Computer and experimental modelling of the contact behaviour of prosthetic knee implants

Transcription

1 Computer and experimental modelling of the contact behaviour of prosthetic knee implants T M McGloughlin Department of Mechanical and Aeronautical Engineering University of Limerick, Ireland Abstract Recent experience with prosthetic knee implants has shown that despite the widespread success of the surgical procedure and the restoration to activity it provides to patients suffering from arthritic disorders, certain key design problems remain to be solved. Perhaps the most serious of these problems is the high wear rate of the polymeric insert in the tibial component of the joint replacement. This high wear rate has been attributed to high levels of contact stress at the metal to polymer interface and also to the fact that this contact stress condition can cause the polymer surface to oscillate from tension to compression during the sliding and rolling motions which occur at the joint during normal walking. These oscillating stresses can induce fatigue type failures in the polymer. In order to obtain a better understanding of these contact conditions an experimental and theoretical investigation of the contact situation has been undertaken. The investigation involved the use of embedded strain gauges to evaluate subsurface stresses in an experimental model of the contact condition occuring at the implant surfaces. Both normal contact loads and normal contact loads coupled with sliding loads were studied as this combined loading situation is known to occur during the movement of the knee. In addition, the experimental model was simulated using Finite Element Analysis (MARCK6.2, Marc Analysis Research Corp.) and the results of the two procedures were compared. The Finite Element method was also used to critically examine a number of parameters associated with the contact behaviour of the Ultra- High Molecular Weight Polyethylene (UIIMWPE) tibial component of knee implants, both in two-dimensions and in three-dimensions. The effect of polymer thickness on contact stress levels was critically examined and it was found to be important. The sliding action which occurs at the knee joint was also found to influence the contact stress levels in the implant polymer. In almost all recent designs of total knee joint implants, a metallic tray is used for retaining and supporting the UIIMWPE component in the tibial implant. Certain design features associated with the metal tray were investigated to assess their influence on the contact stress levels in the polymeric insert and the results of the study indicated that the metal tray may have a major influence on the long-term performance of the implant.

2 222 Simulations in Biomedicine IV 1 Introduction Joint replacement surgery for the alleviation of the pain and malfunction caused by arthritic diseases is now the accepted clinical procedure for restoration of function in patients with such knee disorders. Despite the clear success of the procedure in the vast majority of cases, there remain significant levels of failure. The knee joint is significantly more complex in both form and motion than the hip joint and the engineering challenges that remain are complex and demanding. The material combinations most widely used for total knee replacement surgery are a cobalt chrome molybdenum alloy for the femoral component and an ultra high molecular weight polyethylene for the tibial component as shown in Fig 1. Fig.l A typical total knee implant Most current designs of implant have a low level of conformity which gives a greater range of motion and reduces shear stresses at the interface between the implant and the bone. A consequence of the low conformity between the femoral and tibial components has been higher wear rates due to the higher levels of contact stress introduced by the non-conforming contact condition present in the prosthesis. In early 1993, Tsao et al [ 1 ] following examination of retrieved tibial components found extensive delamination caused by fracture of the polyethylene at a depth of about one millimetre below the surface. Cracks in the polyethylene were also found and these cracks contributed to fracture in the polyethylene in two of the components. In the products examined the articular surfaces of the femoral condyles and the tibial plateaux were flat in the medial-lateral direction. The tibial plateaux were also partially flat in the antero-posterior direction. The authors argued that these geometric aspects produced high stresses within the polyethylene. In contrast Argenson and O'Connor [2] achieved low wear rates using a highly congruent interface bet ween the femoral and tibial components. Serious levels of polyethylene wear and associated complications have also been reported in a number of other studies. All of the failures reported [3,4,5] were of components which were highly non-conforming and Engh et al, [4] found that five distinct design variables may have contributed to this accelerated wear. Both Engh et al [4] and Jones et al [5] suggested that the polyethylene thickness should not be less than 6 mm in tibial implants based on these reviews. The stress analysis conducted by Wright and Bartel [6, 7 and 8] examined the question of contact stress in some depth. Using experimental analysis, theoretical analysis and finite element analysis they concluded that 1. Since propagation of surface cracks perpendicular to the surface is related to cyclic tensile and compressive stresses acting tangentially to the surface and the maximum principal stress in the polyethylene occurs at the surface, the magnitude and oscillating nature of this stress has significant implications for the fatigue life of the polyethylene. 2. Propagation of subsurface cracks associated with shear stress and the maximum shear stress is a function of the conformity between the metal and polyethylene components.

