the effect of bearing congruency, thickness and alignment

8/10/2019 The Effect of Bearing Congruency, Thickness and Alignment

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The effect of bearing congruency, thickness and alignmenton the stresses in unicompartmental knee replacements

D.J. Simpson a, H. Gray a, D. DLima b, D.W. Murray a,c, H.S. Gill a,*

a Nuffield Department of Orthopaedic Surgery, University of Oxford, Nuffield Orthopaedic Centre, Windmill Road, Oxford OX3 7LD, UKb Orthopaedic Research Laboratories, Shiley Centre for Orthopaedic Research and Education at Scripps Clinic,

11025 N Torrey Pines Road, 140 La Jolla, CA 92037, USAc Nuffield Orthopaedic Centre, Oxford, OX3 7LD, UK

Received 8 February 2008; accepted 4 June 2008

Abstract

Background.Unicompartmental knee replacement offers an effective treatment for patients with single compartment knee disease andis becoming an increasingly popular alternative to total knee replacement. An important cause of failure in a unicompartmental kneereplacement implant is polyethylene wear. Significant contributory factors to the amount of polyethylene wear are contact stress, bearingalignment, congruency and thickness.

Methods. Four different unicompartmental knee replacement implant designs (Fully-Congruent; Partially-Congruent; Non-Congru-ent-metal-backed; Non-Congruent-all-polyethylene) were inserted into a validated finite element model of a proximal tibia. The effectthat bearing congruency, alignment and thickness had on the polyethylene stresses during a simulated step-up activity for each designwas investigated. Additionally, contact pressures were compared to those calculated from Hertz elastic theory.

Findings.Only the Fully-Congruent bearing experienced peak von Mises and contact stresses below the lower fatigue limit for poly-

ethylene during the step-up activity. The highest polyethylene contact stresses were observed for the Partially-Congruent and Non-Con-gruent-metal-backed designs, which experienced approximately three times the polyethylene lower fatigue limit. Increasing the bearingthickness from 3.5 mm to 8.5 mm of the Non-Congruent design decreased the contact stresses in the bearing; however they did not fallbelow the lower fatigue limit for polyethylene. Good agreement between finite element and Hertz contact pressures was found.

Interpretation.Fully congruent unicompartmental knee replacement bearings can be markedly thinner without approaching the mate-rial failure limit, have a greater potential to preserve bone stock and are less likely to fail mechanically. 2008 Elsevier Ltd. All rights reserved.

Keywords: Unicompartmental; Knee; Finite element; Contact stress; Polyethylene; Bearing; Step up

1. Introduction

Unicompartmental knee replacement (UKR) is becom-ing an increasingly popular alternative to total kneereplacement (TKR) because of its improved functional out-come, favourable long term clinical results and the benefitsof minimally invasive surgical techniques (Gioe et al., 2003;Berger et al., 2005). In particular, UKR offers a more effec-tive solution than TKR for more active patients with single

compartment knee disease, because the mechanics of theknee are better preserved, and more functional anatomy

is maintained (Goodfellow et al., 2006).One of the most important causes of failure in UKR ispolyethylene wear, (Palmer et al., 1998; Ashraf et al.,2004) which can disrupt the surface geometry of thereplaced plateau, altering joint stability and alignment(Hernigou and Deschamps, 2004; Wright, 2005). A signifi-cant contributory factor to polyethylene wear is the contactstress on the polyethylene articulating surface, which inturn is affected by bearing congruency, polyethylene thick-ness and contact area (Bartel et al., 1986; Engh et al., 1992;Kuster et al., 2000).

0268-0033/$ - see front matter 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.clinbiomech.2008.06.001

* Corresponding author.E-mail address: [email protected](H.S. Gill).

www.elsevier.com/locate/clinbiomech

Available online at www.sciencedirect.com

Clinical Biomechanics 23 (2008) 11481157
mailto:[email protected]:[email protected]


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Considerable differences exist in contemporary UKRdesign. Metal backed tibial components were introducedto address the issues of polyethylene wear and subsidence(Deshmukh and Scott, 2001). However, the use of metal-backed tibial components may mean that a thinner poly-ethylene insert will be required, or that more bone must

be resected.A consequence of using thinner bearings is that higherstresses can be generated, (Bartel et al., 1986, 1995).Indeed, several retrieval studies have shown bearing fail-ures related to polyethylene wear, where the original tibialinsertion thickness was less than 6 mm (Engh et al., 1992;McAuley et al., 2001). Maximum tensile stresses in polyeth-ylene bearings have been hypothesised to create stress fieldsnecessary to propagate cracks and large von Mises stresseshave been implicated in subsurface failures such as delam-ination (Bartel et al., 1986; Estupinan et al., 1998).

Other UKR designs use an all polyethylene tibial com-ponent to maximise the bearing thickness, or a mobile

bearing to maximise the bearing contact area. Importantly,these UKR designs are also intended to minimise theamount of bone that is resected, which is of particularadvantage if the UKR needs to be revised to a TKR (John-son et al., 2007).

Experimental measurements cannot predict the stressdistributions within polyethylene components for UKRs.This limitation can be overcome by using finite element(FE) analysis. Previous FE analyses of UKR designs havehad some important limitations. Iesaka et al. (2001) usedFE analysis to investigate tibial component inclination onbone stress with a simplified two-dimensional (2D) model.

A significant disadvantage of this work was that no valida-tion was given for the FE model. Bearing congruency in asingle plane has also been investigated with FE analysisusing 2D models (Estupinan et al., 1998; Kuster et al.,2000; Rawlinson and Bartel, 2001) without any validation.Other FE studies of knee replacements have used three-dimensional (3D) FE models to investigate tibial tray incli-nation (Sawatari et al., 2005) and the effects of gait onpolyethylene stresses (Morra and Greenwald, 2003). How-ever, all the FE models used in these 3D studies were notvalidated.

