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Research Papers

Two-Dimensional Surrogate Contact Modeling for Computationally Efficient Dynamic Simulation of Total Knee Replacements

[+] Author and Article Information
Yi-Chung Lin, Raphael T. Haftka

Department of Mechanical and Aerospace Engineering, University of Florida, 231 MAE-A Building, P.O. Box 116250, Gainesville, FL 32611-6250

Nestor V. Queipo

Applied Computing Institute, University of Zulia, Maracaibo, Zulia 4005, Venezuela

Benjamin J. Fregly1

Department of Mechanical and Aerospace Engineering, Department of Biomedical Engineering, and Department of Orthopaedics and Rehabilitation, University of Florida, 231 MAE-A Building, P.O. Box 116250, Gainesville, FL 32611-6250fregly@ufl.edu

1

Corresponding author.

J Biomech Eng 131(4), 041010 (Feb 04, 2009) (8 pages) doi:10.1115/1.3005152 History: Received November 19, 2007; Revised August 22, 2008; Published February 04, 2009

Abstract

Computational speed is a major limiting factor for performing design sensitivity and optimization studies of total knee replacements. Much of this limitation arises from extensive geometry calculations required by contact analyses. This study presents a novel surrogate contact modeling approach to address this limitation. The approach involves fitting contact forces from a computationally expensive contact model (e.g., a finite element model) as a function of the relative pose between the contacting bodies. Because contact forces are much more sensitive to displacements in some directions than others, standard surrogate sampling and modeling techniques do not work well, necessitating the development of special techniques for contact problems. We present a computational evaluation and practical application of the approach using dynamic wear simulation of a total knee replacement constrained to planar motion in a Stanmore machine. The sample points needed for surrogate model fitting were generated by an elastic foundation (EF) contact model. For the computational evaluation, we performed nine different dynamic wear simulations with both the surrogate contact model and the EF contact model. In all cases, the surrogate contact model accurately reproduced the contact force, motion, and wear volume results from the EF model, with computation time being reduced from $13minto13s$. For the practical application, we performed a series of Monte Carlo analyses to determine the sensitivity of predicted wear volume to Stanmore machine setup issues. Wear volume was highly sensitive to small variations in motion and load inputs, especially femoral flexion angle, but not to small variations in component placements. Computational speed was reduced from an estimated $230hto4h$ per analysis. Surrogate contact modeling can significantly improve the computational speed of dynamic contact and wear simulations of total knee replacements and is appropriate for use in design sensitivity and optimization studies.

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Figures

Figure 1

Overview of surrogate contact model creation and implementation process. (a) 300 points (black dots) are sampled in the (X,θ) design space. (b) Five static analyses using five axial loads are performed at each sample point location using an elastic foundation contact model to calculate Y and Fx. (c) Generalized Hertzian contact theory is used to model Fy as a function of Y while Fx is modeled as proportional to Fy. (d) The values of Y10N, ky, ny, and ratio from the 300 sample points are fitted as functions of X and θ using Kriging. (e) During a dynamic simulation, the surrogate contact model calculates Fy and Fx from four Kriging models given the current values of X, Y, and θ.

Figure 2

Overview of global and local sensitivity analyses of predicted wear volume performed with the surrogate contact model. (a) Large variations in nominal component placements (labeled A–I) used for the global sensitivity analysis. (b) Small variations in component placements, input loads, and input motion used for local sensitivity analysis involving Monte Carlo methods applied to each nominal component placement.

Figure 3

Root-mean-square errors in joint motions and contact forces for each nominal component placement. Errors are computed by comparing dynamic simulation results generated with the elastic foundation contact model and the surrogate contact model.

Figure 4

Predicted wear volume as a function of large variations in component placements as calculated from 400 dynamic simulations performed with the surrogate contact model. Wear increases linearly when the femoral flexion axis is translated superiorly and quadratically when the tibial slope is increased anteriorly or posteriorly.

Figure 5

Box plot distribution of predicted wear volume generated by four Monte Carlo analyses using the surrogate contact model. Each box has (from bottom to top) one whisker at the 10th percentile, three lines at the 25th, 50th, and 75th percentile, and another whisker at the 90th percentile. Outliers are indicated by black crosses located beyond the ends of the whiskers. For the first and second Monte Carlo analyses, motion and load inputs and component placements are varied together within (a) 100% or (b) 10% of their maximum ranges, respectively. For the third and fourth Monte Carlo analyses, (c) motion and load inputs or (d) component placements are varied separately within 100% of their maximum ranges, respectively.

Figure 6

Predicted wear volume as a function of variations in (a) anterior-posterior load and femoral flexion angle and (b) axial load and femoral flexion angle. Both plots were created by performing dynamic simulations with the surrogate model and changing the weight of the first principal component for each input profile variation away from the ISO standard. Each weight was normalized to be between 0 and 1. The cross marker (×) represents the ISO standard input with no superimposed input profile variations (i.e., weights of 0) while the circle marker () represents the ISO standard input with maximum superimposed input profile variations (i.e., weights of 1).

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