3 Simulations in Biomedicine IV 223 With highly conforming geometries [hip implants] the maximum shear stress occurs at the surface and in non conforming geometries [knee implants] the maximum shear stress occurs below the surface. Since Wright et al [6] found that the higher contact stresses which occur in knee prostheses were not of themselves a sufficient reason for causing the damage modes observed in knee components such as pitting and delamination, they postulated that the combination of a large range of principal stress acting in an oscillating tensile to compressive condition and the occurrence of high subsurface shear stresses were the major causes of the failures in vivo that have been already described. They further suggested that a minimum thickness of 8-10 mm of polyethylene would reduce the likelihood of failure and that a greater degree of conformity between components in the medical-lateral direction was highly desirable. Bartel et al [7 and 8] examined in detail the effect of conformity and thickness on the stress behaviour of polyethylene with metal backing. They argued that the Hertzian theory of contact was inappropriate for this problem since: [a] Only the polyethylene undergoes deformation in the prosthetic situation. [b] That the area of contact is very small with respect to the typical dimensions of the contacting bodies. The experimental measurement of subsurface strains in a CT200 model using embedded strain gauges and the evaluation of stresses due to contact loads has been described in an earlier paper [9], Afiniteelement model of the UHMWPE component was also developed (see ref 9) and contact behaviour of the polymer was examined. 2 Results and Discussion 2.1 Strain Gauge Results Strain gauge readings were obtained from the loaded CT200 block for normally applied loads and results for gauges 2 and 3 are shown in Figs. 2 and 3. (Gauge directions shown in inset). The magnitude of the principal stresses were calculated and compared with the corresponding stresses obtained fromfiniteelement analysis. FE analysis was performed using MARCK6.2 software, (MARC Analysis Research Corporation, Palo Alto, CA). The model had 1496 isoparametric, plane strain quad elements, with loads and boundary conditions set to match the experimental conditions as described in refs [9,10 and 1 l].the principal stresses in the CT200 block for gauges 2 and 3 are shown in Figs. 4 and 5 along with corresponding values for principal stresses obtained from the FE model. The CT200 model was also subjected to normal and horizontal loads simultaneously to simulate the sliding condition known to occur in the implant situation. Strain results and the corresponding principal stress data are shown in Figs. 6 and 7. In relation to the normal loads, the strain readings were in line with expectations. Since Strain Gauge 2 was positioned 2.25mm from the centreline of the CT200 test block and 4.45mm below the surface, significant strains could be expected to occur in gauge 2. The gauge recorded no change in strain e, in leg 1, whereas legs 2 and 3 showed increasingly negative strains in e, and e, as the normal load increased as shown in Fig. 2. The applied load was purely compressive at the centreline of the CT200 block, and thus this strain behaviour seemed reasonable. Gauge 3, on the other hand, was positioned at approximately the same depth in the block [4.14mm] but was 4.81 mm off the centreline and this would explain the rise in tensile strain e, in leg 1 and the smaller magnitude of the compressive strains in e% and E; in legs 2 and 3 of the gauge.

