Coupled simulations and parameter inversion for neural system and electrophysiological muscle models

Abstract

The functioning of the neuromuscular system is an important factor for quality of life. With the aim of restoring neuromuscular function after limb amputation, novel clinical techniques such as the agonist-antagonist myoneural interface (AMI) are being developed. In this technique, the residual muscles of an agonist-antagonist pair are (re-)connected via a tendon in order to restore their mechanical and neural interaction. Due to the complexity of the system, the AMI can substantially profit from in silico analysis, in particular to determine the prestretch of the residual muscles that is applied during the procedure and determines the range of motion of the residual muscle pair. We present our computational approach to facilitate this. We extend a detailed multi-X model for single muscles to the AMI setup, that is, a two-muscle-one-tendon system. The model considers subcellular processes as well as 3D muscle and tendon mechanics and is prepared for neural process simulation. It is solved on high performance computing systems. We present simulation results that show (i) the performance of our numerical coupling between muscles and tendon and (ii) a qualitatively correct dependence of the range of motion of muscles on their prestretch. Simultaneously, we pursue a Bayesian parameter inference approach to invert for parameters of interest. Our approach is independent of the underlying muscle model and represents a first step toward parameter optimization, for instance, finding the prestretch, to be applied during surgery, that maximizes the resulting range of motion. Since our multi-X fine-grained model is computationally expensive, we present inversion results for reduced Hill-type models. Our numerical results for cases with known ground truth show the convergence and robustness of our approach.