Cardiff School of Engineering                   Coursework Cover SheetPersonal DetailsStudent No: 1056984Family Name: Dive...
Stress shielding in the proximal tibiaof a stemmed knee prosthesis is amajor problemHiren Maganlal DivechaCandidate Number...
Table of ContentsAbstract ...................................................................................................
1. IntroductionStemmed tibial prostheses are used mainly in revision total knee replacement (TKR) surgery.Prosthesis fixat...
2. Stress analysesIn these analyses, the following assumptions are made:        1. The proximal tibia is modelled as a cyl...
Stem (0.013m)                                                                       Cement Mantle (0.015m)                ...
The proportion of the total axial load (F) experienced by each constituent can be determined bythat constituent’s relative...
a. Proximal tibia without prosthesisBefore analysing the situation with a prosthesis in situ, the distribution of load, an...
b. Influence of stem materialThe following analyses shall demonstrate the change in stress distribution amongst theconstit...
c. Influence of stem diameterReducing the stem’s diameter will result in a reduced relative axial rigidity and therefore l...
d. Use of a hollow tibial stemmed prosthesisIf the stem is hollow, the axial rigidity of the stem (EA) will be reduced and...
e. Analysis of an “ideal” material for a stemmed tibial prosthesisAnother approach to developing an ideal stemmed tibial p...
3. DiscussionIn the natural situation, the cortical bone takes the majority of axial load transferred from thetibial plate...
Factors that can be modified or manipulated to reduce the stress shielding effect of the stemmedtibial prosthesis include:...
femoral stem – here there is a proximal load transfer zone between the stem and bone). Throughthe length of the stem, the ...
As per Wolff’s law, bone remodelling is driven, in part, by mechanical loading (stress). The stressshielding experienced a...
using finite element analysis (FEA). This is a computerised method that entails the threedimensional modelling of the obje...
The analysis performed here is a simplistic approximation of the in vivo situation, which is mademore complicated by the f...
4. ConclusionStemmed tibial prostheses are generally only used in revision TKR scenarios where there issignificant bone lo...
5. ReferencesAbu-Rajab, R. B., Watson, W. S., Walker, B., Roberts, J., Gallacher, S. J., & Meek, R. M. (2006). Peri-prosth...
Huiskes, R. (1984). Principles and methods of solid biomechanics. In P. Ducheyne, & G. W.Hastings (Eds.), Functional behav...
6. Appendices      a. Appendix 1 – NomenclatureSymbol               Quantity                          SI UnitL            ...
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Stress shielding in proximal tibia of a stemmed prosthesis

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analysis of the stress shielding effect of stemmed tibial TKR prostheses and how this effect can be varied/ reduced

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Stress shielding in proximal tibia of a stemmed prosthesis

  1. 1. Cardiff School of Engineering Coursework Cover SheetPersonal DetailsStudent No: 1056984Family Name: Divecha First Name: HirenPersonal Tutor: Prof Sam Davies Discipline: MMMModule DetailsModule Name: Engineering Theory 1 Module No: ENT536Coursework Title: Stress shielding in the proximal tibia of a stemmed knee prosthesis is a majorproblemLecturer: Dr D O’DohertySubmission Deadline: 8/1/2011DeclarationI hereby declare that, except where I have made clear and full reference to the work of others,this submission, and all the material (e.g. text, pictures, diagrams) contained in it, is my own work,has not previously been submitted for assessment, and I have not knowingly allowed it to becopied by another student. In the case of group projects, the contribution of group members hasbeen appropriately quantified.I understand that deceiving, or attempting to deceive, examiners by passing off the work ofanother as my own is plagiarism. I also understand that plagiarising anothers work, or knowinglyallowing another student to plagiarise from my work, is against University Regulations and thatdoing so will result in loss of marks and disciplinary proceedings. I understand and agree that theUniversity’s plagiarism software ‘Turnitin’ may be used to check the originality of the submittedcoursework.Signed: …..…………………………………….………... Date: ………………………
