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Comparative study on a 3D patient-specific Evans calcaneal wedge implants made from different materials

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Title:
Comparative study on a 3D patient-specific Evans calcaneal wedge implants made from different materials
Creator:
Regmi, Nikesh Kumar
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Mechanical Engineering, CU Denver
Degree Disciplines:
Mechanical engineering
Committee Chair:
Yakacki, Christopher
Committee Members:
Carpenter, Dana
Yu, Kai

Notes

Abstract:
Flat feet, also known as “Pes Planus,” is a generic type of foot problem where the entire sole of the foot touches the ground when an individual is standing. In other words, the curvature of the foot doesn’t follow a normal arch and is straight. The Evans calcaneal osteotomy provides multi-planal correction of foot pes plano-valgus deformities in both children and adults [2]. Evans calcaneal osteotomy is a lateral column lengthening procedure that preserves the calcaneocuboid joint. The treatment consists of using an Evans wedge about 1-1.5 cm proximal to the calcaneocuboid joint, where a surgeon makes the osteotomy and secures the wedge using a locking plate [1, 2]. The influence of the Evans wedge material composition on bone regeneration in the hollow space of the wedge is still a question of significant importance. In the current study, finite element (FE) analysis was performed to understand the nature of mechanical stress distribution from the initial stage of in vivo bone regeneration to fully developed cortical bone within the Evans wedge. The accumulation of bone mineral in the regenerating bone was simulated by implementing progressively stiffer bone material properties at seven time points. Evans wedges made of cortical bone, titanium (Ti), polyether ether ketone (PEEK), and PEEK with Ti endplates were modeled to determine how material composition affected stress levels in the regenerating bone. The study utilized a computed tomography (CT) image of a Sawbones foot model to create the anatomical geometry in ScanIP. Bone and joint anatomy were meshed using tetrahedral elements, and ligaments were modeled using one-dimensional, non-compressible truss elements. A mesh convergence analysis confirmed that the mesh size used in the final set of models was enough. To ensure that the foot model provided reasonable results, stresses in the intact foot model were compared with a previous study by J.M. Garcia on load transfer mechanism in metatarsals [22]. Using different materials for the Evan’s wedge demonstrated that the von Mises stress levels in the regenerating bone reaches levels like those in cancellous bone of an intact foot when the regenerating bone accumulates enough mineral to achieve a Young’s modulus of 5 GPa. The graft made from cortical bone produced stresses 7% higher than those in a normal bone. The Ti implant produced von Mises stress in the regenerating bone at a level 47% lower than the cancellous bone stress in the intact foot model, whereas the PEEK implant produced stresses in the regenerating bone that were 36% higher than those in the intact foot model. PEEK implants with Ti endplates produced stress levels 16.8% lower than those the normal foot model. These results suggest that both cortical bone wedges and Ti-PEEK wedges create a more osteoconductive environment within the Evans wedge open space than wedges made solely of titanium or PEEK.

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University of Colorado Denver
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Auraria Library
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Full Text
COMPARATIVE FE STUDY ON 3D PATIENT-SPECIFIC EVANS CALCANEAL WEDGE IMPLANTS MADE FROM DIFFERENT MATERIALS
by
NIKESH KUMAR REGMI B.E., Kathmandu University, 2014
A thesis submitted to the Department of Mechanical
Engineering of the University of Colorado in partial
fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN MECHANCIAL ENGINEERING
May 2019
Mechanical Engineering


©2019
NIKESH KUMAR REGMI
ALL RIGHTS RESERVED


This thesis for the Master of Science degree by Nikesh Kumar Regmi has been approved for the Mechanical Engineering Program by
Christopher Yakacki, Chair Dana Carpenter, Advisor Kai Yu
Date: May 18, 2019


ACKNOWLEDGEMENTS
I would first like to acknowledge my thesis advisor Professor Dana Carpenter for giving me the opportunity to work with him. Secondly, I would like to thank the Smart Materials and Biomechanics (SMAB) Lab family, who have provided a very cordial working environment. I am thankful to them for at times ignoring my existence and allowing me to give all my hours to this tedious task of thesis preparation and at times entertaining me with all kinds of conversation. Thank you to Nicholas, Ross, Sabina, Ravi, and Sam, who have contributed so much to the SMAB Lab and are loving the work they do. I must say, this is one of the super cool labs I have worked ever in the United States.
I would like to thank Binh Dao, a CU Denver Graduate Alumnus. He is surely an example to follow as I graduate now.
I would also like to thank the members of my thesis committee: Professor Christopher Yakacki, one of the coolest professors I have met to date, who devotes an enormous amount of his energy to his students. Also, Prof. Kai Yu, whose appraisal of my work during the classes I have taken with him has surely had an impact on my dedication to this work.
I’d like to thank my mother and father, Namrata Khatiwada and Dipak Regmi, and my sister, Dikshin Regmi, for your love and support throughout my college career.
And finally, thanks to my homie Umang Khatiwada who has been with me during the entire time of my Graduation career and who is also a Civil Engineering graduate student here in CU Denver. Besides that, I would like to thank every individual in the whole Department of Mechanical engineering, Natalya, Tanya, Dr. Welch, Dr. Jenkins, Dr. Rorrer, and everyone behind the curtains whom I have missed. Because of your dedication to the work you do every


day at the University, students like us get this opportunity to begin another phase in our careers.
IV


Regmi, Nikesh Kumar (MS, Mechanical Engineering)
Comparative FE Study on 3D Patient-Specific Evans Calcaneal Wedge Implants made from different materials
Thesis directed by Associate Professor Dana Carpenter
ABSTRACT
Flat feet, also known as “Pes Planus,” is a generic type of foot problem where the entire sole of
the foot touches the ground when an individual is standing. In other words, the curvature of the
foot doesn’t follow a normal arch and is straight. The Evans calcaneal osteotomy provides multi-
planal correction of foot pes plano-valgus deformities in both children and adults [2], Evans
calcaneal osteotomy is a lateral column lengthening procedure that preserves the calcaneocuboid
joint. The treatment consists of using an Evans wedge about 1-1.5 cm proximal to the
calcaneocuboid joint, where a surgeon makes the osteotomy and secures the wedge using a
locking plate [1,2]. The influence of the Evans wedge material composition on bone
regeneration in the hollow space of the wedge is still a question of significant importance. In the
current study, finite element (FE) analysis was performed to understand the nature of mechanical
stress distribution from the initial stage of in vivo bone regeneration to fully developed cortical
bone within the Evans wedge. The accumulation of bone mineral in the regenerating bone was
simulated by implementing progressively stiffer bone material properties at seven time points.
Evans wedges made of cortical bone, titanium (Ti), polyether ether ketone (PEEK), and PEEK
with Ti endplates were modeled to determine how material composition affected stress levels in
the regenerating bone. The study utilized a computed tomography (CT) image of a Sawbones
foot model to create the anatomical geometry in ScanIP. Bone and joint anatomy were meshed
using tetrahedral elements, and ligaments were modeled using one-dimensional, non-
v


compressible truss elements. A mesh convergence analysis confirmed that the mesh size used in the final set of models was enough. To ensure that the foot model provided reasonable results, stresses in the intact foot model were compared with a previous study by J.M. Garcia on load transfer mechanism in metatarsals [22], Using different materials for the Evan’s wedge demonstrated that the von Mises stress levels in the regenerating bone reaches levels like those in cancellous bone of an intact foot when the regenerating bone accumulates enough mineral to achieve a Young’s modulus of 5 GPa. The graft made from cortical bone produced stresses 7% higher than those in a normal bone. The Ti implant produced von Mises stress in the regenerating bone at a level 47% lower than the cancellous bone stress in the intact foot model, whereas the PEEK implant produced stresses in the regenerating bone that were 36% higher than those in the intact foot model. PEEK implants with Ti endplates produced stress levels 16.8% lower than those the normal foot model. These results suggest that both cortical bone wedges and Ti-PEEK wedges create a more osteoconductive environment within the Evans wedge open space than wedges made solely of titanium or PEEK.
The form and content of this abstract are approved. I recommend its publication.
Approved: Dana Carpenter
VI


Table of Contents
ACKNOWLEDGEMENTS.........................................................iii
ABSTRACT...................................................................v
LIST OF TABLES...........................................................vii
LIST OF FIGURES.........................................................viii
CHAPTER 1: INTRODUCTION....................................................1
CHAPTER 2: MATERIALS AND METHODS...........................................7
Geometry andMesh Construction............................................7
Material Properties......................................................8
Loads andBoundary Conditions.............................................9
Literature Comparison...................................................10
Mesh Sensitivity Test...................................................11
Evans Calcaneal Osteotomy...............................................11
Evan’s Wedge Implant....................................................12
CHAPTER 3: RESULTS........................................................16
Literature Comparison...................................................16
Mesh Sensitivity Analysis...............................................20
Evans Calcaneal Osteotomy Comparative Study.............................21
CHAPTER 4: DISCUSSION.....................................................22
CHAPTER 5: CONCLUSION.....................................................25
REFERENCES................................................................27
vii


LIST OF TABLES
Table 1: Materials and mechanical properties used in Evans wedge implant......................14
Table 2: Anatomical measurements of Sawbones foot model.......................................18
Table 3: Maximum principal stress values in all the metatarsals for different mesh sizes in Sawbones foot
model..........................................................................................19
Table 4: Maximum tensile and compressive stresses (MPa) in each metatarsal for the different conditions
analyzed by Garcia [22]........................................................................19
Table 5: Variation in stress values calculated with different mesh sizes......................20
viii


LIST OF FIGURES
Figure 1: Two separate feet, one on the left showing a normal arch and defective foot on the right
showing a flat arch [33]............................................................................1
Figure 2: Transverse plane deformity in flat foot [31]..............................................3
Figure 3: A post-operated Evans calcaneal foot with locking plate [32]..............................4
Figure 4: Locking plate made from Titanium (Ti) [28], a posterior dynamic stabilization of the spine
using PEEK rods [26], a Ti-PEEK implant [29], and wedge implants made from cortical bone [30].......6
Figure 5: Full geometric model of the foot and mesh construction....................................8
Figure 6: Connecting ligaments in ABAQUS.............................................................8
Figure 7: Loading and boundary conditions in the foot model.........................................10
Figure 8: Position of Evans wedge insertion.........................................................12
Figure 9: Isometric, front and side views of Evans wedge (left to right)............................13
Figure 10: Isometric, top and front view of the H-shaped locking Ti-plate designed in Solidworks (left to
right)..............................................................................................13
Figure 11: Positioning ofH-locking plate in ScanIP..................................................14
Figure 12: Ligament-augmented FE foot model with Evans wedge implant................................15
Figure 13: Measurements of Maestro’s Parameter for foot categorization [23]........................17
Figure 14: Mesh convergence results................................................................20
Figure 15: Variation of bone Young's modulus with increasing bone mineral density...................21
Figure 16: Variation of average von Mises stress generated in regenerating bones using different Evans wedge materials.....................................................................................22
IX


