Parameterizing history-dependent dynamics of skeletal muscle with a new nonlinear stiffness and damping formulation

Abstract

This paper introduces a novel mathematical modeling framework for skeletal muscle (SM), capturing its history-dependent characteristics during submaximal contractions and exploring the influence of muscle mechanical parameters and related diseases. The proposed model utilizes a history-dependent nonlinear second-order system, encompassing various contractions: isometric, isotonic, and cyclic. Unlike previous approaches, it incorporates nonlinear stiffness-damping formulation (NSDF) to accurately represent SM's passive properties, independent of neural excitation. Allowing SM mass deflection for realistic bilateral movement, the model incorporates force-length and force-velocity relationships, yielding accurate SM dynamics predictions with less than 10% normalized force error deviation compared to neural excitation-based model. In addition, it exposes the time-varying natural frequency (TV-NF) of SM using the NSDF and damper coefficients, contributing to our understanding of SM diseases. The model shows a 28.07% rise in initial passive stiffness (IPS) and a 13.18% increase in TV-NF during passive stretching for both healthy and Osgood-Schlatter disease scenarios. During cyclic contraction, IPS increases by 9.19%, TV-NF by 4.49%, and collaborative stiffness by 7.52%. Despite slight disparities in force and muscle length, the healthy muscle generates more power due to the diseased muscle's higher stiffness limiting length change. This research enhances biomechanical understanding in developing robotics and prostheses by considering SM's history-dependent dynamics.