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Technical Forum

A Subject-Specific Musculoskeletal Modeling Framework to Predict In Vivo Mechanics of Total Knee Arthroplasty

[+] Author and Article Information
Marco A. Marra

Orthopaedic Research Laboratory,
Radboud Institute for Health Sciences,
Radboud University Medical Center,
P.O. Box 9101,
HB Nijmegen 6500,
The Netherlands
e-mail: Marco.Marra@radboudumc.nl

Valentine Vanheule

N. V. Materialise,
Technologielaan 15,
Leuven 3001, Belgium
e-mail: Valentine.Vanheule@kuleuven.be

René Fluit

Faculty of Engineering Technology,
Laboratory of Biomechanical Engineering,
University of Twente,
P.B. 217, Gebouw Horstring,
Enschede 7500 AE, The Netherlands
e-mail: R.Fluit@utwente.nl

Bart H. F. J. M. Koopman

Faculty of Engineering Technology,
Laboratory of Biomechanical Engineering,
University of Twente,
P.B. 217, Gebouw Horstring,
Enschede 7500 AE, The Netherlands
e-mail: H.F.J.M.Koopman@ctw.utwente.nl

John Rasmussen

Department of Mechanical
and Manufacturing Engineering,
Aalborg University,
Fibigerstrade 16,
Aalborg East DK-9220, Denmark
e-mail: jr@m-tech.aau.dk

Nico Verdonschot

Orthopaedic Research Laboratory,
Radboud Institute for Health Sciences,
Radboud University Medical Center,
P.O. Box 9101,
HB Nijmegen 6500, The Netherlands
e-mail: Nico.Verdonschot@radboudumc.nl

Michael S. Andersen

Department of Mechanical
and Manufacturing Engineering,
Aalborg University,
Fibigerstraede 16,
Aalborg East DK-9220, Denmark
e-mail: msa@m-tech.aau.dk

1Corresponding author.

Manuscript received October 2, 2014; final manuscript received November 25, 2014; published online January 26, 2015. Editor: Beth A. Winkelstein.

J Biomech Eng 137(2), 020904 (Feb 01, 2015) (12 pages) Paper No: BIO-14-1490; doi: 10.1115/1.4029258 History: Received October 02, 2014; Revised November 25, 2014; Online January 26, 2015

Musculoskeletal (MS) models should be able to integrate patient-specific MS architecture and undergo thorough validation prior to their introduction into clinical practice. We present a methodology to develop subject-specific models able to simultaneously predict muscle, ligament, and knee joint contact forces along with secondary knee kinematics. The MS architecture of a generic cadaver-based model was scaled using an advanced morphing technique to the subject-specific morphology of a patient implanted with an instrumented total knee arthroplasty (TKA) available in the fifth “grand challenge competition to predict in vivo knee loads” dataset. We implemented two separate knee models, one employing traditional hinge constraints, which was solved using an inverse dynamics technique, and another one using an 11-degree-of-freedom (DOF) representation of the tibiofemoral (TF) and patellofemoral (PF) joints, which was solved using a combined inverse dynamic and quasi-static analysis, called force-dependent kinematics (FDK). TF joint forces for one gait and one right-turn trial and secondary knee kinematics for one unloaded leg-swing trial were predicted and evaluated using experimental data available in the grand challenge dataset. Total compressive TF contact forces were predicted by both hinge and FDK knee models with a root-mean-square error (RMSE) and a coefficient of determination (R2) smaller than 0.3 body weight (BW) and equal to 0.9 in the gait trial simulation and smaller than 0.4 BW and larger than 0.8 in the right-turn trial simulation, respectively. Total, medial, and lateral TF joint contact force predictions were highly similar, regardless of the type of knee model used. Medial (respectively lateral) TF forces were over- (respectively, under-) predicted with a magnitude error of M < 0.2 (respectively > −0.4) in the gait trial, and under- (respectively, over-) predicted with a magnitude error of M > −0.4 (respectively < 0.3) in the right-turn trial. Secondary knee kinematics from the unloaded leg-swing trial were overall better approximated using the FDK model (average Sprague and Geers' combined error C = 0.06) than when using a hinged knee model (C = 0.34). The proposed modeling approach allows detailed subject-specific scaling and personalization and does not contain any nonphysiological parameters. This modeling framework has potential applications in aiding the clinical decision-making in orthopedics procedures and as a tool for virtual implant design.

