Surrogate-based worst-case analysis of a knee joint model using Genetic Algorithm

Abstract

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Verification, validation, and uncertainty quantification is generally recognized as a standard for assessing the credibility of mechanical models. This is especially evident in biomechanics, with intricate models, such as knee joint models, and highly subjective acquisition of parameters. Propagation of uncertainty is numerically expensive but required to evaluate the model reliability. An alternative to this is to analyze the worst-case models obtained within the specific bounds set on the parameters. The main idea of the paper is to search for two models with the greatest different response in terms of displacement-load curve. Real-Coded Genetic Algorithm is employed to effectively explore the high-dimensional space of uncertain parameters of a 2D dynamic knee model, while Radial Basis Function surrogates reduce the computation by orders of magnitude to near real-time, with negligible impact on the quality. It is expected that the studied knee joint model is very sensitive to uncertainty in the geometrical parameters. The obtained worst-case knee models showcase unrealistic behavior with one of them unable to fully extend, and the other largely overextending. Their relative difference in extension is up to 35% under ±1 mm bound set on the geometry. This unrealistic behavior of knee joint model is confirmed by the large standard deviation obtained from a classical sampling-based sensitivity analysis. The results confirm the viability of the method in assessing the reliability of biomechanical models. The proposed approach is general and could be applied to other mechanical systems as well.

Keywords

• sensitivity analysis
• uncertainty quantification
• biomechanics
• tibio-femoral joint
• multibody model
• model reliability