Journal of Biomechanics 46 (2013) 19001906Contents lists available at SciVerse ScienceDirectjournal homepage: www.elsevier.com/locate/jbiomech

Journal of Biomechanics0021-92http://d

n Corrter ScieTel.: +61

E-mwww.JBiomech.comA large scale finite element study of a cementless osseointegratedtibial tray

Francis Galloway a, Max Kahnt b, Heiko Rammb, Peter Worsley a, Stefan Zachowb,Prasanth Nair c, Mark Taylor a,d,n

a Bioengineering Sciences Research Group, Faculty of Engineering and the Environment, University of Southampton, UKb Medical Planning Group, Zuse Institute Berlin (ZIB), Germanyc University of Toronto Institute for Aerospace Studies, Toronto, Canadad Medical Device Research Institute, School of Computer Science, Engineering and Mathematics, Flinders University, Adelaide, Australiaa r t i c l e i n f o

Article history:

Accepted 23 April 2013

The aim of this study was to investigate the performance of a cementless osseointegrated tibial tray(P.F.C. s Sigmas, Depuys Inc, USA) in a general population using finite element (FE) analysis.Keywords:Population based studyFinite element modellingCementless fixationTotal knee replacementAutomated implantation90/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.jbiomech.2013.04.021

esponding author at: Medical Device Researcnce, Engineering and Mathematics, Flinders U8 8201 5732.

ail address: mark.taylor@flinders.edu.au (M. Ta b s t r a c t

Computational testing of total knee replacements (TKRs) typically only use a model of a single patientand assume the results can be extrapolated to the general population. In this study, two statistical models(SMs) were used; one of the shape and elastic modulus of the tibia, and one of the tibiofemoral jointloads over a gait cycle, to generate a population of FE models. A method was developed to automaticallysize, position and implant the tibial tray in each tibia, and 328 models were successfully implanted andanalysed. The peak strain in the bone of the resected surface was examined and the percentage surfacearea of bone above yield strain (PSAY) was used to determine the risk of failure of a model. Using anarbitrary threshold of 10% PSAY, the models were divided into two groups (higher risk and lower risk)in order to explore factors that may influence potential failure. In this study, 17% of models were in thehigher risk group and it was found that these models had a lower elastic modulus (mean 275.7 MPa), ahigher weight (mean 85.3 kg), and larger peak loads, of which the axial force was the most significant.This study showed the mean peak strain of the resected surface and PSAY were not significantly differentbetween implant sizes.

& 2013 Elsevier Ltd. All rights reserved.1. Introduction

Due to the increasing number of total knee replacement (TKR)procedures, assessment of TKR performance in the general popu-lation is becoming more important. To evaluate the performanceof a tibial tray, computational models are often used. Many studiesonly use a model of a single patient (Keja et al., 1994; Tissakhtet al., 1995; Taylor et al., 1998; Hashemi and Shirazi-Adl, 2000;Barker et al., 2005; Perillo-Marcone and Taylor, 2007; Chong et al.,2010). A problem with such an approach is that populationvariability is not taken into account and the results cannot beapplied to the general population.

Studies using multiple patients have investigated tibial trayperformance. Perillo-Marcone et al. (2004) modelled four patients,ranking the models using percentage volume of bone at risk offailure. The rank order matched the measured implant migrationll rights reserved.

h Institute, School of Compu-niversity, Adelaide, Australia.

aylor).from radiostereometric analysis. Wong et al. (2010) looked at thefactors influencing the risk of subsidence, modelling four speci-mens in neutral and varus alignment. The volume of bone at risk ofdamage was significantly higher for varus alignment, despite thevariation among specimens. Rawlinson et al. (2005) carried outexperimental tests and finite element (FE) analyses on ninepaired-tibiae to compare stemmed and un-stemmed tibial trays.From the FE analyses, it was seen that a stem reduced the stressesand strains in the bone beneath the tibial tray. However, due to thebiological variability between specimens, the displacementbetween the bone and implant was highly variable and the effectof the stem inconclusive. Despite the use of multiple patientgeometries, the loading was limited to a single magnitude for allspecimens.