CHAPTER 1: INTRODUCTION
Flat feet, also known as “Pes Planus,” is a common condition in which the foot does not have a normal arch, and so the entire foot touches the floor when the patient is standing (Figure 1). According to the 2012 National Foot Health Assessment conducted by the NPD Group (a global research organization) for the Institute for Preventive Foot Health, 8 percent of U.S. adults ages 21 and older (about 18 million people) have the condition. Another 4 percent, or about 8 million U.S adults, have fallen arches [11], There are different types of flat feet, namely, flexible flat foot, short Achilles tendon and posterior tibial tendon dysfunction [12],
Figure 1: Two separate feet, one on the left showing a normal arch and defective foot on the right showing a flat arch [33]
Among these, posterior tibial tendon dysfunction is acquired in adulthood when the tendon that connects the calf muscle to the ankle is injured or swollen. If the foot arch doesn’t receive the support it needs, one can have pain on the inside of their foot and ankle, as well as on the outside of the ankle [12], Treatment of these problems is customized to the individual patient and tailored according to the clinical examination.
In general, conservative measures like using simple analgesia, non-steroidal antiinflammatories, physiotherapy and orthoses in the shape of a corrective medial arch support
1


insole with a neutral heel cup for a flexible deformity are suggested as first measures [13], However, if the recommended trail of conservative measures fails over a period of 6 months then the patient should consider surgical options [13], Various factors like the degree of deformity and its flexibility, the patient’s age, and functional requirements to the problem, condition of the soft tissues and presence of arthritis need to be considered before selecting the mode of a surgical option. Different techniques include tendon debridement, tendon transfer, tibiotalocalcaneal fusion, cotton medial cuneiform osteotomy [13], and Evans calcaneal osteotomy, a widespread procedure used in treatment of a flexible calcaneovalgus foot in patients [14],
Evans calcaneal osteotomy is a lateral column lengthening technique that preserves the calcaneocuboid joint. This laterally-based opening wedge osteotomy is historically known to achieve transverse plane correction for pes plano-valgus deformities (Figure 2).
Evans [1] verified that the medial and lateral columns of the foot must be equal in length to maintain the load balance. Evans [1] described that a symptomatic flatfoot can be improved in alignment by inserting a wedge of tibial bone into an anterior calcaneal section by creating a wedge opening osteotomy. Long term follow-up reports have shown Evans osteotomy process to be highly effective as most of the correction obtained through this process was maintained over time [2], The osteotomy was however revised by cutting the facets between the anterior and middle part of the calcaneus and then inserting a trapezoid-shaped tricortical wedge instead of tibial bone [3], However, there are potential problems that can lead to the failure of the osteotomy process.
There has been long term follow up reports of deteriorating changes in the
2


Transverse Plane View
L.MJ.A.
Longitudinal Mid Tarsal Joint Axis Oblique Mid Tarsal Joint Axis
The more oblique this axis leads to more 1st Ray hypermobility
• More instability
• More Pronatory Disease
• More Transverse Plane Rotation is present
• Oblique Midtarsal Joint Axis
LMJA= Longitudinal Midtarsal Joint Axis
Figure 2: Transverse plane deformity in flat foot [31]
Calcaneocuboid joint [2], particularly because there has been reports of increased pressure in the calcaneocuboid joint after the wedge opening surgery [4], The Evans procedure discovered an increase in the contact pressures across the posterior and anteromedial facets [5], The increase in pressure at the joints and facets location can result in long term pain and disability due to rapid arthrosis. Besides this, the osteotomy for the Evans procedure might also violate the anterior or middle calcaneal facet movement. Some studies have demonstrated failures in 20% of the osteotomy cases, resulting in loss of correction, chronic lateral column pain, and occasionally, even in the failure of the hardware [6, 7], It is therefore highly imperative to carefully construct the wedge surfaces, with the right choice of graft material that provides tight attachment with the cancellous bone. Also, an H-shaped locking plate is used exterior to the lateral opening of the wedge osteotomy to provide more rigid stabilization and avoid dorsal displacement of the graft or dislocation of the anterior section of the calcaneus (Figure 2) [3, 6, 8],
3


Figure 3: A post-operated Evans calcaneal foot with locking plate [32]
In recent time, due to advancement in 3D printing technology, one can easily design custom-made implants for ankle surgery [9], Bony defects, and deformities in lower extremity of human body including high-risk arthrodesis situations can be difficult to treat and often requires a critical size or shape structural graft which may not be available with allograft bones [9], Patient-specific wedge graft development is thus essential to avoid the problems of misalignment and tractional movement between the articulating surfaces. This will ensure a secure fit between the wedge and surrounding bone area. Also, H-plates can be designed to achieve a tight fit respective to the lateral surface of the wedge opening.
Appropriate selection of the implant material is a key factor for long term success of implants. It is well known that the stress transfer between an implant device and a bone is not homogeneous when Young’s moduli of the implant material and the bone are different; this is defined as stress shielding. In such cases where an implant shields a bone from stress, bone atrophy occurs and can lead to the loosening of the implant and refracturing of the bone [10], Therefore, it is desirable to find the right wedge and locking plate material for the osteotomy
4


such that the wedge material allows healthy levels of stress to occur in the bone.
The different types of biomaterials can be categorized into metals, polymers, composites and ceramics. Due to advancement in material science technology, nowadays almost all orthopedic implants comprise a composition of metals, polymers, and ceramics. The first corrosion-resistant alloy to be proven very effective in surgical implants were Cobalt- chromium alloys [27], Also, stainless steel is a common alloy, which has been very successful as a surgical implant material. Titanium (Ti) alloys are primarily type Ti-6A1-4V, which contains 6% aluminum, 4% vanadium, and 90% titanium. This metal has become ever more popular in the last decade because of its strength similarity to stainless steel and cobalt chrome however only half as stiff as them. This is one of the significant features of Titanium alloy over the other two, because it would minimize the disparity in elastic modulus between implants and bones and hence prevent stress shielding [27], Also, polymers like ultra-high-molecular-weight polyethylene (UHMWPE) have low wear characteristic with metals, and hence can be used as bearing surface in implants. Recently, polyether ether ketone, commonly known as PEEK, has utmost achievement in the field of spine implant design with follow-up reports from clinical examinations. It has been prevalent as a radiolucent alternative to metallic biomaterials in the spine community [26] (Figure 4).
5


Figure 4: Locking plate made from Titanium (Ti) [28], a posterior dynamic stabilization of the spine using PEEK rods [26], a Ti-PEEK implant [29], and wedge implants made from cortical bone [30]
The objective of the current study was to compare the effects of four different material compositions in an Evans wedge on the amount of stress generated in regenerating bone as it grows over time in the open spaces. The study began with the development of a patient-specific foot model. The geometric model of the foot bones and joints were augmented with ligaments, and the ligamentous model was compared with a previously published research paper on load transfer mechanisms in foot metatarsals [23], Mesh convergence testing was carried out to determine the optimum size of mesh to test the stiffness of different materials composition of Evans wedge as compared to allograft wedge osteotomy. The stress in regenerating bone was computed at multiple time points with the simulated wedge composed of cortical bone allograft, PEEK, Ti-PEEK combination, and Ti. The hypothesis of this study is that the Ti-PEEK implants provides closest stress distribution to an intact bone.
6


CHAPTER 2: MATERIALS AND METHODS Geometry and Mesh Construction
The geometry of the FE model was obtained from CT scan of a Sawbones foot model (Figure 5). The images were segmented using ScanIP (Simpleware, Synopsys, Mountain View, CA), and a cortex of uniform thickness of 5 mm was created to surround trabecular bone cores. The connections between the cortical-cancellous bones were modeled with cartilaginous joints. Linear tetrahedral mesh elements were used to discretize the foot model. The FE foot model along with mesh is depicted in Figure 5. The entire foot model is a composition of 26 bones namely, calcaneus, talus, cuboid, navicular, 3 cuneiforms, 5 metatarsals and 14 small bones that form the phalanges. The phalanges don’t constitute any relative movement because of negligible influence on the stage of forefoot, thus are fused together in the foot model [18], The full foot model was exported to ABAQEiS (Simulia, Dassault Systemes, and Johnston, RI) for FE analysis. ID non-compressible truss elements were added to the model to simulate the ligaments. Ligaments include plantar fascia, the deep and superficial long plantar ligaments (LPL), posterior talus-calcaneus ligament, exterior and interosseous ligaments, low calcaneus-navicular ligament, superior, interosseous and external ligaments, joints talus and inter ligaments, Lisfranc’s ligament, calcaneus-cuboid ligament, and calcaneus navicular ligament. Figure 6 shows the connecting locations of these ligaments in the model in ABAQEIS. Ligaments are modeled by using the ABAQUS input file (INP). In the input file, ligaments are defined as an element type of T3D2 and the connecting points of ligaments are modeled with the following syntax:
* ELEMENT, TYPE=T3D2
7


(Element number), (node number of the origin), (node number of the insertion).
Figure 5: Full geometric model of the foot and mesh construction
L.
Figure 6: Connecting ligaments in ABAQUS Material Properties
Bones were modeled as homogeneous, elastic and isotropic with cortical bone having a Young’s modulus of 17,000 MPa and 0.3 Poisson ratio, whereas trabecular bone was assigned a Young’s modulus of 700 MPa and 0.3 Poisson ratio [15], Ligaments were modeled with noncompression ID truss elements and distinguished between two materials: a stiffer one (superficial deep LPL and fascia ligaments) with Young’s modulus of 350 MPa and Poisson’s ratio of 0.4 and cross-sectional area of 290.7 mm2
8


