UC San Diego

This work focuses on electro-chemical-mechanical multi-scale simulation of the excitation-contraction of skeletal muscle, including electro-chemical excitation process in the neural system which activates the contraction of muscle fibers, the combined effects of active fiber contraction and passive extracellular matrix (ECM) mechanical deformation, and their resulting force generation in the muscle components. In the neural systems, the Fitzhugh-Nagumo (FHN) equation is solved to simulate the propagation of neural signals (action potential) in neural trees and muscle fibers using multi-dimensional FHN discretizations. The calculated neural signal is consequently used as the input for the calcium dynamics model, which describes the chemical processes in the muscle fibers. Based on the calculated calcium concentration, the activation distribution in the muscle tissue is then obtained, which determines the active force muscle fiber can generate voluntarily. To study the mechanics associated with the composition of muscle fibers and ECM, the microstructure of skeletal muscle is reconstructed from images, from which the homogenized material property in the continuum level is calculated. By varying the microstructure model, their morphological effect on the muscle performance is studied and compared with experimental observation.

Computationally, the physiological models in excitation dynamics are solved by finite difference methods, and their accuracy, efficiency and stability conditions are studied respectively. For the cellular and component scale models, the 3-dimensional reproducing kernel particle method (RKPM) together with stabilized conforming nodal integration are employed. The simulation models are constructed based on medical images, where the pixel points are directly used as meshfree nodes. This computational model has been used to investigate the source of reduced force generation associated with ageing or diseases within muscles due to the malfunctioning in the subscale units. Through the proposed computational models, this research demonstrates how the stiffened connective tissue reduces force generation and how the frequency of neural stimulation affects force generation in the skeletal muscle.