Improving the fitness of high-dimensional biomechanical models via data-driven stochastic exploration.
The field of complex biomechanical modeling has begun to rely on Monte Carlo techniques to investigate the effects of parameter variability and measurement uncertainty on model outputs, search for optimal parameter combinations, and define model limitations. However, advanced stochastic methods to perform data-driven explorations, such as Markov chain Monte Carlo (MCMC), become necessary as the number of model parameters increases. Here, we demonstrate the feasibility and, what to our knowledge is, the first use of an MCMC approach to improve the fitness of realistically large biomechanical models. We used a Metropolis-Hastings algorithm to search increasingly complex parameter landscapes (3, 8, 24, and 36 dimensions) to uncover underlying distributions of anatomical parameters of a "truth model" of the human thumb on the basis of simulated kinematic data (thumbnail location, orientation, and linear and angular velocities) polluted by zero-mean, uncorrelated multivariate Gaussian "measurement noise." Driven by these data, ten Markov chains searched each model parameter space for the subspace that best fit the data (posterior distribution). As expected, the convergence time increased, more local minima were found, and marginal distributions broadened as the parameter space complexity increased. In the 36-D scenario, some chains found local minima but the majority of chains converged to the true posterior distribution (confirmed using a cross-validation dataset), thus demonstrating the feasibility and utility of these methods for realistically large biomechanical problems.
Santos
Veronica J
VJ
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA. veronica.santos@asu.edu
Bustamante
Carlos D
CD
Valero-Cuevas
Francisco J
FJ
D000465:Algorithms; D001499:Bayes Theorem; D001696:Biomechanical Phenomena; D003198:Computer Simulation; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D016011:Normal Distribution; D015203:Reproducibility of Results; D013933:Thumb / Q000502:physiology