  2. 2. Stress shielding in the proximal tibiaof a stemmed knee prosthesis is amajor problemHiren Maganlal DivechaCandidate Number: 1056984ENT536 – Engineering Theory 1AbstractStemmed tibial prostheses are used in revision total knee replacements as a means of by-passingareas of bony deficiency in the proximal tibia. They allow for maintenance of proper alignmentand provide distal fixation where there is good bone stock. An unfortunate side-effect of usingintra-medullary stemmed prostheses is stress shielding. This occurs because the stem is muchstiffer than surrounding bone and therefore takes a greater proportion of the axial load, leavingthe surrounding bone stress shielded. As a result, this bone will gradually resorb as it does notexperience mechanical loading sufficient to stimulate positive remodelling. The magnitude of thisstress shielding shall be explored, as well as modifications to the prosthesis that can reduce itsmagnitude. 1
  3. 3. Table of ContentsAbstract .............................................................................................................................................. 11. Introduction ...................................................................................................................... 32. Stress analyses .................................................................................................................. 4 a. Proximal tibia without prosthesis .......................................................................................... 7 b. Influence of stem material ..................................................................................................... 8 c. Influence of stem diameter .................................................................................................... 9 d. Use of a hollow tibial stemmed prosthesis .......................................................................... 10 e. Analysis of an “ideal” material for a stemmed tibial prosthesis .......................................... 113. Discussion ........................................................................................................................ 124. Conclusion ....................................................................................................................... 185. References....................................................................................................................... 196. Appendices ...................................................................................................................... 21 a. Appendix 1 – Nomenclature ................................................................................................ 21 b. Appendix 2 – Abbreviations ................................................................................................. 21 2
  4. 4. 1. IntroductionStemmed tibial prostheses are used mainly in revision total knee replacement (TKR) surgery.Prosthesis fixation and alignment using a standard non-stemmed tibial component would be poorin the revision TKR due to bone loss/ defects that arise as a result of prosthetic loosening orosteolysis. The function of the stem is to provide better fixation, allow for maintenance of correctalignment and off-load/ bypass bony deficiencies (Bourne & Crawford, 1998) (Mabry & Hanssen,2007). An unfortunate side-effect of using stemmed prostheses is stress shielding. Stress shieldingoccurs around implants whereby the implant load-shares with the surrounding bone. This resultsin reduced stresses within the bone and results in osteopenia. The mechanism accounting for thisis conceptualised in Wolff’s law (Wolff, 1892) translated to English (Maquet & Furlong, 1986): Every change in the function of a bone is followed by certain definite changes in its internal architecture and its external conformation.Thus, by off-loading the proximal tibia, bone density decreases as there is less stimulation ofosteoblastic activity (i.e.: bone formation) compared to osteoclastic activity (i.e.: boneresorption). The resulting osteopenia has the following consequences: 1. Loss of fixation of prosthesis, leading to progressive prosthesis loosening and migration 2. Increased bone loss/ bone defects which makes further revision surgery even more difficult (often requiring bone grafting, metallic augments or even custom prostheses) 3. Increased risk of peri-prosthetic fractureThe following analysis aims to demonstrate the magnitude of stress shielding that occurs in theproximal tibia with a stemmed tibial prosthesis in situ. 3
