finite element analysis of osseointegrated transfemoral...

IN DEGREE PROJECT MEDICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2018

Finite Element Analysis of Osseointegrated Transfemoral Implant

Indentification of how the Length of Implant Affects the Stress Distribution in Cortical Bone and Implant

ANNA POGOSIAN

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES IN CHEMISTRY, BIOTECHNOLOGY AND HEALTH

Finite Element Analysis ofOsseointegratedTransfemoral ImplantIndentification of how the Length of Implant Affectsthe Stress Distribution in Cortical Bone and Implant

Finita element analys avosseointegrerat transfemoraltimplantatIdentifiering av hur längden på implantat påverkarspänningsfördelningen i det kortikala benet ochimplantatet

ANNA POGOSIAN

Master in Biomedical EngineeringDate: October 31, 2018Supervisor: Madelen FahlstedtExaminer: Svein KleivenSchool of Engineering Sciences in Chemistry, Biotechnology andHealth

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Abstract

An alternative method of conventional prosthesis is osseointegratedtransfemoral implant, in where the prosthesis is fixated directly to thebone. The benefits with this system is increased range of motion, sen-sory feedback and reduced soft tissue problem. One of the drawbacksof this method is the effect of stress shielding, which could in longterm lead to bone loss and bone resorption. The aim of this studyis to investigate how the length of the fixture (60, 80 and 100 mm)of OPRA system (Osseointegrated Prosthesis for the Rehabilitation ofAmputees) affects the stress distribution in femoral bone and implantduring short walk by using Finite Element Methods.

The finite element model used in this study was constructed of threemajor parts: THUMS model (Total Human Model of Safety) of leftthigh, implant and bone graft. The analysis was performed throughthe software LS-DYNA, with an implicit solver. The loading of the to-tal gait cycle was applied in the distal end of the implant, whereas theproximal end of the thigh was fixed.

The FE simulation revealed lower stress distribution in the distal endof femoral bone, and higher in the proximal end. Implant 60 had low-est effect of stress shielding. The highest stress distribution in OPRAimplant was shown in the abutment shaft, in the interface with bonegraft. The length of the fixture did not have any impact on the stressdistribution in the implant.

Keywords: Osseointegrated, Implant, Transfemoral, Finite ElementMethods

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Sammanfattning

En alternativ metod för konventionell protes är osseointegrerad trans-femorala implantat, där protesen är direkt skelettfixerad. Fördelarnamed denna system är ökad rörelseomfång, sensorisk feedback och re-ducerad mjukvävnads problem. En av nackdelarna med denna metodär effekten av stress shielding, vilket kan på lång sikt leda till förlustav ben och benresorption. Syftet med denna studie är att undersökahur längden av fixturen (60, 80 och 100 mm) av OPRA syststemet (Os-seointegrated Prosthesis for the Rehabilitation of Amputees) påverkarspänningsfördelningen i lårbenet och implantatet.

Finita element modellen bestod av tre huvuddelar: THUMS-modell(Total Human Model of Safety) av vänstra benet, implant och ben-transplantat. Analysen utfördes genom mjukvaran LS-DYNA, med enimplicit lösare. Den distala delen av implantatet belastades med kraf-ter från normal gång, medan den proximala änden av låret fixerades.

FE-simuleringen påvisade lägre spänningsfördelning i distal änden avlårbenet och högre i proximal änden. Implantat 60 hade lägst effekt avstress shielding. Den högsta spänningsfördelningen i OPRA implan-tan var i abutment, vid gränssnittet med bentransplantat. Fixturenslängd hade ingen inverkan på spänningsfördelningen i implantatet.

Nyckelord: Osseointegrerad, Implantat, Transfemoral, Finita ElementMetoden

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Acknowledgements

First of all, I would like to thank my supervisor at KTH, MadelenFahlsted. Thank you for guiding and supporting me through out theproject. This project would be hard to complete without your encour-agements and ideas. I would also like to thank Yan Li, Li Felländer-Tsai, Hans Berg, and Rickard Brånemark for giving me the opportunityto be part of this project. Finally I would like to thank my beloved fam-ily who have always been there for me. You have always motivated meto work harder and never give up.

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Terminology

Gait - WalkTransfemoral - Across or through the femurTranstibial Across or through the tibiaAnisotropic - Different properties in different directions (x, y, z)Isotropic - The same properties in all directions (x, y, z)Viscoelasticity - The material behaves both viscous and elastic whenit is deformedYoung’s modulus - Material resistance of elastic deformation underloading

Abbrevation

OI - OsseointegrationROM - Range of MotionOPRA - Osseointegrated Prosthesis for the Rehabilitation of AmputeesFEM - Finite Element MethodFEA - Finite Element Analysis

Directional References

Figure 1: Anatomical directions [1]

Contents

1 Introduction 11.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Methods 32.1 Finite Element Modelling . . . . . . . . . . . . . . . . . . 3

2.1.1 Bone . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 Implant . . . . . . . . . . . . . . . . . . . . . . . . 52.1.3 Implant fixation in Femur . . . . . . . . . . . . . . 6

2.2 Material Properties . . . . . . . . . . . . . . . . . . . . . . 72.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 92.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Results 133.1 Cortical Bone . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Discussion 174.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Conclusions 21

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Chapter 1

Introduction

Losing a limb due to amputation is an economic, social and physiolog-ical consequence for the patient [2]. The physiological consequences isnot only because of the loss of a limb, but also because of the need toadapt to a limited lifestyle [3]. The conventional prosthesis used af-ter an amputation consist of a stump-fitting socket, where the limb isfixed into [4, 5]. However, patients using socket prosthesis often ex-perience pain, sores, rashes, etc. It is also perceived difficult to controlthe prosthetic limb because the whole-body weight is supported bysoft tissue. Patients with short residual limb, scars, or damaged tissueare not suitable for prosthetic sockets [6].

A solution to these problems is to use direct skeletal fixation throughosseointegrated transfemoral implant, where a direct bond betweenthe bone and implant is formed [7] (Figure 1.1). The benefits with thissystem is increased range of motion, sensory feedback, and reducingsoft tissue problem [4]. However, the drawbacks of bone anchoredprosthesis are the risks of fracture of the implant or the bone [4]. Thereis also a risk of infection, especially in the area where the implant pen-etrates through the skin [5]. Another major problem with osseoin-tegrated implants is the effect of stress shielding of the bone, whichcauses thinner and more porous bone [8]. Stress shielding happenswhen there is a reduced loading on the bone because of load absorp-tion by the implant. Previous studies have shown high level of stressshielding in the distal part of femur, and bone growth in the proximalpart [9, 10, 11].

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2 CHAPTER 1. INTRODUCTION

Figure 1.1: Osseointegrated transfemoral implant [12] (Image courtesy ofIntegrum AB).