In addition, the above analyses were carried out for asmall number of load cases representing discrete points ofan activity. It has been shown that the medial lateral loadsplit on the tibial plateau can vary considerably throughouta motion cycle (Hurwitz et al., 1998).

The current study examined the influence that four dif-ferent UKR design geometries have on polyethylene stres-ses experienced throughout a functional activity using avalidated FE model. The four designs investigated wereFully-Congruent, Partially-Congruent, Non-Congruent-metal-backed and Non-Congruent-all-polyethylene UKRs.These implants were modelled as they represent commoncontemporary UKR designs. In clinical practice, a particu-lar implant is used following careful consideration of the

patients condition and requirements as well as the compe-

tence and familiarity that a surgeon has with a particularimplant and associated procedure. Ultimately the choiceis that of the surgeon performing the procedure.

The aims were to improve understanding of the effectsthat bearing congruency, thickness and alignment haveon stresses in a UKR bearing, and to give indications of

how the longevity of UKR bearings can be optimised.

2. Methods

The FE model used in this work was based on a vali-dated whole tibia model (Gray et al., 2007). The full detailsof this validation have been given elsewhere (Gray, 2007); abrief description is provided here.

Three-dimensional geometry for the whole tibia wasderived from computed tomography (CT) scans of a cadav-eric tibia (male donor, age 60 years, height 178 cm, weight82 kg, left side). The computer aided design (CAD) geom-etry for the tibia was reconstructed from the CT dataset

using SliceOmatic software (v4.2 Rev-9b, TomoVision,Magic Inc., Montreal, Canada). A mesh consisting of 10-noded tetrahedral elements was created and the CT datawere used to map orthotropic material properties to indi-vidual elements (Rho et al., 1995; Viceconti, 2000; Gray,2007).

Seventeen triaxial rosettes (Mod. KFG-3-120-D17-11L3M2S, Kyowa, Tokyo, Japan) were attached (Vicecontiet al., 1992) to the prepared tibia, and it was then subjectedto nine axial loading conditions, two four-point bendingloading conditions and one torsional loading condition.Axial loading was repeated after implantation of a medial

Oxford Unicompartmental Knee Replacement (OUKR)(Biomet UK Ltd, Swindon, UK). The tests were performedusing a materials testing machine (MTS 858 MiniBionix,MTS Systems Corporation, Minneapolis, Minnesota,USA).

Measured principal strains were compared to their cor-responding FE values using linear regression. The experi-mental results correlated well with those of the FEanalysis (axial loading; R2 = 0.97, root mean square error(RMSE) = 8.8%; bending loading R2 = 0.96, RMSE =9.0%) (Gray 2007).

2.1. Proximal tibia model

A reduced model measuring 75 mm from the tibial pla-teau was created to represent the proximal end of the tibia.Orthotropic material properties were assigned based on theaxial distribution of Youngs modulus along the wholetibia, and relationships established by Rho et al. (1995)and Gray (2007). Seven material properties were assignedto the proximal tibia model in the axial, mediolateral andanteroposterior directions (Table 1). Maximum and mini-mum principal strain data were compared between thereduced proximal model and the whole tibia model forone axial load condition (Gray, 2007). This reduction in

model size had little effect on the principal strains at the

D.J. Simpson et al. / Clinical Biomechanics 23 (2008) 11481157 1149


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locations considered. The slope of the linear regression linecomparing the FE and experimental strains was 0.999, theintercept 0.0001 micro-strain with an R2 value of 1.000.

Mean correlation coefficients of 0.989 and 0.976 wasobtained for the maximum and minimum principal strainsrespectively, for the axial load case.

The proximal tibia model consisted of 282,188 10-nodedtetrahedral elements.

2.2. UKR geometry and mesh

Four UKRs were modelled:

1. Fully-Congruent a spherical femoral component artic-ulating on a spherical, mobile bearing. The mobile bear-

ing articulated on the metal tibial component, which wasbonded to the tibia.

2. Partially-Congruent a poly-radial femoral componentarticulating on a fixed concave bearing. The bearing wasfixed to the metal tibial component, which was bondedto the tibia. The conformity ratio in the sagittal planewas 0.05 (Kuster et al., 2000).

3. Non-Congruent-metal-backed a spherical femoralcomponent articulating on a flat bearing. The bearingwas fixed to the metal tibial component, which wasbonded to the tibia.

4. Non-Congruent-all-polyethylene a spherical femoralcomponent articulating on a flat, all-polyethylene tibialcomponent. The bearing (tibial component) was bondedto the tibia.

In the above definitions the term bonded is used todescribe the kinematic constraint between two bodieswhereby no sliding is permitted between the two surfaces(l= 1), but separation is allowed.

These models will be hereafter respectively referred to as

1. Fully-Congruent.2. Partially-Congruent.3. Non-Congruent-MB.

4. Non-Congruent-AP.

The same cementing technique used for the validatedimplanted whole tibia model (Gray, 2007) was modelledfor each UKR. To minimise the differences between eachFE model, the same surgical procedure was simulated forcreating each UKR FE model, (Goodfellow et al., 2006).Each UKR was implanted in a neutral position; the femo-

ral component, bearing and tibial component were allaligned with the long axis of the tibia.The same tibial tray was used for the Fully-Congruent,

Partially-Congruent and the Non-Congruent-MB UKRmodels (Biomet UK Ltd, Swindon, UK). The Non-Con-gruent-MB and Non-Congruent-AP UKR models usedthe same bearing transverse cross-sectional geometry.

