estimating totalkneereplacementjointloadratiosfromkinematics

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Estimating total knee replacement joint load ratios from kinematics

Clare K. Fitzpatrick n, Paul J. Rullkoetter

Center for Orthopaedic Biomechanics, University of Denver, 2390 S. York St., Denver, CO 80208, USA

a r t i c l e i n f o

Article history:

Accepted 1 July 2014

Keywords:

Total knee replacement

Finite element

Joint load ratios

Kinematics

Force prediction

Fluoroscopy

a b s t r a c t

Accurate prediction of loads acting at the joint in total knee replacement (TKR) patients is key to

developing experimental or computational simulations which evaluate implant designs under physio-

logical loading conditions. In vivo joint loads have been measured for a small number of telemetric TKR

patients, but in order to assess device performance across the entire patient population, a larger patient

cohort is necessary. This study investigates the accuracy of predicting joint loads from joint kinematics.

Specically, the objective of the study was to assess the accuracy of internal–external (I–E) and anterior–

posterior (A–P) joint load predictions from I–E and A–P motions under a given compressive load, and to

evaluate the repeatability of joint load ratios (I–E torque to compressive force (I–E:C), and A–P force to

compressive force (A–P:C)) for a range of compressive loading proles. A tibiofemoral nite element

model was developed and used to simulate deep knee bend, chair-rise and step-up activities for ve

patients. Root-mean-square (RMS) differences in I–E:C and A–P:C load ratios between telemetric

measurements and model predictions were less than 1.10e–3 Nm/N and 0.035 N/N for all activities.

I–E:C and A–P:C load ratios were consistently reproduced regardless of the compressive force prole

applied (RMS differences less than 0.53e–3 Nm/N and 0.010 N/N, respectively). When error in kinematic

measurement was introduced to the model, joint load predictions were forgiving to kinematic

measurement error when conformity between femoral and tibial components was low. The prevalence

of kinematic data, in conjunction with the analysis presented here, facilitates determining the scope of

A–P and I–E joint loading ratios experienced by the TKR population.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

It is important to evaluate prospective total knee replacement

(TKR) devices under physiological joint loading conditions so that

in vivo mechanics can be accurately evaluated during pre-clinical

experimental or computational simulation. Loads acting at the joint

affect kinematics, wear and micromotion of the components, inu-

encing the clinical performance and longevity of these devices.

However, due to the complex nature of the knee joint (six degrees-

of-freedom (DOF), ligamentous structures, and muscle redundancy),

estimating joint forces from numerical models remains a challenge(Kinney et al., 2013; Fregly et al., 2012). The current standard in joint

force prediction from numerical models is rigid body musculoskeletal

optimization in combination with nite element (FE) modeling (Kim

et al., 2009; Shelburne et al., 2005; Taylor et al., 2004). Due to the

iterative nature of these simulations, they are computationally

intensive and can take days to solve. In recent years, direct measure-

ment of in vivo tibiofemoral (TF) joint forces during dynamic activity

has been achieved. Telemetric tibial trays have been implanted in a

number of TKR patients and TF joint loads have been recorded while

the patients perform activities of daily living (Kutzner et al., 2010;

D’Lima et al., 2011). However, in vivo joint load data has been

collected for just a handful of TKR patients. In order to develop

population-based analyses to assess device performance across the

entire TKR patient population, a larger patient cohort in conjunction

with computationally ef cient simulations is desirable.

There is a wealth of kinematic data available from TKR patients.

In vivo kinematics are acquired through a variety of techniques,

with varying levels of accuracy in joint motion measurement. Jointkinematics are frequently measured using motion capture analysis

in the gait laboratory, typically using reective or infra-red

markers attached to the skin to measure whole body motion

during dynamic activity, and applying inverse kinematics methods

to predict the motion of the underlying bones (D’Lima et al., 2012;

Lloyd and Besier, 2003). Video uoroscopy tracks the bone or

implant geometry with improved accuracy over motion capture

systems; single plane systems have reported measurement of

joint motions with accuracy in the order of 0.5 mm or 0.51 for in-

plane translations and rotations, respectively (Banks and Hodge,

1996; Mahfouz et al., 2003; Fregly et al., 2005; Prins et al., 2010;

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jbiomechwww.JBiomech.com

Journal of Biomechanics

http://dx.doi.org/10.1016/j.jbiomech.2014.07.002

0021-9290/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: þ 1 303 871 6435; fax: þ 1 303 871 4450.