The Swedish company Integrum AB manufactures this type of im-plants called Osseointegrated Prothesis for the Rehabilitation of Am-putees (OPRA) implant system [7]. OPRA consist of three major parts:fixture, abutment and abutment screw. The standard length of the fix-ture is 80 mm for transfemoral prosthesis, whereas the diameter is acustom-fit property, and is between 16-20 mm.

Bone anchored prosthesis are today not the primary choice of trans-femoral treatment, thus only patients with major difficulties with socketprosthesis are target group [4]. By reducing the issues more patientscould benefit of osseointegrated fixation.

1.1 Objective

The objective of this project is to determine how the length of the fix-ture affects the stress distribution in femur and implant, during a dy-namic motion. This will be done by performing finite element analysisof femur and implant, each with different length of the fixture. A moreoptimal length of the implant may reduce the effect of stress shielding.

Chapter 2

Methods

A literature study was performed in order to get deeper understand-ing about the characteristics of bone, osseointegrated implants andwhat previous finite element analysis that have been performed onosseointegrated implants (see Appendix).

2.1 Finite Element Modelling

The FE model used for the analysis was constructed of three majorparts thigh, implant (abutment and fixture) and bone graft. The FEanalysis was performed through the software LS-DYNA (LSTC, Liver-more, US) revision 9.1, with an implicit solver.

2.1.1 Bone

The FE model of the thigh used for the analysis were the Total HumanModel of Safety (THUMS), Academic version 4.02, developed by Toy-ota Motor Corporation and Toyota Center R&D in 2015 and modifiedby previous studies [13, 14, 15]. The model was created based on highresolution CT scan, and is based on an average adult male, with theheight of 175 cm and weight of 77 kg [16]. The full THUMS model ofleft thigh was used for the FE analysis, but only the stress distributionin the cortical bone was analysed in this study (Figure 2.1).

The FE model of femur was constructed of two parts: cortical boneand trabecular bone. The cortical bone was made of hexahedron el-ements, whereas the trabecular bone was made of tetrahedrons. The

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4 CHAPTER 2. METHODS

element size was 3 to 5 mm. The trabecular bone was modelled as acombined part with the yellow marrow. Thus the length of the trabec-ular bone in the FE model depends on the length of the implant. Theshorter the implant is, the longer the trabecular bone will be.

The THUMS model was first uniformly rescaled with +1.05, so that thesurfaces of implant and bone would not overlap each other. The cho-sen amputation length of the FE model of thigh was based on CT im-ages of a patient with the amputation length of 230 mm (from femoralhead to the distal shaft of femur), fixated with OPRA implant. The CTimages were provided by Yan Li (Surgeon at Karolinska UniversityHospital Huddinge, from the Division of Orthopedics and Biotech-nology). The length of the bone was measured through the softwareSECTRA. All modifications on THUMS model of left thigh were per-formed through the software HyperMesh 13.0 (Altair, Michigan, US).Other modifications of the model have been performed, in order to fitfrom an explicit model to an implicit model (see section 2.2).

Figure 2.1: A1) Full THUMS (posterior view). A2) Full THUMS (isometricview). B1) Amputated thigh (posterior view). B2) Amputated Thigh (isomet-ric view).

CHAPTER 2. METHODS 5

2.1.2 Implant

A 3D CAD model of the OPRA implant was obtained from IntegrumAB. The fixture and the abutment was modelled as one solid unit andthe threaded region of the fixture was already removed. The abutmentscrew was not included in the model.

The geometry of the implant was simplified by removing all the round-ing of the structure, in order to facilitate the meshing. This was donein Solid Edge ST9 (Siemens PLM Software, Munich, Germany). Thediameter of the abutment shaft was 12 mm and the total length of theabutment was 56 mm. The diameter of the fixture was 16 mm, whereasthe three lengths of the fixture were 60, 80 (standard length of OPRAtransfemoral implant) and 100 mm.

To eliminate the potential influences of mesh sizes on the results, thesame mesh was used in all three models. The longest implant wasmeshed with mixed element type (hexahedron and tetrahedron), withan element target size 2.7 mm. The meshing was done in Altair Hy-permesh. By removing elements at the proximal end of the fixture themesh could be used for the other two implants as well (Figure 2.2).The total number of elements for the three implants was 1032, 1184and 1336 elements respectively for the 60, 80 and 100 mm implants.

Figure 2.2: The cross section of the FE model in frontal view (brown=corticalbone; red=trabecular bone; blue= implant; pink=bone graft). The arrows in-dicated the different lengths of the fixture.


2.1.3 Implant fixation in Femur

The implant was placed in medular cavity of the femoral bone so thatthe surfaces of bone and implant did not overlap each other (Figure2.3 image c ), with about 20 mm embedment. A bone graft was thencreated between the cortical bone and implant at the distal end of thecortical bone. The mesh of bone graft was tetrahedon with the elementtarget size 3.2 mm. The total number of elements of bone graft was282 elements. The full model of was placed so that the distal end ofabutment head was parallel to the x-y plane. The contact betweenthe femoral bone and implant, bone graft and implant, bone graft andcortical bone was set to TIED_SURFACE_TO_SURFACE_OFFSET inorder to represent osseointegration.

Figure 2.3: Image a) shows the satisfactory position according to IntegrumAB. However, in this study the implant have been places according to imagec) with a smaller fixture diameter so there are no overlaps between implantand cortical bone (Imgage courtesy Integrum AB).


2.2 Material Properties

In this study it was assumed that the patient has been directly fittedwith bone anchored prosthesis after a trauma accident. Hence, the ma-terial properties of the thigh model did not depend on level of activityand the time between the amputation and implementation of the im-plant. The material properties of the left thigh could therefore be takenfrom THUMS model. However, in this study there have been severalmodifications of the material models, in order to fit the model from anexplicit model to an implicit (Table 2.1). The bone graft is of trabecularbone, and is often taken from iliac crest (hipbone) [7]. Thus the mate-rial properties was taken from THUMS model for trabecular bone fromhipbone. OPRA implant is made of titanium alloy Ti-6Al-4V (grade 5)and is modelled as homogeneous isotropic elastic material [17].

The lower part of the thigh was made of three parts of flesh tissues,surrounded by fat tissue. In the original THUMS model the three fleshtissues shared nodes in the proximal and distal ends. However af-ter eliminating elements (amputation), the three flesh tissues were notconnected to each other at the distal end. Therefore, in order to havea controlled movement the material properties of the fat tissue andthe lowest row of flesh tissue (blue part Figure 2.4) were changed tothe material properties of skin, with the material model ELASTIC. Allparts with the material models PIECEWISE_LINEAR_PLASTICITY andMAT_DAMAGE_2 from THUMS model were changed to ELASTIC inorder to improve the convergence, and reduce the simulation time.