4 224 Simulations in Biomedicine IV Mlcrostroln Gauge No.2 Load 1169N Load 1474N Load 1779N Load 2109N Load 2389N Fig. 2 Strain gauge readings for Gauge 2 for a range of loads. Mlcroitfdln Gauge 3 Load 1169N Load 1474N Load 1779N Load2109N Load 2389N Fig. 3 Strain gauge readings for Gauge 3 for a range of loads. Principal Stresses teuge 2 and FE - Max Priitc Stress O2 -* Min Princ Stress G2 A Max Princ Stress FE (2 Values) D Min Pnnc Stress FE (2 Val.es) Fig.4 Principal Stresses at Gauge 2 and for corresponding FE node Principal Stresses Gauge 3 and ME SMS 717 M.9S _^--^^ ^^-^ -* " Tt ; -05 " M 2.5 ^^^^"" ^^^^^ IOAD (N/rrm) MuPriicSlrMi Giug«) -*-Mm Prhc Siren n«jg«3 -*-Mw Priic Sites* FE(2 Vikj«>) F/g.5 Principal Stresses at Gauge 3 and for corresponding FE node

5 Simulations in Biomedicine IV 225 The stress values obtained from the experimental data shown in Figs 4 and 5 were in reasonable agreement with the results obtained from the finite element analysis. This demonstrated cleary the usefulness of this experimental technique for assessing the quality of FE data. Furthermore, these results suggest that embedded strain gauging can also provide a guideline as to the stress distribution in the contact region of mating solids. The strain results from the blocks subjected to sliding loads (Fig 6) showed that compression was occurring at the leading edge in agreement with Johnson [12] although in this case there were significant differences between the principal stresses obtained from strain data and the FE analysis.(fig.7) Fig.6 Strain gauge data for Gauge 2, Normal and Sliding Loads Max Principal Stresses and Max Shear Stress Gauge 2 and FE Sliding Loads?,49H H H Load (N/mm and N HOT) /<7#. 7 Principal Stresses and Shear Stresses Gauge 2, Normal and Sliding Loads and FE Analysis The severe strain gradients which occur within the contact zone make precise measurement of strains and stresses in the contact region experimentally very difficult. The reasonably good level of con elation between the stress values obtained from the experimental data and the FE data suggests that the simplification of the problem to a Plane Strain analyis of the CT200 block did not introduce excessive errors. The positioning of the strain gauge rossettcs in a vertical plane within the CT200 ensured precise alignment of all the gauges in a single plane. A further table of results for stresses at the gauge points is shown in Table 1 alongside corresponding maximum and minimum principal stresses obtained at nodal points in the FE model. This demonstrates the reasonable correlation between the techniques. While the technique of embedded strain gauging has significant experimental limitations, it appears that the method can provide reasonable guidelines regarding the stress levels in the contact region when the CT200 block is subjected to

6 226 Simulations in Biomedicine IV Gauge No NODAL STRESSES EXPERIMENTAL AND FE CT200 BLOCK Normal Load Oma* (N/mtrf) On.n (N/ram>) FBNode (N/mn») (Tmin (N/mtrf) Table 1 Stresses obtained from strain gauge data and corresponding FE stresses. Normal loading. In this study the analysis of strains in the CT200 block was confined to a single vertical axis in the block. This was a significant simplification of the contact problem being considered and the purpose of this simplification was to reduce the analysis to that of plane strain. Johnson [12] indicates that for this assumption to be valid in a contact situation, the thickness of the solid should be large compared to the size of the loaded region. The CT200 block had a thickness dimension of 65mm while the contact width dimensions, which could not be obtained from strain gauge data,were measured experimentally using Presensor film [13,14, and 15] and calculated using Hertz theory. These dimensions for the width of the contact region, which were also found to be in good agreement with predictions from FE analysis, ranged from 3.45mm to 7.0mm i.e. between 5 and 10 % of the thickness dimension as shown in Table 2. These results were obtained for Normal loading only and the values from Hertzian analysis and FE analysis are also shown. The strains obtained from the CT200 block were also compared with strain values predicted by the FE model. Strains measured at a gauge location corresponding to gauge 5 in the CT200 block had values of strain E, = 1094 istrain, c, = -1758p,Slrain while the FE model predicted strains of e, = 980u,Strain and &, = istrain. This proved that the experimental readings from the embedded strain gauges were in good agreement with the FE figures. In relation to the measurement of strains in the contact zone, the technique of embedded strain gauging has certain limitations due to the severe strain gradients in the vicinity of the contact Finite Element Analysis Normal Loading, UHMWPE Material The effect of thickness on UHMWPE material was examined using FE methods. The material was treated as elastic for this analysis and for the range of loads being considered, this was felt to be a reasonable assumption. Bartel et al [8] and Pappas et al [18] both conducted analyses which did not take account of the time dependency effects of the polymer and treated it as an elastic material for the purposes of their analyses, which further supports the approach adopted in tliis study. Similar plots of the maximum shear stresses (Figures 8 (a) and (b)) revealed that the thin component had a greater propensity to failure due to high subsurface shear stresses. The plots of the maximum shear stress show that the peak value of 3.785MPa for the 21mm component and 3.62MPa for the 7mm are both larger than the peak value (3.601MPa) for the 63mm component. In the case of the 7mm component the applied load was lower and notably for both of the thin components the position of the peak moves toward the surface. Of greater significance could be the fact that the peak value occurs more than 0.5mm closer to the surface of the block