[16], and a more compliant one that corresponds to the rest of ligaments with Young’s modulus of 260 MPa, Poisson’s coefficient of 0.3, and cross-sectional area of 18.4 mm2 [16], Cartilage was also considered as homogeneous, elastic and isotropic with Young’s modulus of 10 MPa and Poisson’s coefficient of 0.4 [17], It is labelled in color red in Figure 5.
Loads and Boundary Conditions
The loads applied on the foot varies upon the magnitude, direction and areas of application [19], Thus, the stance phase of foot gait can be divided into different stages depending upon the requirement of the study. For example, Gefen et al. [19] proposed to divide it into six phases: initial contact, heel-strike, midstance, forefoot-contact, push-off and toe-off In this study, we only consider the standing foot [15, 16, and 20] where the forefoot is totally in contact with the ground. Therefore, we constrain the heel movement by constraining the vertical and horizontal displacement of the node at the calcaneal base. However, only the vertical movement of the five metatarsal heads are constrained. The constrained calcaneus node acts as the reference for the movement of all other nodes in the foot.
The scenarios for the loading and boundary conditions were based off Garcia’s paper of load transfer mechanism in the foot metatarsals (Figure 7) [22], The same loading and boundary conditions were used to obtain computational results on Evans calcaneal osteotomy. A 300-N load was applied on the foot, corresponding to the weight of a person of approximately 60 kg [15], and the site of application of the force is uniformly distributed on the areas in contact with the tibia and the fibula. The load is applied at an angle of 10 degrees with respect to the normal to the ground due to the inclination of the tibia and fibula at this stage of the gait cycle. Moreover, a similar load exists in the opposite direction in the talus due to the action of the Achilles’ tendon. Simkin [21] calculated that this force is approximately half of the force that
9


applies the body on the foot; therefore, in our model, a force of 150 N was uniformly distributed in the region where the Achilles’ tendon inserts on the calcaneus [22] with a similar inclination of 10 degrees. (See fig. 7)
Achilles tendon tension
Hinged Joint
Roller Joint
Applied Load
Figure 7: Loading and boundary conditions in the foot model
Literature Comparison
Garcia-Aznar in 2009 published a study analyzing the load transfer mechanism across the bones of the human foot [23], The study used a 3D foot model without soft tissues and augmented with several ID truss elements as ligaments. Our study used similar methodologies, material properties, loading and boundary conditions, and we therefore compared our results for maximum tensile and compressive stresses were in each of the metatarsals to Garcia’s results to ensure that our model produced realistic results.
10


The foot model used in our study was also measured anatomically to classify any foot deformities, like how J.M. Garcia classified the models in his paper [22],
Mesh Sensitivity Test
Mesh convergence was tested by calculating the average values of von Mises stress, maximum principal stress and resultant displacement in metatarsal-1 (Ml). ScanIP was used to vary the element numbers from coarser 694,557 to finer number of 2,817,702 elements.
Evans Calcaneal Osteotomy
Evans calcaneal osteotomy is a surgical technique to treat flat foot deformities. In this study, we make use of the validated foot model and perform a virtual osteotomy 1.4 cm proximal to the calcaneocuboid joint with a varying depth of 1.3 cm to 2 cm at bottom and top of Evans wedge respectively (Figure 8).
11


Evan’s Wedge Implant
The Evans wedge was masked in Scan IP with three different layers of mask distinguishing between the two endplate layers and a wedge-shaped layer sandwiched in between (Figure 8).
The geometry of the tri-layer wedge was in accordance with the geometry of the Sawbones model. An open space in the Evan’s wedge is designed for post-operative bone growth.
There has been recent development of wedges made of different materials like Ti, polymers and their combinations. Companies like DePuy Synthes, TyberMedical, CONMED, Anthrex, and many more now manufacture wedges composed of a combination of Ti and polymer, with a PEEK body between two Ti alloy endplates [29],
Figure 8: Position of Evans wedge insertion
12


Figure 9: Isometric, front and side views of Evans wedge (left to right)
After the wedge was successfully modeled in ScanIP, an H-shaped locking plate was modeled in Solidworks (Figure 10) and then exported as a .stl file in ScanIP.
Figure 10: Isometric, top and front views of the H-shaped locking Ti-plate designed in
Solidworks (left to right)
The locking plate was exported to ScanIP and positioned at the lateral surface of the wedge opening to prevent lateral movement (Figure 11). Due to the dissimilarities in anatomy between the locking plate and bone surface, their attachment is further masked in ScanIP to prevent any openings. The implant augmented model is then exported to ABAQUS for ligament modelling at the suggested mesh element size of negative 30.
13


Figure 11: Positioning of H-locking plate in ScanIP
Evans wedge material properties were varied as follows:
Table 1: Materials and mechanical properties used in Evans wedge implant
Cortical bone E = 17000 MPa, Poisson’s ratio = 0.3
Titanium E = 109000 MPa, Poisson’s ratio = 0.33
PEEK E = 3000 MPa, Poisson’s ratio = 0.33
Ti-PEEK Titanium dnd plates, PEEK wedge
14


Figure 12: Ligament-augmented FE Foot model with Evans wedge implant
The fully developed FE Evans calcaneal osteotomy model was then tested to determine von Mises stress in the region of bone regeneration, and the stress in the regenerating bone was compared with the amount of von Mises stress generated in the same region of interest for an intact foot. Seven time points were used to simulate bone mineralization and subsequent increases in Young’s modulus: 2, 6, 9, 12, 24, 41, and 112 days. The corresponding Young’s moduli (0.001, 0.1, 0.5, 1, 5, 10, and 17 GPa, respectively) were computed based on a previous study of bone ingrowth into titanium and PEEK materials [24],
15


CHAPTER 3: RESULTS
Literature Comparison
The categorization of the selected foot model was done based on Maestro’s formula
[22] as discussed by Garcia [23],
Terminology of the classification of Maestro [23]:
• Cl = Transition distance between Ml and M2
• C2 = Transition distance between M2 and M3
• C3 = Transition distance between M3 and M4
• C4 = Transition distance between M4 and M5
• SM4 line = line from the center of the lateral sesamoid perpendicular to the axis of the foot.
16


Figure 13: Measurements of Maestro’s Parameter for foot categorization [23]
17


Table 2: Anatomical measurements of Sawbones foot model
NOMENCLATURE DISTANCE (mm)
Ml 60.394
M2 84.218
M3 78.123
M4 74.928
M5 71.658
Cl 12.102
C2 7.166
C3 14.736
C4 16.358
Angle between 1st MTP and 2nd MTP 10.971 degrees
Based on these measurements and Maestro’s classification [23], the foot model is categorized as a symptomatic 10 degrees foot model, with SM4 line proximal to MT4. It is a harmonious forefoot morphotype which is characterized by a SM4 line passing through the center of the fourth metatarsal head, associated to a geometrical progression of a factor 2 of the lesser metatarsals. Thus, it resembles to a foot model somewhere between symptomatic 12 deg (S12) and symptomatic 8 deg (S8) model as described by Garcia [22],
The maximum compressive and tensile principal stresses in the metatarsals in our model are provided in Table 3, and the corresponding values from Garcia’s model are provided in Table4.
18


Table 3: Maximum principal stress values in all the metatarsals for different mesh sizes in Sawbones foot model
Model Max Principal Stress values in Metatarsals (MPa) Displacement (mm)
Vertical Horizontal
1st 2nd 3rd 4th 5th Min Max Min Max
Neg mesh 50 Tension 12.3027 5.4368 5.87122 6.4115 4.61863 â– 0.2565 0.0277 â– 0.187 0.0085773
Compression â– 3.76683 â– 1.99397 â– 2.43 â– 3.6204 â– 1.0589

Neg mesh 30 Tension 10.6854 10.1801 5.61 5.48213 6.32244 â– 0.1654 0.01728 â– 0.122 0.000896
Compression â– 1.3011 â– 2.01205 â– 1.43743 â– 0.842704 â– 1.01876

Neg mesh 25 Tension 17.2566 15.9758 10.9151 7.98025 6.41636 â– 0.1408 0.01413 â– 0.09 9.541E-05
Compression â– 1.73237 â– 1.63966 â– 0.127872 â– 1.16971 â– 0.939581

Neg mesh 20 Tension 30.0748 15.2642 9.93443 8.91096 10.1187 â– 0.1517 0.02048 â– 0.123 0.0002694
Compression â– 1.59484 â– 1.62983 â– 1.02747 â– 1.84171 â– 1.67741

Neg mesh 15 Tension 13.2929 34.4813 18.9735 9.98577 5.56566 â– 0.1151 0.0227 â– 0.102 0.0001692
Compression â– 2.82036 â– 2.65058 â– 2.34517 â– 1.59632 â– 0.787549
Table 4: Maximum tensile and compressive stresses (MPa) in each metatarsal for the different analyzed condition by Garcia [22]
Unit: MPa Ml M2 M3 M4 M5
Initial Case Maximal tension stress 5.7 4.3 4.9 5.3 4.2
(IC) Maximal Compression Stress -10 -11.6 -11.7 -10.0 -9.0
Parabola of Maximal Tension stress 4.5 4.6 5.3 4.9 4.3
Maestro et. Al. [23] (MP8) Maximal compression stress -9.5 -11 -11 -9 -10
Symptomatic Maximal Tension Stress 3.8 5.3 5.6 5.0 4.8
(12 deg) (S12) Maximal Compression Stress -8.5 -11.7 -11.4 -10.5 -12.5
Symptomatic Maximal Tension stress 4.0 4.7 5.0 4.8 4.4
(Bdeg)(S8) Maximal Compression stress -9.2 -10.5 -11.2 -9.1 -11
Peak stress magnitudes in our model ranged from 0.1 to 34.5 MPa, while the stress magnitudes obtained by Garcia ranged from 3.8 to 12.5 MPa. Thus, our model had a wider range of stresses, with Garcia’s stresses falling within the range of ours. Given the fact that our
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model was based on a different foot anatomy and given the unavoidable differences in points of load application and ligament attachment locations, the stress levels in our model appear to be reasonable in comparison with those found by Garcia.
Mesh Sensitivity Analysis
Computational results obtained from the mesh convergence test are provided in Table 5 and Figure 14.
Table 5: Variation in stress values calculated with different mesh sizes
Unit: MPa Properties Calculated
No. Of elements in the mesh Avg. Von Misses Stress Max. Principal Stress Resultant Displacement (mm)
694557 1.1047531 0.423155 0.17304983
1.069,251 0.45892084 0.15000945 0.055755291
1,308,795 0.48702907 0.22052226 0.077199021
1,847, 713 0.46265142 0.18576198 0.083124595
2,817,702 0.45834972 0.18101422 0.065516558
Number of Elements in the mesh
â–  Avg. Von M isses Stress
â–  Max. Principal Stress
â–  Resultant Displacement
Figure 14: Mesh convergence results
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The graph above clearly shows that after mesh element size of negative 30, there is minimal difference in the calculated values. The mesh size of -30 yields 1,069,251 tetrahedral elements in total. This is the threshold element numbers for meshing, at which the values are converged. Therefore, all models used in the study were meshed at a setting of -30.
Evans Calcaneal Osteotomy Comparative Study
The time-dependent variation of bone mineral density and Young’s modulus in the regenerating bone is shown in Figure 15.
Figure 15: Variation of bone Young's modulus with increasing bone mineral density
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Bone Layer Age (days)