Geometry from CAD models was used to construct theFE models of the Fully-Congruent UKR (Biomet UK,Ltd, Swindon, UK). The geometry for the Partially-Con-gruent UKR (Zimmer Inc, Warsaw, USA), was obtainedfrom 3D scanning of the components (THE SCAN TEAM,Hertfordshire, UK). The scanned component models were

decimated into 40,000 faces and the binary stereolithogra-phy files were rendered and smoothed to accurately repre-sent the surface topology (Solidworks 2007, SolidworksCorporation, Concord, MA). For the Non-Congruent-MB and Non-Congruent-AP UKRs, a hypothetical flatbearing was modelled with the same spherical femoral com-ponent as the Fully-Congruent UKR.

The bearing in the Fully-Congruent model had a mini-mum thickness of 3.5 mm, and the bearing in the Par-tially-Congruent model had a minimum thickness of4.5 mm. The bearing in the Non-Congruent-MB modelhad a minimum thickness of 3.5 mm, comparable to the

bearing in the Fully-Congruent model. The bearing in theNon-Congruent-AP model had a thickness of 15.0 mm.This was comparable to the combined thickness of theother FE models cement layer, tibial tray and bearing; thisis also the maximum thickness used in the all-polyethyleneUKR, the St. Georg Sled (Waldemar Link, Hamburg, Ger-many) (Gleeson et al., 2004).

The tibial tray and femoral component in all the FEmodels was modelled as linear elastic and isotropic withthe material properties for cast cobalt-chromium (E=195,000 MPa (Lewis, 1997), m= 0.3 (Cheal et al., 1985)).The cement was modelled as a linear elastic isotropic mate-rial (E= 1940 MPa (Lewis, 1997), m= 0.4 (Orr et al.,2003)).

Linear material models for polyethylene have been usedin previous studies (Walker, 1988; Sathasivam and Walker,1994); however the stresses obtained using this approxima-tion are considerably higher than for nonlinear models,indicating that a linear approximation is not accurateenough for careful evaluation of polyethylene loadresponse (Kuster et al., 2000). A multi-linear, kinematichardening, elastoplastic material model (Mroz, 1967)was implemented in ANSYS, v11.0 (Ansys Inc., Canons-burg, PA, USA) for the polyethylene. Experimental datawere entered into the polyethylene material model from

literature (Kurtz et al., 1996), with eight points defining

Table 1Orthotropic material properties for the proximal tibia model

Material property Bone section properties

1 2 3 4 5 6 7

E medial-lateral (X)(MPa)

7600 5564 5459 606 2926 2907 479

E anterio-posterior(Y) (MPa) 7652 5595 5489 610 2943 2923 481

E proximal-distal (Z)(MPa)

13,263 9698 9514 1056 5100 5067 835

m(XY) 0.427 0.427 0.427 0.427 0.427 0.427 0.427m(YZ) 0.234 0.234 0.234 0.234 0.234 0.234 0.234m(XZ) 0.405 0.405 0.405 0.405 0.405 0.405 0.405

G(XY) (MPa) 2591 1895 1859 206 996 990 163

G(YZ) (MPa) 3509 2565 2517 279 1349 1340 220G(XZ) (MPa) 3566 2534 2486 276 1333 1324 218

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the polyethylene true stressstrain material response. TheYoungs modulus was entered as 1048 MPa.

2.3. Boundary conditions

In vivo kinematic data measured using fluoroscopy, dur-

ing a step-up activity, was used to determine the relativetibial-femoral positioning for each model; this was deter-mined as a function of knee flexion angle. The data werecollected from 10 patients with an OUKR (Pandit et al.,2008), and used to position the bearing in all the FE mod-els. The fluoroscopic measurement methodology has beendescribed in detail elsewhere (Pandit et al., 2005; vanDuren et al., 2007). The knees flexion angles ranged from20 to 55 for the step up activity, as this correspondedto the flexion range for which force data were available.

The load data were adapted from loads measuredin vivo using an instrumented implant during a step-upactivity (Zhao et al., 2007). This load condition was chosen

as it represents a functional high intensity activity withlarge knee flexion angles, and it has been shown to corre-late better to outcome score parameters than walking(Morlock et al., 2001). Separate loads were applied to themedial and lateral compartment and these were scaled toa subject of mass 82 kg (mass of tibia donor). The loadon the lateral compartment was applied at the nodes inthe vicinity of the central point of the compartment. Theload on the medial compartment was applied to the femo-ral component, on nodes located on the internal surfacegeometry, on a cross-sectional line in the coronal plane.Force vectors were applied perpendicular to the tibial tray

and the distal end of the proximal tibia model was rigidlyconstrained.

2.4. Contact constraints

A Coulomb friction contact model (l= 0.07 (Shen andDumbleton, 1974)) was used to simulate the femoral com-ponent/bearing contact surfaces for all UKR models. Forthe Fully-Congruent UKR model a Coulomb friction con-tact model was used to simulate the bearing/tibial tray con-tact surface. The polyethylene was bonded to the tibial trayfor the Partially-Congruent and Non-Congruent-MB mod-els. The Non-Congruent-AP bearing was bonded to thecement layer. The implant/cement and cement/bone inter-faces were modelled as bonded contact for all four UKRFE models. An Augmented Lagrange multiplier contactalgorithm was implemented in the contact algorithm (Simoand Laursen, 1992). A contact stiffness of 70 kN/mm wasassigned initially within the contact algorithm, and wasupdated at each solution sub-step. The affect of varyingthis parameter on the model output was investigated.

The FE models were solved using Ansys v11.0, using apre-conditioned conjugate iterative solver algorithm. Theanalyses were performed on an Intel Dual CoreTM work-station (2.66 GHz, 4GB RAM), running a Suse Linux 9.2

operating system.

2.5. Analyses

For all four UKR FE models, the peak contact, vonMises and principal stresses in the polyethylene bearingwere evaluated over the step-up activity and compared tothe upper (32 MPa) and lower (17 MPa) limits of polyeth-

ylene fatigue failure stress obtained from tensile testing(Ries et al., 1996). Although this loading regime is differentfrom that experienced in UKR bearings, it was chosenbecause the yield properties of polyethylene have beenshown to be very similar in compression and tension(Kurtz et al., 1997).