Larger scale studies have focussed on the hip; two studies of ahip resurfacing used 16 patient specific models to investigatevarusvalgus alignment (Radcliffe and Taylor, 2007a) and cement-ing technique (Radcliffe and Taylor, 2007b). A statistical shape andintensity model (SSIM) of the femur (Bryan et al., 2010) has beenused to analyse hip fracture risk (Bryan et al., 2009) and influenceof head diameter of a hip resurfacing (Bryan et al., 2012). Using the

www.elsevier.com/locate/jbiomechhttp://www.JBiomech.comhttp://www.JBiomech.comhttp://dx.doi.org/10.1016/j.jbiomech.2013.04.021http://dx.doi.org/10.1016/j.jbiomech.2013.04.021http://dx.doi.org/10.1016/j.jbiomech.2013.04.021http://crossmark.dyndns.org/dialog/?doi=10.1016/j.jbiomech.2013.04.021&domain=pdfhttp://crossmark.dyndns.org/dialog/?doi=10.1016/j.jbiomech.2013.04.021&domain=pdfhttp://crossmark.dyndns.org/dialog/?doi=10.1016/j.jbiomech.2013.04.021&domain=pdfmailto:mark.taylor@flinders.edu.auhttp://dx.doi.org/10.1016/j.jbiomech.2013.04.021

F. Galloway et al. / Journal of Biomechanics 46 (2013) 19001906 1901SSIM, variability of both the femur geometry and elastic moduluswas captured and a large numbers of FE-ready meshes repre-senting a population were easily generated.

Inter-patient variability has been observed in clinical measure-ments of knee loads (Kutzner et al., 2010). However, in moststudies variation of loading is not taken into account and a fixedmagnitude static load is applied for all cases. Loads are oftenscaled by body weight (Perillo-Marcone et al., 2004; Rawlinsonet al., 2005; Perillo-Marcone and Taylor, 2007) which does notrepresent the significant variation in the ratio of the load compo-nents (e.g. anteriorposterior to axial force) known to occurbetween subjects (Kutzner et al., 2010). To capture this inter-patient variability, a statistical model (SM) has been used togenerate a population of load cycles (Galloway et al., 2012).

In this study, the inter-patient variability of both the bone andloading is considered to assess a cementless osseointegrated tibialtray (P.F.C. s Sigmas, Depuys Inc, USA) in a large population.The outcome of a TKR is dependent on many factors; pre-operativefunction, surgical technique, fixation type, implant design, and thephysical, emotional and social health of the patient (Wylde et al.,2007). Cementless fixation is of interest as it is thought to providelong-term fixation for younger more active patients without theproblems associated with cement degradation (Lombardi et al.,2007) and studies have reported good survivorship rates of around95% after 10 years for cementless tibial trays (Hofmann et al.,2001; Oliver et al., 2005; Baker et al., 2007; Epinette and Manley,Fig. 1. Comparison of the internal joint reaction forces from Orthoload (light) andmusculoskeletal data have been scaled by 0.5. The heavy line represents the mean ofmoments act in the directions defined in Fig. 4.2007). The objective of the present work is to develop a metho-dology for carrying out population based studies and to investigatefactors which increase the failure risk of the tibial tray.

2. Methods

A SSIM of the complete tibia incorporating both geometry and elastic modulusvariation was created using principal component analysis (PCA), following themethod of Bryan et al. (2010) as detailed in the Appendix A. A set of 32 leftcomputed tomography (CT) scans of mixed resolution and an unknown demo-graphic were used to train the SSIM. The full tibia from each CT scan was semi-automatically segmented using Avizo (Visualization Sciences Group, Bordeaux,France) and a tetrahedral mesh of each was generated using Ansys ICEM CFD(Ansys Inc., PA, USA). The maximum element size for the proximal and distalregions was set to 1.5 mm and 5 mm, respectively. The baseline volume mesh,which consisted of 65,655 nodes and 337,205 tetrahedra, was then morphed to eachtraining case in a two-step process, first through elastic registration of the surfacemesh and then volumetric morphing of the tetrahedral mesh. Having establishedcorrespondence between each member of the training set, PCAwas then performed togenerate the SSIM. The SSIM was then used to generate a large population of tibiamodels, where each tibia model is described by a tetrahedral mesh and associatedelement material properties, based upon the smaller training population of tibiamodels. A population of 500 tibiae was generated by sampling the first 24 of 32 PCweights, which explained 95% variance, assuming each had a normal distributionwithmean and standard deviation s for each PC and truncated to 73s. The generatedpopulation was considered to be realistic in shape, size, and modulus distribution (seeAppendix A).

