Proceedings of the Institution of Mechanical Engineers, Part H- Journal of Engineering in...

251

Elasto-plastic contact analysis of an ultra-highmolecular weight polyethylene tibial component basedon geometrical measurement from a retrieved kneeprosthesis

C H Cho1*, T Murakami2, Y Sawae2, N Sakai2, H Miura3, T Kawano3 and Y Iwamoto31Department of Mechanical Systems and Environmental Engineering, The University of Kitakyushu, Japan2Department of Intelligent Machinery and Systems, Kyushu University, Fukuoka, Japan3Department of Orthopaedic Surgery, Kyushu University, Fukuoka, Japan

Abstract: The wear phenomenon of ultra-high molecular weight polyethylene (UHMWPE) in kneeand hip prostheses is one of the major restriction factors on the longevity of these implants. Especiallyin retrieved knee prostheses with anatomical design, the predominant types of wear on UHMWPEtibial components are delamination and pitting. These fatigue wear patterns of UHMWPE arebelieved to result from repeated plastic deformation owing to high contact stresses. In this study, theelasto-plastic contact analysis of the UHWMPE tibial insert, based on geometrical measurement forretrieved knee prosthesis, was performed using the nite element method (FEM) to investigate theplastic deformation behaviour in the UHMWPE tibial component. The results suggest that the maxi-mum plastic strain below the surface is closely related to subsurface crack initiation and delaminationof the retrieved UHMWPE tibial component. The worn surface whose macroscopic geometricalcongruity had been improved due to wear after joint replacement showed lower contact stress atmacroscopic level.

Keywords: knee prosthesis, ultra-high molecular weight polyethylene (UHMWPE), fatigue wear,nite element method (FEM), elasto-plastic contact analysis, plastic strain

1 INTRODUCTION and eventual loosening of knee and hip prostheses. Thesereactions restrict the longevity of the knee and hipprostheses [24]. Despite quite a number of studies onUltra-high molecular weight polyethylene (UHMWPE)the wear of UHMWPE [512], the wear mechanism ishas been generally used as a bearing material of thenot clear yet. Therefore, the wear phenomenon ofarticulating surface in total joint replacements for overUHMWPE components in total joint replacements40 years. It possesses excellent properties, such asis regarded not only as one of major concern to bothnotably high abrasion resistance, low friction, highorthopaedists and engineers, but also as a research sub-impact strength, excellent toughness, low density, bio-ject that requires urgent solutions and comprehensivecompatibility, and biostability, which make it particu-studies. In order to minimize the wear of UHMWPElarly attractive for use as bearing surfaces in total jointand to improve the longevity of articial joints, it isreplacements. In fact, UHMWPE is the sole polymericnecessary to clarify the factors inuencing the wearmaterial currently used for the liner of the acetabularmechanism of UHMWPE.cup in total hip replacements and the tibial insert and

Especially for the articial knee joint with anatomicalpatellar component in total knee replacements [1].design, the contact stresses in the UHMWPE tibial com-However, the wear of UHMWPE causes serious prob-ponent are generally higher than the yield stress of thelems both clinically and mechanically, such as osteolysismaterial during normal gait. In addition, the predomi-nant types of wear on reported simulator-tested andThe MS was received on 30 April 2003 and was accepted after revision

for publication on 7 April 2004. retrieved UHMWPE tibial components are delamination* Corresponding author: Department of Mechanical Systems and and pitting [1317]. Figure 1(a) shows such an exampleEnvironmental Engineering, Faculty of Environmental Engineering, The

of a retrieved UHMWPE tibial insert with severe wear,University of Kitakyushu, 1-1, Hibikino, Wakamatsu-ku, Kitakyushu,Fukuoka, 808-0135, Japan. including delamination and pitting [18]. The consensus