The peak stresses in the Fully-Congruent and Non-Con-gruent-MB bearing were assessed as a function of bearingthickness, for the maximum load state, which occurred at35 of knee flexion. The thickness of the Non-Congruent-MB bearing was varied from 2.5 mm to 8.5 mm, in1.0 mm increments. The thickness of the Fully-Congruentbearing was varied from 2.5 mm to 5.5 mm, in 1.0 mm

increments.Each femoral component was rotated about the sagittal

plane, relative to the tibial tray, (whilst maintaining thesame initial contact condition with the bearing) to repre-sent varusvalgus mal-alignment often seen in clinical prac-tice (Swienckowski and Pennington, 2004; Cool et al.,2006). The femoral component was rotated up to a maxi-mum of 20 and the stresses in the polyethylene bearingexamined.

To investigate the effect of the stiffness parameter, thecontact stiffness was varied from 53 to 280 N/mm, andthe results using the Non-Congruent-MB model were

examined.

2.6. Contact validation

The results from the FE contact representation werecompared to those calculated using Hertzs theory of elas-tic contact (Johnson, 1987). Hertz contact theory is limitedby the assumptions and restrictions concerning an elastichalf-space, and the relative dimensions of the contactingbodies and their resulting contact region (Johnson, 1987).Therefore comparisons were made for a sphere-on-planemodel and for the Non-Congruent-MB FE model.

The sphere-on-plane model consisted of a sphere ofradius 20 mm in contact with a rectangular substrate(dimensions 20 20 50 mm); this FE model had exactlythe same contact parameters as those used for all the UKRmodels. This sphere-on-plane model is analogous to thespecial case in classical contact mechanics of two cylindersin contact with their axes perpendicular (Johnson, 1987). Aload of 100 N directed perpendicularly to the substrate sur-face acted on the sphere such that contact between it andthe substrate occurred. The sphere was modelled as linearelastic with an elastic modulus of 195,000 MPa and Pois-sons ratio 0.3 (material properties of cobaltchrome).The substrate was modelled as linear elastic, with an elastic

modulus of 1048 MPa and a Poissons ratio of 0.3 (material



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properties of polyethylene). The FE calculated contactpressure and contact width were compared to those calcu-lated from Hertz theory using the following relationships:

a 3PR

4E

1=3and p0

6PE2

p3R2

1=3

where a is contact width, Pis normal load and p0is maxi-mum contact pressure, 1

E

1v21

E1

1v22

E2(E

n and vn are the

respective elastic modulus and Poissons ratio of the twobodies). 1

R

1R1

1R2

is the relative curvature (R1 and R2are principal radius of curvature).

Following this comparison, the peak contact pressureand contact width in the Non-Congruent-MB UKR bear-ing were compared to those calculated from Hertz theoryfor the peak load condition (knee flexion angle = 35).For this comparison the polyethylene bearing was mod-elled as linear elastic (E= 1048 MPa).

3. Results

For all models the peak contact stress was observed atthe contact region between the femoral component andthe polyethylene bearing. The magnitude of this contactstress was similar for the bearings in the Partially-Congru-ent, Non-Congruent-MB and Non-Congruent-AP models(mean peak contact stress, 44.3 MPa, 48.6 MPa and45.9 MPa, respectively). Considerably lower contact stres-ses were observed in the Fully-Congruent model bearing(mean peak contact stress, 2.7 MPa). The contact stressfor the Partially-Congruent, Non-Congruent-MB and

Non-Congruent-AP bearing was concentrated in a smallarea, and was more widely distributed in the Fully-Congru-ent bearing (Fig. 1).

Only the Fully-Congruent bearing experienced peakcontact stresses below the polyethylene lower fatigue limit(17 MPa). All other models had peak contact stresses ofapproximately three times the lower fatigue limit (Fig. 2).For the Non-Congruent-MB, Non-Congruent-AP andPartially-Congruent UKR models, the area on the bearingcontact surface that experienced contact stresses above the

lower fatigue limit was 28.2 mm2, 36.2 mm2 and36.85 mm2, respectively. This related to a total contact sur-face area of 1038.5 mm2, 1038.5 mm2 and 1045.2 mm2,respectively.

Peak von Mises stresses in the Fully-Congruent bearingwere considerably smaller than in the Partially-Congruent,

Non-Congruent-MB and Non-Congruent-AP bearings,and were well below the lower fatigue limit of the polyeth-ylene (Fig. 3). Peak von Mises stresses for the Partially-Congruent, Non-Congruent-MB and Non-Congruent-APbearings were above the polyethylene lower fatigue limitfor all flexion angles over the step-up activity.

Similar trends were observed for the 3rd principal stres-ses in the polyethylene bearing. The bearing in the Fully-Congruent model experienced a considerably lower peakcompressive stress than the other bearings (Fig. 4a).

The mean peak 1st principal stress observed in theFully-Congruent bearing over the step-up activity was1.9 MPa and this was well below the lower fatigue limit

for polyethylene. For the Non-Congruent-MB and Non-Congruent-AP bearings the mean peak 1st principal stresswas 8.3 MPa and 5.5 MPa, respectively. The Partially-Con-gruent polyethylene bearing experienced a mean peak 1stprincipal stress of 7.2 MPa (Fig. 4b).

3.1. Variation in bearing thickness

As the thickness of the Non-Congruent-MB bearing wasincreased, the peak von Mises stress decreased (Fig. 5a).Increasing the bearing thickness from 2.5 mm to 8.5 mmresulted in the peak von Mises stress decreasing from

26.6 MPa to 20.7 MPa; this lower value was still abovethe lower fatigue limit of polyethylene. For a bearing thick-ness of 3.5 mm, the peak von Mises stress occurred2.25 mm below the bearing surface, beneath the centralcontact point with the femoral component. This distanceincreased to 2.83 mm below the surface for a bearing thick-ness of 8.5 mm.

