Multiphysics Simulations of the Process of Neuromuscular Activation

Abstract

In this Master's thesis, we consider the problem of mathematical modelling and computer simulations of neuromuscular activation. We describe the biological and biochemical processes that result in a muscle contraction. For each of them, we derive a mathematical model, established in the literature. In particular, we consider: the Hodgkin-Huxley model of neural transmission; a reaction-diffusion model for the process of neurotransmitter release in the synaptic gap between a nerve and a muscle cell; an ODE system, based on chemical reaction schemes, proposed by Williams, for the process of calcium dynamics inside the muscle cell; Hill’s model for the generation of muscle force, triggered by calcium dynamics. We study the models numerically to illustrate the behaviour of the model solutions and to interpret them from a biological point of view. For the model of calcium dynamics, we also make qualitative analysis and obtain original results for the asymptotic behaviour of the model solutions. Further, we propose a framework for coupling the models, mentioned above, so that we can obtain new integrated multiphysics simulations of the whole process. Our initial motivation for the study is the future application of the proposed approach for modelling neuromuscular diseases. Therefore, the framework we propose is based on the idea of modelling micro-scale processes and studying their effect on the macro-scale muscle action.