7 LOAD(N/mm) Fuji Presensor Film Contact Width (2a mm) Simulations in Biomedicine IV 227 Hertz analysis Contact Width (2a mm) FE Analysis Contact Width (2a mm) 3A (Load in FE 55N/mm) 5.0 (Load in FE 82N/mm) 5.08 (LoadinFE130N/mm) Table 2 Contact Dimensions from Presensor Film, Hertz Analysis and Finite Element Analysis CT200 Block, Indentor Width 20mm, Rigid Indentor MM Shear Strew, Va Depth along Centreline UHMWPE Block 63mm Thick PJote offtfexshea Stress Vs Depth along Centreline UHMWPE Block 21mm and 7mm Thick Fig. 8 Plots of Maximum Shear Stress versus depth along the centreline of UHMWPE blocks (a) 63mm block; Peak value 3.601MPa, Depth 4.28mm and (b) 21mm block; Peak value 3.785MPa, Depth 3.78mm, 7mm block; Peak Value 3.62MPa, Depth 2.62mm. As previously discussed, the proximity of this peak to the surface could induce breakdown of the material. The distribution and magnitude ofc^ was also found to be significantly influenced by the component thickness. The stress distributions were similar to those found in the analysis of CT200 blocks but the differences in the magnitude of the peak tensile value were more marked, with a value of 1.988MPa for the 21mm component as against a value of 1.296MPa for the 63mm components, again indicating that polymer may be susceptible to thickness effects. 2.3 Normal and Sliding Loads. Sliding is believed to play a significant role in the failure mechanism of the UHMWPE inserts in knee implants as indicated by Blunn et al [ 19] and B artel et al [8] and thus the behaviour of the FE models when they undergo Normal and Sliding contact loads could provide important new insights into the prosthetic behaviour. Further treatment of the contact stresses associated with a contact condition involving Normal and Sliding loads was therefore conducted using Finite Element analysis. 2.4 FE Analysis Normal and Sliding Contact The FE models and meshes used to investigate Normal and Sliding loads were described in an earlier paper [8] and FE tests were conducted for different coefficients of

