaging 5:378{387,2012. [64]InekePStolze,DavidRMole,andPeterJRatclie.Regulationofhif:prolyl hydroxylases.In NovartisFoundationSymposium ,volume272,page15.Chichester;NewYork;JohnWiley;1999,2006. [65]DianaMTabima,AlejandroRoldan-Alzate,ZhijieWang,TimothyAHacker, RobertCMolthen,andNaomiCChesler.Persistentvascularcollagenaccumulationaltershemodynamicrecoveryfromchronichypoxia. Journalofbiomechanics ,45:799{804,2012. [66]LianTianandNaomiCChesler.Invivoandinvitromeasurementsofpulmonary arterialstiness:Abriefreview. Pulmonarycirculation ,2:505,2012. 64

PAGE 81

[67]LianTian,StevenRLammers,PhilipHKao,MarkReusser,KurtRStenmark, KendallSHunter,HJerryQi,andRobinShandas.Linkedopeningangleand histologicalandmechanicalaspectsoftheproximalpulmonaryarteriesofhealthy andpulmonaryhypertensiveratsandcalves. AmericanJournalofPhysiologyHeartandCirculatoryPhysiology ,301:H1810{H1818,2011. [68]RubinMTuder,JeongHYun,AnilBhunia,andIwonaFijalkowska.Hypoxiaand chroniclungdisease. JournalofMolecularMedicine ,85:1317{1324,2007. [69]PaulNWatton,YiannisVentikos,andGerhardAHolzapfel.Modellingthe mechanicalresponseofelastinforarterialtissue. Journalofbiomechanics 42:1320{1325,2009. [70]CraigEWeinberg,JeanRHertzberg,DDunbarIvy,KScottKirby,KChen Chan,LilliamValdes-Cruz,andRobinShandas.Extractionofpulmonaryvascularcompliance,pulmonaryvascularresistance,andrightventricularworkfrom single-pressureanddopplerowmeasurementsinchildrenwithpulmonaryhypertension:anewmethodforevaluatingreactivityinvitroandclinicalstudies. Circulation ,110:2609{2617,2004. [71]EKennethWeirandAndreaOlschewski.Roleofionchannelsinacuteand chronicresponsesofthepulmonaryvasculaturetohypoxia. Cardiovascularresearch ,71:630{641,2006. [72]MarcoPEWenger,LaurentBozec,MichaelAHorton,andPatrickMesquida. Mechanicalpropertiesofcollagenbrils. Biophysicaljournal ,93:1255{1263, 2007. [73]XQXuandZCJing.High-altitudepulmonaryhypertension. EuropeanRespiratoryReview ,18:13{17,2009. 65

PAGE 82

TableA.1:ComponentsofAvertin.Take0.25mlofthissolutionanddissolvein10 ml1XPhosphatebueredsalinePBS. ComponentAmount 2-Methyl-2-butanol5ml 2,2,2-Tribromoethanol5g APPENDIXA.FiguresandTables FigureA.1:Theheartblockisextractedandthepre-hilarleftpulmonaryarteryis disectedandlungsareisolatedforsubsequentanalysis.Timepointsof3weekhypoxia, 3weekhypoxia+6weekreturn,andagematchedcontrolsaretobeperformed. 66

PAGE 83

TableA.2:Modulusofcollagenandelastindominatedregionsofthestress-strain curveforeachrat. CTRLHPXRTN E e E c E e E c E e E c RatkPakPaRatkPakPaRatkPakPa 1115.9313.71124.4583.41126.0738.1 2190.5399.12112.1679.12160.3697.9 3106.8480.93159.3623.03154.4669.0 4191.4220.14123.5439.64111.0696.2 5136.2248.95163.3619.75129.4635.7 TableA.3:MaterialconstantsdeterminedforeachratintheCTRLcohort. Rat C 1 kPa a 1 a 2 a 4 2 p-value 12.441.01.372.44237 : 7p > 0.05 22.061.01.142.06149 : 4p > 0.05 33.281.202.223.36118 : 5p > 0.05 42.451.181.742.51194 : 5p < 0.05 67