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252 C H CHO, T MURAKAMI, Y SAWAE, N SAKAI, H MIURA, T KAWANO AND Y IWAMOTO

is that both surface failures are the results of fatigue, UHMWPE tibial component and the femoral compo-nent of the retrieved knee prosthesis used in this studywith delamination being caused when subsurface cracks

continue to propagate in a tangential path relative to the are shown in Figs 1(a) and (b). This retrieved MG I-type knee prosthesis had a lower degree of conformitysurface and pitting being caused by cracks that emanate

at the surface and then propagate into the UHMWPE between the femoral component and the UHMWPEtibial component (the virgin component is nearly at).component [1]. These facts suggest that the fatigue

fracture that causes microcracks both on and below the The medial side of the retrieved UHMWPE tibial insertshown in Fig. 1(a) demonstrated more excessive wearsurface of the UHMWPE tibial component and the gen-

eration of wear particles as fatigue type are closely and higher plastic deformation than the lateral side.related to the cyclic plastic-strain accumulation, alsoknown as ratcheting or incremental collapse [19].

The primary objective of this study was to investigate 2.2 FEM modelling and analysis conditionsthe fatigue wear mechanism of the UHMWPE tibial

On the basis of the geometrical measurement for thecomponent. In this study, the elasto-plastic contact

femoral component and the UHMWPE tibial compo-analysis of the UHMWPE tibial component based on

nent of the retrieved MG I-type knee prosthesis, a three-three-dimensional geometric measurement for retrieved

dimensional FEM model of the retrieved knee prosthesisknee prosthesis was performed using the nite element

was produced, as shown in Fig. 2. A three-dimensionalmethod (FEM) in order to investigate the plastic defor-

coordinate measuring machine (BH-V504, Mitsutoyo,mation behaviour in the UHMWPE tibial insert. The

Japan) was used to measure the geometrical congur-determinative method of the contact position between

ations of the femoral and tibial components in thethe femoral component and the UHMWPE tibial com-

macroscopic level. Three-dimensional computer graphicsponent for the retrieved knee prosthesis was developed.

software (Rhinoceros, Robert McNeel and Associates)The three-dimensional FEM model of the retrieved knee

and FEM modeling software (HyperMesh, Altair Com-prosthesis with worn contact surfaces was also produced.

puting Inc.) were used to generate meshes of bothOnly the static contact condition between the femoral

components.and tibial components in the standing position was con-

The UHMWPE tibial insert was assumed to be ansidered in this study; the inuence of change of contact

elasto-plastic body that has the Poissons ratio of 0.4position and the kinematic contact condition will be con-

and meshed using six-node solid elements. It was alsosidered in a further study.

assumed that the bottom surface of the UHMWPEtibial insert was entirely xed to the rigid metallic tibialtray. The contacting metallic femoral component was

2 MATERIALS AND METHODSassumed to be a rigid body and meshed using three-noderigid surface elements. The contact between the femoral

2.1 Materialscomponent and the UHMWPE tibial component wassimulated as a rigid body (the metallic femoral compo-In this study, the metallic femoral component and the

UHMWPE tibial component of a retrieved Miller- nent) deforming a soft body (the UHMWPE tibialcomponent).Galante I (MG I) porous total knee system (right

side, Zimmer Inc., USA) were used to produce the It is well known that the loads on the UHMWPEtibial components can reach peak values of three timesthree-dimensional FEM model of the retrieved knee

prosthesis. The knee prosthesis was retrieved from a 68- the body weight during normal walking conditions andcan reach between four and ve times the body weightyear-old man (162 cm, 93 kg) and the in vivo duration

of the retrieved knee prosthesis was 133 months. The during more stressful activities, such as walking upstairs

Fig. 1 Components of a retrieved MG I-type knee prosthesis (right side): (a) UHMWPE tibial component,(b) femoral component

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253CONTACT ANALYSIS OF A UHMWPE TIBIAL COMPONENT

an extension rate of 50 mm/min. using a material testingmachine (AGS-10kNG, Shimadzu, Japan). Elongationbetween gauge marks during the tensile tests wasmeasured by a video-type, non-contact extensometer(DVE-100/200, Shimadzu, Japan). Five or more speci-mens were tested for determination of material proper-ties of the UHMWPE. Results of the tensile testsperformed to failure were also analyzed to generate truestressstrain curves in a similar method to the previousliterature [21].