E-mail address: [email protected] (C.K. Fitzpatrick).

Journal of Biomechanics 47 (2014) 3003–3011

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Acker et al., 2011; Prins et al., 2011). However, some of these studies

report accuracy of the absolute position of an individual component

in space. When evaluating knee kinematics, it is the relative pose

between components that is of interest. Of single-plane studies

which have evaluated relative TF motion, errors of 0.2–1.3 mm and

1.1–1.51 have been reported in internal–external (I–E) and anterior–

posterior (A–P) motions (Banks and Hodges, 1996; Mahfouz et al.,

2003; Prins et al., 2011; Acker et al., 2011). Dual-plane systems

demonstrate improved accuracy over single-plane systems, withaccuracy of relative motion reported as 0.1–0.3 mm and 0.1–0.41 in

all DOFs (Li et al., 2004; Short et al., 2005; Hanson et al., 2006;

Bingham and Li 2006; Kaptein et al., 2007; Torry et al., 2011; Zhu and

Li, 2012). Kinematic information provides valuable insight into the

performance of different TKR component designs, but does not

describe the loads and interface mechanics at the joint.

Prior researchers have sought to establish relationships bet-

ween joint loads and joint kinematics. D’Lima et al. (2011)

investigated the concept of a unique relationship between implant

position and contact loads. They simultaneously recorded compo-

nent position and contact loads in an AMTI testing machine and

used joint loads to predict kinematics. I–E and A–P joint kine-

matics were predicted with an accuracy of 0.51 and 0.5 mm. The

current study investigates the inverse to this relationship: how

accurately joint load ratios can be predicted from more easily

obtained joint kinematics. A number of prior studies have demon-

strated that compressive and valgus-varus (V –V) loads are highly

sensitive to component position (Lin et al., 2006; Fregly et al.,

2008; Lin et al., 2010a). Fregly et al. (2008) showed that a change

of 70.1 mm in S–I o r V –V position altered S–I and V –V load

predictions by 205% and 77%, respectively. Hence, current kine-

matic measuring systems do not provide enough accuracy to

facilitate direct prediction of loading in these DOFs from kinematic

data. However, Fregly et al. (2008) and Lin et al. (2010a) also

demonstrated that when a combination of kinematics (in insensi-

tive DOFs) and assumed loads (in sensitive DOFs) were applied,

changes in pose of 70.5 mm or 0.51 have minimal changes in

resulting loads. Hence, in the current study, we hypothesize that

for most activities, I–E torque and A–P force were a function of I–E

rotation, A–P translation and compressive force. Specically, the

objective of this study was to assess the accuracy of I–E and A–P

joint load predictions from I–E and A–P motions under a given

compressive load, and to evaluate the consistency of joint load

ratios (I–E torque to compressive force (I–E:C) and A–P force to

compressive force (A–P:C) ratios) for a range of compressive

loading proles. Improved prediction of joint load ratios would

facilitate evaluation of joint mechanics over the range of potential

load ratios likely to be encountered in vivo and provide valuable

information for experimental and computational testing.

2. Methods

In-vivo joint load data, which included 6-DOF joint loads but no kinematic joint

data, was obtained from published tibial tray telemetric data from ve TKR patients

performing three activities of daily living: deep knee bend, chair-rise and step-up

(Kutzner et al., 2010). Knee exion-extension (F–E) was adopted from video

recordings of each patient performing the activity (Bergmann, 2008). These

activities were chosen as activities which are typically measured in uoroscopy

studies as knee position is reasonably stationary and stays within the eld of view

of the uoroscopy system.