To generate loading for each tibia, a SM of internal tibiofemoral joint loads for asingle gait cycle (heel strike to heel strike) was generated following Galloway et al.(2012). The training data were taken from musculoskeletal models of 20 olderhealthy subjects (9 male, 11 female, age 5579) (Worsley et al., 2011). The loadsmusculoskeletal models (dark). The AP force, FE and VV moments of theeach component and the shaded area is 71 standard deviation. The forces and

F. Galloway et al. / Journal of Biomechanics 46 (2013) 190019061902consisted of anteriorposterior (AP), mediallateral (ML), and axial (AX) forcesand flexionextension (FE), varusvalgus (VV), and internalexternal (IE) rota-tion moments, time normalised from 0 to 100% gait (sampled at 1% intervals), andnormalised by body weight. The AP force, FE moment, and VV moment werescaled by a factor of 0.5 to make the peak magnitudes more comparable totelemetric implant data (Fig. 1). A set of 500 gait cycles were generated from the SMby sampling the first 13 of 20 PC weights, which explained 95% variance, againassuming each had a normal distribution with mean and standard deviation s foreach PC and truncated to 73s. The sampled gait cycles were seen to be similar inpattern to the original training data (Galloway et al., 2012).

Each tibia was associated with one gait cycle. To compute the actual loads itwas necessary to estimate the weight of each model. Using the full leg CT scans,from which the training tibiae were taken, a regression relationship was foundbetween tibia and femur length. This was modified with a femurstature ratio(Feldesman and Fountain, 1996) to predict model height. A BMI for each model wassampled from a distribution based on NHANES data (NHANES, 1999) and used withthe predicted height to calculate the mass.

The alignment of the tibia, tibial tray position, and tibial tray implantation wereall performed automatically using ZIBAmira 2010.07-rc7 (Zuse Institute Berlin (ZIB),Berlin, Germany http://amira.zib.de). Each tibia was aligned in a coordinatesystem, such that +x is medial, +y is anterior, and +z is superior (Fig. 2), using thetransformation described by Fitzpatrick et al. (2007). The tibia was resected 1.5 mmbelow the lowest point of the condyles (Fig. 3a). The resected surface posteriorcondylar line (line joining the most posterior medial and lateral points of theresected surface) was used to determine the IE rotation angle (Moreland, 1988)and the ML width of the resected surface was measured to size the tibial tray(Fig. 3b). The tibial tray was translated to align with the centre of the ML width inML direction and the centre of the resected surface in the AP direction (Fig. 3b).Models were excluded from the study if the implant overhung the bone, becausethe implant could impinge on a ligament and cause pain.

Mesh operations were performed to implant the tibial tray (Fig. 3c). The tibiawas (i) resected using mesh cutting operations, (ii) merged with the tray geometryusing a mesh union operation, and (iii) remeshed to ensure good element qualityFig. 2. Alignment of the tibia to the global axis.(a) Inferior view and (b) Medialview.

Fig. 3. Selected steps of implanting the tibial tray: (a) shows the position of the cutting pland (c) is an exploded view of mesh components (Tetra).(Zilske et al., 2008; Kahnt et al., 2011). A first order tetrahedral mesh was generatedin ZIBAmira with element sizes of 2 mm and 1.5 mm for the tibia and trayrespectively, and the elastic modulus was interpolated to the new mesh. Thecombined mesh of tibia and tray was imported into Abaqus 6.9 (Simulia, RI, USA).The elastic modulus of the tibia was grouped into 10 MPa bands and the tibial traywas modelled as cobalt chrome with a modulus of 210 GPa. The interface betweenthe tray and tibia was assumed to be tied, simulating complete osseointegration.