The variation in average von Mises stress in the cortical and cancellous regions of a normal foot is compared with the average von Mises stress in regenerating bone region for different Evans graft materials in Figure 16.
Titanium Evans wedge Model
i PEEKEvanswedgeModel iTi-PEEKWedge Model i Cortical Bone Wedge Model
â–  Cortical bone Stress in Normal intact foot at the wedge location
â–  Cancellous bone Stress in Normal intact foot at the wedge location
Figure 16: Variation of average von Mises stress generated in regenerating bones using
different Evans wedge materials
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CHAPTER 4: DISCUSSION
The objective of this study was to investigate the effects of different types of implant materials on the regenerating bone in an Evans wedge. This study also focused on development of a new FE model of the human foot using an optimized mesh element size to improve accuracy in results and optimum utilization of processing memory simultaneously, also defined as mesh sensitivity. According to FEA theory, FE models with fine mesh (small element size) yield highly accurate results but take longer computing time and memory space. On the contrary, those FE models with coarse mesh (large mesh size) may lead to less accurate results but do save significant computing time [25], The mesh sensitivity test for our foot model found that an average mesh element size of 1.25 mm with 214,589 nodes and 1,069,251 elements is enough to provide accurate results in FEA, beyond which there is minimal changes to the properties calculated.
The stresses in our foot model had magnitudes like those found in a previous study by Garcia [22], The foot model was also anatomically measured to categorize it based on Maestro’s Formula [22], In Garcia’s study, he calculated the maximum tensile and compressive stress on all the five metatarsals in different categories of foot. Garcia’s study found the overall highest tensile and compressive stress on the third metatarsal. In our study, the highest tensile stress occurs in the first metatarsal. The FE foot model inevitably includes stress risers like notches and corners in the foot model, which may explain the higher maximum stresses found in our model. Given the differences in anatomical geometry and overall modeling techniques between our study and Garcia’s, the fact that Garcia’s results fit within the range of our results suggests that our model provides reasonable, realistic results.
The Evans calcaneal osteotomy simulations were performed assuming that regenerating
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bone tissue mineralizes within the Evans graft gradually with time. It was found that implants made from Ti alone produced the lowest von Mises stress values in the regenerating bone at all time points. The implant made from PEEK substantially increased the von Mises stress values in the newly formed bone. A previous load sharing study in our laboratory showed that, when bone grows into a porous PEEK implant, bone bears majority of the load (66.5%) at the onset of mineralization along the implant surface at 4 weeks as compared to Ti implants that allow only 12.7% of the total load transferred to the bone under compression [24], The current study showed that composite implants with Ti endplates and a PEEK wedge allow higher stress distribution in the regenerated bone, but stresses in these implants do not reach levels seen in wedges made of PEEK alone.
The stress levels in the cortical and trabecular regions of the calcaneus of the intact foot model can be compared with the Evans wedge models to help determine whether different implants may be more conducive to healthy bone formation. The average von Mises stress at the osteotomy location in the intact foot was 0.2 MPa in the cancellous bone and 0.5 MPa in the cortex (Figure 16). This magnitude of stress was acquired in the regenerating bone in the Evans wedge model when bone reached a Young’s modulus of 5 GPa. Our model suggests that it takes 24 days for the bone mineral to accumulate and stiffen the tissue to this level. At this point of time, the Evans graft made from cortical bone produced stress 7% higher than in the intact bone. The Ti-PEEK implant produced an average stress 17% lower than the intact bone at this same time point. The Ti implant, the stiffest material tested in our study, produced a stress magnitude lower by 47%. This large difference suggests that the degree of stress shielding in this implant may be high enough to preclude maintenance of healthy bone tissue, as previous studies on stress transfer between an implant device and bone have demonstrated that stress shielding
occurs if the difference between the stiffness (Young’s modulus) between the material and bone
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is too high [34], The PEEK wedge on the other hand produced an average stress 36% higher than in the intact bone. Note that, after 41 days bone mineralizes to achieve a modular strength of 10 GPa where Ti-implants show closest stress distribution to cancellous bone stress by 16% lower value from a normal bone. However, it is evident that a normal cancellous doesn’t even get that stiffer. But, provided with consistent physiotherapies for a prolonged period can induce more mineralization and increase bone modular strength at least to the strength of 5 GPa.
The underlying idea in Ti-PEEK wedge design is that the Ti surface provides better adhesion to surrounding bone tissue while providing stress shielding environment more like that obtained by using a PEEK wedge. Our study suggests that a Ti-PEEK wedge does indeed lead to stress levels more like that in intact bone at the 24th day time point, as compared to wedges made of Ti or PEEK alone. One of the shortcomings of this study is that, the foot model does not include all the tendons, muscles and soft tissues present in a normal, intact foot. However, this study is focused on comparing different materials used in the field of implant development.
Since the exact same model was used while only varying the implant material, we can be confident that including additional anatomic details (tendons, etc.) would not change the overall conclusions of the study. Also, the design of the Evans wedge in this study was based directly on the site of insertion’s area geometry, rather than a commercially available wedge design. However, the differences in stress levels seen using different materials in this study should still apply to wedges with other geometric designs. Furthermore, this study can be used as a reference for experimental setups that can simulate the stress requirement for bone remodeling after a surgery. A range of bone material properties were tested to simulate time-dependent bone mineralization, the amount of stress generated in the masked region of interest at every stage is hypothetically the minimum amount of stress required for bone remodeling.
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CHAPTER 5: CONCLUSION
Flat foot is a common problem where a foot doesn’t have a normal arch. Evans calcaneal osteotomy is a lateral column lengthening procedure that achieves transverse plane correction for pes plano-valgus deformities. The influence of the Evans wedge material composition on bone remodeling in the hollow space of the wedge is still a question of significant importance. Finite element (FE) analysis was performed to understand the nature of mechanical stress distribution from the initial stage of in-vivo bone regeneration to fully developed cortical bone within the Evans wedge made from different materials. It took 24 days for the regenerating bone within the Ti-PEEK Evans wedge graft to acquire the modulus of 5 GPa that yielded stress distribution lower in magnitude than normal cancellous bone by 17%. At this same time point, the Evans wedge made from cortical bone approximated the stress level of the intact calcaneous with a stress only 7%, higher in magnitude than the normal bone. Thus, the hypothesis that Ti-PEEK implants provide closest stress distribution to a normal bone stress isn’t correct as Cortical made implants are reported to have minimum difference to the cancellous stress in an intact foot bones.
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REFERENCES
[1] Evans D. Calcaneo-valgus deformity. J Bone Joint Surg 1975; 57B:270-8
[2] Philips GE. A review of elongation of os calcis for flat feet. J Bone Joint Surg 1983 ;65B: 15-8
[3] Mosca VS. Calcaneal lengthening for valgus deformity of the hindfoot. J Bone Joint Surg 1995;77A:500-12
[4] Cooper PS, Nowak MD, Shaer J. Calcaneocuboid Joint pressures with lateral column lengthening (Evans) procedure. Foot Ankle Int 1997; 18(4): 199-204.
[5] Sarrafin SK. Anatomy of the foot and ankle: descriptive, topographic, functional, Philadelphia: J.B. Lipincott; 1983.
[6] Thomas RL, Wells BC, Garrison RL, et al. Preliminary results comparing two methods of lateral column lengthening. Foot Ankle Int 2001; 22:107-19
[7] ToolanBC, Sangeorzan B J, HansenS. Complex reconstruction for the treatment of dorsolateral peritalar subluxation ofthe foot. J Bone Joint Surg 1999;81A:1545-60
[8] Dalton GP, Wapner KL, Hecht PJ. Complications of Achilies and posterior tibial tendon surgeries. Clin Orthop 2001; 391:133-9.
[9] Wee, James & Thevendran, Gowreeson. (2017). “The role of orthobiologics in foot and ankle surgery: Allogenic bone grafts and bone graft substitutes.” EFORT Open Reviews. 2. 272-280. 10.1302/2058-5241.2.160044.
[10] N. Sumitomo, K. Noritake, T. Hattori et al., “Experiment study on fracture fixation with low rigidity titanium alloy: plate fixation of tibia fracture model in rabbit”, Journal of Materials Science, vol. 149, no. 4, pp. 1581-1586, 2008.
[11] Foot Conditions: Flat Feet. Available at https://www.ipfh.org/foot-conditions/foot-conditions-a-z/flat-feet. Accessed August 2018.
[12] What causes Flat Foot? Posterior Tibial Tendon Dysfunction. Available at https://www.healthline.com/symptom/flat-foot. Accessed July 2018.
[13] C.J. Lever, M.S. Hennessy. Adult flat foot deformity. Orthop. Trauma, 30 (2016), pp. 41-50
[14] Dayton, P, Prins, DB, Smith, DE, Feilmeier, MJ. Effectiveness of a locking plate in preserving midcalcaneal length and positional outcome after Evans calcaneal osteotomy: a retrospective pilot study. J Foot Ankle Surg. 2013; 52(6):710-713.
[15] Gomez-Benito, M. J., Fornells, P., Garcia-Aznar, J. M., Serai, B., Seral-Innigo, F., and Doblare, M., 2007, “Computational Comparison of Reamed Versus Undreamed Intramedullary Tibial Nails,” J. Orthop. Res., 25, pp. 191-200.
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[16] Cheung, J. T., Zhang, M., Leung, A. K., and Fan, Y., 2005, “Three-Dimensional Finite Element Analysis of the Foot During Standing-A Material Sensitivity Study,” J. Biomech., 38, pp. 1045-1054.
[17] Gefen, A., 2002, “Stress Analysis of the Standing Foot Following Surgical Plantar Fascia Release,” J. Biomech., 35, pp. 629-637
[18] 19 Scott, S. H., and Winter, D. A., 1993, “Biomechanical Model of the Human Foot: Kinemetics and Kinetics During the Stance Phase of Walking,” J. Biomech., 26, pp. 1091-1104.
[19] Gefen, A., Megido-Ravid, M., Itzchak, Y., and Arcan, M., 2000,“Biomechanical Analysis of the Three-Dimensional Foot Structure during Gait: A Basic Tool for Clinical Applications,” ASME J. Biomech. Eng., 122, pp. 630-639
[20] Scott, S. H., and Winter, D. A., 1993, “Biomechanical Model of the Human Foot: Kinemetics and Kinetics During the Stance Phase of Walking,” J. Biomech., 26, pp. 1091-1104.
[21] Simkin, A., 1982, “Structural Analysis of the Human Foot in Standing Posture,” Ph.D. thesis, Tel Aviv University, Tel Aviv, Israel
[22] Garcia-Aznar JM, Bayod JJ, Rosas AA, et al. Load Transfer Mechanism for Different Metatarsal Geometries: A Finite Element Study. ASME. J Biomech Eng. 2008; 131 (2):021011-021011-7. doi: 10.1115/1.3005174
[23] Maestro, M., Besse, J. L., Ragusa, M., and Berthonnaud, E., 2003, “Forefoot Morphotype Study and Planning Method for Forefoot Osteotomy”, Foot and Ankle Clinics, 8(4), pp. 695-710
[24] Carpenter, R & Klosterhoff, Brett & Brennan Torstrick, F & T Foley, Kevin & Burkus, John & S D Lee, Christopher & Gall, Ken & E Guldberg, Robert & Safranski, David. (2018). “Effect of porous orthopaedic implant material and structure on load sharing with simulated bone ingrowth: A finite element analysis comparing titanium and PEEK.” Journal of the mechanical behavior of biomedical materials. 80. 68-76. 10.1016/j.jmbbm.2018.01.017
[25] Liu, Yucheng. (2013). Effects of Mesh Density on Finite Element Analysis. SAE Technical Papers. 2. 10.4271/2013-01-1375.
[26] Kurtz, Steven M and John N Devine. “PEEK biomaterials in trauma, orthopedic, and spinal implants” Biomaterials vol. 28, 32 (2007): 4845-69.
[27] Dominique G. Poitout, 2004. Biomechanics and Biomaterials in Orthopedics. Springer, London. DOI 10.1007/978-1-4471-3774-0
[28] Depuy Synthes: Products. Available at https://www.dqiuysynthes.com/hcp/timima/pioducts/qs^Small-Fragment-LCP#tab2. AccessedJanuary2019
[29] Tyber Medical: Tywedge System. Available at http://tybermedical.com/products/tywedge-system/. Accessed January 2019
[30] Wright: Allopure- Allograft Bone Wedges. Available at http://www.wright.com/footandankleproducts/allopure-allograft-bone-wedges. AccessedJanuary2019.
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[31] Medical Case Histories and Treatment: Transverse Plane View. Available at http ://medicalcasehistories.blogspot. com/2012/11/hypermobile-versus-rigid-pathomechanics.html. Accessed January 2019.
[32] TriMed: Evans Osteotomy Plate. Available at https://trimedortho.com/product-stm-detail/evans-osteotomy-plate. Accessed January 2019.
[33] Mayo Clinic: Flatfeet. Available at https://www.mayoclinic.org/diseases-conditions/flatfeet/symptoms-causes/syc-20372604. Accessed February 2019.
[34] N. Sumitomo, K. Noritake, T. Hattori et al., “Experiment study on fracture fixation with low rigidity titanium alloy: plate fixation of tibia fracture model in rabbit,” Journal of Materials Science, vol. 19, no. 4, pp. 1581-1586, 2008.
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Full Text