A TF FE model was developed which consisted of the same femoral and tibial

components as those implanted in the telemetric patients; this was a cruciate

sacricing design with an ultracongruent tibial insert ( Heinlein et al., 2007). The

femoral component was meshed with rigid triangular shell elements, while the

tibial component was meshed using hexahedral continuum elements. Material

properties have been shown to have minimal effect on kinematics, so for

computational ef ciency, components were modeled as rigid with a pressure–

overclosure relationship (Halloran et al., 2005a; Fitzpatrick et al., 2010 ). A friction

coef cient of 0.04 was assumed between femoral and tibial components ( Godest

et al., 2002; Halloran et al., 2005b). In order to determine corresponding joint

kinematics for the telemetric loading conditions, an FE simulation was initiallyperformed where loads, as measured in the telemetric patients, were applied and

the resulting kinematics were recorded. The femoral component was kinematically

constrained in all 6-DOF, while 5-DOF loads (compressive, A–P, medial–lateral

(M–L), I–E, and V –V) and F–E kinematics were applied to the tibial insert ( Fig. 1).

The resulting I–E and A–P joint motions during the activity were recorded. This

analysis was carried out for each subject performing each of the three activities.

This analysis resulted in a matched set of joint kinematics and loads, equivalent to

data obtained from simultaneous measurement of telemetric loads and uoro-

scopic kinematics in the experimental setting, but without any kinematic

measurement error.

In order to evaluate the ability of the model to predict joint loads from

kinematics that could be measured from uoroscopy, the analysis was subse-

quently repeated by applying only compressive joint force and reproducing I –E, A–

P and F–E joint motions, while the remaining DOFs were unconstrained (Fig. 1).

Resulting I–E and A–P joint loads were compared to the original telemetric loads to

assess how accurately I–E and A–P joint loads could be predicted from applied

kinematics. While V –

V motions were thought to be too subtle to be measured withsuf cient accuracy uoroscopically, quantifying the effect of V –V motion on joint

loads was still of interest. Additional simulations were performed whereby V –V

motions were also included in the analyses; compressive load, I–E, A–P, V –V and

F–E motions were applied in the analyses and predicted I–E, A–P and V –V joint

loads were compared to the original telemetric loads. Compressive load is too

sensitive to superior–inferior (S–I) position to be accurately predicted from

kinematic joint measurements; hence this study focused on prediction of joint

load ratios rather than absolute joint load magnitudes. I–E:C and A–P:C load ratios

Fig. 1. TF model showing loading conditions for the telemetric (left) and kinematically-driven (right) analyses; applied loads shown in red, applied motions shown in green.

C.K. Fitzpatrick, P.J. Rullkoetter / Journal of Biomechanics 47 (2014) 3003– 30113004


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were calculated for each simulation. To evaluate the consistency of joint load ratio

prediction under different compressive loads, further analysis was performed

whereby the same I–E and A–P joint motions were simulated, with a variety of

compressive force proles. Specically, compressive forces were held constant at

1000 N, 2000 N, and 3000 N, with F–E, I–E and A–P motions kinematically

prescribed and all other DOFs unconstrained for each subject during each activity.

Joint loads and joint load ratios (I–E:C and A–P:C) were compared for different

compressive force analyses.

There is uncertainty in the estimation of joint kinematics from experimental

studies. Single plane uoroscopy studies have reported accuracy of 0.51 for

rotations and 0.5 mm for in-plane translations (S–

I and A–

P), which may be largerstill when the relative pose between components, rather than a single component

position in space, is the measurement of interest (Banks and Hodge, 1996; Hoff et

al., 1998; Dennis et al., 2003; Mahfouz et al., 2003; Fregly et al., 2005; Prins et al.,

2010; Acker et al., 2011; Prins et al., 2011). Thus far, the analysis performed in this

study has assumed ideal kinematics (zero measurement error). To evaluate how

well the method outlined in the current study would perform with real experi-

mental kinematic data, rather than ideal computational data, error in kinematic

measurement was introduced into the analyses. In order to assess the effect of

measurement error on joint load prediction, I–E and A–P motions were shifted by

70.51 and 70.5 mm, and 71.01 and71.0 mm, respectively, in separate analyses.

