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Introduction

•Since the calculation of joint contact forces is often carried

out using expensive finite-element or elastic-foundation

models, concurrent simulation of body-level dynamics and

detailed joint mechanics is computationally demanding.

•Simulation time for a single activity of daily living may reach

several hours, as shown in a recent Total Knee Arthroplasty

(TKA) musculoskeletal (MS) model [1].

•To speed up the computation, surrogate modeling techniques

have been proposed to replace the original contact model

(OCM) with a faster surrogate model (SCM)[2,3].

•Overhead may also arise from the computation of muscle and

ligament lines of action over obstacles, which require the

solution of a contact problem. Simple wrapping conditions

can be solved both analytically and numerically.

Objective

We developed and tested a surrogate contact model of TKA and

we assessed its performance during gait simulation using both

numerical and analytical wrapping algorithm.

Materials and Methods

•Sampling. 135.000 sample points were randomly generated

using a multi-domain approach [3]. The OCM (Fig. 1) was

created in the AnyBody Modeling System (AnyBody

Technology A/S, Aalborg, Denmark) and used to calculate the

TF loads resulting from the TF pose for each sample.

Additionally, 20.000 samples were evaluated for testing.

•Training. Feed-forward artificial neural networks (FFANN)

were trained until convergence to learn the implicit relations

between TF loads and pose (Fig. 2) [2,3].

•Gait simulation. A gait trial from a publicly available dataset

[4] was simulated using the OCM, the SCM, numerical and

analytical wrapping algorithm¹. Simulation times were noted.

M.A. Marra¹, M.S. Andersen², H.F.J.M. Koopman³, D. Janssen¹, N. Verdonschot¹,³

¹Orthopaedic Research Lab, Radboud University Medical Center, Nijmegen, The Netherlands, ²Department of Mechanical and

Manufacturing Engineering, Aalborg University, Aalborg East, Denmark, ³Department of Biomechanical Engineering, University of

Twente, Enschede, The Netherlands

Results

Surrogate model accuracy

a b

Gait simulation

Discussion and Conclusion

•Approximately 213 hours were necessary on an Intel® Core™

i5-4570 quad-core computer with 16 gigabytes of RAM for

the creation of the surrogate model. This time was paid up

front and could be reduced using parallel-computing.

•There were no substantial differences in predicted versus

experimental TF forces during a gait simulation using either

contact models and wrapping algorithms (Fig. 4).

•The SCM provided the largest acceleration in conjunction

with the analytical wrapping algorithm (Fig. 4). The latter is

preferable over the more general numerical algorithm when

computation time is a concern.

Conclusion

When used together with an analytical wrapping algorithm, our

surrogate contact model could reduce simulation time by 67%.

Figure 1. The original contact model used to

evaluate sample points by repeated static analyses.

The TF pose is defined by the relative position

between the femur (blue frame) and tibial (red

frame) component.

Figure 2. 2-stage FFANN used to learn the relations between TF pose (input) and

TF loads (output). In stage I (left half) MedFy, MedTx, LatFy, LatTx were fit as

functions of TF pose. In stage II (right half) the remaining TF loads were fit as

functions of the TF pose and the TF loads of stage I. HL: hidden layer, W: network

weight, b: network bias.

Figure 4. Left: proximo-distal component of tibiofemoral force predictions during

gait. Right: simulation times and the musculoskeletal model used.

Legend: eTibia: experimental TF force; NumWrp, numerical wrapping; AnlWrp,

anlytical wrapping; OCM, original contact model; SCM, surrogate contact model.

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Figure 3. Accuracy of the surrogate model on a testing dataset of ca. 20.000

sample points. (a) Regression plot of output versus target loads and (b) root-

mean-square errors of predicted medial and lateral forces and moments.

[1] Marra et al., “A Subject-Specific Musculoskeletal Modeling Framework to Predict in Vivo Mechanics of Total Knee

Arthroplasty”, J Biomech Eng. 2015 Feb 1;137(2):020904; [2] Eskinazi and Fregly, “Surrogate modeling of deformable joint

contact using artificial neural networks.”, Med Eng Phys. 2015 Sep;37(9):885-91; [3] Lin et al., “Surrogate articular contact

models for computationally efficient multibody dynamic simulations.”, Med Eng Phys. 2010 Jul;32(6):584-94; [4] Fregly et

al., “Grand challenge competition to predict in vivo knee loads.”, J Orthop Res. 2012 Apr;30(4):503-13

¹ The analytical wrapping algorithm was made available to us by AnyBody Technology A/S in a prototype version of the

AnyBody Modeling System for the solution of a cylindrical wrapping case.

Evaluation of a surrogate contact model of TKA.

Marco Marra, MSc

Marco.Marra@radboudumc.nl

Orthopaedic Research Laboratory, Radboud umc

P.O. Box 9101, 6500 HB Nijmegen, The Netherlands

The research leading to these results has received funding from the

European Research Council under the European Union's Seventh

Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 323091

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