  5. 5. 2. Stress analysesIn these analyses, the following assumptions are made: 1. The proximal tibia is modelled as a cylinder. In reality, the metaphysis is almost conical with an elliptical cross-section and narrows at the metaphyseal-diaphyseal junction. The diaphysis is prismoid in cross-section. 2. Bone is made up of outer cortical bone and inner cancellous bone 3. The prosthesis is firmly bonded to the bone via a cement mantle and behaves as a composite, thus in a state of iso-strain 4. The cement mantle (polymethylmethacrylate – PMMA) has a constant thickness of 1mm 5. The prosthesis experiences a compressive axial load (F) of three times body weight (i.e.: for a 70kg subject; 3 x 70 x 9.81 = 2060N), based on modelled maximum tibial plateau contact values in the terminal stance phase of the gait cycle (Wehner, Claes, & Simon, 2009) 6. This axial force is taken as acting through the centre of the tibial plate and stem. Thus no bending moments are experienced 7. Interface, radial, hoop and shear stresses are ignoredFigure 1 demonstrates a cross-section of the modelled proximal tibia with the cemented tibialstem in situ including the diameters of each constituent used henceforth. 4
  6. 6. Stem (0.013m) Cement Mantle (0.015m) Cancellous Bone (0.024m) Cortical Bone (0.03m)Figure 1: Diagrammatic representation of cross-section of proximal tibia with cemented stem in situ (outer diameters in brackets) 5
  7. 7. The proportion of the total axial load (F) experienced by each constituent can be determined bythat constituent’s relative axial rigidity (ϵx) based on the cross-sectional area (A) and Young’smodulus of elasticity (E), as demonstrated below (Huiskes, 1984) (Huiskes, 1984) (Huiskes, 1991):The cross-sectional area of a hollow circle is given by the following equation (rx is the outerdiameter; ry is the inner diameter):Thus, the proportion of the axial load (Lx) experienced by each constituent is given by: 6
  8. 8. a. Proximal tibia without prosthesisBefore analysing the situation with a prosthesis in situ, the distribution of load, and thus stress,between cortical and cancellous bone shall be analysed. Table 1 shows the Young’s moduli, cross-sectional areas, relative axial rigidities, proportion of load and stress experienced by cortical andcancellous bone with an axial load (F) of 2060N. Thus in the natural situation, the cortical bonetakes the majority of the axial load. Young’s Modulus, Cross-sectional Relative axial Load, L /N Stress, σ /MPa E /GPa Area, A /m2 rigidity, ϵCortex 12 0.000254 0.985 2030 79.92Cancellous 0.1 0.000452 0.015 30 0.66 Table 1: Analysis without prosthesis 7
  9. 9. b. Influence of stem materialThe following analyses shall demonstrate the change in stress distribution amongst theconstituents of this composite model with a cemented, stemmed tibial prosthesis in situ. Theinfluence of the material used for the prosthesis shall also be demonstrated. The most commonmaterials used in orthopaedic prostheses are cobalt-chrome (Co-Cr) and titanium alloys (Ti-6Al-4V; referred to as Ti henceforth). The stress distribution between the constituents isdemonstrated for Co-Cr and Ti stems in Tables 2 and 3 respectively. Young’s Cross- Relative axial Load, L/N Stress, σ/MPa Modulus, sectional rigidity, ϵ E/GPa Area, A/m2Cortex 12 0.000254 0.0943 194.25 7.65Cancellous 0.1 0.000276 0.0009 1.75 0.06Cement 2.3 0.000044 0.0031 6.44 1.46(PMMA)Stem (Co-Cr) 220 0.000133 0.9017 1857.56 139.67 Table 2: Analysis with Co-Cr prosthesis Young’s Cross- Relative axial Load, L/N Stress, σ/MPa Modulus, sectional rigidity, ϵ E/GPa Area, A/m2Cortex 12 0.000254 0.1668 343.48 13.52Cancellous 0.1 0.000276 0.0015 3.10 0.11Cement 2.3 0.000044 0.0055 11.38 2.59(PMMA)Stem (Ti) 114 0.000133 0.8262 1702.04 127.97 Table 3: Analysis with Ti prosthesis 8
  10. 10. c. Influence of stem diameterReducing the stem’s diameter will result in a reduced relative axial rigidity and therefore lessenthe stress shielding effect. The stress experienced by the stem will also increase and considerationmust be made in ensuring the stem is adequately strong to endure in vivo loading without failure.Table 4 below shows an analysis using a Ti stem of diameter 0.008m. Young’s Cross- Relative axial Load, L/N Stress, σ/MPa Modulus, sectional rigidity, ϵ E/GPa Area, A/m2Cortex 12 0.000254 0.3436 707.88 27.82Cancellous 0.1 0.000374 0.0042 8.67 0.23Cement 2.3 0.000028 0.0073 15.08 5.33(PMMA)Stem (Ti) 114 0.000050 0.6448 1328.37 264.27 Table 4: Analysis with reduced diameter Ti prosthesis (0.008m) 9