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COMPARATIVE FE STUDY ON 3D PATIENT SPECIFIC EVANS CALCANEAL WEDGE IMPLANTS MADE FROM DIFFERENT MATERIALS b y NIKESH KUMAR REGMI B.E., Kathmandu University, 2014 A thesis s ubmitted to the Department of Mechanical Engineering of the University of Colorado in partial fulfillment o f the requirements for the degree of MASTER OF SCIENCE IN MECHANCIAL ENGINEERING May 2019 Mechanical Engineering

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i © 2019 NIKESH KUMAR REGMI ALL RIGHTS RESERVED

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ii This thesis for the Master of Science degree by Nikesh Kumar Regmi h as been approved for the Mechanical Engineering Program b y Christopher Yakacki , Chair Dana Carpenter, Advisor Kai Yu Date: May 18, 2019

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iii ACKNOWLEDGEMENTS I would first like to acknowledge my thesis advisor Professor Dana Carpenter for giving me the opportunity to work with him. Secondly, I would like to thank the Smart Materials and Biomechanics (SMAB) Lab family, who have provided a very cordial working en vironment. I am thankful to them for at times ignoring my existence and allowing me to give all my hours to this tedious task of thesis preparation and at times entertaining me with all kinds of conversation. Thank you to Nicholas, Ross, Sabina, Ravi, and Sam, who have contributed so much to the SMAB Lab and are loving the work they do. I must say, this is one of the super cool labs I have worked ever in the United States. I would like to thank Binh Dao, a CU Denver Graduate Alumnus. He is surely an example to follow as I graduate now. I would also like to thank the members of my thesis committee: Professor Christopher Yaka ck i, one of the coolest professors I have met to date, who devotes an enormous amount of his energy to his students. Also, Prof. Kai Yu, whose appraisal of my work during the classes I have taken with him has surely had an impact on my dedication to this work. Dikshin Regmi, for your love and suppo rt throughout my college career. And finally, thanks to my homie Umang Khatiwada who has been with me during the entire time of my Graduation career and who is also a Civil Engineering graduate student here in CU Denver. Besides that, I would like to thank every individual in the whole Department of Mechanical engineering, Natalya, Tanya, Dr. Welch, Dr. Jenkins, Dr. Rorrer, and everyone behind the curtains whom I have missed. Because of your dedication to the work you do every

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iv day at the University, student s like us get this opportunity to begin another phase in our careers.

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v Regmi, Nikesh Kumar (MS, Mechanical Engineering) Comparative FE Study on 3D P atient Specific Evans Calcaneal Wedge I mplants made from different materials Thesis directed by Associate Professor Dana Carpenter ABSTRACT the foot touches the ground when an individual is standing. In other words, the curvature of the planal correction of foot pes plano valgus deformities in both children and adults [2]. Evans calcaneal osteotomy is a lateral column leng thening procedure that preserves the calcaneocuboid joint. The treatment consists of using an Evans wedge about 1 1.5 cm proximal to the calcaneocuboid joint, where a surgeon makes the osteotomy and secures the wedge using a locking plate [1, 2]. The influ ence of the Evans wedge material composition on bone regeneration in the hollow space of the wedge is still a question of significant importance. In the current study, finite element (FE) analysis was performed to understand the nature of mechanical stress distribution from the initial stage of in vivo bone regeneration to fully developed cortical bone within the Evans wedge. The accumulation of bone mineral in the regenerating bone was simulated by implementing progressively stiffer bone material propertie s at seven time points. Evans wedges made of cortical bone, titanium (Ti) , polyether ether ketone (PEEK), and PEEK with Ti endplates were modeled to determine how material composition affected stress levels in the regenerating bone. The study utilized a co mputed tomography (CT) image of a Sawbones foot model to create the anatomical geometry in ScanIP. Bone and joint anatomy were meshed using tetrahedral elements, and ligaments were modeled using one dimensional, non -

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vi compressible truss elements. A mesh conv ergence analysis confirmed that the mesh size used in the final set of models was enough . T o ensure that the foot model provided reasonable results, stresses in t he intact foot model were compared with a previous study by J.M. Garcia on load transfer mecha nism in metatarsals [22]. U sing different materials for the wedge demonstrated that the von Mises stress levels in the regenerating bone reaches levels like those in cancellous bone of an intact foot when the regenerating bone accumulates enough mineral to achieve of 5 GPa. The graft made from cortical bone produced stresses 7 % higher than those in a normal bone. The T i implant produced von Mises stress in the regenerating bone at a l evel 4 7 % lower than the cancellous bone stress in the intact foot model, whereas the PEEK implant produced stresses in the regenerating bone that were 3 6 % higher than those in the intact foot model . PEEK i mplants with Ti endplates produced stress levels 16 .8% lower than those the normal foot model. These results suggest that both cortical bone wedges and Ti PEEK wedges create a more osteoconductive environment within the Evans wedge open space than wedges made solely of titanium or PEEK. The form and content of this abstract are approved. I recommend its publication. Approved: Dana Carpenter

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vii Table of Contents AC KNOWLEDGEMENTS ................................ ................................ ................................ .................. iii AB STRACT ................................ ................................ ................................ ................................ ........... v L IST OF TABLES ................................ ................................ ................................ ............................... vii L IST OF FIGURES ................................ ................................ ................................ ............................ viii C HAPTER 1: INTRODUCTION ................................ ................................ ................................ .......... 1 C HAPTER 2: MATERIALS AND METHODS ................................ ................................ .................... 7 G eometry and Mesh Construction ................................ ................................ ................................ ..... 7 M aterial Properties ................................ ................................ ................................ ............................ 8 L oads and Boundary Conditions ................................ ................................ ................................ ........ 9 Literature Comparison ................................ ................................ ................................ .................... 10 M esh Sensitivity Test ................................ ................................ ................................ ........................ 11 E vans Calcaneal Osteotomy ................................ ................................ ................................ ............. 11 E Wedge Implant ................................ ................................ ................................ ..................... 12 C HAPTER 3: RESULTS ................................ ................................ ................................ ..................... 16 L iterature Comparison ................................ ................................ ................................ .................... 16 M esh Sensitivity Analysis ................................ ................................ ................................ ................. 20 E vans Calcaneal Osteotomy Comparative Study ................................ ................................ ............. 21 C HAPTER 4: DISCUSSION ................................ ................................ ................................ ............... 22 C HAPTER 5: CONCLUSION ................................ ................................ ................................ ............. 25 REFERENCES ................................ ................................ ................................ ................................ ... 27

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viii LIST OF TABLES Table 1: Materials and mechanical properties used in Evans w edge i mplant ................................ ........... 14 Ta ble 2: A natomical measurements of Saw bones foot m odel ................................ ................................ . 18 Table 3: M aximum p rincipal s tress values in all the metatarsals for different mesh sizes in S awbones foot model ................................ ................................ ................................ ................................ .................... 19 Table 4: M axim um tensile and compressive stresses (MPa) in each metatarsal for the different condition s analyzed by Garcia [22] ................................ ................................ ................................ .......................... 19 Ta ble 5 : Variation in stress values calculated with different mesh sizes ................................ .................. 2 0