8 228 Simulations in Biomedicine IV friction, for two block thicknesses and for both CT200 and UHMWPE. Variations in the coefficient of friction were found to have only a small effect on the stress distribution in the case of sliding. This was initially felt to be a weakness in the capability of the software in handling sliding contact. Subsequent studies, however, which also considered rolling effects did show that the coefficient of friction influenced the stress distribution, suggesting that frictional effects on the sliding models being examined were indeed small. The coefficient of friction between the metallic femoral component and the polymeric tibial component can be as low as 0.04 and thus the influence of friction in the implant case is also considered to be almost negligible. The thick block of UHMWPE displayed a significant response to sliding loads suggesting that the lower elastic modulus of the UHMWPE may also influence the behaviour of solids in contact. Unlike the thick CT200 block which appeared not to respond significantly to sliding loads, the UHMWPE block clearly did. Plots of the contours of Maximum Shear Stress for Normal loading and for Normal loading with Sliding for the 63mm UHMWPE block are shown in Figure 9 and 10. The values of the peak shear stress rose significantly from 3.60MPa to 4.635MPa and the contours show a distinct tendency to bring the shear stress towards the surface of the block. While much of the attention in the literature has focussed on the failure of very thin polymeric components, it is notable that Apel et al [20] commented on the need to examine the performance of the polymer for thick components also. They noted that the material was prone to breakdown even in the thicker components and while such a breakdown may not necessarily require clinical intervention, there have been some indications that polymeric debris, such as could be produced by the shearing action described above, could cause unwelcome tissue reactions or possibly lead to loosening of the implant (Goodman and Lidgren, [23]). Further indications that the sliding action of the indentor on the polymer could contribute to failure of the UHMWPE was also found when the changes in 0, between the Normal and sliding situations were examined. Results are presented graphically in figures 11 and 12 and again it is clear that the sharp rise in a^, exhibited when there are sliding loads present, would further highlight the shortcomings of the UHMWPE in non-conforming knee joint situations. Further data obtained from the FE studies suggested that, when thin components of UHMWPE are being used, the influence of sliding on the contact stress levels in the material can be even more significant. Figures 13 and 14 show the differences in o, when almost identical loads are applied to the 21mm and 63mm block respectively. The thinner component has a peak tensile value for (J^ of 9.34MPa which is more than double the value (4.20MPa) occurring in the thick component. 2.5 Finite Element Analysis of Full Scale Components The initial analysis focussed on models which were approximately three times the scale of normal prosthetic components. This was to allow a strain gauged model to be constructed and also to take account of the large modulus mismatch between the CT200 and the UHMWPE. Having established a reasonable degree of confidence in the capability of the Finite Element method for analysis of the complex contact conditions previously described, a further detailed examination of some of the critical features of the tibial implants currently used was undertaken.

9 Simulations in Biomedicine IV 229 Fig. 9 Contour plot of Maximum Shear Stress for UHMWPE block 63mm thick, Normal Load. Fig. 10 Contour plot of Maximum Shear Stress for UHMWPE block 63mm thick, Normal and Sliding Loads. Fig.ll Plot of O* for UHMWPE block Fig. 12 Plot of <?* for UHMWPE 63mm thick, Normal and Sliding Loads. block 63mm thick, Normal Load. In particular, the role of rigid trays used to support the UHMWPE insert and the effect of polymer thickness was examined The role of rigid trays used to support the UHMWPE insert and the effect of polymer thickness Clearly, in many implant components in current use there could be an interaction between the metallic tray and the UHMWPE insert as the femoral component presses down into the polymer. To assess these effects finite element meshes of the components were created in which the indentor was treated as a rigid cylinder, as in earlier work, the polymer was treated as a plane strain elastic solid and the tray was considered to be a rigid body as shown in Figure 15.

10 230 Simulations in Biomedicine IV Tension at trailing edge tor moving vertically down Compression at leading edge I" Tangential gentlal or or Sliding Load Surface Stunt Sx Vt Position Normal and Sliding Loads UHMWPE Block 21mm Thick Poclllon tlong Si»U<«Fig. 13 Plot of 0* for UHMWPE block 21mm thick, Normal and Sliding Loads, Peak value 9.34MPa. Sliding as shown above. Surface Stress Vs Position Normal and Sliding Load UHMWPE Block 63mm Thick Fig.14 Plot of O* for UHMWPE block 63mm thick, Normal and Sliding Loads, Peak value 4.20MPa. Sliding as shown above. The influence of the bony support and the bone cement was not included in this analysis. Initially Normal loads were considered and two thicknesses of polymer were examined, namely, 14mm and 7mm. The 7mm insert corresponded to the minimum insert thickness recommended by Bartel [8] and others based on clinical and analytical findings. The magnitude of the applied loads corresponded to those occurring at the knee joint during normal walking, obtained from Morrison [21]. The insert in this case was retained by the two upright clips shown in Eigure 15. A plot of the Maximum Shear Stress along the central axis of the 14mm insert is shown in figure 16. The peak value was found to be 4.17MPa and this occurred at a depth of only mm. The presence of such a significant shear stress so close to the surface would clearly give rise to concern. In addition to investigating the position of the shear stresses, the deflection behaviour of the upper surface was also studied. A plot of displacement of the upper surface of the 7mm block is shown in Figure 17 and while the magnitude of the displacement is small at O.lmm, the geometry profile of the deflected surface suggests that the surface could be subjected to a significant tensile condition. This surface is also subjected to oscillating loads during walking and thus there appears to be a distinct possibilty that fatigue type failures of the polymer could occur.

