Musculoskeletal dynamics simulation using shape-varying muscle mass models

Abstract

Recent studies have shown that the constant inertia assumption made in typical muscle dynamic models can lead to significant discrepancies in accuracy of simulation or inverse dynamics. This paper proposes a general framework for musculoskeletal dynamic simulation that takes into account changes in muscle inertia that occur during movement. We first develop a general shape-varying muscle mass model in which muscle deformations are modeled via linear volume-preserving transformations, and derive a corresponding muscle mass matrix and Jacobian in a Lagrangian setting. A dynamic musculoskeletal model is then constructed, in which each muscle is segmented into multiple segments that are each modeled using our earlier muscle deformation model. Depending on the extent of muscle segmentation, the musculoskeletal dynamics can be simulated to arbitrary resolution. To improve the computational efficiency of the simulation, we propose a spline-based dynamics algorithm consisting of an offline and online computation stage. In the offline stage, a parametrized B-spline surface on the space $\mathcal{P}(n)$ of n×n symmetric positive-definite matrices is constructed so as to fit a set of sampled values of the system mass matrix. In the online computation stage, given an arbitrary configuration, the mass matrix for that configuration is obtained as a weighted average of the nearest sampled values (i.e., the control points of the B-spline surface). The Coriolis forces are evaluated directly from the partial derivatives of the B-spline approximation of the mass matrix. Our method ensures that the online computational costs effectively remain fixed independently of the system dimension or complexity. Detailed case studies involving planar arms with multiple shape-varying muscles attached demonstrate the feasibility and computational advantages of our proposed method for musculoskeletal modeling and simulation.