Joint Surface Modeling With Thin-Plate Splines

[+] Author and Article Information
S. K. Boyd, J. L. Ronsky

Department of Mechanical Engineering, University of Calgary, 2500 University Drive, N.W., Calgary, T2P 1N4 Canada

D. D. Lichti

School of Spatial Sciences, Curtin University of Technology, GPO Box U1987, Perth, WA 6845 Australia

D. Šalkauskas

Department of Mathematics and Statistics, University of Calgary, 2500 University Drive, N.W., Calgary, T2P 1N4 Canada

M. A. Chapman

Department of Geomatics, University of Calgary, 2500 University Drive, N.W., Calgary, T2P 1N4 Canada

J Biomech Eng 121(5), 525-532 (Oct 01, 1999) (8 pages) doi:10.1115/1.2835083 History: Received May 28, 1998; Revised May 18, 1999; Online January 23, 2008


Mathematical joint surface models based on experimentally determined data points can be used to investigate joint characteristics such as curvature, congruency, cartilage thickness, joint contact areas, as well as to provide geometric information well suited for finite element analysis. Commonly, surface modeling methods are based on B-splines, which involve tensor products. These methods have had success; however, they are limited due to the complex organizational aspect of working with surface patches, and modeling unordered, scattered experimental data points. An alternative method for mathematical joint surface modeling is presented based on the thin-plate spline (TPS). It has the advantage that it does not involve surface patches, and can model scattered data points without experimental data preparation. An analytical surface was developed and modeled with the TPS to quantify its interpolating and smoothing characteristics. Some limitations of the TPS include discontinuity of curvature at exactly the experimental surface data points, and numerical problems dealing with data sets in excess of 2000 points. However, suggestions for overcoming these limitations are presented. Testing the TPS with real experimental data, the patellofemoral joint of a cat was measured with multistation digital photogrammetry and modeled using the TPS to determine cartilage thicknesses and surface curvature. The cartilage thickness distribution ranged between 100 to 550 μm on the patella, and 100 to 300 μm on the femur. It was found that the TPS was an effective tool for modeling joint surfaces because no preparation of the experimental data points was necessary, and the resulting unique function representing the entire surface does not involve surface patches. A detailed algorithm is presented for implementation of the TPS.

Copyright © 1999 by The American Society of Mechanical Engineers
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