All loads were assumed to act at the centre of the knee relative to the tibia. Thethree forces, +FAP, +FML, and +FAX, act in the medial (+x), anterior (+y), and superior(+z) directions (Fig. 4). The three moments, +MFE, +MVV, and +MIE, act clockwise inthe median (yz), frontal (xz), and horizontal (xy) planes (Fig. 4). The forces andmoments were split across groups of nodes positioned medial, lateral, anterior, andposterior relative to the centre of the tibial tray (Table 1).

To assess the risk of failure, the equivalent strain (, referred to as strain) wascomputed from the principal strains (1, 2, and 3),

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi122 232 312

2

s

Only the resected surface was considered in the analysis and this was definedas the tibial bone directly in contact with the tibial tray, excluding the stem of thetray, based on the assumption that for the tibial tray to migrate or subside, theresection surface must fail (Perillo-Marcone et al., 2004; Perillo-Marcone andTaylor, 2007). Two metrics were computed for the resection interface; thecomposite peak strain (CPS) which is the peak strain of each element which occursduring the complete gait cycle, and the percentage surface area with strain aboveyield (PSAY). The compressive yield strain of trabecular bone was used and taken as7300 microstrain (Morgan and Keaveny, 2001).

A mesh convergence study was performed using a single model with theelement sizes ranging from 5 mm for the bone and 3 mm for the tray (coarsest), to1.75 mm for bone and 1 mm for the tray (finest). The mean CPS and PSAY changedby less than 5% between mesh densities, and the distribution of both metrics wasane, (b) shows the landmarks used on the resected surface to position the tibial tray,

Fig. 4. The directions of the applied forces and node groups to which loads areapplied of the FE model.

Table 1Split of loads over the four groups of nodes on the tibial tray. The fraction and direction of a load are given for the positive direction. x, y, and z are the directions in which theforce is applied. ra, rp, rm, and rl are the moment arms from the centre to the anterior, posterior, medial, and lateral group of nodes respectively.

Load Group of nodes

Medial Lateral Anterior Posterior

Anteriorposterior force (FAP) +0.5y +0.5yMediallateral force (FML) +0.5x +0.5xAxial force (FAX) +0.5z +0.5zFlexionextension moment (MFE) +0.5raz 0.5rpzVarusvalgus moment (MVV) 0.5raz +0.5rpzInternalexternal rotation moment (MIE) +0.25rmy 0.25rly 0.25rax +0.25rpx

F. Galloway et al. / Journal of Biomechanics 46 (2013) 19001906 1903similar for all mesh densities. This was used as a guide to select an appropriatemesh density because each model varies in shape, size, and modulus distribution,and different loading was applied. The choice of mesh density was a compromisebetween solution time and solution accuracy.

To estimate the models at risk of failure, the models were split into two groups,lower risk and higher risk, using a threshold of 10% PSAY. To visualise differencesbetween the two groups of models, the correlation between CPS, PSAY, andmodulus was examined and the resection surface for models representing a lowerrisk case, border case (with a PSAY close to 10%), and higher risk cases wasvisualised. A paired t-test with a Bonferroni correction factor was performed to testif factors were significantly different between the two groups (5%). The factorsconsidered were mean elastic modulus of the resected surface, weight, BMI, andpeak forces and moments in all directions (e.g. the peak anterior force is themaximum of FAP and the peak posterior force is the minimum of FAP). Further, aone-way ANOVA test was used to test if mean CPS and PSAY were differentbetween the series of implant sizes (5%).Fig. 5. Distribution of the mean CPS and 95th percentile CPS.

