Miller, L. and Penta, R. (2024) Homogenization of a coupled electrical and mechanical bidomain model for the myocardium. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865231207600)
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Abstract
We propose a coupled electrical and mechanical bidomain model for the myocardium tissue. The structure that we investigate possesses an elastic matrix with embedded cardiac myocytes. We are able to apply the asymptotic homogenization technique by exploiting the length scale separation that exists between the microscale where we see the individual myocytes and the overall size of the heart muscle. We derive the macroscale model which describes the electrical conductivity and elastic deformation of the myocardium driven by the existence of a Lorentz body force. The model comprises balance equations for the current densities and for the stresses, with the novel coefficients accounting for the difference in the electric potentials and elastic properties at different points in the microstructure. The novel coefficients of the model are to be computed by solving the periodic cell differential problems arising from application of the asymptotic homogenization technique. By combining both the mechanical and electrical behaviors, we obtain a macroscale model that highlights how the elastic deformation of the heart tissue is influenced and driven by the difference in the electric potentials at various points in the material.
| Item Type: | Articles |
|---|---|
| Additional Information: | R.P. is partially supported by EPSRC Grants EP/S030875/1 and EP/T017899/1 and conducted the research according to the inspiring scientific principles of the national Italian mathematics association Indam (“Istituto nazionale di Alta Matematica”), GNFM group. |
| Keywords: | Multiscale modelling, myocaridum, electrical activity, asymptotic homogenization, bidomain models. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Miller, Dr Laura and Penta, Dr Raimondo |
| Authors: | Miller, L., and Penta, R. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Mathematics and Mechanics of Solids |
| Publisher: | SAGE Publications |
| ISSN: | 1081-2865 |
| ISSN (Online): | 1741-3028 |
| Published Online: | 17 January 2024 |
| Copyright Holders: | Copyright © 2024 The Author(s) |
| First Published: | First published in Mathematics and Mechanics of Solids 2024 |
| Publisher Policy: | Reproduced under a Creative Commons license |
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