Design and Analysis of Robust Total Joint Replacements: Finite Element Model Experiments With Environmental Variables

[+] Author and Article Information
Paul B. Chang, Kanwaljeet Singh Bawa Bhalla, Thomas W. Belknap, Donald L. Bartel

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853

Brian J. Williams, Thomas J. Santner, William I. Notz

Department of Statistics, The Ohio State University, Columbus, OH 43210

J Biomech Eng 123(3), 239-246 (Jan 11, 2001) (8 pages) doi:10.1115/1.1372701 History: Received January 23, 2000; Revised January 11, 2001
Copyright © 2001 by ASME
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Reduced midstem implant design. The implant design comprised a cementless cobalt chrome Ranawat–Burstein implant proximal geometry (Biomet, Inc., Warsaw IN) with a retrofitted 16 mm diameter, 100 mm long distal stem. Two example (b,d) configurations are shown. Nine distal stems were constructed for use in the physical experiment corresponding to all combinations of b={25,50,75} mm and d={7,10,13} mm. Finite element models of this geometry were constructed in which (b,d) could assume a continuous set of values.
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Composite material analogs of an adult male femur (“Sawbones,” Pacific Research Laboratories, Vashon, WA). The Sawbones, used in place of cadaver bones, consisted of an epoxy shell filled with polyurethane foam with one of three elastic moduli (E=60, 200, or 400 MPa). Also shown to the left is the definition of joint angle, Θ, meauserd from a neutral joint angle determined from a telemetric hip force study 8. To the right, an idealized distribution, g, was assumed for the combinations of (E,Θ). Five alternate distributions are also displayed.
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Three-dimensional nonlinear finite element models. The implant was modeled as linearly elastic and isotropic with the properties of cobalt chrone (ECoCr=220,000 MPa). Bone properties were also assumed to be linearly elastic and isotropic but with an inhomogeneous distribution. Material properties for bone were determined using CT scans of the Sawbones femurs. The bone–implant interfaces were modeled with zero-tension Coulomb-friction interface elements enabling an estimate of relative motion.
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Experimental test specimen and fixture schematic. Three strain gage rosettes were placed on both the medial and lateral sides of the bones. Load was applied with an MTS-858 Mini Bionix servohydraulic tester. The abductor force was simulated by a cable attached to a rod inserted through the greater trochanter. The adjustable fixture coupled the head load and abductor load in such a way that the relative loading magnitudes in the computer models and the physical experiment were the same.
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The predicted objective function is presented for each stage of the optimal search. The (b,d) projections corresponding to the training sites are shown for the first-stage (8 circles), second-stage (8 circles plus 8 squares), and third-stage predictors (16 circles and squares plus 6 diamonds). Eight sites were insufficient to predict the effects of the design fabricators. The 16-point second-stage and third-stage predictors indicated an optimal design in the lower left quadrant of the design space corresponding to a minimal bullet tip length and midstem diameter. The predicted optimal (b,d) combination is denoted by a star.
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The standard error of the objective function prediction is presented for each stage of the optimal search. The (b,d) projections corresponding to the training sites are shown for the first stage (8 circles), 16 point second-stage (8 circles plus 8 squares), and third-stage predictors (16 circles and squares plus 6 diamonds). Eight sites were insufficient to predict the effects of the design factors. The prediction error for the objective function diminished with increasing training sites. The third-stage predictor was specifically accurate in the region of objective function minima denoted by a star.
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The predicted tangential relative motion is presented for the third-stage training data
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Percent combination of factors. The main effects of design and environmental factors on the bone remodeling signal response function (Y) and tangential relative motion (Dt) are shown. Interaction effects were generally small. The percent contribution estimates are based on the third-stage (22-site) Latin hypercube sample.
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Comparison of finite element predictions (averaged over values of bullet tip length, b) of the objective function with physical experiments. The predicted bone remodeling signal was re-computed from the finite element model results by considering strain energy density sites in the regions corresponding to strain gage placement in the physical experiments. Both results predict a minimum midstem diameter, d=7 mm. The effects of bullet tip length, b, were not presented because its contribution to the variation in the bone remodeling signal was approximately 1 percent.



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