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ix LIST OF FIGURES Figure 1 : Two separate feet, one on the left showing a normal arch and defective foot on the right show ing a flat arch [33] ................................ ................................ ................................ ........................... 1 F igure 2: Transverse plane deformity in flat foot [31] ................................ ................................ ............... 3 F igure 3: A post operated Evans calcaneal foot with locking plate [32] ................................ .................... 4 Figure 4: L ocking plate made from Titanium (Ti ) [28], a posterior dynamic stabilization of the spi ne using PEEK rods [26], a Ti PEEK implant [29], and wedge implants made from cortical bone [30] 6 F igure 5: F ull geometric model of the foot and mesh construction ................................ ............................ 8 F igure 6: C onnecting ligaments in ABAQUS ................................ ................................ ........................... 8 F i gure 7: L oading and b oundary condition s in the foot model ................................ ................................ ....... 10 F igure 8: P osition of Evans wedge insertion ................................ ................................ ........................... 12 F igure 9: Isometric, front and side view s of Evans wedge (left to right) ................................ .................. 13 Figure 10: I sometric, top and front view of the H shaped locking Ti plate designed in S olidworks (left to right) ................................ ................................ ................................ ................................ ..................... 13 F igure 11: P ositioning of H locking plate in S can IP ................................ ................................ ............... 14 F igure 12: L igament augmented FE foot model with Evans wedge implant ................................ ............ 15 F igure 13: M easurements of for foot categorization [23] ................................ ........ 17 F igure 14: M esh convergence results ................................ ................................ ................................ ..... 20 F igure 15: V ariation of bone Young's modulus with increasing bone mineral density ............................. 21 Figure 16: V ariation of average von Mises stress generated in regenerating bones using di fferent Evans wedge materials ................................ ................................ ................................ ................................ ..... 22

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1 CHAPTER 1: INTRODUCTION have a normal arch, and so the entire foot touches the floor when the patient is standing (Figure 1). According to the 2012 National Foot Health Assessment conducted by the NPD Group (a global research organization) for the Institute for Preventive Foot Health, 8 percent of U.S. adults ages 21 and older (about 18 million people) have the condition. Another 4 percent, or about 8 million U.S adults, have fallen arches [11] . There are different types of flat feet, namely, flexible flat foot, short Achilles tendon and posterior tibial tendon dysfunction [12]. Figure 1: Two separate feet, one on the left showing a normal arch and defective foot on the right showing a flat ar ch [33] Among these, posterior tibial tendon dysfunction is acquired in adulthood when the receive the support it needs, one can have pain on the inside of their foot and ankle, as well as on the outside of the ankle [12]. Treatment of these problem s is customized to the individual patient and tailored according to the clinical examination. In general, conservative measures like using simple analge sia, non steroidal anti inflammatories, physiotherapy and orthoses in the shape of a corrective medial arch support

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2 insole with a neutral heel cup for a flexible deformity are suggested as first measures [13]. However, if the recommended trail of conserva tive measures fails over a period of 6 months then the patient should consider surgical options [ 13]. Various factors like the degree of deformity soft tis sues and presence of arthritis need to be considered before selecting the mode of a surgical option. Different techniques include tendon debridement, tendon transfer, tibiotalocalcaneal fusion, cotton medial cuneiform osteotomy [13] , and Evans calcaneal os teotomy, a widespread procedure used in treatment of a flexible calcaneovalgus foot in patients [14]. Evans calcaneal osteotomy is a lateral column lengthening technique that preserves the calcaneocuboid joint. This laterally based opening wedge osteotomy is historically known to achieve transverse plane correction for pes plano valgus deformities (Figure 2). Evans [1] verified that the medial and lateral columns of the foot must be equal in length to maintain the load balance. Evans [1] described that a s ymptomatic flatfoot can be improved in alignment by inserting a wedge of tibial bone into an anterior calcaneal section by creating a wedge opening osteotomy. Long term follow up reports have shown Evans osteotomy process to be highly effective as most of the correction obtained through this process was maintained over time [2]. The osteotomy was however revised by cutting the facets between the anterior and middle part of the calcaneus and then inserting a trapezoid shaped tricortical wedge instead of tibi al bone [3]. However, there are potential problems that can lead to the failure of the osteotomy process. There has been long term follow up reports of deteriorating changes in the

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3 Figure 2: Transverse plane deformity in flat foot [31] Calcaneocub oid joint [2], particularly because there has been reports of increased pressure in the calcaneocuboid joint after the wedge opening surgery [4]. The Evans procedure discovered an increase in the contact pressures across the posterior and anteromedial face ts [5]. The increase in pressure at the joints and facets location can result in long term pain and disability due to rapid arthrosis. Besides this, the osteotomy for the Evans procedure might also violate the anterior or middle calcaneal facet movement. S ome studies have demonstrated failures in 20% of the osteotomy cases, resulting in loss of correction, chronic lateral column pain, and occasionally, even in the failure of the hardware [6, 7]. It is therefore highly imperative to carefully construct the w edge surfaces, with the right choice of graft material that provides tight attachment with the cancellous bone. Also, an H shaped locking plate is used exterior to the lateral opening of the wedge osteotomy to provide more rigid stabilization and avoid dor sal displacement of the graft or dislocation of the anterior section of the calcaneus (Figure 2) [3, 6, 8].

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4 Figure 3: A post operated Evans calcaneal foot with locking plate [32] In recent time, due to advancement in 3D printing technology, one can easily design custom made implants for ankle surgery [9]. Bony defects, and deformities in lower extremity of human body including high risk arthrodesis situations can be difficult to treat and often requires a critical size or shape structural graft which may not be available with allograft bones [9]. Patient specific wedge graft development is thus essential to avoid the problems of misalignment and tractional movement between the articulating surfaces. This will ensure a secure fit between the wedge and surrounding bone area. Also, H plates can be designed to achieve a tight fit respective to the lateral surface of the wedge opening. Appropriate selection of the implant material is a key factor for long term success of implants. It is well known that the stress transfer between an implant device and a bone is not defined as stress shielding. In such cases where an implant shields a bone from stress, bone atrophy occ urs and can lead to the loosening of the implant and refracturing of the bone [10]. Therefore, it is desirable to find the right wedge and locking plate material for the osteotomy

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5 such that the wedge material allows healthy levels of stress to occur in the bone. The different types of biomaterials can be categorized into metals, polymers, composites and ceramics. Due to advancement in material science technology, nowadays almost all orthopedic implants comprise a composition of metals, polymers, and ceramic s. The first corrosion resistant alloy to be proven very effective in surgical implants were Cobalt chromium alloys [27]. Also, stainless steel is a common alloy, which has been very successful as a surgical implant material. Titanium (Ti) alloys are prim arily type Ti 6Al 4V, which contains 6% aluminum, 4% vanadium, and 90% titanium. This metal has become ever more popular in the last decade because of its strength similarity to stainless steel and cobalt chrome however only half as stiff as them. This is one of the significant features of Titanium alloy over the other two, because it would minimize the disparity in elastic modulus between implants and bones and hence prevent stress shielding [27]. Also, polymers like ultra high molecular weight polyethylene (UHMWPE) have low wear characteristic with metals, and hence can be used as bearing surface in implants. Recently, polyether et her ketone, commonly known as PEEK, has utmost achievement in the field of spine implant design with follow up reports from clinical examinations. It has been prevalent as a radiolucent alternative to metallic biomaterials in the spine community [26] (Figu re 4).

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6 Figure 4: L ocking plate made from Titanium (Ti) [28], a posterior dynamic stabilization of the spine using PEEK rods [26], a Ti PEEK implant [29], and wedge implants made from cortical bone [30] The objective of the current study was to compare the effects of four different material compositions in an Evans wedge on the amount of stress generated in regenerating bone as it grows over time in the open spaces. The study began with the development o f a patient specific foot model. The geometric model of the foot bones and joints were augmented with ligaments, and the ligamentous model was compar ed with a previously published research paper on load transfer mechanisms in foot metatarsals [23]. Mesh co nvergence testing was carried out to determine the optimum size of mesh to test the stiffness of different materials composition of Evans wedge as compared to allograft wedge osteotomy. The stress in regenerating bone was computed at multiple time points w ith the simulated wedge composed of cortical bone allograft, PEEK, Ti PEEK combination, and Ti. The hypothesis of this study is that the Ti PEEK implants provides closest stress distribution to a n intact bone.

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7 CHAPTER 2: MATERIALS AND METHODS Geometry and Mesh Construction The geometry of the FE model was obtained from CT scan of a Sawbones foot model (Figure 5). The images were segmented using ScanIP (Simpleware, Synopsys, Mountain View, CA), and a cortex of uniform thickness of 5 mm was created to surround trabecular bone cores. The connections between the cortical cancellous bones were modeled with cartilaginous joints. Linear tetrahedral mesh elements were used to discretize the foot model. The FE foot m odel along with mesh is depicted in Figure 5. The entire foot model is a composition of 26 bones namely, calcaneus, talus, cuboid, navicular, 3 cuneiforms, 5 metatarsals and 14 small bones that e movement because of negligible influence on the stage of forefoot, thus are fused together in the foot model [18]. The full foot model was exported to ABAQUS (Simulia, Dassault Systemes, and Johnston , RI) for FE analysis. 1D non compressible truss elemen ts were added to the model to simulate the ligaments. Ligaments include plantar fascia, the deep and superficial long plantar ligaments (LPL), posterior talus calcaneus ligament, exterior and interosseous ligaments, low calcaneus navicular ligament, superi or, interosseous and external ligaments, joints talus and inter ligaments, cuboid ligament, and calcaneus navicular ligament. Figure 6 shows the connecting locations of these ligaments in the model in ABAQUS. Ligaments are mo deled by using the ABAQUS input file (INP). In the input file, ligaments are defined as an element type of T3D2 and the connecting points of ligaments are modeled with the following syntax: *ELEMENT, TYPE=T3D 2

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8 ( Element number ) , ( node number of the origin ) , ( node number of the insertion). Figure 5: F ull geometric model of the foot and mesh construction Figure 6: C onnecting ligaments in ABAQUS Material Properties Bone s were modeled as homogeneous, elastic and isotropic with cortical bone having a 17 , 000 MPa and 0.3 Poisson ratio , whereas t rabecular bone was assigned a 700 MPa and 0.3 Poisson ratio [15]. Ligaments were modeled with n on compression 1D truss elements and distinguished between two materials: a stiffer one (superficial modulus ratio of 0.4 and cross sectional area of 290.7 mm 2

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9 [16] , a nd a more compliant , and cross section al area of 18.4 mm 2 [16]. 10 MPa and P Figure 5. Loads and Boundary Conditions The loads applied on the foot varies upon the magnitude, direction and areas of application [19]. Thus, the stance phase of foot gait can be divided i nto different stages depending upon the requirement of the study. For example, Gefen et al. [19] proposed to divide it into six phases: initial contact, heel strike, midstance, forefoot contact, push off and toe off. In this study, we only consider the sta nding foot [15, 16, and 20] where the forefoot is totally in contact with the ground. Therefore, we constrain the heel movement by constraining the vertical and horizontal displacement of the node at the calcaneal base. However, only the vertical movement of the five metatarsal heads are constrained. The constrained calcaneus node acts as the reference for the movement of all other nodes in the foot. The scenarios for the loading and boundary conditions were based off of load transfer mechani sm in the foot metatarsals (Figure 7) [2 2 ]. The same loading and boundary conditions were used to obtain computational results on Evans calcaneal o steotomy. A 300 N load was applied on the foot, corresponding to the weight of a person of approximately 60 k g [15], and the site of application of the force is uniformly distributed on the areas in contact with the tibia and the fibula. The load is applied at an angle of 10 degrees with respect to the normal to the ground due to the inclination of the tibia and fibula at this stage of the gait cycle. Moreover, a similar load exists in the opposite direction in the talus due to the action of the tendon . Simkin [21] calculated that this force is approximately half of the force that

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10 applies the b ody on the foot; therefore, in our model, a force of 150 N was uniformly distributed tendon inserts on the calcaneus [22] with a similar inclination of 10 degrees. (See fig. 7) Figure 7: L oading and b oundary condition s in the foot model Literature Comparison Garcia Aznar in 2009 published a study analyzing the load transfer mechanism across the bones of the human foot [23]. The study used a 3D foot model without soft tissues and augmented with several 1D truss elements as ligaments. Our study us ed similar methodologies , material properties, loading and boundary conditions, and we therefore compared our results for maxim um tensi le and compressi ve stre sses were in each of the metatarsals ensure that our model produced realistic results.