Figure 4 shows the mean results of these tensile teststogether with the simplied elasto-plastic material modelof the UHMWPE used in the FEM analysis. The linearelastic modulus of 498 MPa and the yield stress of

Fig. 2 Three-dimensional FEM model of the retrieved knee 13.3 MPa were determined from this true stressstrainprosthesis curve.

or running [2]. In this FEM analysis, the femoral2.4 Experiment for determination of contact positioncomponent was simply pressed into the UHMWPE tibial

component with a constant normal load of 3 kN A preoperative radiograph of the retrieved knee pros-(approximately three times the patients body weight). thesis (right side, standing position) is shown in Fig. 5.A coecient of friction between the femoral component Estimating from the clearance gap between the metallicand the UHMWPE tibial component was assumed to be femoral component and the tibial tray, the medial side0.1. The FEM analysis in this study was performed using has a narrower clearance gap than the lateral side. Thisthe commercial FEM analysis software ABAQUS/ fact corresponds to the excessive wear and high plasticStandard version 5.8[20]. deformation observed in the medial side. However, it is

dicult to determine the three-dimensional contactposition between the femoral and tibial components in2.3 Experiment for FEM material modelthe human body with only a sheet of radiograph.

In this study, UHMWPE was assumed to be an incom- In this study, it was assumed that the contact positionpressible elasto-plastic material and simple tensile tests between the femoral and tibial components in the exten-of the UHMWPE (compression molding, molecular sion position is the position that maximizes the contactweight#4106) were carried out in a temperature- area between both components. In order to determinecontrolled container lled with physiological saline this contact position, the experimental apparatus shown(0.9 per cent NaCl ) at 37 C (body temperature), which in Fig. 6. was constructed. For ease of the experiment,simulates in vivo conditions, in order to establish an the retrieved knee prosthesis was set up in an invertedelasto-plastic material model of the UHMWPE used in position as shown in Fig. 6. A material testing machinethe FEM analysis.

The experimental apparatus for the simple tensile testsis shown in Fig. 3. Tensile test specimens were tested at

Fig. 4 True stressstrain curve of UHMWPE used in theFig. 3 Material testing machine with a container for simu-lation of in vivo condition FEM analysis (in saline 37 C)



lational motions. A ball joint and an XY table wereused to allow the rotational, varusvalgus, and trans-lational degrees of freedom of movement to the femoraljig. The UHMWPE tibial component was entirely xedon the tibial jig (upper at plate for compression), whichwas constrained for all motions with the exception ofthe axial movement for tibial axis load.

A pin was xed vertically on each jig surface of bothcomponents, as shown in Fig. 6, in order to determinean initial position of the femoral component prior tocontact of both components. A point that brings bothpin tips in line under unloaded condition was set as areference point, and then a position of the femoral com-ponent at this point was determined as an initial positionat the extension position (Fig. 7).

The retrieved knee prosthesis used in this study had ahigher degree of conformity between the femoral andtibial components than the virgin one, because of severewear and high plastic deformation of the UHMWPEtibial component.

After contacting of both components, the contact areawas measured by a computerized contact pressure andcontact-area measurement system, including a tactilesensor for knee prostheses (K-SCAN, Nitta, Japan)under a constant tibial axis load of 1 kN. In order todetermine the most conforming contact position by per-forming the compensations to friction of the contact sur-

Fig. 5 Preoperative radiograph of the retrieved case (right faces and friction of the ball joint, the position and theside, standing position) attitude of the femoral component were changed from

the initial position in the range of anteriorposterior displacement of 6 mm, mediallateral displace-(AGS-10kNG, Shimadzu, Japan) was used to apply thement of 3 mm, exionextension angle of three degrees,tibial axis load.internalexternal rotation angle of 12 degrees andThe femoral component cemented on the femoral jig

was allowed the rotational, varusvalgus, and trans- adductionabduction angle of two degrees. Ten or more

Fig. 6 Schematic drawing of the experimental apparatus for determination of contact position between thefemoral component and the UHMWPE tibial component



As a result of this test, there was a slight error in thetranslation distance only in a horizontal direction ofFig. 8. This error was appropriately corrected by theuse of a photographic image with markers shown inFig. 8 using a 3.34 mega pixel digital camera (DSC-S70,Sony, Japan).