11 cbody2 cbody3 Simulations in Biomedicine IV 231 Fig.15 FE mesh for Tray, UHMWPE inset and rigid indentor, 7mm insert shown, An examination of the distribution of pressure on the upper surface of the 7mm insert also showed that the stress distribution was no longer Hertzian probably due to the influence of the rigid metal tray. A plot of this distribution is shown in Figure 18 and the reaction to the rigid cylindrical indentor resembles the response of an elastic material to a rigid flat punch as described by Galin [22]. It is worth noting that the contact pressure predicted here is close to the yield strength of the material of 23MPa. The displacement of the lower surface of the polymer (Figure 17) when subjected to normal loads also displayed a response which although different from that found for the 14mm did, nonetheless, indicate that the retention mechanism and the thickness of the component may both contribute to high stresses in the polymer. This further highlights a thickness effect and suggests that the relatively large displacements for the thinner insert are causing the deviation from the predicted values. 2.6 Discussion of FE Analysis and Thickness Many authors have indicated that when the thickness of the UHMWPE insert in an implant is less than 8mm, the likelihood of failure increases. Tests were conducted on FE models of CT200 and UHMWPE to assess the influence of thickness on the stress levels and satisfactory adherence to Hertzian theory was demonstrated for the thicker components. With decreasing component thickness Hertz theory is unlikely to be capable of predicting stress levels since the half-space condition no longer applies. This was found to be the case and further investigations concerning thickness were conducted. Reduction of thickness of both CT200 and UHMWPE revealed interesting trends.for normal loads as the block thickness was reduced the peak shear stress magnitude increased and notably in the case of the UHMWPE model, the FE predicted that the position of the peak shear stress moved towards the surface. The more severe condition occurring in the UHMWPE material due to the reduction in thickness is clearly seen in Figure 8 (a) and (b) for the normal loading case. The value of the maximum shear stress increases as thickness decreases and perhaps, more critically for the implant situation, the position of the peak moves towards the surface and thus if oscillating loads were present, the likelihood of a fatigue type failure of the material would increase. Thickness of the UHMWPE was further examined using models subjected to normal and sliding loads. The peak shear stress increased due to sliding as indicated on Figures 9 and 10 and also due to the reduction in thickness.

12 232 Simulations in Biomedicine IV Max Shear Stress Vs Depth along Centreline UHMWPE Insert In Tray 14mm Thick -Max Shear Sire (MPa) v t< d Depth along Centreline Fig. 16 Plot of Maximum Shear Stress versus Depth along centre line, UHMWPE insert 14mm thick, Peak value 4.17MPa, Position mm from surface. Displacement of lower insert surface (Y) 7mm UHMWPE Insert 06E-01 > * P 05E-01 7\ /\ 2 04E-01 7 > / \ +* 1 03E-01 - / \ f V o> -\ Q2E-01 - ^» \ ti 01E-01 - \ f T -DisplacemQnl(Y) «1 HOP m 4 / UMIIHIIIIIIHIU/ Q- g 9QE E E 02 ^ Q fiaf-ap II t H 1 1 t *.**.# I i 1 ( T- cd CM i CM 10 CM od CO cvi CO LO Position rusmuii Fig.17 Plot of Displacement in the y- direction versus Position along the lower surface, 7mm UHMWPE insert in Tray, Normal Load, Peak Displacement mm Plot of Stress In Y direction Ve Position along Surfao* UHMWPE, 7mm Insert In Tray, Normal Load Fig. 18 Plot of 0^ Stress versus Position along surface, 7mm UHMWPE insert in Tray, Normal Load. Figure 13 and 14 demonstrate clearly that the surface stress also rises sharply and a severe tensile condition can occur in the surface at. the edge of the contact region as a