Part Material Model Young’s Modulus Poisson’s Ratio DensityCorticalBone

Elastic 17.4 GPa 0.3 2 g/cm3

TrabecularBone

Elastic 40 MPa 0.45 0.862g/cm3

Bone Graft Elastic 1 GPa 0.45 0.862g/cm3

Ti-6Al-4V(grade 5)

Elastic 113.8 GPa 0.342 4.43g/cm3

Table 2.1: Material properties of the FE model.

Figure 2.4: Image A) is of left thigh with skin tissue (pink and blue) sur-rounding the flesh tissues. Image B) is of left thigh without the skin.


2.3 Boundary Conditions

In order to achieve realistic boundary conditions the FE model con-tained full THUMS model of the left leg. The other parts besides fe-mur, e.g. hipbone, muscle, cartilage, thigh flesh, fat, ligament etc., wasused to control the movement of the femoral bone, and to create morerealistic rotational movement in the interface between the bone headand hipbone. The full THUMS model was fixated at the proximal endin all direction (Figure 2.5).

Figure 2.5: THUMS model of left thigh with implant fixated in femur. Theproximal part of the model is fixed in all directions (black markers).


The loads applied on the implant were of normal self-sett gait cycle,taken from a previous study [18]. The participant of the study was a 41year old male patient using OPRA implant, with the wight of 96.55kg.The implant was connected to two types of prosthesis (mechanical andmicroprocessor-controlled). The forces and moments of different dy-namic motions (incline ascent and descent; stair ascent and descent;walking in long and short walkway) were recorded directly for eachprosthesis, by using multi-axial transducers connected. However, onlythe loading case of microprocessor-controlled prosthesis during shortwalkway (5 m) was used for this analysis (Figure 2.6 and Figure 2.7).The stride time of the gait cycle was 1.07 s [19].

Figure 2.6: Loads applied to the distal part of the implant in x, y, z direction.The stride time of the gait cycle is 1.07 s. Mean Toe-off at 62 % of gait cycle.

Figure 2.7: Loads applied to distal end of abutment. Fx is in posterior direc-tion, Fy in lateral direction and Fz in superior direction.


2.4 Data Analysis

In this study only the stress distribution of cortical bone and implanthas been analysed, by comparing the results of the three implants (60,80, and 100 mm).

The cortical bone was divided into ten sections (Figure 2.8 A). TheVon Mises stress of each section was analysed seperatly for all threeimplants. Implant 60 ends in section 4, implant 80 ends in section 5and implant 100 ends in section 6.

The three implants were divided into three parts: fixture, abutmentshaft and abutment head (Figure 2.8 B).

Figure 2.8: A) Cortical bone divided into ten sections in posterior view. B)Implant divided into three parts: fixture, abutment shaft and abutment head.This figure is of 100 mm implant in frontal view.

Chapter 3

Results

In this chapter the results will be presented of Von Mises stress in cor-tical bone and implant.

3.1 Cortical Bone

The simulation revealed higher stress distribution in proximal end ofcortical bone than at the distal end for all three implants (Figure 3.1).The highest stress value were found in femoral neck, close to lessertrochanter.

Figure 3.1: The stress distribution of cortical bone at 0.50 s of the gait cycle.The fringe levels are in MPa.

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14 CHAPTER 3. RESULTS

The simulation demonstrates that implant 60 has higher stress valuesat the distal end (section 1 to 5) than implant 80 and 100 (Figure 3.2and Figure 3.3). Implant 80 has lower stress distribution than implant60 and larger than implant 100 at section 3 to 5. Implant 100 has thelowest stress distribution at the distal end, compared to the other twoimplants. Implant 60 (ends in section 4), has the highest stress value insection 4 compared to the other two implants. Implant 80 (ends in sec-tion 5) gets equal stress value at section 5 as implant 60, while implant100 is still the lowest. Finally at section 6, where implant 100 ends,all three implants get equal stress distribution. At the proximal end ofcortical bone (section 6 to 10), the stress distribution in cortical bone isalmost identical for all three implants.

Figure 3.2: The maximum stress values of Von Mises stress for the threeimplant in section 1 to 10.

CHAPTER 3. RESULTS 15

Figure 3.3: The maximum stress values of Von Mises stress for the threeimplant in section 1 to 10.

16 CHAPTER 3. RESULTS

3.2 Implant

The simulation demonstrated highest Von Mises stress at the abutmentshaft, at the interface with bone graft, for all three implants (Figure 3.4and 3.5). The stress distribution of the the total gait cycle is almostidentical for all three implants.

Figure 3.4: The Von Mises stress distribution the three implants at time 0.50sof the gait cycle. The fringe levels are in MPa.

Figure 3.5: The Von Mises stress distribution of fixture, abutment shaft andabutment head, of the three implants.

Chapter 4

Discussion

In this study a finite element analysis was performed in order to com-pare how the length of the fixture (60, 80 and 100 mm) of OPRA im-plant influence on the stress distribution on cortical bone and implant.The FE analysis demonstrates a difference in the maximum Von Misesstress in all ten sections of cortical bone, for the three implants. Thehighest stress value were found in femoral neck, close to lesser troch-anter and the lowest in the distal end at the interface with bone graft.Thus the result agrees with previous studies about uneven stress dis-tribution in cortical bone due to stress shielding [4, 11, 20, 21]. Themaximum Von Mises stress was 82 MPa which is less than the failurestress of cortical bone, about 131 MPa [22].

The results showed that in some sections, the three implants had iden-tical stress values, whiles in others it varied. This could be because theimplants end at different sections in the cortical bone. The longer theimplant, the greater part of the cortical bone is exposed to stress shield-ing, which means a lower stress distribution on that part. Accordingto Figure 3.3 it can be seen that implant 60, which ends at section 4,has the highest stress values of all three implants. Implant 80 (ends insection 5) gets equal stress values at section 5 as implant 60, while im-plant 100 is still the lowest. And finally at section 6 all three implantsget equal stress where implant 100 ends.

Previous studies have shown that high stress distribution occurs atthe proximal part of femoral shaft, the place where the implant ended[11, 20]. However, the results obtained from this study does not agree

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18 CHAPTER 4. DISCUSSION

with this. One of the reasons could be because the loads applied in thisstudy were lower than the previous studies, since no moment load wasapplied in this study. Another reason could be that the boundary con-ditions in this study differ from previous studies (see appendix TableC2). In order to achieve realistic boundary conditions the FE modelin this study contained full THUMS model of the left thigh. The sur-rounding tissues around cortical bone was used to fixate the corticalbone and create more realistic rotational movement in the interfacebetween the bone head and hipbone. Non of the previous studies in-cluded the surrounding tissues around the cortical bone. In all ninestudies, the FE model was either fixed at the distal end of implant orproximal end of cortical bone. The disadvantage of fixating directlyto the cortical bone is that it arises a high stress concentration in thefixation point. Thus the femoral head was not analysed due to the un-realistic high stress concentration [4, 20].

