A Bayesian approach to biomechanical modeling to optimize over large parameter spaces while considering anatomical variability

Abstract

We present the Markov chain Monte Carlo (MCMC) approach in the context of a musculoskeletal model of the thumb. With special consideration for the complexities of biomechanical modeling, we present this approach as an alternative to standard parameter estimation techniques that produce a single, in some way optimal, set of parameter values. In contrast, MCMC methods are derived from a Bayesian philosophy, in which each "true" model parameter is actually a random variable with its own probability distribution. With MCMC we can (1) address challenges of model parameter estimation that are difficult for gradient-based methods to meet, (2) estimate the inherent biomechanical capabilities of a specific "model topology" for large, variable parameter spaces (e.g. 50-dimensional for the assumed thumb model), and (3) determine the functional consequences of the unavoidable anatomical variability across subjects in a population. Using the MCMC approach with a Metropolis-Hastings sampling algorithm we explored a 50-D musculoskeletal parameter space and successfully achieved convergence. We found the relatively small subspace of the expansive 50-D space that, for a hinged serial linkage model of the thumb, predicts functional outcomes that best-fit the experimental data.