Fig. 6. Correlation between mean CPS, PSAY, and mean modulus of the resectedsurface, with yield and ultimate strain of cancellous bone marked. Three examplecases are highlighted, one lower risk case, one border case, and one higherrisk case.3. Results

From the population of 500 tibiae, 328 (65.6%) were included inthe study and 172 (34.4%) were not. Of the excluded models, for134 (26.8%) the tibial tray was found to overhang the resectedsurface. The implantation process failed for the remaining 38(7.4%) due to geometric limitations. FE analysis was successfullycompleted for 328 models.

The distribution of the mean CPS shows that the majority ofmodels (95.1%) were below the yield strain limit (Fig. 5). For alarge proportion of models (70.7%) the 95th percentile CPS is alsobelow yield strain (Fig. 5). The mean of the mean CPS for allmodels is 2843 microstrain, below yield strain, with a range of64817060 microstrain.

The mean CPS was correlated with PSAY, indicating the mod-ulus of each model (Fig. 6). Using a threshold of 10% PSAY, 56models (17.1%) were in the higher risk group with a minimummean CPS of 3510 microstrain and maximum of 17,060 micro-strain. The majority of models in this group have a mean elasticmodulus of less than 400 MPa, with several models in the 400600 MPa range.

It was observed that the distribution of the CPS changed as thePSAY increased. For models with a low PSAY (e.g. lower risk caseFig. 7), higher strains were seen around the anterior and posterioredges. As the PSAY increases, models around the 10% threshold(e.g. border case Fig. 7) tended to have bone above yield strainaround the periphery. The strains on the lateral side tended to behigher in comparison to the medial side. In the higher risk group,bone above yield tended to be distributed over the whole resectedsurface (e.g. higher risk case Fig. 7), although in some cases onlythe lateral side was above yield.

Using a paired t-test, only the mean modulus and peak flexionmoment were found to be significantly different between thelower risk and higher risk groups (Table 2). The one-way ANOVAtest showed no significant difference of mean CPS or PSAYbetween the series of implant sizes (p0.28 and p0.45respectively).

Fig. 7. Three example cases of the resected surface. Top is a lower risk case (PSAY1.45%), middle is a border case (PSAY9.05%), and bottom is a higher risk case(PSAY39.75%). Each is plotted with the CPS (left), the point in the gait cycle at which the peak strain occurs (middle), and modulus (right). These cases are highlighted in Fig. 6.

F. Galloway et al. / Journal of Biomechanics 46 (2013) 1900190619044. Discussion

A large scale, multi-subject study was performed of a cement-less osseointegrated tibial tray incorporating inter-patient varia-bility of bone geometry and elastic modulus, and gait cycleloading. The process was fully automated, allowing an FE meshto be generated in 510 min using ZIBAmira and configured usingAbaqus in a further 10 min. The solution and post-processing timewas around 30 min per model. The system was designed such thateach stage was automated and could run multiple processesunattended.

In examining the strain of the proximal tibia during a gait cycle,Perillo-Marcone and Taylor (2007) reported the PSAY of theresected surface between 59 and 70% when using the minimumprincipal strain as the failure criteria. In this study the mean PSAYof the population was 6% (minimum 0%, maximum 83%). Thedifference is likely because Perillo-Marcone and Taylor (2007)modelled a 116 kg patient, whereas in this study the mean weightof a model was 79 kg resulting in smaller applied loads. However,the pattern of strain on the resected surface is comparablebetween Perillo-Marcone and Taylor (2007) and this study; higherstrains were seen around the anterior and lateral edges. Thepattern of strain is most likely due to the difference in modulusbetween the lateral and medial side of the resection surface asseen in Fig. 7.

Models were determined to be at risk of failure using the PSAYmetric. Loosening is the leading cause of tibial tray failures(Sharkey et al., 2002; National Joint Registry for England andWales, 2010), and it is reasoned that if a large proportion of bonesupporting the tray fails because it experiences a high strain, thetray could migrate and loosen. Using the 10% PSAY threshold, theproportion of models in the higher risk group was 17.1%, anoverestimation in comparison to the reported survivorship rates;96.3% at 5 years for all cementless TKRs (National Joint Registry forEngland and Wales, 2010) and 93.3% at 10 years for the PFCimplant (Baker et al., 2007). This could be because the chosenPSAY threshold is too conservative. Defining a more accuratethreshold would require matched clinical data. The tray is perhapsundersized to avoid overhangs between it and the bone, resultingin the tray not being supported by stronger cortical bone andincreasing the strain in the cancellous bone. Further to this, boneremodelling was not simulated, which would affect the straindistribution in the tibia. It is expected that models in this studywould be at lower risk of failure because the tray was assumed tobe fully osseointegrated, which takes time to occur in vivo.

