•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 .
•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.
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 . 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
 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
Surrogate model accuracy
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.
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
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.
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.
 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;  Eskinazi and Fregly, “Surrogate modeling of deformable joint
contact using artificial neural networks.”, Med Eng Phys. 2015 Sep;37(9):885-91;  Lin et al., “Surrogate articular contact
models for computationally efficient multibody dynamic simulations.”, Med Eng Phys. 2010 Jul;32(6):584-94;  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
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
0 20 40 60 80 100
TF Force (N)
% Gait Cycle