Resulting I–E and A–P joint loads and joint load ratios were compared to analyses

with the original joint kinematics.

3. Results

Comparing telemetric I–E and A–P joint loads with model

predictions based on I–E and A–P motions and compressive loads,

root-mean-square (RMS) differences in I–E torque and A–P force

across subjects averaged 1.27 Nm and 31.0 N for deep knee bend,

1.12 Nm and 31.4 N for chair-rise, and 1.99 Nm and 68.3 N for step-

up activities, respectively. RMS differences in I–E:C and A–P:C joint

load ratios across subjects averaged 0.90e–3 Nm/N and 0.022 N/N

for deep knee bend, 0.89e–3 Nm/N and 0.027 N/N for chair-rise,

and 1.10e–3 Nm/N and 0.035 N/N for step-up activities, respec-

tively (Table 1; Figs. 2 and 3). When V –V motions were also

included in the analyses, RMS differences in I–E torque and A–P

force across subjects improved to 0.34 Nm and 6.1 N for deep knee

bend, 0.18 Nm and 4.9 N for chair-rise, and 0.45 Nm and 10.4 N for

step-up activities, respectively. RMS differences in I–E:C and A–P:C joint load ratios across subjects improved to 0.24e–3 Nm/N and

0.006 N/N for deep knee bend, 0.25e-3 Nm/N and 0.008 N/N for

chair-rise, and 0.38e–3 Nm/N and 0.015 N/N for step-up activities,

respectively. V –V:C joint loads ratios were predicted with an RMS

accuracy of 0.002e–3, 0.003e–3, 0.004e–3 Nm/N for deep knee

bend, chair-rise, and step-up activities, respectively (Fig. 4).

Comparing joint load ratios for a variety of compressive

proles, I–E:C and A–P:C joint load ratios were consistently

reproduced regardless of compressive force prole. When I–E

and A–P motions were applied for different compressive force

proles (telemetric, constant 1000 N, constant 200 0 N and con-

stant 3000 N), RMS differences in I–E:C and A–P:C ratios for all

constant proles compared to the telemetric prole were less than

0.28e–3 Nm/N and 0.010 N/N for deep knee bend, 0.53e–3 Nm/N

and 0.008 N/N for chair-rise, and 0.22e–

3 Nm/N and 0.010 N/N forstep-up activities, respectively, for all subjects (Fig. 5).

When measurement error was introduced into the kinematic

data, small changes in joint loads were observed when knee

exion was greater than 251. At knee exion greater than 251,

the worst RMS differences in I-E:C and A-P:C ratios for all

kinematic error conditions evaluated (shifts of 70.51 in I-E rota-

tions and70.5 mm in A-P translations) averaged 1.20e–3 Nm/N

and 0.049 N/N for deep knee bend, 1.34e–3 Nm/N and 0.048 N/N

for chair-rise, and 1.88e–3 Nm/N and 0.080 N/N for step-up activ-

ities. In early exion, small changes in kinematics resulted in a

large shift in the point of contact between femoral and tibial

components and as a result had a substantial impact on joint load

predictions; at low exion (less than 251) kinematic data were

unable to accurately predict joint loads (Table 2; Fig. 6).

4. Discussion

Historically, a combination of rigid body musculoskeletal mod-

els and detailed FE models has been used to predict in vivo joint

loads during dynamic activity (Kim et al., 2009; Shelburne et al.,

2005; Taylor et al., 2004). These studies require an extensive

clinical dataset (whole body kinematics, ground reaction forces,

EMG, muscle strength, dynamic imaging) and optimization simu-

lations which can take multiple days to complete (Kinney et al.,

2013; Fregly et al., 2012). Recently, the availability of measured

in vivo joint loads from patients with telemetric implants has

provided validation data for these models. Overall, medial and

lateral contact forces have been predicted with RMS accuracy in

the order of 150–300 N (Guess et al., 2014; Kinney et al., 2013; Kimet al., 2009; Lin et al., 2010b). These studies have primarily focused