An increase in the minimum thickness of the Fully-Con-gruent bearing from 3.5 to 5.5 mm resulted in the peakcontact stress decreasing from 3.21 MPa to 3.18 MPa. A

Fig. 1. Contact stress (MPa) contour plot in each polyethylene bearing for the peak load case: (a) Fully-Congruent, (b) Partially-Congruent, (c) Non-

Congruent-MB and (d) Non-Congruent-AP.



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decrease in thickness from 3.5 mm to 2.5 mm resulted in anincrease in peak contact stress from 3.21 MPa to 3.40 MPa(Fig. 5b), and a small bearing deformation.

3.2. Varusvalgus alignment

A varusvalgus mal-alignment of up to 15between thefemoral component and tibial tray had no effect on thepeak stresses in the Partially-Congruent, Non-Congruent-MB and Non-Congruent-AP bearings. A 20 mal-align-ment led to an increase in peak contact stress from49.04 MPa to 52.31 MPa in the Partially-Congruent bear-ing. A varusvalgus mal-alignment of 10 between theFully-Congruent femoral component and tibial tray pro-

duced an increase in contact stress from 3.21 MPa to

5.00 MPa in the Fully-Congruent bearing. Any furtherincrease in mal-alignment had no additional consequenceon the peak stresses.

3.3. Contact validation and stiffness

The maximum contact pressure and contact width pre-dicted by the sphere-on-plane finite element model was34.01 MPa and 1.39 mm, respectively. The classical Hertztheory predicted a peak contact pressure and width of39.89 MPa and 1.09 mm, respectively. For the Non-Con-gruent-MB UKR with an elastic bearing the FE model pre-dicted a contact pressure of 85.7 MPa, Hertz theorypredicted 85.2 MPa.

For the UKR model with a non-linear polyethylenematerial model, varying the initial contact stiffness betweenthe polyethylene and femoral component from 53 N/mm to280 N/mm decreased the contact penetration from0.045 mm to 0.040 mm. The contact stress increased from

45.7 MPa to 47.0 MPa. The five fold increase in contactstiffness resulted in a 2.8% and 12.5% increase in contactstress and contact penetration, respectively.

4. Discussion

Unicompartmental knee replacement offers a more effec-tive treatment for patients with isolated single compart-ment knee disease as more functional anatomy ispreserved. Some contemporary UKR designs maximisethis preserved anatomy by minimising the amount of bonestock resected. A significant failure mechanism of UKR

implants is wear of the polyethylene bearings (Palmeret al., 1998; Ashraf et al., 2004), which is associated withhigh contact stress, small bearing thickness and mal-align-ment (Bartel et al., 1986, 1995). By applying physiologicalkinematic and loading conditions to a validated finite ele-ment model of an implanted tibia, it was possible to inves-tigate the effect that bearing congruency, thickness andalignment had on the stresses in four polyethylene bearingdesigns. Furthermore, it was possible to determine whichtype of UKR design had the greater potential to maximisethe amount of preserved bone stock followingimplantation.

The data obtained from the finite element models in thispaper support the findings of previous computational stud-ies. Contact and von Mises stresses in the polyethylenebearing for the Partially-Congruent, Non-Congruent-MBand Non-Congruent-AP bearings were similar in magni-tude to those reported elsewhere (Estupinan et al., 1998;Kuster et al., 2000; Rawlinson and Bartel, 2001). The bear-ing in the Fully-Congruent design experienced much lowercontact and von Mises stresses, compared to the otherUKR designs, due to the increased congruency, and therelationship between congruency and contact stress is wellunderstood (Bartel et al., 1986). We were also able to com-pare the results for Non-Congruent-MB with Hertz elastic

theory of contact and found a good agreement.

Fig. 2. Comparison of peak contact stress in each bearing over the step-upactivity.

Fig. 3. Comparison of peak von Mises stress in each bearing over the step-up activity.



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Results obtained from the four UKR finite elementmodels also support the findings of previous clinical stud-ies. The Fully-Congruent bearing experienced very lowcontact stresses, which indicates that this type of UKRdesign will have favourable wear characteristics. Therehas been a number of clinical studies confirming that lowwear is observed in fully congruent designs (Psychoyioset al., 1998; Callaghan, 2001; Price et al., 2005). The con-siderably higher contact stresses observed in the Partially-Congruent, Non-Congruent-MB and Non-Congruent-APbearings suggest that this type of bearing is more suscepti-ble to excessive polyethylene wear, and this has beenreported previously (Bartley et al., 1994; Palmer et al.,

1998; Callaghan, 2001). However, it must be noted that

Fully-Congruent, mobile bearing designs are susceptibleto different failure modes, such as bearing dislocation.

The Fully-Congruent bearing is less likely to fail fromfatigue. The bearing in the Partially-Congruent, Non-Con-gruent-MB and Non-Congruent-AP designs experiencedpeak von Mises stresses above the lower fatigue failurestress for polyethylene throughout the functional activityanalysed. These bearing designs are therefore more suscep-tible to material failure, such as delamination. The mech-anism for subsurface failure of polyethylene has beendescribed elsewhere (Bartel et al., 1995; Estupinan et al.,1998), and retrieval analysis of UKRs has shown fatiguefailure of non-conforming polyethylene components (Kop

and Swarts, 2007).

Fig. 4. (a) Comparison of peak 3rd principal stress in each bearing over the step-up activity and (b) comparison of peak 1st principal stress in each bearingover the step-up activity.

Fig. 5. (a) Variation of peak von Mises stress in the Non-Congruent-MB polyethylene bearing with bearing thickness and (b) variation of stress in theFully-Congruent bearing with bearing thickness.