The simulations revealed more even stress distribution in cortical bonefor implant 60, compared to the other two implant. Implant 60 hashigher stress values in the distal end. This implies the effect of stressshielding (bone loss) is lower in the distal end of cortical bone whenusing a shorter implant compared to the standard length (80 mm). Thestress distribution at the proximal end of the femoral bone is almostidentical for the three implants. The results also demonstrate that thelength of the fixture does not affect the stress distribution on the totalimplant.

The FE model contains several simplifications which could have aninfluence on the results. One of the shortcomings of this study is thatno moment load was applied to the abutment in x, y and z direction,due to limitations of the implicit solver. This implies that the load ap-plied in this study is lower than for a normal gait, of an OI patient. Themaximum moment load for short walk of an OI patient is in x direction13 Nm, y direction 16 Nm and in z direction 3.3 Nm [18]. However,the moments are lower in relation to the forces, and should thereforehave low impact on the stress distribution.

The material properties of THUMS model represents an average adultindividual, which means that it can not be used to predict behavior ofa specific amputated patient. The bone quality changes over time after

CHAPTER 4. DISCUSSION 19

an amputation. The less the bone is loaded the more bone resorption[23]. Long rehabilitation time (about 18 months) leads to unloadedbone and could lead to softer bone due to bone resorption [4], hencethe material properties would not match the material properties fromTHUMS model. Another limitation of the THUMS model is that theyellow marrow and trabecular bone is modeled as a combined part.This means that the material properties of trabecular bone is an av-erage value of both parts, and is therefore much lower than for justtrabecular bone [24, 25].

Another shortcoming of this study is that the implant is not ideal placedaccording to the criterion set by Integrum AB [26] (Figure 2.3). The im-plant should be in direct contact with cortical bone so that osseointe-gration can be formed. The diameter of the fixture (a custom-fit prop-erty based on the dimensions of the cortical bone) should be set so thatthere are minimum gap between the implant and cortical bone. In thisstudy the the implant has been placed in the medullary cavity, so thatno initial penetration occurs between bone and implant. Hence thediameter is less than the criterion. According to previous studies thethickness of the implant has an influence on the level of stress shield-ing. The thinner the material is, the lower effect of stress shielding[27, 28].

The recommendations to optimize the simulation time and improveconvergence are to ignore initial penetration, change material mod-els and element formulation and properties of implicit solver, such asILIMIT and MAXREF (the stiffness matrix are reformed maxref timeswith the limit iterations between each reformation) [29]. Sometimes,in hard problems the, convergence is improved by setting ILIMIT=1(full Newton) [30]. The simulation time for this FE analysis was about2 weeks, even though all of the recommendations were carried out,except ILIMIT and MAXREF. An overly high ILIMIT and MAXREFcaused many iteration steps, thus longer simulation time. At low val-ues (ILIMIT = 1), LS-DYNA warned that ILIMIT is too low. Hence,no further investigation were made on what values of MAXREF andILIMIT that are most optimal for this particular study.

20 CHAPTER 4. DISCUSSION

4.1 Future Work

The recommendation for future work is to verify the model by analyz-ing the mesh density and material properties. It is essential to investi-gate how much the results were affected when changing the materialmodels from damaged to elastic. The FE model also needs to be mod-ified in order to be able to apply moment load to the implant. It isalso of great interest to perform a patient specific FE analysis of an OIpatient, by creating a FE model of the bone based on the patient, andhaving correct dimensions and placement of the implant. The simu-lation time could also be optimized in the future, by modifying theimplicit solver properties and model properties. Furthermore, otherdynamic motions are of interest in this field, such as stair ascent anddescent, to rise up from chair, and falls in different directions.

Chapter 5

Conclusions

The conclusion of this study is that implant 60 has more even stressdistribution in the cortical bone than implant 80 and 100. The stressvalues in the proximal part of femur is almost identical for all threeimplants. The length of the implant does not influence on stress distri-bution on implant.

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[18] L. Frossard and E. Häggström, “Load applied on bone-anchored trans-femoral prosthesis: Characterization of a prosthesis— A pilot study,”JRRD, vol. 50, no. 5, pp. 619–634, 2013.

[19] D. S. J. Choi, J. Kang and G. Tack, “Reliability of the walking speed andgait dynamics variables while walking on a feedback-controlled tread-mill,” Journal of Biomechanics, vol. 48, pp. 1336–1339, 2015.

[20] W. C. C. Lee, J. M. Doocey, R. Brånemark, C. J. Adam, J. H. Evans, M. J.Pearcy, and L. A. Frossard, “FE stress analysis of the interface betweenthe bone and an osseointegrated implant for amputees - Implications torefine the rehabilitation program,” Clinical Biomechanics, vol. 23, no. 10,pp. 1243–1250, 2008.

BIBLIOGRAPHY 25

[21] B. Helgason, H. Pálsson, T. P. Rúnarsson, L. Frossard, and M. Viceconti,“Risk of failure during gait for direct skeletal attachment of a femoralprosthesis: A finite element study,” Medical Engineering and Physics,vol. 31, no. 5, pp. 595–600, 2009.

[22] “Review Article The Mechanical properties of Cortical Bone, year =1974, journal = Wolters Kluwer, author = A.Albert, issue=5 volume =56,.”

[23] X. Wang, J. Nyman, X. Dong, H. Leng, and M. Reyes, Fundamental Biome-chanics in Bone Tissue Engineering, 2010, vol. 2, no. 1.

[24] B. Thomas and F. Albert, “Mechanical Property Distributions in the Can-cellous Bone of the Human Proximal Femur ,” Acta Orthopeaedica Scan-dinavica, vol. 51, no. 1-6, pp. 429–437, 1980.

[25] P. M.Martens, R.Vanaudekerckep, “The Mechanical Characteristics ofCancellous Bone at the upper Femoral Region ,” J.Biomechanics, vol. 16,no. 12, pp. 971–982, 1983.

[26] I. AB, “OPRA Implant System Instructions for Use,” Tech. Rep.

[27] L. Newcombe, M. Dewar, G. W. Blunn, and P. Fromme, “Effect of am-putation level on the stress transferred to the femur by an artificial limbdirectly attached to the bone,” Medical Engineering and Physics, vol. 35,no. 12, pp. 1744–1753, 2013.

[28] R. Huiskes and E. Y. Chao, “A survey of finite element analysis in ortho-pedic biomechanics: The first decade,” Journal of Biomechanics, vol. 16,no. 6, pp. 385–409, 1983.

[29] K. U. S. Manual, KEYWORD USER ’ S MANUAL, 2007.