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Figures

Grahic Jump Location
Fig. 1

Steps for obtaining a subject-specific MS model. (a) Pre-operative bone segmentation from CT images. Partial bones were merged with postoperative bone geometries to generate complete 3D pre-operative bone models, (b) morphing of the generic tlem 2.0 bone meshes to the patient-specific pre-operative bones (note the variation in muscle insertion sites), (c) registration of postoperative bone geometries to the morphed pre-operative bones, (d) analytical joint fitting of postoperative bone geometries to obtain patient-specific hip joint center, TF, PF, ankle, and subtalar joint axes.

Grahic Jump Location
Fig. 2

Simplified schematic of the modeling workflow. Marker trajectories are input to an inverse kinematics-based analysis that computes joint angles. Inverse dynamics like models are developed, in which GRFs are input together with joint angles. Two types of knee models are simulated: A hinged model and an FDK model. The hinged model employed idealized constraints, whereas the FDK model finds a quasi-static kinematic configuration, α(FDK), in the FDK DOFs under the influence of the forces, F(FDK), acting in the respective DOFs. Predictions are independently produced by each model. The FDK model provides, in addition to muscle forces and joint reactions, also ligament and contact forces, and secondary knee kinematics.

Grahic Jump Location
Fig. 3

The 11-DOF knee model used in the FDK simulations. Knee flexion is driven using joint angle from an inverse kinematic-based analysis. The remaining 10DOFs are handled by the FDK solver. Ligaments are modeled as one-dimensional string elements wrapping around geometrical shapes (abbreviations as described in the text). Medial and lateral contacts were modeled using rigid–rigid contact formulation. Patellar ligament (PL) consists of a rigid linkage between patella and tibia.

Grahic Jump Location
Fig. 4

Reference frames used to express the knee planar knee kinematics during the leg-swing trial in the fluoroscopy images (left) and in the MS model (right). The PF flexion is defined as the rotation of the femoral frame (Of) relative to the patellar frame (Op); PT flexion is the rotation of the tibial frame (Ot) relative to the patellar frame; TF tip and PT shift are given by the two coordinates of displacement (posterior–anterior and distal–proximal) of femoral frame and patellar frame, respectively, relative to the tibial frame. Muscles are hidden in the model view and the hinged model version is shown.

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Fig. 5

Total, lateral and medial compressive TF contact forces predicted during one gait trial (left column) and one right-turn trial (right column) using an idealized knee joint model and the FDK knee model. Experimental measurements are reported for the same trial. Overall good agreement between measured and predicted total forces is noted. Lateral (respectively medial) forces are slightly underpredicted (respectively overpredicted) in the gait trial. Lateral (respectively medial) forces are slightly overpredicted (respectively underpredicted) in the right-turn trial.

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Fig. 6

Ligament forces predicted during gait (left) and right-turn (right) trials using the FDK model. Each force shown in the graphs was computed as the root of the summed squares of each ligament individual bundle force. The PCL is being activated after toe-off in both trials, and MPFL, MCL, and LEPL exert considerable amount of force throughout the trials.

Grahic Jump Location
Fig. 7

Experimental versus predicted PF flexion (top left) and PT flexion (bottom left), plotted relative to knee flexion angle; TF tip shift (top right) and PT shift (bottom right). The FDK model predictions are generally more accurate than hinged model predictions. Note the inability of the hinged model to predict PT shifts, due to the absence of femoral roll-back.

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