13 Simulations in Biomedicine IV 233 result of the reduction in thickness in the presence of sliding loads. This too is a cause for concern in implant situations and in the light of these indicators, further analysis of models which had dimensions, boundary conditions and loads closer to those found in total knee implants were also examined as indicated in section Conclusions 1. The experimental methods of embedded strain gauging can be used to obtain preliminary values for the strain and subsequently the stress behaviour of contacting solids. 2. The technique has been found to be a moderately sucessful reference method for assessing the validity of results obtained when using computational techniques. This was found to be the case when two loading conditions were examined, namely [a] Normal Loads [b] Normal and Sliding Loads The benchmarking of the software and of the models again used Hertzian theory for comparisons and the results which have previously been reported McGloughlin et al. [8,9] demonstrated that both the model and the software were providing satisfactory responses to the applied loads. 3. The presence of the metallic tray appears to influence the response of the UHMWPE insert to contact loads and this may be further aggravated by the sliding action. Since the sliding load is not stationary and the point of application moves forward and back along the surface of the polymer, the prediction of significant deflections raises issues concerning the material behaviour at the tray to insert interface. There appears to be a strong likelihood that the surface will cycle from tension to compression, a condition which is known to give rise to fatigue type failures. There was a change in the pattern of loading between the thicker (14mm) and the thinner (7mm) component when the polymer was supported by a rigid metal tray. In addition to the difference in shear stress behaviour mentioned above which showed increases in magnitudes as thickness reduced, the FE models also predicted that the deflections of the components within the trays changes markedly with changes in thickness. For the 14mm insert, FE predicted that the position of the maximum shear stress was a mere 1.31 mm from the surface of the polymer. The clinical data reported by B artel et al [8] indicated subsurface cracking of the polymer at approximately 1.5mm which would suggest that the FE predictions are very good. Indeed the FE predictions for the behaviour of the UHMWPE insert provide valuable new insights into the behaviour of the polymer when supported by the tray and pose many new questions concerning the use of metal trays for retaining the UHMWPE tibial insert in knee implants. 4. The results presented suggest that the mechanical properties of UHMWPE maybe inadequate when the material is subjected to the contact loads and stresses described and that there is a need for a bearing material for knee implants which has a better tribological and bearing performance. 5. The results from the FE analysis confirm that sliding contact plays a significant part in the failure mechanism of the UHMWPE tibial insert. Sliding involving non conforming geometries appears to raise stress levels considerably and when the further influence of reducing polymer thicknes is considered, this effect becomes more severe. These findings quantitatively and qualitatively agree with the theoretical treatments of Jin et al.[24], Johnson [25], Hamilton [26] and Smith and Liu [27] and with the clinical evidence presented by Blunn et al [ 19] and Engh et al [4].