on prediction of total, medial and lateral contact forces, rather

than shear forces and torques (A–P force and I–E torque) which are

important to implant design assessment, for example, in the

development of realistic loading conditions for experimental wear

and micromotion simulations. In addition, the volume of clinical

Table 1

RMS differences in joint loads and joint load ratios between telemetric measurements (taken from Kutzner et al., 2010) and model (with I–E and A–P kinematics and

compressive load) predictions for each subject during deep knee bend (top), chair-rise (center), and step-up (bottom) activities.

Patient # IE torque (Nm) IE:C load ratio (Nm/N) (e-3) AP force (N) AP:C load ratio (N/N)

1 0.40 0.26 10.7 0.006

2 0.77 0.78 32.8 0.036

3 0.23 0.18 34.1 0.018

4 4.11 2.91 47.7 0.035

5 0.82 0.40 29.7 0.015

Mean7SD 1.2771.61 0.9071.15 31.0713.3 0.02270.013

1 0.75 0.56 14.3 0.010

2 0.74 0.80 33.2 0.032

3 0.26 0.69 30.5 0.040

4 3.54 2.17 44.8 0.029

5 0.31 0.22 33.9 0.022

Mean7SD 1.1271.37 0.8970.75 31.4711.0 0.02770.011

1 2.45 0.98 90.2 0.033

2 3.29 1.77 84.8 0.038

3 1.33 0.98 96.9 0.050

4 2.13 1.19 40.9 0.036

5 0.74 0.59 28.8 0.018

Mean7SD 1.9970.99 1.1070.44 68.3731.1 0.03570.012

C.K. Fitzpatrick, P.J. Rullkoetter / Journal of Biomechanics 47 (2014) 3003– 3011 3005


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data and computational resources required for long-running

optimizations limits the number of patient-specic simulations

which may be performed. In order to develop population-based

simulations to assess device performance across the entire TKR

patient population, a larger patient sample, in conjunction with

computationally ef cient simulations, is required.

The current study utilizes a simple TF nite element modelwhich simulates an activity cycle on a single CPU in approximately

six minutes. FE model predictions with imposed I–E and A–P

motions and compressive force demonstrated excellent agreement

in both trend and magnitude with telemetric I–E torque and A–P

force measurements, with RMS accuracy in prediction of I–E

torque and A–P force of less than 2 Nm and 70 N across three

activities. There were some portions of the analysis, notably the

step-up activity at approximately 80% of the cycle, which showed

large errors in I–E torque predictions (Fig. 2). These discrepancies

between telemetric measurements and model predictions

occurred when V –V torque from the telemetric data was large,

and exion angle was low. The curvature of the contacting

surfaces, in combination with a large V –V torque (compared to

the models with neutral V –

V torque), resulted in substantial

differences in I–E torque. When V –V motions were also applied

in the analyses, RMS accuracy in prediction of I–E torque and A–P

force improved to less than 0.5 Nm and 11 N across the three

activities. However, overall V –V motions were small (o21),

resulting from the curvature of the tibial implant rather than

condylar lift-off, and the differences in V –V motions between

these sets of analyses (V –V motion unconstrained, and V –V motion kinematically prescribed) were in the order of 0.11, which

is likely too subtle to be accurately measured with current

uoroscopy systems. Analyses where V –V motions were not

included in the simulations are perhaps a better reection of joint

load accuracy that can realistically be expected from clinically

obtained data with current uoroscopy measurement accuracy.

In the rst set of analyses, compressive force measured from the

telemetric patients was applied to the models. Unfortunately,

changes in relative TF superior–inferior position in the order of

microns have a large effect on compressive force (Fregly et al., 2008),

so S–I kinematic measurements are not accurate enough to facilitate

prediction of compressive force. Therefore, this study focused on

joint load ratios, rather than absolute joint loads – the hypothesis of

this study being that although compressive force may vary, I–

E and

Fig. 2. Comparison of I–E and A–P joint loads and joint load ratios (I–E:C and A–P:C) from telemetric loads and kinematic model predictions for one representative subject

for each activity (deep knee bend (DKB), chair-rise and step-up). Each representative subject was chosen as the subject with RMS differences closest to the mean values for

that activity.



