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Research Papers

Computationally Efficient Finite Element Evaluation of Natural Patellofemoral Mechanics

[+] Author and Article Information
Clare K. Fitzpatrick, Mark A. Baldwin

Department of Mechanical and Materials Engineering, Computational Biomechanics Laboratory, University of Denver, Denver, CO 80208

Paul J. Rullkoetter1

Department of Mechanical and Materials Engineering, Computational Biomechanics Laboratory, University of Denver, Denver, CO 80208prullkoe@du.edu

1

Corresponding author.

J Biomech Eng 132(12), 121013 (Dec 08, 2010) (8 pages) doi:10.1115/1.4002854 History: Received February 12, 2010; Revised October 10, 2010; Posted October 25, 2010; Published December 08, 2010; Online December 08, 2010

Finite element methods have been applied to evaluate in vivo joint behavior, new devices, and surgical techniques but have typically been applied to a small or single subject cohort. Anatomic variability necessitates the use of many subject-specific models or probabilistic methods in order to adequately evaluate a device or procedure for a population. However, a fully deformable finite element model can be computationally expensive, prohibiting large multisubject or probabilistic analyses. The aim of this study was to develop a group of subject-specific models of the patellofemoral joint and evaluate trade-offs in analysis time and accuracy with fully deformable and rigid body articular cartilage representations. Finite element models of eight subjects were used to tune a pressure-overclosure relationship during a simulated deep flexion cycle. Patellofemoral kinematics and contact mechanics were evaluated and compared between a fully deformable and a rigid body analysis. Additional eight subjects were used to determine the validity of the rigid body pressure-overclosure relationship as a subject-independent parameter. There was good agreement in predicted kinematics and contact mechanics between deformable and rigid analyses for both the tuned and test groups. Root mean square differences in kinematics were less than 0.5 deg and 0.2 mm for both groups throughout flexion. Differences in contact area and peak and average contact pressures averaged 5.4%, 9.6%, and 3.8%, respectively, for the tuned group and 6.9%, 13.1%, and 6.4%, respectively, for the test group, with no significant differences between the two groups. There was a 95% reduction in computational time with the rigid body analysis as compared with the deformable analysis. The tuned pressure-overclosure relationship derived from the patellofemoral analysis was also applied to tibiofemoral (TF) articular cartilage in a group of eight subjects. Differences in contact area and peak and average contact pressures averaged 8.3%, 11.2%, and 5.7% between rigid and deformable analyses in the tibiofemoral joint. As statistical, probabilistic, and optimization techniques can require hundreds to thousands of analyses, a viable platform is crucial to component evaluation or clinical applications. The computationally efficient rigid body platform described in this study may be integrated with statistical and probabilistic methods and has potential clinical application in understanding in vivo joint mechanics on a subject-specific or population basis.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Hexahedral mesh of patient-specific articular cartilage incorporated into the FE model (left) and isolated FE model of the patellofemoral joint including vasti, rectus femoris, patellar tendon, and medial and lateral patellofemoral ligaments (right)

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Figure 2

The effect of changing the slope of the pressure-overclosure relationship on the difference in peak contact pressure and contact area between rigid and deformable models

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Figure 3

Comparison of patellar kinematics (patellar flexion, A-A rotation, I-E rotation, and M-L translation) for deformable and rigid body analyses of the group mean (and one standard deviation) plus a representative subject. Results are shown separately for the subject group used to tune the rigid body relationship and the additional test group. Representative subjects were chosen as outliers to the group mean to show the broad range of the rigid body representation.

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Figure 4

Mean (and one standard deviation) for PF contact area and peak and average contact pressure for deformable and rigid body analyses. Results are shown separately for the subject group used to tune the rigid body relationship and the additional test group. Inset: PF contact patch for a representative subject (contact area and peak and average contact pressure similar to the mean values) shown at a 90 deg flexion.

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Figure 5

PF contact mechanics comparisons for a representative subject. Results are shown for a subject used to tune the rigid body relationship and a test subject. Representative subjects were selected with deformable-rigid differences similar to the mean values of each group. Inset figures (top: rigid, bottom: deformable) demonstrate excellent qualitative agreement between representations.

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Figure 6

Comparison of PF contact area and peak and average contact pressures between deformable and rigid analyses with varying loading. Patellar contact patches for each loading condition are at shown at a 90 deg flexion (top right), demonstrating excellent qualitative agreement between representations.

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Figure 7

Comparison of TF contact area and peak and average contact pressure between deformable and rigid analyses. Results are shown for three representative subjects (demonstrating a range of contact area and pressure values). Inset: deformable and rigid contact patch for a single subject at a 90 deg flexion.

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Figure 8

Comparison of PF contact area and peak and average contact pressures predictions with experimental measurements (and standard deviations) reported in the literature. Inset: representative PF contact patches at 0 deg, 30 deg, 60 deg, 90 deg, and 120 deg for a subject with contact mechanics predictions similar to the mean values.

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