The contact position between the femoral componentand the UHMWPE tibial component shown in Fig. 8was reproduced in the three-dimensional computergraphics software. Figure 9 shows the contact positionthat was reproduced through the use of the dataobtained from this experiment mentioned above.

In reality, it is thought that the medial side and thelateral side of the UHMWPE tibial component havedierent load-carrying ratios respectively in vivo. How-ever, it is impossible to calculate the load-carrying ratioswith only a sheet of radiograph shown in Fig. 5. Theretrieved case shown in Fig. 5 was judged to be a nearlynormal knee alignment because the femorotibial angleFig. 7 Initial position between the femoral component andwas 170 degrees and the Mikuliczs line passed throughthe UHMWPE tibial componentnear the centre of the knee joint in the preoperativeroentgenographic measurement. Therefore, a constantnormal load of 3 kN was applied to a centroid of thecontact-area measurements were performed for determi-

nation of the contact position between both components. femoral component in the nally determined contactposition shown in Fig. 9.A position that showed the largest contact area was

determined as a rational contact position at the extensionposition, and then the translation distances and therotation angles of the femoral component from the initial 3 RESULTSposition to this contact position were measured.

In this study, the three-dimensional electromagnetic The validity of the reproduced contact position of theFEM model shown in Fig. 2 was rst examined in thetracking device (3SPACE FASTRAKTM, Polhemus

Inc., USA) was used to measure the translation distances contact analysis. For this purpose, a comparison betweenthe contact pressure distribution obtained from the FEMand the rotation angles of the femoral component.

Electromagnetic sensors are used to determine positions analysis and the measurement result obtained from theand directions of an object in this device. Two sensors(receivers in Fig. 6) were used in this experiment. Onewas attached on an acrylic arm xed in the femoral jigfor the position measurement of the femoral componentafter contacting of both components. The other wasattached on an acrylic needle bar and used to measurethe initial position of the reference point (the tip of thelower pin in Fig. 6).

The accuracy of this device is particularly susceptibleto metallic instruments and electric equipments aroundthe sensors. In order to minimize the eects of theseequipment, the sensors were kept as far away from themetallic jig, material testing machine, and personal com-puters as possible by the use of the acrylic extension armand the acrylic needle bar.

However, there was no guarantee that the eects ofthese equipment on the sensors were completely removedby this method. Therefore, the accuracy of the electro-magnetic tracking device was examined under theseexperimental conditions by means of a comparisonbetween the measurement results in a place that has nometallic or electromagnetic materials and the measure- Fig. 8 Contact position between the femoral component and

the UHMWPE tibial componentment results under the material testing machine.



Fig. 12 An example of element set and the position of cross-sections shown in Fig. 13

and 13. Figures 10 and 11 show the contour plots of thevon Mises equivalent stress and the equivalent plasticFig. 9 Reproduced contact position in the three-dimensionalstrain on the surface of the UHMWPE tibial component.computer graphics software

In this contact analysis, in order to investigate thecontact-stress distribution and the plastic-deformationtactile sensor was performed. The contact regionsbehaviour in the cross-sections of the UHMWPE tibialobtained from both methods were nearly corresponding.component, element sets of the cross-sections in theThe results of the elasto-plastic contact analysismedial side and the lateral side were constructed.between the metallic femoral component and theFigure 12 shows such an example of the element set.UHMWPE tibial component are shown in Figs 10, 11,

Figure 13 shows the cross-sections that have maxi-mum values of the von Mises equivalent stress and theequivalent plastic strain in the medial and the lateralsides of the UHMWPE tibial component. The positionsof these cross-sections and the direction of view are alsoshown in Fig. 12.

In the case of the retrieved UHMWPE tibial compo-nent in this study shown in Fig. 1(a), the medial sidedemonstrated more excessive wear and higher plasticdeformation than the lateral side. For this reason, themedial side had higher surface conformity for thefemoral surface than the lateral side, and thus the medialside demonstrated wider contact area and lower con-tact stress than the lateral side, as shown in Fig. 10.