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A–P to compressive load ratios remain relatively consistent for a

specic relative position. Our analysis conrmed this; for all tele-

metric patients and activities, when a different compressive forceprole was applied with the same set of I–E and A–P kinematics, I–E:

C and A–P:C joint load ratios were consistent regardless of applied

compressive force. More detailed analysis of joint loading conditions

such as compressive force, muscle force or muscle co-contraction

predictions would require more complex analyses such as tradition

musculoskeletal and optimization simulations.

In this study, perfect kinematics were initially assumed in the

predictive model when compared to the telemetric patient simu-

lations. In reality, there is measurement error associated with the

experimental process of obtaining joint kinematics. Accuracy of

single-plane uoroscopy systems is in the order of 0.5–1.01 and

0.5–1.0 mm (Banks and Hodge, 1996; Hoff et al., 1998; Mahfouz

et al., 2003; Dennis et al., 2003; Fregly et al., 2005; Prins et al.,

2010; Acker et al., 2011; Prins et al., 2011). This was similar to

errors reported in a complementary study from D’Lima et al. (2011)

where telemetric joint loads were used to predict I–E and A–P joint

kinematics with an accuracy of 0.51 and 0.5 mm. In the current study,the effect of measurement error was introduced by varying applied I–E

and A–P kinematics by 70.5 and 1.01 and 70.5 and 1.0 mm. In later

exion (after 251 of TF exion), errors in joint loads were small and

consistent. However, in early exion, joint load predictions varied

widely from the telemetric measurements. This was due to high

congruency between femoral and tibial components in early exion; a

small change in joint kinematics resulted in a large change in the point

of contact between the components (Fig. 7). The implant geometry

used in this study was an ultra-congruent xed-bearing design;

implant designs with lower conformity between components would

be more forgiving of kinematic measurement error. In addition, data

from dual-plane uoroscopy systems would reduce the measurement

error associated with motion tracking, facilitating more accurate joint

load ratio predictions.

Fig. 3. Comparison of average (light) and 71 standard deviation (dark) joint load ratios (I–E:C and A–P:C) from telemetric loads and kinematic model predictions across all

subjects for each activity (deep knee bend (DKB), chair-rise and step-up).



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No initial implant position information for the telemetricimplants was available. In this study, tibial posterior slope was

assumed to be zero, and knee exion was adopted from video

recordings, which is less accurate than uoroscopy measurement.

Overall, implant alignment does not impact the results, as a

perfectly matched set of kinematics and kinetics has been devel-

oped. An initial simulation in 5-DOF load control was performed to

determine the corresponding kinematics to this combination of

loads, implant design and implant alignment. Simulations include

a variety of patients and activities, which start in different initial

positions and under different loading conditions, with all showing

similarly accurate results in joint load ratio predictions. In practice,

when uoroscopy data rather than model data is used to predict

joint load ratios, the uoroscopy data with provide initial implant

information, reducing or eliminating this source of uncertainty.

In order for experimental and computational simulations toprovide data that is reective of the clinical performance of TKR

devices, these simulations must be representative of the loading

conditions encountered in vivo. Telemetric tibial trays have been

implanted in TKR patients and have provided valuable information

regarding in vivo TF joint loading; however, the number of patients

for which data is available is limited (Kutzner et al., 2010; D’Lima

et al., 2011). Initial results from this study demonstrate the

potential applicability of using widely available kinematic data to

predict joint load ratios. Kinematic data has been collected from

thousands of TKR patients. If this kinematic data could be

converted into joint load information, loading proles for experi-

mental and computational simulators may be greatly enhanced to

evaluate device performance under mean loading conditions, but

perhaps more importantly, under outlying loading conditions

Fig. 4. Comparison of I–E, A–P and V –V joint loads ratios from telemetric loads and kinematic model predictions for one representative subject for each activity (deep knee

bend (DKB), chair-rise and step-up). Left: model simulations applied compressive force, I–E and A–P motions. Right: model simulations included the addition of V –V motions

(applied compressive force, I–E, A–P and V –V motions).