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Increasing the thickness of the bearing for the Non-Con-gruous-MB UKR resulted in a decrease in the peak vonMises stress. Interestingly, the peak von Mises stressremained above the polyethylene lower fatigue failurestress limit (17 MPa) for a bearing thickness above8.5 mm. In addition, the Non-Congruent-AP bearing,

which had a thickness of 15.0 mm, experienced peak vonMises stresses above 17 MPa.There have been several retrieval studies showing bear-

ing failures where the original tibial insertion thicknesswas less than 6 mm (Engh et al., 1992; Palmer et al.,1998; McAuley et al., 2001). This has led to the assertionby many clinicians that a bearing thickness of above6.5 mm is safe. The results from the current study suggestthat even for a bearing thickness of 8.5 mm, the peak vonMises stresses remain above the polyethylene lower fatiguelimit, and this affect is seen with or without metal-backing.If a Partially-Congruent, Non-Congruent-MB or Non-Congruent-AP bearing is used, a minimum bearing thick-

ness of 8.5 mm would be recommended on the basis ofour finite element model results. However, our results sug-gest that there is no safe limit for the polyethylene thick-ness in lesser congruent designs. Where dishing occurs,the peak bearing stresses may be alleviated because a morecongruent articulating area will be generated as a conse-quence of polyethylene wear. However, the concern willbe that the subsurface material on an un-worn bearingprior to dishing would have been subjected to stressesabove the fatigue failure stress. This same subsurface mate-rial becomes the surface after dishing, and therefore hasan increased likelihood of fatigue failure. In addition, the

process of dishing will give rise to a considerable volumeof polyethylene debris and will lead to the recurrence ofvarus which may increase loading.

It must be borne in mind however that bearing choicewill be balanced against the patient cohort. More elderlyand typically less active patients will transfer lower loadsto the bearing, and will subject the bearing to fewer stresscycles over their lifetime, compared to younger patients.Therefore the choice of a Non-Congruent UKR designmay be appropriate for a patient cohort that is less activeand elderly, but would not be appropriate for a younger,more active population. This is probably the reason thatsome Non-Congruent UKR designs have an adequateclinical performance.

Fully-Congruent UKR bearings are preferential whentrying to minimise stresses that may lead to catastrophicwear and can also be markedly thinner without approach-ing the material failure limit. A Fully-Congruent UKRdesign therefore has a greater potential to preserve bonestock during implantation. A minimum thickness of3.5 mm was used for the Fully-Congruent bearing in thecurrent study. Compared to the minimum safe thicknessof 6.5 mm for a Non-Congruous-MB UKR design, apotential 3.0 mm of bone stock can be preserved duringimplantation. This bone stock saving increases to 8.5 mm

when compared to the Non-Congruent-AP bearing. Fur-

thermore, the peak von Mises stresses in the Fully-Congru-ent bearing were still well below the lower fatigue limit ofpolyethylene when a minimum thickness of 2.5 mm wasmodelled.

The modelling process used in vivo measured kinematicand load data, and great care was taken to model the tibial-

femoral positioning for each UKR design. This is impor-tant for two reasons: firstly, the stresses in the bearing wereable to be assessed throughout an entire activity; secondly,the kinematic data determined where the femoral compo-nent and polyethylene contacted with each other. If ananalysis does not use kinematic data measured in vivo, thenmisleading results can be obtained.Morra and Greenwald(2003)reported very similar contact and von Mises stressesin a partially congruent and a fully congruent UKR bear-ing. In the absence of kinematic data, the partially congru-ent UKR may have been analysed in its most conformingposition. This would explain the low stresses found in thepartially congruent bearing.

Following implantation with a UKR, there is oftensome degree of varusvalgus mal-alignment of the replacedjoint (Swienckowski and Pennington, 2004; Cool et al.,2006). This will inevitably have an effect on the restoredkinematics of the implanted knee, but the affect of mal-alignment on bearing stress has not, to the authors knowl-edge, been reported elsewhere. The current study hasshown that the stress raising affects that were observedfor up to a 20varusvalgus mal-alignment were extremelysmall. This may have important implications for clinicalpractice, because the varusvalgus mal-alignment investi-gated in this study does not increase the likelihood of the

bearing failing mechanically.The tibia was modelled in this work to more accurately

assess the polyethylene stresses in each UKR design. Thepolyethylene material properties used in this paper weretaken from readily available data in the literature. Thematerial properties of contemporary polyethylene may dif-fer from this data; further study should be performed toexamine these effects.

Only the proximal tibia was modelled, which is a limita-tion of the current study. This simplification meant that anartificial modelling restraint had to be placed on the distaltibia, so that the condition of equilibrium was not violated.Using a proximal tibia model was justified because we werepredominantly interested in what happens in the polyethyl-ene bearing. Using a proximal model had the added advan-tage of allowing us to use a much more refined meshwithout increasing computational time. The kinematic dataused in this study was obtained from only one of the UKRdesigns. In reality each UKR design may have differentkinematics, and may have subtly different loading. Theloading used in this study was taken from in vivo measureddata, and is somewhat simplified in that the soft tissueforces are not considered. The load data were capturedusing an instrumented TKR, and the normal force vectorson the medial and lateral plateau were adapted for the

UKR finite element models. As such, no lateral force was



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applied to the UKR models and this is a simplification ofthe in vitro situation. However, this is the first study touse internally measured load data for the medial-lateralsplit on a UKR model. Most previous load data has beenbased on estimates derived from models that are very sen-sitive to errors (Zhao et al., 2007). The loading conditions

applied in this study therefore provide an insight into thestresses experienced by different polyethylene bearings incontemporary UKR designs. A high intensity load casewas used in this paper. A more complete investigationwould compare the relative activity level of a patientcohort. However, the choice of only using a high intensityload case is justified because bearing design should bebased upon the worst case scenario.