[30] Tobias Erhart, “Tips and tricks for successful im-plicit analyses with LS-DYNA,” 2016. [Online]. Available:https://www.dynamore.de/de/download/presentation/dokumente/download-informationstag-Implizit-2016/05-2016-02-dynamore-infotag-implizit-tipstricks.pdf

Appendix

Finite Element Analysis ofOsseointegrated TransfemoralImplant

Identification of how the Length of the Implant

Affects the Stress Distribution in Cortical Bone

and Implant

ANNA POGOSIAN

Content

A Anatomy and Biomechanics 31A.1 Structure and Characteristics of Bone . . . . . . . . . . . . 31A.2 Bone Remodeling . . . . . . . . . . . . . . . . . . . . . . . 32A.3 Femur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

B Amputation and Prosthesis 35B.1 Prosthetic Stump Fitting Socket . . . . . . . . . . . . . . . 35B.2 Osseointegrated Implant . . . . . . . . . . . . . . . . . . . 37B.3 Current Challenges in Osseointegrated Implants . . . . . 39

C FEM-Finite Element Method 41C.1 Finite Element Method . . . . . . . . . . . . . . . . . . . . 41C.2 Previous FE Analysis of Osseointegrated Transfemoral

Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Appendix A

Anatomy and Biomechanics

A.1 Structure and Characteristics of Bone

Bone is one of the hardest tissues in the body. It is composed withboth organic and inorganic material [1]. The inorganic part consistsprimarily of calcium, which contributes to the hardness, stiffness andhigh compression stress. The majority of organic material is of colla-gen, which provides high tensile strength and flexibility to the bone[2]. In additional to collagen, bone also consists of bone cells (osteo-clast, osteoblast and osteocytes), which are responsible for the bone torepair, rebuilt, remodel, reshape and grow [1].

Bone tissue consists of cortical bone and cancellous bone. Corticalbone is compact, dense and provides mechanical strength [3]. It hashigh resistance to bending and torsion, and forms the outer part ofbone. Cancellous bone (also called trabecular bone or spongy bone),can be found in the ends of long bone. It has lower density and higherelasticity than cortical bone. Bone tissue is an anisotropic material,which implies that the mechanical behaviour differ in different direc-tions, e.g. femur is stronger in longitudinal direction than transversaldirection [2]. It has also a viscoelastic behaviour, which means that theresponse of a load depends on the rate and the duration of the load [2].The higher speed of load the stronger and stiffer bone behaves.

31

32 APPENDIX A. ANATOMY AND BIOMECHANICS

A.2 Bone Remodeling

Bone is an active organ. It is constantly renewed throughout the life-time thanks to its ability to remodel. The remodelling process hasthree phases: resorption- when old bone is digested by the osteoclast,reversal- when mononuclear cells get on the bone surface, and formation-when osteoblast built up new bone matrix [3]. Bone requires mechan-ical loading in order to grow and strengthen [4]. The external loadingstimulates bone cells to build new bone matrix, maintain the tissueand remodel as needed. On the contrary, bone loss will occur whenit is underloaded, which will make it thinner and weaker. The boneremodelling process can be explained by Wolff’s law [5]: bone adaptsto the changes in the loading by altering its structure.

APPENDIX A. ANATOMY AND BIOMECHANICS 33

A.3 Femur

Femur is the strongest and longest bone in the body. Its function isto support the body by transferring the upper body weight from thehip joints to the knee joints [6]. The shaft of femur is called diaphysis,and the outer part of diaphysis consist of cortical bone, (Figure A.1)[1]. The centre of the diaphysis, medullar cavity, consists of yellowmarrow, which is energy in form of fat cells. The epiphysis, which islocated in the ends of long bone, has an outer shell of cortical boneand a middle part consisting of trabecular bone and red marrow. Theproximal epyphysis consist of a spherical shaped head. Femur has anasymmetric shape. One third of femoral shaft is cylindrical, whereasthe rest of the lower shaft is broader [7]. The anterior part of femur isto some extent convex and the posterior is concave. The beam shapeof femur makes it stronger so it can handle bending loads [2].

Figure A.1: Anatomical structure of femur [8].

Appendix B

Amputation and Prosthesis

Amputation is done as the last choice when the limb is dead/dyingor when it threatens the patient’s life. The cause of amputation variesbetween developing and developed countries [9]. The main reasonsto amputation in developing countries are trauma, infections, uncon-trolled diabetes and malignancies, whereas in developed countries themain cause is peripherial vascular diseases. Elderly patients, under-goes amputees more often in developed countries, whereas in devel-oping countries younger patients are more common. Losing a limbcan have economic, social and physiological consequences on patients[9]. According to Swedeamp (a national register for amputations andprosthesis in Sweden) 1102 lower limb amputations were performedduring 2016 in Sweden [10]. In Netherlands each year around 600 pa-tients undergoes amputation, which is about 3.7 amputees per 100 000inhibitor [11], and in Australia about 8000 lower limb amputation areperformed each year [12].

B.1 Prosthetic Stump Fitting Socket

The conventional prosthesis used after an amputation consist of a stump-fitting socket, where the limb is fixed into, (Figure B.1) [11]. Today,most of the prosthetic sockets consists of silicone elastomers which isa soft and linear elastic material [13]. The silicone creates a comfort-able interface between the prosthesis and the skin. However, despitethe soft material of the socket, patients using conventional prosthesisoften experience pain, sores, rashes etc. [11, 14]. It is also perceiveddifficult to control the prosthetic limb because the whole-body weight

35

36 APPENDIX B. AMPUTATION AND PROSTHESIS

is supported by soft tissue. In addition, patients using prosthetic sock-ets often experience sitting discomfort, and reduced range of motion(ROM). Patients with short residual limb, scars, or damaged soft tis-sue are not suitable for stump fitting sockets [15]. The most importantfactors of a prosthesis is the quality and the interference between thelimb and the prosthesis [13]. The fit of the socket affects the comfortand the ability to control the prosthesis, and depends on the volumet-ric matching of the socket and the limb. Heat tends to swell the limb,which reduces the fitting to the socket. Weight changes of the patientalso affect the fitting.

Figure B.1: Conventional prosthesis- stump fitting socket (Image courtesyof Yan Li, surgeon at Karolinska University Hospital Huddinge, from thedivision of Orthopedics and Biotechnology).

APPENDIX B. AMPUTATION AND PROSTHESIS 37

B.2 Osseointegrated Implant

An alternative method of prosthetic limb attachment is to use directskeletal fixation through osseointegrated transfemoral implant. Theimplant is made of screw shaped titanium, and an osseointegrationwill form a direct bond between bone and implant [16]. The phenom-ena was first discovered by the Swedish professor Per-Ingvar Bråne-mark [17]. He revealed that pure titanium had a stable bonding withliving bone tissue, and called this phenomena osseointegration. Os-seointegrated implants have been used for more than 40 years in den-tal clinics worldwide. Today it can be used for many other applica-tions such as: bone anchored hearing aids, joint prosthesis, prosthesisfor head and neck defects etc. The first osseointegrated transfemoralprosthesis for amputation treatment were done in 1990 at SahgrenskaUniversity Hospital, in Sweden [17].