PAGE 84

TableA.4:MaterialconstantsdeterminedforeachratintheHXcohort. Rat C 1 kPa a 1 a 2 a 4 2 p-value 18.788.811.001.16103 : 8p > 0.05 216.5416.681.002.21560 : 2p > 0.05 310.8310.581.001.32478 : 6p > 0.05 413.8313.280.991.40164 : 4p > 0.05 56.866.760.991.04679 : 6p > 0.05 TableA.5:MaterialconstantsdeterminedforeachratintheRTNcohort. Rat C 1 kPa a 1 a 2 a 4 2 p-value 112.4412.521.001.25815 : 7p > 0.05 219.8420.141.02.51164 : 4p > 0.05 310.7510.801.001.21122 : 3p > 0.05 49.299.371.001.12135 : 9p > 0.05 TableA.6:Modulusofcollagenandelastindominatedregionsofthestress-strain curveforeachrat. CTRLHPXRTN S e S c S e S c S e S c RatkPa*mmkPa*mmRatkPa*mmkPa*mmRatkPa*mmkPa*mm 11.4891.11911.0881.98910.7622.729 20.8030.68121.6633.16320.9331.837 31.3501.32031.2992.80630.9432.746 41.7271.36340.7792.21341.0482.184 52.7351.06251.5863.17550.9422.296 68

PAGE 85

FigureA.2:ANOVAcomparisonofthethicknessesofeachcohort. 69

PAGE 86

FigureA.3:ANOVAcomparisonofpercentagesofcollagenbetweeneachcohort. 70

PAGE 87

FigureA.4:ANOVAcomparisonofpercentagesofelastinbetweeneachcohort. 71

PAGE 88

FigureA.5:ANOVAcomparisonofpercentagesofthecircumferentialwallstresses foreachcohort. 72

PAGE 89

FigureA.6:ANOVAcomparisonof E e betweencohorts. 73

PAGE 90

FigureA.7:ANOVAcomparisonof E c betweencohorts. 74

PAGE 91

FigureA.8:ANOVAcomparisonofresidualstressesbetweencohorts. 75

PAGE 92

FigureA.9:ANOVAcomparisonofelastindominatedregionstiness. 76

PAGE 93

FigureA.10:ANOVAcomparisonofelastindominatedregionstiness. 77

PAGE 94

APPENDIXB.MatlabCode B.1ImageThresholdingforCollagenQuantication Forsimplicity,thecalculationsareonlyshownforonerat,controlratone. clearall closeall %callintheimages %Controls masstri cntl1=imreadamcntl s1 6.8.14.tif; MT cntl1 red=doublemasstri cntl1:,:,1; MT cntl1 green=doublemasstri cntl1:,:,2; MT cntl1 blue=doublemasstri cntl1:,:,3; %blue %figure,imagescMT cntl1 red; MT cntl1 redMT cntl1 red > =150=255; MT cntl1 redMT cntl1 red < 130=0; areablue MT cntl1=nnzMT cntl1 red==0; %figure,imshowMT cntl1 red; blueperc MT cntl1=areablue MT cntl1/areatotes MT cntl1 100; col perc CNTL=[blueperc MT cntl1;blueperc MT cntl2;blueperc MT cntl3;... blueperc MT cntl4;blueperc MT cntl5]; col avg cntrl=meancol perc CNTL; amnt col cntl=[areablue MT cntl1;areablue MT cntl2;areablue MT cntl3;... areablue MT cntl4;areablue MT cntl5]; B.2WallStressCalculations 78