14 234 Simulations in Biomedicine IV References 1 Tsao, A., Mintz, L., McRae, C., Stulberg, D. and Wright, T.M.; Failure of the Porous- Coated Anatomic Prosthesis in Total Knee Arthroplosty due to severe Polyethylene Wear. JBJS Vol. 75-A NO 1 January pp Argenson, J.N. and O'Connor, J.J.; Polyethylene wear in meniscal knee replacement. JBJS Vol. 74-B N<>2 March pp Nolan, J.F. and Bucknill, T.M.; Aggressive granulomatosis from Polyethylene failure in an uncemented knee replacement. JBJS Vol. 74-B N l Jan pp Engh, G.A., Dwyer, K. and Hanes, C.; Polyethylene wear of metal backed tibial components in total and unicomparunental knee prostheses. JBJS Vol 74-B N l Jan pp Jones, S.M.G., Finder, I.M., Moran, C.G. and Malcolm, A.J.; Polyethylene wear in uncemented knee replacements. JBJS Vol. 74-B N l Jan pp Wright, T.M. and Bartel, D.L.; Surface damage in polyethylene joint components in The Changing Role of Engineering in Orthopaedics. I Mech E, London pp Bartel, D.L., Bicknell, V.L. and Wright,T.M.; The effect of conformity, thickness and material on stresses in ultra-high molecular weight components for joint replacement JBJS Vol 68-A, NO 7, September pp Bartel, D.L., Burstein, A.M., Toda, H.H., and Edwards, D.L.; The effect of conformity and plastic thickess on contact stresses in metal-backed plastic implants. Journal of Bioniechanical Engineering, August 1985, Vol 107, pp McGloughlin T. and Monaghan J., Contacts Stresses in Tibial Components of Knee Implants in Computational Methods and Experimental Measurements VII, Capri, Italy, 16-18th May 1995 pp Eds Carlomagno, G.M. and Brebbia, C.A., Computational Mechanics Publications, McGloughlin T. and Monaghan J., Finite element analysis of the Contact behaviour of Metal to Plastic interfaces in Total Knee Joints in Contact Mechanics II Computational Techniques, Ferrara, Italy, ll-13th July 1995 pp Eds Aliabadi, M.H. and Alessandri, C., Computational Mechanics Publications, McGloughlin T. M., ; Contact Stress Analysis of Tibial Components of Prosthetic Knee Implants, Ph.D. Thesis, 1995, University of Dublin, Trinity College. 12 Johnson, K.L.; One hundred years of Hertz contact. Proceedings l.mech.e, Vol 196, pp Hale, J.E. and Brown, T.D.; Contact stress gradient detection limits of Presensor film. Journal of Biomechanical Engineering, Trans ASME, Vol. 114, August pp Lee, J.W. and Rim, K.; A new method for measurement of finger-phalangeal force. Experimental Mechanics, December, 1990.pp Hasler, E.M., Hertzog, W., Fick, G.H., Appropriateness of plane pressure-sensitive film calibration for contact stress measurements in articular joints. Clinical Biomechanics Vol.11, No.6, pp , Hamilton,G.M. and Goodman, L.E.; The stressfieldcreatedf by a circular sliding contact. Journal Appl. Mech. Vol. 33 [1966] pp Hanson, M.J. and Keer, L.M.; Cyclic tangential loading of dissimilar elastic bodies. Int. Journal Mech Sci 1989 Vol. 31 No Pappas, M.J. Hakris, G. and Buechel, F.F. ; "Evaluation of contact stresses in metalplastic total knee replacements" in Biomaterials and Clinical applications. Eds Pizzoferroto, A., Marchetti, P.G., Ravaglioli, A.and Lee, A.J.C. Elsevier Blunn, G.W., Walker, P.S., Joshi, A. and Hardinge, K. ;"The dominance of cyclic sliding in producing wear in total knee replacements"; Clinical orthop. and Rel. Research, 1991, No. 273, Apel, D.M., Toggi, J.M. and Dorr, L.D. ; "Clinical comparison of all polyethylene and metal-backed tibial components in total knee arthroplasty"; Clinical Orthop. and Rel. research, 1991 No. 273,

15 Simulations in Biomedicine IV Morrison, J.B.; "The mechanics of the knee joint in relation to normal walking"; Journal of Biomechanics. 1970, Vol Galin, L.A.,; Contact Problems in the Theory of Elasticity, Moscow, 1953 (English Translation, H.Moss (1961)) 23. Goodman, S. and Lidgren, L.; "Polyethylene wear in knee arthroplasty, a review"; Acta Orthop. Scand Vol 63, No Jin, Z.M.,Stewart, T., Auger, D.D., Dowson, D., and Fisher, J.; " Contact Pressure prediction in total knee joint replacements Part: application to the design of total knee joint replacements"; Proc. I. Mech. E., 1995 Part H Vol.209 (HI) Johnson, K.L.,; Contact Mechanics Cambridge University Press Hamilton, G.M. and Goodman, L.E.; "The stress field created by a circular s l i d i n g contact" Trans ASME, Journal of App. Mech Vol 33, Smith, J.O. and Liu, C.K.; "Stresses due to tangential and normal loads on an elastic solid with application to some contact stress problems"; Trans ASME, Journal of Applied Mechanics, 1953 Vol 20 Pt