The Swedish company Integrum manufactures this type of implants,called Osseointegrated Prosthesis for the Rehabilitation of Amputees(OPRA) implant system. OPRA consists of three major parts: a threadedfixture that is attached to the bone, an abutment (titanium extension)that penetrates through the skin, and an abutment screw which theprosthesis is attached to (Figure B.2) [16]. The implant is made of ti-tanium, and an osseointegration will form a direct bond between thebone and the implant. The diameter of the fixture is between 16-20mm and the length of abutment between 72-77 mm [18, 19]. The thick-ness of cortical bone, around the implant, should not be less than 2mm [18]. The implementation of OPRA system includes two surgi-cal session [16, 17]. During the first session the fixture is inserted intothe bone, with about 20 mm embedment. The healing time is about6 months. After the wound has healed, the patient can use conven-tional sockets until next surgery session. The second session is whenthe abutment is attached to the distal part of the fixture. Due to therisk of loosening of the implant, the bone should gradually be loadedfor best rehabilitation [17]. Pain experience in the leg during rehabili-tation, may indicate that the bone is exposed to excessive stress.


Figure B.2: Osseointegrated transfemoral implant [20] (Image courtesy ofIntegrum AB).

In addition to OPRA system, there are two other implants availableon market: ILP Endo/Exo (Integral Leg Prosthesis, developed in Ger-many) and OPL (Osseointegrated Prosthetic Limb, developed in Aus-tralia) [21]. In addition to these, there are a number of new implantsunder development. Four of these new implants, ITAP (IntraosseousTranscutaneous Amputation Prosthesis, developed in United King-dom), Keep Walking Advances (developed in Spain), POP (Percuta-neous Osseointegrated Prosthesis, developed in USA) and COMPRESS(developed in USA), have been experimented on humans. The re-maining implants have only been tested on animals. The main dif-ferences between the implants are the choice of material and shape.ILP is made of porous cobolt-chromium-molybdenium and is slightlycurved, whereas the rest of the implants are made of titanium alloy Ti-6A1-4V. The bone-implant interface also varies between the differentsystems. OPRA has a threaded fixtures, whereas the rest is press-fitinto the femur.

APPENDIX B. AMPUTATION AND PROSTHESIS 39

B.3 Current Challenges in OsseointegratedImplants

The direct connection between the implant and bone provides a stableand long term attachment, which makes the prosthesis easier to han-dle [16]. The implant can be used all day and there is an increasedROM in the proximal joint. It is also easier to control the prosthesisdue to sensory feedback, thanks to the direct bond to the bone [11].The OI prosthesis reduces skin related problems and enhances com-fort. The patient can sit more comfortable and also cross their legs[15, 22, 23]. However, the drawbacks of bone anchored prosthesis arethe risks of fracture of the implant or the bone, loosing of the implant,or bone-implant interface disruption [11]. There is also a risk of in-fection, especially in areas where the implant penetrates through theskin. Patients with high risk factors for infections are patients sufferingfrom diabetic, rheumatoid arthritis, renal failure, malnutrition, woundinfection. Studies has also shown that smoking weakens the bone heal-ing process, and that diabetes has an inhibitory effect of osseointegra-tion [14]. The long healing time (approximately 16 months when us-ing OPRA implants) may cause bone fracture, because the bone getsweaker when it is not loaded [11].

Another problem with OI transfemoral implants is the effect of stressshielding on the bone. Stress shielding occurs because of the differ-ence in the stiffness between the implant and bone [24]. The loadingtransfer on the bone will be reduced due to load absorption by theimplant. This is because stresses that was before carried by the boneis now also carried by the implant. The reduced loading contributesto thinner and more porous bone, which could lead to bone loss orbone resorption [25]. This phenomena can be explained by Wolff’s law[5, 22, 25]. Previous studies have shown that stress shielding causesweaker and thinner cortical bone in the distal part of femur, when us-ing transfemoral implants [22, 26, 27]. It has also been shown that thereis a bone growth in the proximal end of femur, due to increased stresslevel, (Figure B.3) [27]. Previous studies have shown that the distri-bution and rate of the strain, and the number of strain cycles have animpact on the bone remodelling process [22]. The material propertiesand the thickness of the implant have also shown to have an impact of


the level of stress shielding. Thin and elastic material have less effectto stress shielding [25, 28]. By reducing the stiffness of the implant theeffect of stress shielding can be reduced. However, this will lead to in-crease stress level on the bone-implant interface, which could inhibitthe fixation of the implant [24]. Other factors that could influence onthe bone remodelling process are bone properties, bone geometry andthe thickness of cortical bone [29].

Figure B.3: Due to uneven stress distribution in femur the cortical bone indistal part of femur gets weaker and thinner, whereas in proximal part therewill be bone growth. Image is taken five years after surgery (Image courtesyof Yan Li, surgeon at Karolinska University Hospital Huddinge).

Today bone anchored prosthesis are not the primary choice of treat-ment for amputation, thus only patients with major difficulties withsocket prosthesis are target group [11]. Studies have shown that pa-tients with amputation caused by trauma or tumor are more suitablefor osseointegrated implants, because they have lower risk of infec-tion [30]. Children and patients over 70 years old are not acceptablefor this type of treatment. There are still many unresolved problemswith the implant system [11]. By reducing the issues, more patientscould benefit from osseointegrated fixation.

Appendix C

FEM-Finite Element Method

C.1 Finite Element Method

Finite element methods is a powerful tool to analyse bone biomechan-ics [31]. The stress analysis provides an understanding of the boneremodelling process. When a load is applied to a structure, it gener-ates stresses in the material. However, the magnitude and stress dis-tribution does not only depend on the loading, but also the materialproperties and the geometry of the structure. In addition to this, theenvironment interacting to the structure also influence on the stressdistribution (i.e. boundary conditions). The accuracy of FEA of bonedepends of how detailed the structure is modeled, the material prop-erties of the bone structure, and how realistic the loading condition is.

FE method is used to solve complex problem by finding an approxi-mated solution. The FE analysis is done in three steps: pre-processing,numerical analysis and post-processing [32]. In the pre-processingstep the structure, material properties, loading and boundary condi-tions are defined to the system. The structure is simplified by di-viding (meshing) it into smaller substructures, called finite elements[32, 33, 34]. Elements are connected to each other by nodes, which lieson the boundary between the elements [35]. Generally, a larger num-ber of elements gives more accurate approximated solution [35, 33].However, a large number of elements also increase the computationaltime. In the second step, numerical analysis, the problem is solved byusing the input data from the pre-processing step [32]. The final step,post-processing is when the result is displayed.