PAGE 95

Forsimplicity,thecodeforthecontrolcohortisshownhere,withcalculationsfor onerat. %Callintherawpressure )]TJ0 g 0 G.133 .545 .133 rg .133 .545 .133 RG/F39 9.9626 Tf 6.863 0 Td [(diameterdata. Pressure cntl1=xlsreadallDataMechStudy.xlsx,G776:G796;%rat#1 Diameter cntl1=xlsreadallDataMechStudy.xlsx,H776:H796; Pressure cntl2=xlsreadallDataMechStudy.xlsx,G2:G26;%rat#2 Diameter cntl2=xlsreadallDataMechStudy.xlsx,H2:H26; Pressure cntl3=xlsreadallDataMechStudy.xlsx,G141:G159;%rat#3 Diameter cntl3=xlsreadallDataMechStudy.xlsx,H141:H159; Pressure cntl4=xlsreadallDataMechStudy.xlsx,G160:G178;%rat#4 Diameter cntl4=xlsreadallDataMechStudy.xlsx,H160:H178; %TOTALPRESSURESANDDIAMETERS Tote Pressure=[Pressure cntl1;Pressure cntl2;Pressure cntl3;... Pressure cntl4]; Tote Diam=[Diameter cntl1;Diameter cntl2;Diameter cntl3;... Diameter cntl4]; %FITTING [p PRESS t1,S PRESS t1]=polyfitTote Diam,Tote Pressure,2; %datacicumferentialstress fit PRESS t1=polyvalp PRESS t1,Tote Diam; Stress cntl1=/760 Pressure cntl1; Stress cntl2=/760 Pressure cntl2; Stress cntl3=/760 Pressure cntl3; Stress cntl4=/760 Pressure cntl4; %circumferentialstrain circum cntl1=pi Diameter cntl1 )]TJ/F39 9.9626 Tf 7.395 0 Td [(pi minDiameter cntl1... ./pi minDiameter cntl1; circum cntl2=pi Diameter cntl2 )]TJ/F39 9.9626 Tf 7.395 0 Td [(pi minDiameter cntl2... 79

PAGE 96

./pi minDiameter cntl2; circum cntl3=pi Diameter cntl3 )]TJ/F39 9.9626 Tf 7.395 0 Td [(pi minDiameter cntl3... ./pi minDiameter cntl3; circum cntl4=pi Diameter cntl4 )]TJ/F39 9.9626 Tf 7.395 0 Td [(pi minDiameter cntl4... ./pi minDiameter cntl4; %rat#1 delta diameter1=Diameter cntl1 )]TJ/F39 9.9626 Tf 6.863 0 Td [(minDiameter cntl1/minDiameter cntl1; %1.23isL0. %interpolationtofitacurve [p hx,S hyp]=polyfitdelta diameter1,Stress cntl1,3; fit hx=polyvalp hx,delta diameter1; %determinationofderivative hx derivative=polyderp hx;hx der=... polyvalhx derivative,delta diameter1:8; hx der2=sumhx der:/3; disp[TheElasticModuliforthehypoxiccohortis:... ,num2strhx der2,mmHg/strain]; %computetotalareaofcross )]TJ0 g 0 G.133 .545 .133 rg .133 .545 .133 RG/F39 9.9626 Tf 6.863 0 Td [(sectionofPAs %converttograyscale I1=rgb2graymasstri cntl1; %figure,imshowI1; %binarizetheimage I1I1 > =170=255;%firstrat I1I1 < 170=0; %figure,imshowI1; %computetheareaofblack,iethetissue areatotal I1=nnzI1==0;area mils I1=areatotal I1 .68/; 80

PAGE 97

%#1 disp[Thetotalareaforrat#1is,num2strarea mils I1,... milimeterssquare]; %RAT#1 r large1=Diameter cntl1./2; %therangeofouterradiusasdeterminedbyPDtesting outer diam1=2 r large1; A large1=pi r large1.;%areaofoutercircle A small1=A large1 )]TJ/F39 9.9626 Tf 7.231 0 Td [(area mils I1; %relationshipforconstanttissuearea r small1=sqrtA small1/pi;%radiusofinnercircle delta thick1= r large1 )]TJ/F39 9.9626 Tf 7.496 0 Td [(2 r small1; %formulaforthickness [p thick1,S thick1]=polyfitouter diam1,delta thick1,2; fit hx thick1=polyvalp thick1,outer diam1; %calculationofwallstress )]TJ0 g 0 G.133 .545 .133 rg .133 .545 .133 RG/F39 9.9626 Tf 6.864 0 Td [(thinapproximation %RAT#1 WallStress1=Stress cntl1. Diameter cntl1./2./delta thick1... ./1000; %valueinkPa [p wallstress1,S wallstress1]=polyfitcircum cntl1,WallStress1,2; fit rtn wallstress1=polyvalp wallstress1,circum cntl1; %assumestraininxdirectionis0=del L/L %linearalgebraapproachishy.... stresses1=[wallstress thick1,1;radstress thick1,1]; 81