In this study, two separate training sets were used to create theSMs, consisting of 32 tibiae for the tibia SSIM and 20 healthysubjects for the gait cycle SM. These sets represent only a smallproportion of the general population, and sampling the PC weightsto 73s increases the chances of generating outlier cases. How-ever, these cases are of interest, because they represent the worst-case scenarios, important to consider in the assessment of a TKR.

By using separate SMs of the tibia and gait cycle, the two-wayinteraction between tibia morphology and loading, and loadingand tibia strength are neglected. The weight of a model (used tocompute the magnitude of the loads) was estimated from thelength of the tibia and BMI. This provides a link between the tibiamorphology and loading, but the BMI of a model was sampledfrom an independent population and is not directly related to eachmodel. There is a chance that models of a small tibia with a lowmodulus could have an inappropriately high BMI, which might beconsidered unrealistic and result in the model being classified ashigher risk. The relationship between bone properties and load-ing are complex. Tibial bone properties are known to be a functionof age, gender, applied loads and activity levels. To better capturethe interactions between the tibia, loading, and patient factors (e.g.height, weight, BMI, age, gender), a data set of CT scans, motioncapture data and patient information would be required for a SM.

Comparing factors between the two groups (Table 2), it wasfound that the higher risk group was subjected to larger peak

Table 2The significance of factors between the lower risk and higher risk groups for a PSAY threshold of 10%. Result was significant po0.0036 with Bonferroni correction factor.

Factor P Lower risk, n272 Higher risk, n56

Min Mean Max Min Mean Max

Mean modulus*(MPa) 0.000 180.7 590.0 1169.0 106.0 275.7 526.5Peak flexion moment*(Nm) 0.002 5.3 19.5 60.8 5.8 22.8 40.3Peak axial force (N) 0.004 5206.5 2588.3 1247.7 5622.4 2875.9 1456.2Model weight (kg) 0.005 37.8 77.9 149.2 52.8 85.3 138.7Model BMI (kg/m2) 0.006 17.0 28.6 47.7 19.8 30.9 48.5Peak posterior force (N) 0.007 843.4 353.1 101.9 778.4 401.5 147.5Peak extension moment (Nm) 0.023 31.3 9.8 2.2 29.4 11.6 4.1Peak varus moment (Nm) 0.030 11.1 25.8 61.9 11.6 28.5 61.8Peak internal moment (Nm) 0.039 0.8 7.7 32.7 1.8 9.1 28.4Peak external moment (Nm) 0.047 21.7 5.7 2.2 18.0 6.7 0.1Peak medial force (N) 0.167 10.2 130.9 333.8 55.6 141.5 320.8Peak anterior force (N) 0.875 3.8 43.3 452.3 4.9 44.7 271.9Peak lateral force (N) 0.926 120.7 30.4 25.6 136.5 30.9 34.6Peak valgus moment (Nm) 0.550 23.9 2.5 1.9 17.0 2.8 1.3

F. Galloway et al. / Journal of Biomechanics 46 (2013) 19001906 1905loads, implying a greater contact force in the knee. The magni-tudes of the loads applied are dependent on weight. In the higherrisk group the mass of the models ranged from 52.8 kg to 138.7 kgand the BMI range was 19.848.5 kg/m2, not unrealistic for apopulation. If the peak loads are normalised by weight, they arecomparable between the lower risk and higher risk groups.Strain of the resected surface is also dependent on the bonemodulus and a two-fold difference in the mean modulus ofresection interface was found between the lower risk and higherrisk groups (590.0 MPa compared to 275.7 MPa respectively). Themodulus of cancellous bone in the proximal tibia has beenmeasured to be around 500 MPa (Keaveny et al., 2001), with upto an order of magnitude difference within the proximal tibia(Goldstein et al., 1983). It was also seen that the medial side of theresected interface was stronger than the lateral side (examplemodels Fig. 7), a pattern found by Goldstein et al. (1983).