41

42 APPENDIX C. FEM-FINITE ELEMENT METHOD

C.2 Previous FE Analysis of OsseointegratedTransfemoral Implant

Over the past 20 years, there is an increased focus on OI prosthesis[36]. Several FEA of bone anchored prosthesis have been performed,and the most common ones were about transfemoral and transtibialimplants. Nine previous FEA of OI implants are summarized in TableC.1 and C.2. All nine studies were on femur with different types ofimplants (OPRA, ISP, ITAP and two new designs). The main goals ofthese studies were to evaluate the implant by analyzing the stress andstrain distribution in femur in order to investigate the risk of failureor bone resorption. Two of the studies performed FEA with differentamputation levels [28, 37]. The remaining seven studies analyzed ata single amputation level. None of the studies investigated how theshape of the implant influence the stress distribution.

The studies have carried out numerous simplifications, e.g. materialproperties, contact between implant and bone, loading and boundaryconditions. The loading condition differed between the nine studies.Seven studies analyzed the stresses during normal gait. However, onlytwo of these seven performed dynamic analysis of the entire gait cycle[38, 39]. The other five studies selected the maximum load or a par-ticular segment of the gait cycle [11, 22, 27, 29, 40]. One study choseloading that did not correspond to any specific loading from a motion[22]. Only one of these nine studies performed dynamic analysis offorward fall [40]. All models were fixed, either in the proximal headof femur, or distal end of abutment. Thus the load was only appliedto one end of the structure. The contact between the bone and implantwas assumed to be bonded, in order to represent full osseointegration.This implies that the bone and implant models shared same nodes atthe contact surface. None of the studies included the effect of sur-rounding tissue on the bone.

Another limitation of the studies was the choice of material proper-ties. All studies assumed femur to be transversely isotropic. Onlyfour of the studies took into account of both cortical and trabecularbone in the analysis [11, 27, 29, 40]. The rest of the studies assumedbone to be formed by one type of material. The E-modulus of titanium

APPENDIX C. FEM-FINITE ELEMENT METHOD 43

implants varied between the studies as well (between 105 - 115GPa).The higher E-modulus the higher stress distribution to the bone, theless effect of stress shielding [24]. The FE model of bone and implantwas simplified in some studies, either by modelling both bone andimplant as cylinders [28], or by removing the threaded region of thefixture [37]. The dimensions of OPRA implant differed between thestudies, in where the length of fixture varied between 80-110mm, andthe abutment length between 20-72mm. One of the reasons could bebecause the size of the implants are custom-fit to the patients, since thelength and thickness of femoral bone varies between patients. The di-mensions of bone and implant have an impact on the analysis, hencewrong dimensions could lead to incorrect results.

Four of the nine studies showed highest stress level in the proximalend, and lowest in the distal end of femur [11, 27, 38, 39]. It was alsoshown high bone resorption in the distal part of femur, in the inter-face with the abutment [22, 27]. The failure risk was highest in theproximal part [40]. One of the previous studies demonstrated thatthe amputation level had an impact on the stress distribution in bone[37]. The higher amputation level the higher stress in the bone aroundthe implant. The three studies evaluating different types of implantshowed that OPRA implant had lower and more uneven distributioncompared to the other two implants [11, 29, 40]. It was also shownmore bone resorption when using OPRA.

44 APPENDIX C. FEM-FINITE ELEMENT METHOD

TableC

.1:N

ineprevious

FEAof

transfemoral

OI

implants.

Thestudy

design/parameter,

loadingand

re-sult/conclusion

fromeach

studyR

eferenceIm

plantStudy

design/Param

eterLoading

Result/C

onclusion

[22]O

PRA

-Boneshape

-Propertiesof

bone-Properties

ofbone

transplant

Maxim

umload

ofa

gaitcycle.

Mom

entw

as52.3

Nm

indistalend

ofimplant;longitudinalforce

FLw

as831

N

Boneresorption

andrem

odelingof

boneat

theinterface

with

abut-m

ent.Theloads

causedbending

ofimplantw

hichlead

toseparation

frombone

tissue.Increased

E-modulus

ofbone

reduceddisplace-

mentofthe

implant

[39]T

hreadedtitaniumim

plant

LoadingThree

loadingcases:

1.Axialforce

(200N

,400N

and900

N)

2.Loadon

threeaxes

3.Loadduring

normalgaitcycle.

Loadsw

ereapplied

todistalend

ofabutment

Higheststress

was

inproxim

alendofim

plantinallthree

cases.R

e-sultshow

eddifference

instress

distributionin

thethree

cases.Axial

forceprovided

quiteeven

stressdistribution;load

onthree

axeshad

lessuniform

distribution.Higheststress

was

at55%

ofgaitcycle.

[11]O

PRA

ISP-Im

plants-Loading

Two

loadcases

ofnormalgait:

1.25%

ofgaitcycle(heelstrike)

2.55%

ofgaitcycle(rightbefore

toe-off)Loads

were

appliedto

distalendofim

plant

Higheststress

concentrationw

asin

theproxim

alend,andlow

estinthe

distalendofthe

bone.ISPhad

more

even,buthigherstressdistri-

butionthan

OPR

A.H

owever,O

PRA

hasa

lower

riskto

bonefracture

[29]O

PRA

ISPSam

eas

[11]Sam

eas

[11]M

orebone

lossw

asfound

inthe

distalregionthan

theproxim

alforboth

implants.M

orebone

resorptionw

henusing

OPR

Asystem

thanISP

[40]O

PRA

ISPN

ewdesign

Same

as[11]

Threeload

cases:1.25

%ofgaitcycle

(heelstrike)2.55

%ofgaitcycle

(rightbeforetoe-off)

3.Forward

fallLoads

were

appliedto

distalendofim

plant

Highestfailure

riskw

asin

theproxim

alendof

implantfor

bothISP

andO

PRA

.High

boneresorption

indistalend

offemur:-15

%O

PRA

,-17

%ISP

after20

month.The

newdesigned

implanthad

astress

dis-tribution

inthe

boneclose

tothe

physiologicalvalue,duringnorm

algait

[37]O

PRA

Am

putationlevel

Loadson

femur

were

appliedon

thehip

joint(2330

N)

andabductor

muscle

(1022N

),and

theresulting

forceatthe

distalendofabutm

ent(1318N

)

Thehigher

amputation

levelthehigher

equivalentVon

Mises

stressin

thebone

aroundthe

implant

[28]ITA

PA

mputation

levelThree

loadingcases:

1.143N

lateralfromknee

2.664N

axialload3.8

Nm

axialtorqueLoads

were

appliedto

distalendofim

plant

Theproxim

alanddistalend

offemurhad

reducedstress

distribution.Bending

forcecontributed

higherstresses

thanaxialloads

[27]O

PRA

Loading20

%ofnorm

algaitcycle(m

id-stance):axialcom-

pression(3750

N),

torsion(20

Nm

),flexion

(60N

m),abduction

(40N

m).

