Multiphysics Simulations of the Process of Neuromuscular Activation
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.
Copyright (c) 2022 Zdravka Ivanova
This work is licensed under a Creative Commons Attribution 4.0 International License.
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).