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11 The foot model used in our study was also measured anatomically to classify any foot deformities, like how J.M. Garcia classified the models in hi s paper [22] . Mesh Sensitivity Test M esh convergence was tested by calculating the average values of von Mises stress, maximum principal stress and resultant displacement in metatarsal 1 (M1). S can IP was used to vary the element numbers from coarser 694,5 57 to finer number of 2,817,702 elements. Evans Calcaneal Osteotomy Evans calcaneal osteotomy is a surgical technique to treat flat foot deformities. I n this study, we make use of the validated foot model and perform a virtual osteotomy 1.4 cm proximal t o the calcaneocuboid joint with a varying depth of 1.3 cm to 2 cm at bottom and top of Evans wedge respectively (Figure 8 ) .

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12 The Evans wedge was masked in Scan IP with three different layers of mask distinguishing between the two endplate layers and a wedge shaped layer sandwiched in between (Figure 8). The geometry of the tri layer wedge was in accordance with the geometry of the S awbones operative bone growth. T here has been recent development of wedges made of different materials like Ti , polymers and their combinations. Companies like DePuy Synthes, TyberMedical, CONME D, Anthrex, and many mor e now manufacture wedge s composed of a combination of Ti and polymer , with a PEEK body between two Ti alloy endplates [29]. Figure 8: P osition of Evans wedge insertion

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13 Figure 9: Isometric, f ront and s ide view s of Evans wedge (left to right) After the wedge was successfully modeled in S can IP, a n H shaped locking plate was mod eled in Solidworks (Figure 10) and then exported as a .stl file in S can IP. Figure 10: I sometric, top and front view s of the H shaped locking Ti plate designed in Solidworks (left to right) The locking plate wa s exported to S can IP and positioned at the lateral surface of the wedge opening to prevent lateral movement ( F igure 11 ). Due to the dissimilarities in anatomy between the locking plate and bone surface, their attachment is further masked in S can IP to prevent any openings. The implant augmented model is then exported to ABAQUS for ligament modelling at the suggested mesh e lement size of negative 30.

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14 Figure 11: P ositioning of H locking plate in S can IP Evans wedge material properties were varied as follows: Table 1: Material s and mechanical properties used in Evans wedge implant Cortical bone Titanium PEEK Ti PEEK Titanium dnd plates, PEEK wedge

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15 Figure 12: L igament augmented FE Foot model with Evans wedge implant The fully developed FE Evans calcaneal osteotomy model wa s then tested to determine von Mises stress in the region of bone regeneration, and the stress in the regenerating bone was compared with the amount of von M ises stress generated in the same region of interest for an intact foot. Seven time points were used to simulate bone mineralization and subsequent increases in Youn moduli (0.001, 0.1, 0.5, 1, 5, 10, and 17 GPa, respectively) were computed based on a previous study of bone ingrowth into titanium and PEEK materials [24].

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16 CHAPTER 3: RESULTS Liter ature Comparison [22] as discussed by Garcia [23]. Terminology of the classification of Maestro [23]: C1 = Transition distance between M1 and M2 C2 = Transition distance b etween M2 and M3 C3 = Transition distance between M3 and M4 C4 = Transition distance between M4 and M5 SM4 line = line from the center of the lateral sesamoid perpendicular to the axis of the foot. SM4

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17 Figure 13: M categorization [23] M1 M2 M3 M4 M5

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18 Table 2: A natomical measurements of Sa wbones f oot mo del NOMENCLATURE DISTANCE (mm) M1 60.394 M2 84.218 M3 78.123 M4 74.928 M5 71.658 C1 12.102 C2 7.166 C3 14.736 C4 16.358 Angle between 1 st MTP and 2 nd MTP 10.971 degrees Based on these measurements classification [23], the foot model is categorized as a symptomatic 10 degrees foot model, with SM4 line proximal to MT4. It is a harmonious forefoot morphotype which is characterized by a SM4 line passing through the center of the fourth metatarsal head, associated to a geometrical progression of a factor 2 of the lesser metatarsals. Thus, it resembles to a foot model s omewhere between symptomatic 12 deg (S12) and symptomatic 8 deg (S8) model as described by Garcia [22]. The maximum compressive and tensile principal stresses in the metatarsals in our model are provided in Table 3, and the corresponding values from Garcia Table4.

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19 Table 3: M aximum principal stress values in all the metatarsals for different mesh sizes in Sawbones foot model Model Max Principal Stress values in Metatarsals (MPa) Displacement (mm) Vertical Horizontal 1st 2nd 3rd 4th 5th Min Max Min Max Neg mesh 50 Tension 12.3027 5.4368 5.87122 6.4115 4.61863 0.2565 0.0277 0.187 0.0085773 Compression 3.76683 1.99397 2.43 3.6204 1.0589 Neg mesh 30 Tension 10.6854 10.1801 5.61 5.48213 6.32244 0.1654 0.01728 0.122 0.000896 Compression 1.3011 2.01205 1.43743 0.842704 1.01876 Neg mesh 25 Tension 17.2566 15.9758 10.9151 7.98025 6.41636 0.1408 0.01413 0.09 9.541E 05 Compression 1.73237 1.63966 0.127872 1.16971 0.939581 Neg mesh 20 Tension 30.0748 15.2642 9.93443 8.91096 10.1187 0.1517 0.02048 0.123 0.0002694 Compression 1.59484 1.62983 1.02747 1.84171 1.67741 Neg mesh 15 Tension 13.2929 34.4813 18.9735 9.98577 5.56566 0.1151 0.0227 0.102 0.0001692 Compression 2.82036 2.65058 2.34517 1.59632 0.787549 Table 4: Maxim um tensile and compressive stresses (MPa) in each metatarsal for the different analyzed condition by Garcia [22] Unit: MPa M1 M2 M3 M4 M5 Initial Case (IC) Maximal tension stress Maximal Compression Stress 5.7 10 4.3 11.6 4.9 11.7 5.3 10.0 4.2 9.0 Parabola of Maestro et. Al. [23] (MP8) Maximal Tension stress Maximal compression stress 4.5 9.5 4.6 11 5.3 11 4.9 9 4.3 10 Symptomatic Maximal Tension Stress 3.8 5.3 5.6 5.0 4.8 (12 deg) Maximal Compression Stress 8.5 11.7 11.4 10.5 12.5 (S12) Symptomatic Maximal Tension stress 4.0 4.7 5.0 4.8 4.4 (8deg) (S8) Maximal Compression stress 9.2 10.5 11.2 9.1 11 Peak stress magnitudes in our model ranged from 0.1 to 34.5 MPa, while the stress magnitudes obtained by Garcia ranged from 3.8 to 12.5 MPa. Thus, our model had a wider act that our

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20 model was based on a different foot anatomy and given the unavoidable differences in points of load application and ligament attachment locations, the stress levels in our model appear to be reasonable in comparison with those found by Garcia. Mesh Sensitivity Analysis Computational results obtained from the mesh convergence test are provided in Table 5 and Figure 14. Table 5: Variation in stress values calculated with different mesh sizes Unit: MPa Properties Calculated No. Of elements in the mesh Avg. Von Misses Stress Max. Principal Stress Resultant Displacement (mm) 694557 1.1047531 0.423155 0.17304983 1.069,251 0.45892084 0.15000945 0.055755291 1,308,795 0.48702907 0.22052226 0.077199021 1,847, 713 0.46265142 0.18576198 0.083124595 2,817,702 0.45834972 0.18101422 0.065516558 Figure 14: Mesh convergence results Max. Principal Stress Range of Values

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21 The graph above clearly shows that after mesh element size of negative 30, there is minimal difference in the calculated values. The mesh size of 30 yields 1 , 069,251 tetrahedral elements in total. This is the threshold element numbers for meshing, at which the values are converged. Therefore, all models used in the study were meshed at a setting of 30. Evans Calcaneal Osteotomy Co mparative Study The time dependent variation of bone mineral density and in the regenerating bone is shown in Figure 15 . Figure 15: Variation of bone Young's modulus with increasing bone mineral density 0.001 0.1 BMD (mg/cc) Bone Layer Age (days)

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22 The variation in average von M ises stress in the cortical and cancellous region s of a normal foot is compared with the average von Mises stress in regenerating bone region for different Evans graft material s in F igure 16. Figure 16: V ariation of average von Mises stress generated in regenerating bones using different Evans wedge material s PEEK Evans wedge Model Ti PEEK Wedge Model Cortical bone Stress in Normal intact foot at the wedge location Cancellous bone Stress in Normal intact foot at the wedge location Average Von Misses Stress in Regenerating Bones (MPa)