  11. 11. d. Use of a hollow tibial stemmed prosthesisIf the stem is hollow, the axial rigidity of the stem (EA) will be reduced and will reduce further asthe inner diameter approaches the outer diameter. Thus, the stem will theoretically take less ofthe overall axial load resulting in less stress shielding of the proximal tibial bone. This isdemonstrated in Table 5 below with the stem being made of Ti with an outer diameter of 0.013mand an inner diameter of 0.01m. The cross-sectional area of the hollow stem is: Young’s Cross- Relative axial Load, L/N Stress, σ/MPa Modulus, sectional rigidity, ϵ E/GPa Area, A/m2Cortex 12 0.000254 0.3266 672.78 26.49Cancellous 0.1 0.000276 0.0030 6.09 0.22Cement 2.3 0.000044 0.0108 22.34 5.08(PMMA)Stem (Ti) 114 0.000054 0.6596 1358.79 251.63 Table 5: Analysis with hollow Ti stem 10
  12. 12. e. Analysis of an “ideal” material for a stemmed tibial prosthesisAnother approach to developing an ideal stemmed tibial prosthesis is to determine the Young’smodulus of a theoretical material that would result in the cortical bone taking 80% of the overallload (i.e.: a relative axial rigidity ϵcortex of 0.80). This analysis shall be performed for a Ti stem withan outer diameter of 0.013m.Table 6 below shows results of the relative loads and stress distribution using a stem of 0.013mdiameter with a Young’s modulus of 4.76GPa. Young’s Cross- Relative axial Load, L/N Stress, σ/MPa Modulus, sectional rigidity, ϵ E/GPa Area, A/m2Cortex 12 0.000254 0.8 1648.00 64.88Cancellous 0.1 0.000276 0.007244 14.92 0.54Cement 2.3 0.000044 0.026562 54.72 12.44(PMMA)Theoretical 4.76 0.000133 0.166163 342.30 25.74Stem Table 6: Analysis to allow 80% load through cortical bone 11
  13. 13. 3. DiscussionIn the natural situation, the cortical bone takes the majority of axial load transferred from thetibial plateau. The introduction of a stemmed tibial prosthesis results in the proximal tibial bone(cortex and cancellous) becoming stress shielded as the relative rigidity of the stemmedcomponent is much greater than that of the bone. The stem therefore takes a greater proportionof axial load. A comparison of the results obtained from the analyses performed above aresummarised in Figure 2. 350 300 250 Stress (MPa) 200 150 100 Stem 50 Cortex 0 Figure 2: Chart comparing stress experienced in cortex and stem for different stem analyses 12
  14. 14. Factors that can be modified or manipulated to reduce the stress shielding effect of the stemmedtibial prosthesis include: 1. Reduced stiffness of the material used for the stem (i.e.: lower Young’s modulus) 2. Reduced diameter of the stem 3. Making the stem hollow – this results in a reduced cross-sectional area of the stem which reduces the relative axial rigidity but also increases the stress in the stem compared to a solid stem of the same diameterThe results obtained with this simplified analysis show a reduction of stress in the cortex from79.92MPa in the native tibia to 7.65MPa with a Co-Cr stem, 13.52MPa with a Ti stem, 26.49MPawith a hollow Ti stem and 64.88MPa using a solid stem made of a theoretical material with a lowYoung’s modulus (4.76GPa). Examples of materials with a low Young’s modulus in this rangeinclude polystyrene (3.5GPa), nylon (2-4GPa), acrylics (3.2GPa), polyvinylchloride (3.4GPa)polyethylene (0.18-1.6GPa). Such materials would not be strong enough to accommodate theexpected loads transferred and would easily undergo deformation and failure in vivo. Thus, thereis a trade-off in attempting to reduce the relative axial rigidity of the stem. The strength of thestem will also reduce and eventually a point will be reached where the stem’s primary functions(maintaining correct alignment, providing solid fixation, by-passing deficient proximal tibia) will becompromised resulting in early failure.Describing the proportion of load shared by the various constituents in this model using thissimplistic analysis gives an estimate to the in vivo situation. Proximally at the joint itself, the axialforce is transferred to the tibial plate. As shown in Figure 3 below and described by R. Huiskes(Huiskes, 1984) (Huiskes, 1984), the majority of this force is transferred to the stem with a smallerproportion (dependent on the relative axial rigidity) being transferred to the surrounding bonebeneath the plate (compared to the situation where there is no plate such as in an non-collared 13
  15. 15. femoral stem – here there is a proximal load transfer zone between the stem and bone). Throughthe length of the stem, the proportion of load borne by the stem stays proportional to its relativeaxial rigidity. The length of the proximal and distal load transfer zones is dependent on λn whichrefers to the axial fixation exponent and depends on relative axial rigidities and characteristics ofthe cement layer. The stem tip is an area of high stress concentration and the load is transferredacross to the surrounding bone which will experience the full load (F) i.e.: not experience stressshielding. Figure 3: Load transfer characteristics of a straight stem cemented in bone as depicted on p. 398 (Huiskes, 1991). 14