5. Conclusion

The results of this study show that a Fully-CongruentUKR design has bearing stresses that are an order of mag-

nitude lower than other contemporary UKR designs. Per-haps surprisingly, the contact and von Mises stresses inthe Partially-Congruent and Non-Congruent bearings werevery similar, and above the lower fatigue limit for polyeth-ylene. The Fully-Congruent bearing is therefore less likelyto fail mechanically, and can be considerably thinner with-out approaching the material limits.

Conflict of interest statement

The institute of three of the authors DJS, DWM, HSGhas received research support from commercial parties

related to the subject of this paper; one of these authorshas also received benefits for personal and professionaluse from commercial parties related to the subject of thispaper. The other two authors have had no commercialinterest related to the subject of this paper.

Acknowledgements

The lead author was funded by the Furlong ResearchFoundation during the period this work was conducted,other funding was provided by the Hip and Knee Research& Development Fund, Nuffield Orthopaedic Centre Gen-eral Charity. The funding bodies took no role in the writingof this manuscript.

References

Ashraf, T., Newman, J.H., Desai, V.V., Beard, D., Nevelos, J.E., 2004.Polyethylene wear in a non-congruous unicompartmental kneereplacement: a retrieval analysis. Knee 11 (3), 177181.

Bartel, D.L., Bicknell, V.L., Wright, T.M., 1986. The effect of conformity,thickness, and material on stresses in ultra-high molecular weightcomponents for total joint replacement. J. Bone Joint Surg. Am. 68 (7),10411051.

Bartel, D.L., Rawlinson, J.J., Burstein, A.H., Ranawat, C.S., Flynn Jr.,W.F., 1995. Stresses in polyethylene components of contemporary

total knee replacements. Clin. Orthop. Relat. Res. (317), 7682.

Bartley, R.E., Stulberg, S.D., Robb 3rd, W.J., Sweeney, H.J., 1994.Polyethylene wear in unicompartmental knee arthroplasty. Clin.Orthop. Relat. Res. (299), 1824.

Berger, R.A., Meneghini, R.M., Jacobs, J.J., Sheinkop, M.B., Della Valle,C.J., Rosenberg, A.G., Galante, J.O., 2005. Results of unicompart-mental knee arthroplasty at a minimum of ten years of follow-up. J.Bone Joint Surg. Am. 87 (5), 9991006.

Callaghan, J.J., 2001. Mobile-bearing knee replacement: clinical results: areview of the literature. Clin. Orthop. Relat. Res. (392), 221225.

Cheal, E.J., Hayes, W.C., Lee, C.H., Snyder, B.D., Miller, J., 1985. Stressanalysis of a condylar knee tibial component: influence of metaphysealshell properties and cement injection depth. J. Orthop. Res. 3 (4), 424434.

Cool, S., Victor, J., De Baets, T., 2006. Does a minimally invasiveapproach affect positioning of components in unicompartmental kneearthroplasty? Early results with survivorship analysis. Acta Orthop.Belg. 72 (6), 709715.

Deshmukh, R.V., Scott, R.D., 2001. Unicompartmental knee arthro-plasty: long-term results. Clin. Orthop. Relat. Res. (392), 272278.

Engh, G.A., Dwyer, K.A., Hanes, C.K., 1992. Polyethylene wear of metal-backed tibial components in total and unicompartmental kneeprostheses. J. Bone Joint Surg. Br. 74 (1), 917.

Estupinan, J.A., Bartel, D.L., Wright, T.M., 1998. Residual stresses inultra-high molecular weight polyethylene loaded cyclically by a rigidmoving indenter in nonconforming geometries. J. Orthop. Res. 16 (1),8088.

Gioe, T.J., Killeen, K.K., Hoeffel, D.P., Bert, J.M., Comfort, T.K.,Scheltema, K., Mehle, S., Grimm, K., 2003. Analysis of unicompart-mental knee arthroplasty in a community-based implant registry. Clin.Orthop. Relat. Res. (416), 111119.

Gleeson, R.E., Evans, R., Ackroyd, C.E., Webb, J., Newman, J.H., 2004.Fixed or mobile bearing unicompartmental knee replacement? Acomparative cohort study. Knee 11 (5), 379384.

Goodfellow, J.W., OConnor, J., Dodd, C.A.F., Murray, D.W., 2006.Unicompartmental Arthroplasty with the Oxford Knee. OxfordUniversity Press.

Gray, H.A., 2007. Finite Element Analysis of the Human Tibia. D. PhilThesis.Gray, H.A., Zavatsky, A.B., Taddei, F., Cristofolini, L., Gill, H.S., 2007.

Experimental validation of a finite element model of a composite tibia.Proc. Inst. Mech. Eng. [H] 221 (3), 315324.

Hernigou, P., Deschamps, G., 2004. Alignment influences wear in the kneeafter medial unicompartmental arthroplasty. Clin. Orthop. Relat. Res.(423), 161165.

Hurwitz, D.E., Sumner, D.R., Andriacchi, T.P., Sugar, D.A., 1998.Dynamic knee loads during gait predict proximal tibial bone distri-bution. J. Biomech. 31 (5), 423430.

Iesaka, K., Tsumura, H., Sonoda, H., Sawatari, T., Takasita, M., Torisu,T., 2001. The effects of tibial component inclination on bone stressafter unicompartmental knee arthroplasty. J. Biomech. 35, 969974.

Johnson, S., Jones, P., Newman, J.H., 2007. The survivorship and results

of total knee replacements converted from unicompartmental kneereplacements. Knee 14 (2), 154157.Johnson, K.L., 1987. Contact Mechanics. Cambridge University Press.Kop, A.M., Swarts, E., 2007. Quantification of polyethylene degradation

in mobile bearing knees: a retrieval analysis of the AnteriorPosterior-Glide (APG) and Rotating Platform (RP) Low Contact Stress (LCS)knee. Acta Orthop. 78 (3), 364370.