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23 CHAPTER 4: DISCUSSION The objective of this study was to investigate the effects of different types of implant materials on the regenerating bone in an Evans wedge. This study also focus ed on development of a new FE model of the human foot using an optimized mesh element size to improve accuracy in results and optimum utilization of processing memory simultaneously, also defined as mesh sensitivity. According to FEA theory, FE model s with fine mesh (small element size) yield highly accurate results but take longer computing time and memory space. On the contrary, those FE models with coarse mesh (large mesh size) may lead to less accurate results but do save significant computing time [25]. The mesh sensitivity test for our foot model found that an average mesh element size of 1.25 mm with 214,589 nodes and 1,069,251 elements is enough to provide accurate results in FEA, beyond which there is minimal changes to the properties calculated. The st resses in our foot model had magnitudes like those found in a previous study by Garcia [22]. The foot model was also maximum tensile and compressiv e stress on all the five metatarsals in different categories of foot. study found the overall highest tensile and compressive stress on the third metatarsal. In our study , the high est tensile stress occurs in the first metatarsal. The FE foot mode l inevitably includes stress risers like notch es and corners in the foot model, which may explain the higher maximum stresses found in our model. Given the differences in anatomical geometry and overall modeling techniques between our our model provides reasonable, realistic results . The Evans c alcaneal o steotomy simulations w ere performed assuming that regenerating

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24 bone tissue mineralizes within the Evans graft gradually with time . It was found that implants made from Ti alone produced t he lowest von Mises stress values in the regenerating bone at all time points. The i mplant made from PEEK substantially increased the von Mises stress values in the newly formed bone. A previous load sharing study in our laboratory s howed that, when bone grows into a porous PEEK implant , bone bears majority of the load (66.5%) at the onset of mineralization along the implant surface at 4 we eks as compared to Ti implants that allow only 12.7% of the total load transferred to the bone under compression [24]. The current study showed that composite implants with Ti endplates and a PEEK wedge allow higher stress distribution in the regenerated b one , but stresses in these implants do not reach levels seen in wedges made of PEEK alone. The stress level s in the cort ical and trabecular region s of the calcaneus of the intact foot model can be compared with the Evans wedge models to help determine whet her different implants may be more conducive to healthy bone formation . The average von Mises stress at the osteotomy location in the intact foot was 0.2 MPa in the cancellous bone and 0.5 MPa in the cortex (Figure 16). This magnitude of stress wa s acquir ed in the regenerating bone in the Evans wedge model when bone reache d a modulus of 5 GPa. Our model suggests that i t takes 24 days for the b one mineral to accumulate and stiffen the tissue to this level . At this point of time, the Evans graft made from cortical bone produce d stress 7% higher than in the intact bone. The Ti PEEK implant produce d an average stress 17 % lower than the intact bone at this same time point . The Ti implant , the stiffest material tested in our study, produced a stress magnitude lower by 47 % . This large difference suggests that the degree of stress shielding in this implant may be high enough to preclude maintenance of healthy bone tissue, as previous s tudies on stress transfer between an implant device and bone have demonstrated that stress shielding

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25 is too high [34]. The PEEK wedge on the other hand produced an ave rage stress 3 6 % higher than in the intact bone . Note that, after 41 days bone mineralizes to achieve a modular strength of 10 GPa where Ti implants show closest stress distribution to cancellous bone stress by 16% lower value from a normal bone. However, get that stiffer. But, provided with consistent physiotherapies for a prolonged period can induce more mineralization and increase bone modular strength at least to the strength of 5 GPa. The underlying idea in Ti PEEK wedge design is that the Ti surface provides better ad hesion to surrounding bone tissue while providing stress shielding environment more like that obtained by using a PEEK wedge. Our study suggests that a Ti PEEK wedge does inde ed lead to stress levels more like that in intact bone at the 24 th day time point , as compared to wedges made of Ti or PEEK alone . One of the shortcomings of this study is that, the foot model does not include all the tendons, muscles and soft tissues pres ent in a normal, intact foot. However, this study is focused on comparing different materials used in the field of implant development. Since the exact same model was used while only varying the implant material, we can be confident that including addition al anatomic details (tendons, etc.) would not change the overall conclusions of the study. Also, the design of the Evans wedge in this study was based directly on How ever, the differences in stress levels seen using different materials in this study should still apply to wedges with other geometric designs. Furthermore, this study can be used as a reference for experimental setups that can simulate the stress requireme nt for bone remodeling after a surgery. A range of bone material properties were tested to simulate time dependent bone mineralization, the amount of stress generated in the masked region of interest at every stage is hypothetically the minimum amount of s tress required for bone remodeling.

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26 CHAPTER 5: CONCLUSION Flat foot is a common problem where a foot osteotomy is a lateral column lengthening procedure that achieves transverse plane correction for pes plano valgus deformities. The influence of the Evans wedge material composition on bone remodeling in the hollow space of the wedge is still a question of significant importance. Finite element (FE) analysis was performed to understand the nature of mechanical stress distribution from the initial stage of in vivo bone regeneration to fully developed cortical bone within the Evans wedge made from different materials. It took 24 days for the regenerating bone within the Ti PEEK Evans wedge graft to acquire the modulus of 5 GPa that yielded stress distribution lower in magnitude than normal cancellous bone by 17 %. At this same time point, the Evans wedge made from cortical bone approximated the stress level of the intact calcaneou s with a stress only 7 %, higher in magnitude than the normal bone. Thus, the hypothesis that Ti PEEK implants are reported to have minimum difference to the cancellous stress in an intact foot bones.

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27 REFERENCES [1] Evans D. Calcaneo valgus deformity. J Bone Joint Surg 1975; 57B:270 8 [2] Philips GE. A review of elongation of os calcis for flat feet. J Bone Joint Surg 1983;65B:15 8 [3] Mosca VS. Calcaneal lengthening f or valgus deformity of the hindfoot. J Bone Joint Surg 1995;77A:500 12 [4] Cooper PS, Nowak MD, Shaer J. Calcaneocuboid Joint pressures with lateral column lengthening (Evans) procedure. Foot Ankle Int 1997 ; 18 (4):199 204. [5] Sarrafin SK. Anatomy of the foot and ankle: descriptive, topographic, functional, Philadelphia: J.B. Lipincott; 1983. [6] Thomas RL, Wells BC, Garrison RL, et al. Preliminary results comparing two methods of lateral column lengthening. Foot Ankle Int 2001; 22:107 19 [7] Toolan BC, Sangeorzan BJ, Hansen S. Complex reconstruction for the treatment of dorsolateral peritalar subluxation of the foot. J Bone Joint Surg 1999;81A:1545 60 [8] Dalton GP, Wapner KL, Hecht PJ. Complications of Achilies and posterior tibial tendon surgeries. Clin Orthop 2001; 391:133 9. [9] of orthobiologi cs in foot and ankle 280. 10.1302/2058 5241.2.160044. [10] rigidity titanium allo y: plate fixation of Journal of Materials Science, vol. 149, no. 4, pp. 1581 1586, 2008. [11] Foot Conditions: Flat Feet. Available at https://www.ipfh.org/foot conditions/foot conditions a z/flat feet . Accessed August 2018. [12] What causes Flat Foot? Posterior Tibial Tendon Dysfunction. Available at https:// www.healthline.com/symptom/flat foot. Accessed July 2018. [13] C.J. Lever, M.S. Hennessy. Adult flat foot deformity. Orthop. Trauma, 30 (2016), pp. 41 50 [14] Dayton, P, Prins, DB, Smith, DE, Feilmeier, MJ. Effectiveness of a locking plate in pr eserving midcalcaneal length and positional outcome after Evans calcaneal osteotomy: a retrospective pilot study. J Foot Ankle Surg. 2013; 52(6):710 713. [15] Gomez Benito, M. J., Fornells, P., García Aznar, J. M., Seral, B., Seral Innigo, F., and 25 , pp. 191 200.

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28 [16] Cheung, J. T., Zhang, M., Leung, A. Dimensional Finite Element Analysis of t he Foot During Standing A Material Sensitivity J. Biomech., 38 , pp. 1045 1054. [17] Gefen, A., Analysis of the Standing Foot Following Surgical Plantar Fascia 35 , pp. 629 637 [18] 19 Scott, S. H., and Winter, D. A., of the Human Foot: Kinemetics 1091 1104. [19] Gefen, A., Megido Ravid, M., Itzchak, Y., and Arcan, M., 2000, of the Three Dimensional Foot Structure during Gait: A Basic Tool for Clinical Applica ASME J. Biomech. Eng., 122 , pp. 630 639 [20] Scott, S. H., and Winter, D. A., 1993, Model of the Human Foot: Kinemetics and Kinetics During the Stance Phase of 26 , pp. 1091 1104. [21] Simkin, A., 1982, Analysis of the Human Foot in Standing Ph.D. thesis, Tel Aviv University, Tel Aviv, Israel [22] García Aznar JM, Bayod JJ, Rosas AA, et al. Load Transfer Mechanism for Different Metatarsal Geometries: A Finite Element Study. ASME. J Biomech Eng. 2008 ; 131 (2):021011 021011 7. doi:10.1115/1.3005174 [23] Maestro, M., Besse, J. L., Study and Planning Method for Forefoot Ankle Clinics, 8(4), pp. 695 710 [24] Carpenter, R & Klosterhoff, Brett & Brennan Torstrick, F & T Foley, Kevin & Burkus, John & S D Lee, of porous orthopaedic implant material and structure on load sharing with simulated bone of the mecha nical behavior of biomedical materials. 80. 68 76. 10.1016/j.jmbbm.2018.01.017 [25] Liu, Yucheng. (2013). Effects of Mesh Density on Finite Element Analysis. SAE Technical Papers. 2. 10.4271/2013 01 1375. [26] trauma, orthopedic, and spinal Biomaterials vol. 28 , 32 (2007): 4845 69. [27] Dominique G. Poitout, 2004. Biomechanics and Biomaterials in Orthopedics. Springer, London. DOI 10.1007/978 1 4471 3774 0 [28] Depuy Synthes: Products. Available at https://www.depuysynthes.com/hcp/trauma/products/qs/Small Fragment LCP#tab2 . AccessedJanuary2019 [29] Tyber Medical: Tywedge System. Available at http://tybermedical.com/products/tywedge system/. Accessed January 2019 [30] Wright: Allopure Allograft Bone Wedges. Available at http://www.wright.com/footandankleproducts/allopure allograft bone wedges. AccessedJanuary20 19.

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29 [31] Medical Case Histories and Treatment: Transverse Plane View. Available at http://medicalcasehistories.blogspot.com/2012/11/hypermobile versus rigid pathomechanics.html . Accessed January 2019. [32] TriMed: Evans Osteotomy Plate. Available at https://trimedortho.com/product stm detail/evans osteotomy plate. Accessed January 2019. [33] Mayo Clinic: Flatfeet. Available at https://www.mayoclinic.org/diseases conditions/flatfeet/symptoms causes/syc 20372604. Accessed February 2019. [34] on fracture fixation with low rigidity titanium alloy: plate fixation of tibia fracture model of Materials Science, vol. 19, no. 4, pp. 1581 1586, 2008.