PAGE 98

strains1=[radial strain1,1;circum cntl1,1]; elastmat1=strains1/stresses1;%4x4matrix modulus1=1/elastmat1,1; poisson1= )]TJ/F39 9.9626 Tf 7.306 0 Td [(modulus1 elastmat1,1; C1 1=1 )]TJ/F39 9.9626 Tf 7.496 0 Td [(poisson1/modulus1 r small1.. Stress cntl1... ./r large1.2 )]TJ/F39 9.9626 Tf 7.496 0 Td [(r small1.; C2 1=+poisson1/modulus1 r small1.... Stress cntl1. r large1../r large1.2 )]TJ/F39 9.9626 Tf 7.496 0 Td [(r small1.; %modelcomparedtodata stress rad1=modulus1/1 )]TJ/F39 9.9626 Tf 7.454 0 Td [(poisson1 ... +poisson1 C1 1 )]TJ/F39 9.9626 Tf 7.243 0 Td [(1 )]TJ/F39 9.9626 Tf 7.243 0 Td [(poisson1 C2 1./r small1./1000; stress circum1=modulus1/1 )]TJ/F39 9.9626 Tf 7.454 0 Td [(poisson1 +poisson1... C1 1+1 )]TJ/F39 9.9626 Tf 7.495 0 Td [(poisson1 C2 1./r small1./1000; %polyfitting.... array1=[circum cntl1,wallstress thick1]; array1 sorted=sortrowsarray1,1; elast data1=array1 sorted:10,:; col data1=array1 sorted:end,:; %elastin [p wallstress t1,S wallstress t1]=... polyfitelast data1:,1,elast data1:,2,1; %datacicumferentialstress fit rtn wallstress t1=polyvalp wallstress t1,elast data1:,1; %collagen [p wallstress t1col,S wallstress t1col]=... polyfitcol data1:,1,col data1:,2,1; %datacicumferentialstress fit rtn wallstress t1col=polyvalp wallstress t1col,col data1:,1; [p radstress t1,S radstress t1]=... 82

PAGE 99

polyfitcircum cntl1,radstress thick1,2;%dataradialstress fit rtn radstress t1=polyvalp radstress t1,circum cntl1; [p stress circum1,S stress circum1]=... polyfitcircum cntl1,stress circum1,2; %modelcircumferentialstress fit stress circum1=polyvalp stress circum1,circum cntl1; B.3Constitutivemodeling Thissectionofcodeoutlinesusingleastsquaresforstrainenergyfunctiontting. c=[1.1.1.1.]; c0=[1.1.1.1.]; [c,resnorm,residual]=lsqnonlinFITTING,c0,... totalcircumstressCTRL,... totalcircumradiusCTRL; circumstretch avg=0:0.012:1;%strain circum2=.6 ones,lengthcircumstretch avg; sig11=c. c. circumstretch avg+c. circum2. expc... circumstretch avg. circumstretch avg+... c. circum2. circum2+2. c circumstretch avg. circum2; Thisisthefunction'FITTING'thattsusingleastsquares: function[f]=FITTINGc,wallstress,circum circum2=0.6 ones,lengthcircum; fori=lengthcircum %CONTROLHEALTHY f=c c circumi+c circum2i expc circumi circumi... +... c circum2i circum2i+2. c circumi circum2i )]TJ/F39 9.9626 Tf 7.454 0 Td [(wallstressi; 83

PAGE 100

end end 2 valuesarecalculatedasfollows: fori=1:lengthwallstress csort chisquare c,i=sig11 ci )]TJ/F39 9.9626 Tf 13.425 0 Td [(wallstress csorti./... wallstress csorti; end Variancetesting: [h,p,ci,stats]=vartest2wallstress h,wallstress c; [h1,p1,ci1,stats1]=vartest2wallstress r,wallstress c; [h2,p2,ci2,stats2]=vartest2wallstress h,wallstress r; [ht,pt,cit,statst]=vartest2hyp thick,ctrl thick; [ht1,pt1,cit1,statst1]=vartest2rtn thick,ctrl thick; [ht2,pt2,cit2,statst2]=vartest2hyp thick,rtn thick; 84