Fakhrielddine Bader; Mostafa Bendahmane; Mazen Saad; Raafat Talhouk
In: Asymptotic Analysis, 2022.
@article{bader_1995,
title = {Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 - Derivation of the macroscopic tridomain model by unfolding homogenization method},
author = {Fakhrielddine Bader and Mostafa Bendahmane and Mazen Saad and Raafat Talhouk},
url = {https://doi.org/10.3233/ASY-221804},
year = {2022},
date = {2022-09-01},
journal = {Asymptotic Analysis},
abstract = {We study the homogenization of a novel microscopic tridomain system, allowing
for a more detailed analysis of the properties of cardiac conduction than the classical bidomain
and monodomain models. In [5], we detail this model in which gap junctions are considered
as the connections between adjacent cells in cardiac muscle and could serve as alternative
or supporting pathways for cell-to-cell electrical signal propagation. Departing from this mi-
croscopic cellular model, we apply the periodic unfolding method to derive the macroscopic
tridomain model. Several diculties prevent the application of unfolding homogenization
results, including the degenerate temporal structure of the tridomain equations and a nonlin-
ear dynamic boundary condition on the cellular membrane. To prove the convergence of the
nonlinear terms, especially those de ned on the microscopic interface, we use the boundary
unfolding operator and a Kolmogorov-Riesz compactness's result.},
keywords = {},
pubstate = {online},
tppubtype = {article}
}
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