Fig. 10 Contour plot of von Mises stress on the surface of Consequently, additional plastic deformation did notthe UHMWPE tibial component occur on the medial side as shown in Fig. 11. On the

contrary, considerable plastic deformation arose onthe lateral side that had maintained lower surface con-formity due to relatively slight wear and low plasticdeformation.

Though the maximum contact stress occurred in theregion of the surface to 2 mm below the surface in themedial side with improved surface conformity, as shownin Fig. 13(a), the value was lower than the yield stressof the UHMWPE.

In contrast to the medial side, it was found that thehigh contact stress that exceeds the yield stress of theUHMWPE and the considerable plastic strain were gen-erated below the surface in the lateral side with lowersurface conformity (nearly at) as shown in Fig. 13(b)Fig. 11 Contour plot of plastic strain on the surface of the

UHMWPE tibial component and (c).



Fig. 13 Contour plots of von Mises stress and plastic strain in the UHMWPE tibial component

4 DISCUSSION

The previous study [18], which was performed by someof the authors, included static and kinematic FEM con-tact analyses, using a simplied knee prosthesis modelwith a hemispherical rigid ball and an UHMWPE plate,for evaluating the inuence of polyethylene thicknessand slip ratio on the fatigue wear of the UHMWPEtibial component. This previous study suggested that themaximum plastic strain in the UHMWPE tibial compo-nent would occur at approximately 12 mm below thesurface.

In addition, in the case of this static contact analysisbased on geometrical measurement in the macroscopic

Fig. 14 X-ray CT image of the retrieved PFC-typelevel for the retrieved knee prosthesis, the maximumUHMWPE tibial component, including subsurfaceplastic strain in the UHMWPE tibial componentcracksoccurred at approximately 11.5 mm below the surface

of the lateral side. These depths nearly correspond tothe location of subsurface cracks found in the retrieved These microcracks can then propagate at a high rate in

a tangential path relative to the surface by the maximumPress-Fit Condylar (PFC) type UHMWPE tibial com-ponent with anatomical design in the previous study [22] shear stress or shear stress with maximum amplitude that

occurs in the subsurface and eventually produces theas shown in Fig. 14. Work conducted by Sathasivam andWalker [23] has also shown that the damage function delamination. The wear particles of UHMWPE will be

nally generated by this delamination.values, which were used to predict the susceptibility todelamination wear of the polyethylene, peaked at similar It is believed that the UHMWPE wear particles with

various sizes that are completely separated from the sur-depths to the present study.Considering the generation process of the UHMWPE face of the UHMWPE tibial component will intervene

between main contact surfaces of the knee prosthesis aswear particles due to fatigue damages from the resultsobtained in these studies, the maximum plastic strain, third-body wear particles. These wear particles can accel-

erate the wear process of the UHMWPE tibial compo-which occurs below the surface of the UHMWPE tibialcomponent, will increase with every pass of the femoral nent, and these wear particles themselves can become

smaller microscopic wear particles through deformationcomponent under cyclic loading and/or motion. Also,this accumulated residual plastic strain by cyclic loading and split processes.

In the microscopic observation using a laser micro-and/or motion can reach a certain value, that is the duc-tile limit of the UHMWPE, where microcracks will be scope for the retrieved UHMWPE tibial component

shown in Fig. 1(a), a considerable number of micro-initiated in the subsurface of the UHMWPE tibial com-ponent as postulated in the previous literature [19]. scopic surface protuberances, craters, and scratches were



observed in the medial side [17]. On the contrary, several to more exact FEM simulation for the fatigue wearbehaviour of the UHMWPE tibial component.early stages of the delamination (i.e. which have not yet