  16. 16. As per Wolff’s law, bone remodelling is driven, in part, by mechanical loading (stress). The stressshielding experienced around the tibial stem results in osteopenia due to an imbalance betweenosteoblastic and osteoclastic activity, resulting in net bone resorption. Clinically, this effect can beinvestigated using dual energy x-ray absorpitometry (DEXA) which calculates the bone mineraldensity (BMD). Lonner et al found a significantly reduced BMD of the proximal tibia in cementedstems (relative to the patient’s unoperated contra-lateral limb) compared to non-stemmedprostheses at an average follow-up of 94 months indicating significant stress shielding (Lonner,Klotz, Levitz, & Lotke, 2001). Interestingly, Abu-Rajab et al found no difference in relative BMDwhen comparing cemented versus cementless stemmed tibial prostheses at 2 years follow-up(Abu-Rajab, Watson, Walker, Roberts, Gallacher, & Meek, 2006) indicating that the use of cementmay not influence the amount of stress shielding. Sathappan et al found no significant differencein BMD at an average of 87.7 months post-operative when comparing 23 standard with 18stemmed tibial prostheses. They hypothesised that this may be due to the senior author’spreference for only cementing the tibial tray and allowing a press-fit cementless fixation of thestem itself, thus reducing the stress shielding effect over the length of the press-fit stem(Sathappan, Pang, Manoj, Ashwin, & Satku, 2009).Stress/ strain gauge analyses can be performed in vitro to analyse the stress shielding effect, suchas that performed by Bourne and Finlay on cadaveric tibiae, which showed significant proximaltibial stress shielding over the length of the stem (Bourne & Finlay, 1986). In a cadaveric straingauge analysis, Jazrawi et al found that larger diameter and longer press fit tibial stemssignificantly improved stability with improved resistance to lift off of the tibial tray and to shearstresses. There was a statistically non-significant trend towards increased proximal stressshielding with long cemented stems, though stability was greater in this group (Jazrawi, Bai,Kummer, Hiebert, & Stuchin, 2001). A more accurate method of determining stress distribution is 15
  17. 17. using finite element analysis (FEA). This is a computerised method that entails the threedimensional modelling of the object to be studied with nodes that form a mesh frame. Specificmaterial mechanical properties can be assigned to the appropriate regions (bone, implant,cement) and the loading conditions can be specified. The resulting calculations will reveal a stressor strain distribution over the three dimensional model.Completo et al (Completo, Talaia, Fonseca, & Simoes, 2009) performed a FEA comparison ofvarious stem designs and found that Co-Cr long stems (0.11m) had the greatest proximal stressshielding effect (82% of the stress in an intact tibia). With the long Ti stem (0.11m), there wasproximal stress shielding of 79% which reduced to 0% around the mid-stem region. They found a700% increase in stress at the stem tip. The short Ti stem (0.05m) did not experience any proximalstress shielding but did have a 450% increase in stress at the stem tip. A further analysis of a longTi stem (0.095m) with a 0.015m polyethylene (PE) tip revealed no change in the proximal stressshielding, but a significant reduction in stress concentration at the stem tip to 150%.Increased stress concentrations at the tip of the stem may explain the phenomenon of end-of-stem pain and may theoretically increase the risk of a peri-prosthetic fracture (Barrack, Stanley,Burt, & Hopkins, 2004) (Completo, Talaia, Fonseca, & Simoes, 2009).Other methods for reducing stress shielding include using a hollow stem. In a FEA study ofcemented hip prostheses, Gross and Abel found an 18% increase in proximal femur bone stress(compared to a reference 0.01m solid stem) when using a 0.01m hollow stem with an innerdiameter of 0.009m (Gross & Abel, 2001). This effect reduced as the inner diameter of the stemwas reduced. 16
  18. 18. The analysis performed here is a simplistic approximation of the in vivo situation, which is mademore complicated by the following variables that are not accounted for: 1. Three dimensional geometry 2. Non-uniform cement mantle and non-uniform bonding 3. Forces not considered – bending moments, shear stresses, hoop stresses, torsional stresses 4. Dynamic forces during gait 5. Contribution of ligament/ tendon loadingThough a “perfect prosthesis” is far from reality, it certainly seems that FEA is the method ofchoice for designing and experimentally testing the effects of stress shielding in attempt todevelop a suitable compromise. 17
