English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we are dealing with a rigorous homogenization result at twodifferent levels for the bidomain model of cardiac electro-physiology. Thefirst level associated with the mesoscopic structure such that the cardiactissue consists of extracellular and intracellular domains separated by aninterface (the sarcolemma). The second one related to the microscopic structurein such a way that the intracellular medium can only be viewed as a periodicallayout of unit cells (mitochondria). At the interface between intra-andextracellular media, the fluxes are given by nonlinear functions of ionic andapplied currents. A rigorous homogenization process based on unfoldingoperators is applied to derive the macroscopic (homogenized) model from ourmeso-microscopic bidomain model. We apply a three-scale unfolding method in theintracellular problem to obtain its homogenized equation at two levels. Thefirst level upscaling of the intracellular structure yields the mesoscopicequation. The second step of the homogenization leads to obtain theintracellular homogenized equation. To prove the convergence of the nonlinearterms, especially those defined on the microscopic interface, we use theboundary unfolding method and a Kolmogorov-Riesz compactness's result. Next, weuse the standard unfolding method to homogenize the extracellular problem.Finally, we obtain, at the limit, a reaction-diffusion system on a singledomain (the superposition of the intracellular and extracellular media) whichcontains the homogenized equations depending on three scales. Such a model iswidely used for describing the macroscopic behavior of the cardiac tissue,which is recognized to be an important messengers between the cytoplasm(intracellular) and the other extracellular inside the biological cells.Contents 2020 Mathematics Subject Classification. 65N55 and 35A01 and 35B27 and35K57 and 65M..

Three Scale Unfolding Homogenization Method Applied to Cardiac Bidomain Model