Studies of multiple patients have suggested that the variabilityof bone quality and loading affected the volume of bone at risk ofdamage (Wong et al., 2010). The higher risk group had a largerpeak varus moment, which results in a larger medial axial force,suggesting varus alignment. Clinical studies have shown that varusalignment increases the likelihood of revision (Ryd et al., 1995;Fang et al., 2009). FE studies have also shown that with varusalignment, a larger volume of bone is at risk of failure (Perillo-Marcone et al., 2004; Wong et al., 2010). It has also been reportedthat the combination of increased patient BMI (or mass) and asmaller tibial component is associated with the failure of a TKR(Berend et al., 2008). This is perhaps because the stress in the tibiawas simply computed as the ratio of patient weight to tibial trayarea, hence a larger mass and smaller implant will increase stress.In this study, the higher risk group had a larger mass and BMI, butthe mean CPS and PSAY were not significantly different betweenthe series of implant sizes. The populations in each study are alsodifferent, Berend et al., (2008) examined metal-backed and all-polyethylene cemented tibial trays which had failed by asepticloosening, whereas in this study an osseointegrated uncementedtibial tray was modelled.

A limitation of the FE model is that loads are applied directly tothe tibial tray assuming that the forces are evenly distributed andthe tibiofemoral contact area is static. This is not the case in vivo,where the tibiofemoral contact area moves as the knee flexes andextends (Iwaki et al., 2002) and soft tissue constraints influencethe load distribution.

Telemeterised TKRs provide in vivo measurement of the inter-nal forces and moments in the knee, but given the observed inter-patient variability of the telemetric data (Kutzner et al., 2010), thefive available sets of data were not considered enough to create aSM. For this study, the next best available data of internal kneeloads were from musculoskeletal models of 20 healthy subjectsand these were used to create the gait cycle SM. However, theaccuracy of the predicted kinematics is limited by errors andassumption inherent in the MS modelling process, e.g. soft tissueartefacts, use of a generic linear scaling law, and the assumptionthat the knee only has 1 degree-of-freedom (Schwartz et al., 2010;Worsley, 2011). In this study, it was observed that the MSmodelling and in vivo loads had a similar pattern but themagnitudes were overestimated by the MS modelling. Therefore,the loads seen to be most overestimated (the AP force, FEmoment, and VV moment) were scaled by a factor of 0.5 to bringthem more in-line with the in vivo data (Fig. 1).5. Conclusions

This study demonstrates the use of SMs in a population basedstudy assessing the performance of a cementless osseointegratedtibial tray. The process of positioning and implanting a tibial traywas fully automated allowing fast generation of a large number ofmodels. The study showed that the higher risk models have alower mean resected surface modulus, and higher model weightand peak loads; expected for an osseointegrated tibial tray. Theadvantage of a population based study is that inter-patientvariability incorporated in the pre-clinical testing, and by includ-ing additional patient specific information in the SM, populationbased studies can also potentially enable the identification ofclinical factors that influence the performance of a tibial traydesign.Conflicts of interest statement

Mark Taylor is a consultant to DePuy Orthopaedics Inc. None ofthe other authors have any conflicts of interest.Acknowledgements

This project was funded by DePuy (a Johnson & Johnsoncompany), Engineering and Physical Sciences Research Council(EPSRC). Parts of the research leading to these results receivedfunding from the European Union Seventh Framework Programme(FP7/2009-ICT) under grant agreement no. 248693.

F. Galloway et al. / Journal of Biomechanics 46 (2013) 190019061906Appendix A. Supporting information

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A large scale finite element study of a cementless osseointegrated tibial trayIntroductionMethodsResultsDiscussionConclusionsConflicts of interest statementAcknowledgementsSupporting informationReferences