Kurtz, S.M., Jewett, C.W., Moalli, J.E., Edidin, A.A., 1997. An elasticplastic material model for the true stressstrain behavior of ultra-highmolecular weight polyethylene in tension and compression. In:Advances in Bioengineering BED34. American Society of MechanicalEngineers, New York.

Kurtz, S.M., Rimnac, C.M., Santner, T.J., Bartel, D.L., 1996. Exponentialmodel for the tensile true stressstrain behavior of as-irradiated andoxidatively degraded ultra high molecular weight polyethylene. J.

Orthop. Res. 14 (5), 755761.



10/10

Kuster, M.S., Horz, S., Spalinger, E., Stachowiak, G.W., Gachter, A.,2000. The effects of conformity and load in total knee replacement.Clin. Orthop. Relat. Res. (375), 302312.

Lewis, G., 1997. Properties of acrylic bone cement: state of the art review.J. Biomed. Mater. Res. 38 (2), 155182.

McAuley, J.P., Engh, G.A., Ammeen, D.J., 2001. Revision of failedunicompartmental knee arthroplasty. Clin. Orthop. Relat. Res. (392),279282.

Morlock, M., Schneider, E., Bluhm, A., Vollmer, M., Bergmann, G.,Muller, V., Honl, M., 2001. Duration and frequency of every dayactivities in total hip patients. J. Biomech. 34 (7), 873881.

Morra, E.A., Greenwald, A.S., 2003. Effects of walking gait on ultra-highmolecular weight polyethylene damage in unicompartmental kneesystems. A finite element study. J. Bone Joint Surg. Am. 85-A (Suppl.4), 111114.

Mroz, Z., 1967. On the description of anisotropic work hardening. J.Mech. Phys. Solids 15, 163175.

Orr, J.F., Dunne, N.J., Quinn, J.C., 2003. Shrinkage stresses in bonecement. Biomaterials 24 (17), 29332940.

Palmer, S.H., Morrison, P.J., Ross, A.C., 1998. Early catastrophic tibialcomponent wear after unicompartmental knee arthroplasty. Clin.Orthop. Relat. Res. (350), 143148.

Pandit, H., Van Duren, B., Gallagher, J., Beard, D.J., Dodd, C.A.F., Gill,H.S., Murray, D.W., 2008. Combined anterior cruciate reconstructionand Oxford unicompartmental knee arthroplasty: in vivo kinematics.The Knee 15 (2), 101106.

Pandit, H., Ward, T., Hollinghurst, D., Beard, D.J., Gill, H.S., Thomas,N.P., Murray, D.W., 2005. Influence of surface geometry and the cam-post mechanism on the kinematics of total knee replacement. J. BoneJoint Surg. Br. 87 (7), 940945.

Price, A.J., Short, A., Kellett, C., Beard, D., Gill, H., Pandit, H., Dodd,C.A., Murray, D.W., 2005. Ten-year in vivo wear measurement of afully congruent mobile bearing unicompartmental knee arthroplasty. J.Bone Joint Surg. Br. 87 (11), 14931497.

Psychoyios, V., Crawford, R.W., OConnor, J.J., Murray, D.W., 1998.Wear of congruent meniscal bearings in unicompartmental kneearthroplasty: a retrieval study of 16 specimens. J. Bone Joint Surg. Br.80 (6), 976982.

Rawlinson, J.J., Bartel, D., 2001. Flat medial-lateral conformity in totalknee replacements does not minimise contact stresses. J. Biomech. 35,2734.

Rho, J.Y., Hobatho, M.C., Ashman, R.B., 1995. Relations of mechanicalproperties to density and CT numbers in human bone. Med. Eng.Phys. 17 (5), 347355.

Ries, M.D., Weaver, K., Rose, R.M., Gunther, J., Sauer, W., Beals, N.,1996. Fatigue strength of polyethylene after sterilization by gammairradiation or ethylene oxide. Clin. Orthop. Relat. Res. (333), 8795.

Sathasivam, S., Walker, P.S., 1994. Optimization of the bearing surfacegeometry of total knees. J. Biomech. 27 (3), 255264.

Sawatari, T., Tsumura, H., Iesaka, K., Furushiro, Y., Torisu, T., 2005.Three-dimensional finite element analysis of unicompartmental kneearthroplasty the influence of tibial component inclination. J. Orthop.Res. 23 (3), 549554.

Shen, C., Dumbleton, J.H., 1974. The friction and wear behavior ofirradiated very high molecular weight polyethylene. Wear 30 (1), 349364.

Simo, J.C., Laursen, T.A., 1992. An augmented lagrangian treatment ofcontact problems involving friction. Comput. Struct. 42 (1), 97116.

Swienckowski, J.J., Pennington, D.W., 2004. Unicompartmental kneearthroplasty in patients sixty years of age or younger. J. Bone JointSurg. Am., 131142, Suppl. 1 (Pt 2).

van Duren, B.H., Pandit, B.D.J., et al., 2007. How effective are addedconstraints in improving TKR kinematics? J. Biomech. 40, S31S37.

Viceconti, M., 2000. A comparative study on different methods ofautomatic mesh generation of human femurs. Medical Engineeringand Physics 20 (1998): 110. Med. Eng. Phys. 22 (5), 379380.

Viceconti, M., Toni, A., Giunti, A., 1992. Strain Gauge Analysis of HardTissue: Factors Influencing Measurements. Elsevier Science,Amsterdam.

Walker, P.S., 1988. Bearing surface design in total knee replacement. EngMed 17 (4), 149156.

Wright, T.M., 2005. Polyethylene in knee arthroplasty: what is the future?Clin. Orthop. Relat. Res. 440, 141148.

Zhao, D., Banks, S.A., DLima, D.D., Colwell Jr., C.W., Fregly, B.J.,2007. In vivo medial and lateral tibial loads during dynamic and high

flexion activities. J. Orthop. Res. 25 (5), 593602.


the effect of bearing congruency, thickness and alignment

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