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Fig. 5. Comparison of joint loads and joint load ratios predicted by the kinematic model for a variety of compressive force proles: the original telemetric prole, and

constant 1000 N, 2000 N, and 3000 N proles for each activity (deep knee bend (DKB), chair-rise and step-up). Shown for one representative subject for each activity. Each

representative subject was chosen as the subject with RMS differences closest to the mean values for that activity.

Table 2

RMS differences in joint loads and joint load ratios between telemetric measurements (taken from Kutzner et al., 2010) and model (with I–E and A–P kinematics and

compressive load) predictions with error imposed on kinematics (7 0.51 and70.5 mm shift (top) and711 and71 mm shift (bottom) in A–P and I–E motions, respectively)for each activity. Showing mean and standard deviations of the worst kinematic condition for the ve subjects.

Activity IE torque (Nm) IE:C load ratio (Nm/N) (e-3) AP force (N) AP:C load ratio (N/N)

Deep knee bend: full 5.5272.15 4.8571.52 405.27219.9 0.38070.175

Deep knee bend:4251 1.8071.64 1.2071.14 77.3712.9 0.04970.015

Chair-rise: full 10.4072.00 8.8072.49 739.67353.0 0.61570.320

Chair-rise:4251 1.6172.05 1.3471.08 59.4723.1 0.04870.010

Step-up: full 14.0275.22 7.1473.66 513.27278.8 0.29570.164

Step-up:4251 1.6970.26 1.8870.37 85.4725.7 0.08070.028

Deep knee bend: full 6.0972.27 5.3171.42 442.07229.3 0.40970.170

Deep knee bend:4251 2.3171.57 1.4871.14 123.8721.7 0.07770.018

Chair-rise: full 10.2671.97 8.8772.95 786.47361.2 0.64470.315

Chair-rise:4251 1.9572.06 1.5371.10 89.4728.1 0.07070.013

Step-up: full 14.7875.14 7.3673.41 594.77252.2 0.34470.138

Step-up:4251 2.0870.31 2.0970.40 129.1732.7 0.11370.039



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occurring in patients that are likely most vulnerable to complica-

tions and failure. While compressive load may be dif cult to

measure in vivo, computational models can effectively determine

I–E:C and A–P:C load ratios, and absolute I–E torques and A–P

forces can easily and ef ciently be calculated over a design-of-

experiments (DOE) or probabilistic range of compressive force

Fig. 6. Comparison of joint load ratios (I–E:C and A–P:C) from telemetric loads and kinematic model predictions with 70.51 and 70.5 mm (shaded dark) and711

and71 mm (shaded light) of kinematic error in I–E and A–P motions for one representative subject for each activity (deep knee bend (DKB), chair-rise and step-up). Top:

variation in joint load ratio predictions due to kinematic error for the entire activity; bottom: variation in joint load ratio predictions due to kinematic error only shown for TF

exion greater than 251.

Fig. 7. Change in contact location between femoral and tibial components with a 0.51 shift in I–E kinematics. Due to congruency between the components, small changes in

kinematics resulted in a large shift in contact location in early exion (top), while kinematics differences in later exion, when components were less conforming, resulted in

only small changes in contact location (bottom). Sagittal images show a cut-through the mid-point of the lateral condyle.



9/9

proles. The prevalence of kinematic data, in conjunction with the

methods applied in this study, facilitates determining the scope of

A–P a n d I–E loading ratios experienced by the TKR patient

population.

Conict of interest statement

One of the authors (PJR) is a consultant to DePuy Synthes, Inc.

Acknowledgment

This work was supported in part by DePuy Synthes, a Johnson &

Johnson Company.

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