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Research Papers

Dual-Joint Modeling for Estimation of Total Knee Replacement Contact Forces During Locomotion

[+] Author and Article Information
Michael W. Hast

Department of Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802

Stephen J. Piazza

Department of Kinesiology,
Department of Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802;
Department of Orthopaedics and Rehabilitation,
The Pennsylvania State University,
Hershey, PA 17033
e-mail: piazza@psu.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received September 26, 2012; final manuscript received December 31, 2012; accepted manuscript posted January 9, 2013; published online February 7, 2013. Editor: Beth Winkelstein.

J Biomech Eng 135(2), 021013 (Feb 07, 2013) (9 pages) Paper No: BIO-12-1441; doi: 10.1115/1.4023320 History: Received September 26, 2012; Revised December 31, 2012; Accepted January 09, 2013

Model-based estimation of in vivo contact forces arising between components of a total knee replacement is challenging because such forces depend upon accurate modeling of muscles, tendons, ligaments, contact, and multibody dynamics. Here we describe an approach to solving this problem with results that are tested by comparison to knee loads measured in vivo for a single subject and made available through the Grand Challenge Competition to Predict in vivo Tibiofemoral Loads. The approach makes use of a “dual-joint” paradigm in which the knee joint is alternately represented by (1) a ball-joint knee for inverse dynamic computation of required muscle controls and (2) a 12 degree-of-freedom (DOF) knee with elastic foundation contact at the tibiofemoral and patellofemoral articulations for forward dynamic integration. Measured external forces and kinematics were applied as a feedback controller and static optimization attempted to track measured knee flexion angles and electromyographic (EMG) activity. The resulting simulations showed excellent tracking of knee flexion (average RMS error of 2.53 deg) and EMG (muscle activations within ±10% envelopes of normalized measured EMG signals). Simulated tibiofemoral contact forces agreed qualitatively with measured contact forces, but their RMS errors were approximately 25% of the peak measured values. These results demonstrate the potential of a dual-joint modeling approach to predict joint contact forces from kinesiological data measured in the motion laboratory. It is anticipated that errors in the estimation of contact force will be reduced as more accurate subject-specific models of muscles and other soft tissues are developed.

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Figures

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Fig. 1

Illustration of stages in the dual-joint modeling procedure. Ground reaction forces and marker locations are measured in the motion laboratory (left). Following scaling and inverse kinematics, joint angles from the leg of interest ground reaction forces are determined as functions of time (center). These forces and motions (with the exception of the knee motions) are used an inputs to a simulation based on a five-segment, 13-muscle model (right). In this simulation, measured knee flexion angle and measured muscle activity are tracked in order to predict contact forces.

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Fig. 2

Schematic diagram for the inverse dynamics phase in which inverse dynamics are performed on a ball-jointed model of the knee to determine the torque required for tracking knee flexion angle. Static optimization is used to determine excitations for muscles crossing knee that minimize deviation from this torque and from the measured muscle activity. This phase occurs in between forward integration intervals while simulation time is stopped.

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Fig. 3

Schematic diagram for the forward dynamics phase in which equations of motion for a model with a 12-DOF knee are integrated forward in time while tibiofemoral and patellofemoral contact forces are calculated using a rigid body spring model. During each 5 ms forward integration interval, muscle excitations found during the previous inverse dynamics calculation are held constant.

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Fig. 4

Knee flexion angle plotted against percent gait cycle for three trials measured during normal walking gait (dashed lines) and for the corresponding simulations (solid lines)

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Fig. 5

Muscle activations (solid lines) for the 13 muscles included in the model plotted against percent gait cycle for one of the three simulated gait trials. The shaded curves represent the envelopes created by adding ±10% to measured EMG data.

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Fig. 6

Tibiofemoral contact forces plotted against percent gait cycle. Red dashed lines represent simulation results averaged across the three trials, with shading representing plus and minus one standard deviation. Blue curves and shading represent force measurements from the instrumented implant. Results for individual trials are given by thin lines. The subfigures show: (a) the resultant tibiofemoral contact forces; (b) the superior/inferior force component; (c) the anterior/posterior component; and (d) the medial/lateral component.

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Fig. 9

Tibiofemoral contact forces for trunk-swaying gait plotted against percent gait cycle. Red dashed lines represent simulation results averaged across the three trials, with shading representing plus and minus one standard deviation. Blue curves and shading represent force measurements from the instrumented implant. Results for individual trials are given by thin lines. The subfigures show: (a) the magnitude of the resultant tibiofemoral contact force for the medial compartment; (b) the magnitude of the resultant tibiofemoral contact force for the lateral compartment; and (c) the magnitude of the vector sum of the loads for both compartments.

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Fig. 7

Simulated resultant patellofeomoral forces plotted versus percent gait cycle. The dashed lines represents simulation results averaged across the three trials, with shading representing plus and minus one standard deviation. Results for individual trials are given by thin lines.

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Fig. 8

Medial (a) and lateral (b) compartment tibiofemoral contact forces plotted against percent gait cycle. Red dashed lines represent simulation results averaged across the three trials, with shading representing plus and minus one standard deviation. Blue curves and shading represent force measurements from the instrumented implant. Results for individual trials are given by thin lines.

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Fig. 10

Tibiofemoral contact forces (magnitude of the resultant force) plotted against percent gait cycle as maximum isometric force for each muscle was systematically scaled from 100% of the generic value to 75%, 60%, and finally 50%

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