  19. 19. 4. ConclusionStemmed tibial prostheses are generally only used in revision TKR scenarios where there issignificant bone loss. This is a difficult situation because in attempting to achieve a good, stablefixation of the implant, a long stem must be used to provide distal support (as the proximal tibia isdeficient and must be by-passed, especially if it is grafted). This leads to stress-shielding of theproximal tibia, which is already deficient. This bone will not undergo positive bone remodellingand will resorb gradually.Biomechanically, this stress shielding effect can be quantified using static stress analyses (asabove), in vitro stress / strain gauge analyses and, more accurately, with FEA. Whilst this effectcan be reduced by using materials that are less stiff, reducing the diameter of the stem, using ashorter stem (thus shorter length of stress-shielded bone), using hollow stems and possibly byonly cementing proximally beneath the tibial tray, a trade off will be reached where the strengthof the prosthesis and its fixation may become compromised leading to earlier failure and possiblyincreased bony deficit in the process. 18
  20. 20. 5. ReferencesAbu-Rajab, R. B., Watson, W. S., Walker, B., Roberts, J., Gallacher, S. J., & Meek, R. M. (2006). Peri-prosthetic bone mineral density after total knee arthroplasty. Cemented versus cementlessfixation. J Bone Surg Br , 88 (5), 606-613.Barrack, R. L., Stanley, T., Burt, M., & Hopkins, S. (2004). The effect of stem design on end-of-stempain in revision total knee arthroplasty. J Arthroplasty , 19 (7), 119-124.Bourne, R. B., & Crawford, H. A. (1998). Principles of revision total knee arthroplasty. Orthop ClinNorth Am , 29 (2), 331-337.Bourne, R. B., & Finlay, J. B. (1986). The influence of tibial component intramedullary stems andimplant-cortex contact on the strain distribution of the proximal tibia following total kneearthroplasty. An in vivo study. Clin Orthop Relat Res , 208, 95-99.Completo, A., Talaia, P., Fonseca, F., & Simoes, J. A. (2009). Relationship of design features ofstemmed tibial knee prosthesis with stress shielding and end-of-stem pain. Materials & Design ,30 (4), 1391-1397.Gross, S., & Abel, E. W. (2001). A finite element analysis of hollow stemmed hip prostheses as ameans of reducing stress shielding of the femur. J Biomech , 34 (8), 995-1003.Huiskes, R. (1991). Biomechanics of artificial-joint fixation. In V. C. Mow, & W. C. Hayes, BasicOrthopaedic Biomechanics (1st ed., pp. 375-442). New York: Raven Press Ltd.Huiskes, R. (1984). Design, fixation, and stress analysis of permanent orthopaedic implants: Thehip joint. In P. Ducheyne, & G. W. Hastings (Eds.), Functional behavior of orthopaedic biomaterials(1st ed., Vol. II: Applications, pp. 121-162). Boca Raton: CRC Press Inc. 19
  21. 21. Huiskes, R. (1984). Principles and methods of solid biomechanics. In P. Ducheyne, & G. W.Hastings (Eds.), Functional behavior of orthopedic biomaterials (1st ed., Vol. I, pp. 51-97). BocaRaton: CRC Press Inc.Jazrawi, L. M., Bai, B., Kummer, F. J., Hiebert, R., & Stuchin, S. A. (2001). The effect of stemmodularity and mode of fixation on tibial component stability in revision total knee arthroplasty. JArthroplasty , 16 (6), 759-767.Lonner, J. H., Klotz, M., Levitz, C., & Lotke, P. A. (2001). Changes in bone density after cementedtotal knee arthroplasty. Influence of stem design. J Arthroplasty , 16 (1), 107-111.Mabry, T. M., & Hanssen, A. D. (2007). The role of stems and augments for bone loss in revisionknee arthroplasty. J of Arthroplasty , 22 (4), 56-60.Maquet, P., & Furlong, R. (1986). The law of bone remodelling. Berlin: Springer-Verlag.Sathappan, S. S., Pang, H., Manoj, A., Ashwin, T., & Satku, K. (2009). Does stress shielding occurwith the use of long-stem prosthesis in total knee arthroplasty? Knee Surg Sports TraumatolArthrosc , 17, 179-183.Wehner, T., Claes, L., & Simon, U. (2009). Internal loads in the human tibia during gait. ClinBiomech , 24 (3), 299-302.Wolff, J. (1892). Das gesetz der transformation der knochen. Berlin: Hirschwald. 20
  22. 22. 6. Appendices a. Appendix 1 – NomenclatureSymbol Quantity SI UnitL Axial load NE Young’s modulus of elasticity GPaA Cross-sectional area m2ϵ Relative axial rigidityσ Stress MPa b. Appendix 2 – AbbreviationsAbbreviation Full termTKR Total knee replacementFEA Finite element analysisCo-Cr Cobalt-chrome alloyTi Titanium alloy (Ti-6Al-4V)PE PolyethylenePMMA PolymethylmethacrylateDEXA Dual Energy X-ray AbsorpitometryBMD Bone Mineral Density 21

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