In addition, changes of in vivo contact position andled to delamination, but have produced the subsurfacekinematic conditions between the articular bearingcracks on the propagation) were observed in the lateralsurfaces have a direct inuence on the elasto-plasticside, which was atter and smoother than the medialdeformation behaviour of the UHMWPE tibial compo-side. It was found that some of these subsurface locationsnent, and thus its fatigue wear behaviour. Therefore, itof the predelamination nearly correspond to the locationis necessary to investigate the inuence of exionof the maximum plastic strain in this FEM analysis.extension motion and the long-term plastic-strainOn the basis of the results from the FEM analysis inaccumulation. It also requires further improvement, suchthis study and the previous studies [17, 18, 22], theas an addition of the knee-joint ligaments and thefatigue wear process in vivo of the UHMWPE tibial com-patellar component, which can control and limit theponent from the virgin one to the wear pattern of themotion of the femoral component to the FEM knee-retrieved case in this study was estimated as follows.prosthesis model developed in this study to performIn the early stage immediately after the total kneethese repeated kinematic contact analyses.arthroplasty, which has low surface conformity for the

However, considerable plastic strain occurred belowfemoral component, the plastic deformation due tothe surface of the UHMWPE tibial component for evenexcessive contact stress will occur at the subsurface ofthe simple static contact condition at the extensionthe UHMWPE tibial component. The subsurface cracksposition with the largest cotact area, and the depth ofwill be initiated and propagated subsequently by thethe maximum plastic strain nearly corresponded to thecyclic loading and/or motion. The macroscopic delami-location of the subsurface cracks found in the retrievednation wear will eventually occur in this stage.UHMWPE tibial component. These results suggest thatIn the case of the medial side of the retrievedthe maximum plastic strain below the surface has a sig-UHMWPE tibial component in this study, though thenicant inuence on the fatigue wear behaviour of themean contact pressure was decreased by the improve-UHMWPE tibial component, such as subsurface crackment of the macroscopic surface conformity resultinginitiation and delamination. Also, considering that thefrom the subsequent wear, which includes adhesive andmedial side, which had improved the macroscopic sur-abrasive wear, together with the early stage delaminationface conformity due to progression of the wear, showedand the plastic deformation, it would appear that thethe elastic contact for even 3 kN loading, the adoptionmicroscopic pitting nally became a predominant fatigueof the conguration of the worn surface, which has

wear pattern on account of the locally excessive stressin vivo duration of more than a decade, in the original

and the stress concentration at the microscopic surfacesurface design may decrease the fatigue wear of the

protuberances, craters, and scratches.UHMWPE tibial component. In addition, it is necessary

There were some limitations in this study. The to evaluate the various retrieved cases in a further studystressstrain curve used in this study was obtained from since there are considerable dierences in alignment,virgin polyethylene because it was impossible to get the range of movement, and walking condition in each case.tensile test specimens from the retrieved UHMWPEtibial component. Mechanical properties includingstrength of the polyethylene may be altered by gamma- 5 CONCLUSIONirradiation, oxidation, and degradation, as reported inother studies [1, 2, 7]. In this study, three-dimensional FEM models of the

The authors also could not investigate the inuence femoral component and the worn UHMWPE tibialof the microscopic surface asperities, craters, and component based on geometrical measurement for thescratches on the fatigue wear because the three- retrieved knee prosthesis were produced. The elasto-dimensional coordinate measuring machine (BH-V504, plastic contact analysis under static conditions of bothMitsutoyo, Japan) used in this study was the surface components was also performed using the nite elementcontact type that uses a probe with a diameter of 2 mm. method. The medial side of the UHMWPE tibial compo-Therefore, further investigations in terms of the contact nent with improved surface conformity due to excessivestress conditions and the plastic deformation behaviours wear, including delamination, showed the elastic contactat the microscopic surface asperities, craters, and for even 3 kN loading at the extension position. On thescratches in the microscopic level are required. For this other hand, considerable plastic strain occurred belowpurpose, further FEM modeling based on geometrical the surface of the lateral side with low surface conform-measurement using a three-dimensional coordinate ity. It was also found that the depth of the maximummeasuring machine that has higher resolution and accu- plastic strain in the FEM analysis nearly correspondedracy for the worn surface at the microscopic level is also to the location of the subsurface cracks found in therequired. It is believed that a combination of both the retrieved UHMWPE tibial component. From these

results, it was indicated that the maximum plastic strainmacroscopic and the microscopic FEM analyses leads



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