Allloads

were

appliedon

thedistalend

ofabutment

High

stressin

theproxim

alendof

femur,and

lowstress

inthe

dis-tal

end.The

strainlevel

reachedthe

peakvalue

inthe

pointw

herethe

implant

ended.In

thedistalend

thestrain

haslow

erlevelthan

intactfem

ur.FE

analysisshow

edstress/strain

influencedon

boneresorption

offemur

with

implant

[38]Poroustitaniumim

plant

Implant

Loadsfrom

normal

gaitapplied

todistal

endof

abutment.

Thereaction

loadsw

ereapplied

onthree

partsof

proximal

femur:

femoral

head,trochanter

major

andtrochanter

minor

Highest

stressin

proximalpart

offem

ur.The

riskof

failureis

threetim

eshigher

with

implantthan

without,during

normalgait

APPENDIX C. FEM-FINITE ELEMENT METHOD 45Ta

ble

C.2

:Nin

epr

evio

usFE

Aof

tran

sfem

oral

OIi

mpl

ants

.Mat

eria

lpro

pert

ies,

impl

antd

imen

sion

s,co

ntac

tand

boun

dary

cond

itio

nfr

omea

chst

udy

Ref

eren

ceM

ater

ialp

rope

rtie

sIm

plan

tDim

ensi

ons

Bou

ndar

yC

ondi

tion

sB

one

Impl

ant

Youn

g’s

Mod

ulus

Shea

rM

odul

usYo

ung’

sM

odul

us[2

2]16

.7G

Pa(L

ongi

tudi

nal)

11.5

GPa

(Tra

nsve

rse)

-11

0GPa

Thre

aded

fixtu

re(l

engt

h80

mm

,dia

m-

eter

16m

m),

abut

men

t(l

engt

h72

mm

,di

amet

er11

mm

)

Inte

rfac

ebe

twee

nbo

ne,

fixtu

rean

dbo

netr

ansp

lant

was

assu

med

tobo

nded

.T

hein

terf

ace

betw

een

abut

-m

ent

and

abut

men

tsc

rew

was

mod

-el

led

bond

ed,

whe

reas

the

inte

rfac

eto

the

fixtu

rew

asfr

icti

onal

.R

elat

ive

mot

ion

atdi

stal

end

ofab

utm

ent.

[39]

17G

Pa(L

ongi

tudi

nal)

11.5

GPa

115G

PaIm

plan

t(l

engt

h10

0mm

,di

amet

er20

mm

)C

onta

ctbe

twee

nim

plan

tan

dbo

new

asas

sum

edto

bebo

nded

.Th

efe

mor

alhe

adw

asas

sum

edto

befix

ed[1

1]X

-YG

Pa*

-21

0GPa

(ISP

Stem

)1G

Pa(I

SPpo

urs

met

alla

yer)

110G

Pa(O

PRA

)

-O

PRA

fixtu

re(l

engt

h11

0mm

,dia

m-

eter

20m

m),

abut

men

t(l

engt

h30

mm

,di

amet

er11

mm

)-

ISP

fixtu

re(l

engt

h13

2mm

,di

amet

er20

mm

),ab

utm

ent

(len

gth

30m

m,

di-

amet

er35

mm

)

Con

tact

betw

een

impl

ant

and

bone

was

assu

med

tobe

bond

ed.

The

fem

oral

head

was

assu

med

tobe

fixed

[29]

Sam

eas

[11]

-Sa

me

as[1

1]Sa

me

as[1

1]Sa

me

as[1

1]

[40]

Sam

eas

[11]

-Sa

me

as[1

1]fo

rO

PRA

and

ISP

12.5

GPa

(new

desi

gn),

114G

Pa(n

ewde

sign

,st

eam

)

ISP

(len

gth

130m

m),

OPR

A(l

engt

h11

0mm

),ne

wde

sign

(len

gth

75m

m).

All

thre

eha

dsa

me

diam

eter

(20m

m)

Sam

eas

[11]

[37]

X-Y

GPa

**-

105G

PaFi

xtur

e(l

engt

h80

mm

,di

amet

er20

mm

)C

onta

ctbe

twee

nim

plan

tan

dbo

new

asas

sum

edto

bebo

nded

.The

mod

elw

asfix

edat

the

dist

alen

dof

abut

men

t[2

8]20

GPa

(Lon

gitu

dina

l)12

GPa

(Tra

nsve

rse)

-11

0GPa

1.Q

uart

erof

fem

uram

puta

ted

(im

-pl

antl

engt

h16

0mm

,dia

met

er14

mm

)2.

Hal

fof

fem

uram

puta

ted

(im

plan

tle

ngth

160m

m,

diam

eter

14m

m)

3.Th

ree-

quar

ter

offe

mur

ampu

tate

d(i

mpl

ant

leng

th50

mm

,di

amet

er18

mm

)

Con

tact

betw

een

impl

ant

and

bone

was

assu

med

tobe

bond

ed.T

hem

odel

was

fixed

atth

epr

oxim

alen

dof

fem

ur

[27]

18G

Pa(c

orti

calb

one,

lon-

gitu

dina

l)0.

35G

Pa(c

ance

llous

bone

)

7GPa

110G

PaN

otav

aila

ble

inth

ear

ticl

eC

onta

ctbe

twee

nim

plan

tan

dbo

new

asas

sum

edto

bebo

nded

.The

prox

i-m

alen

dof

fem

urw

asfix

ed

[38]

X-Y

GPa

***

-11

0GPa

Fixt

ure

(len

gth

45m

m,

diam

eter

10m

m),

abut

men

t(1

67m

mle

ngth

,di

amet

er6.

5mm

)

Con

tact

betw

een

impl

ant

and

bone

was

bond

ed.

Mod

elw

asfix

edat

the

dist

alen

dof

abut

men

t

*M

odul

usof

fem

urw

asca

lcul

ated

from

its

ash

dens

itie

s.E

=33

900ρ

ash

2.20

forρash

≤0.27

(tra

becu

lar

bone

),E

=102

00,

ρash

2.01

forρash

≤0.6

(cor

tica

lbon

e),ρ

ash

obta

ined

from

CT

data

**Yo

ung’

sm

odul

usof

cort

ical

bone

isEc=

2065ρ

,ρ=

1.54ρCT+0.078

4,w

hereρCT

isth

ede

nsit

yac

cord

ing

toC

Tda

ta**

*Yo

ung’

sm

odul

usof

bone

calc

ulat

edac

cord

ing

dens

ity

rela

tion

shipE

=6.85ρ

app1.49

.Val

ueofρapp=

ρash

0.55

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