About
9
Publications
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22
Citations
Citations since 2017
Introduction
My interests lie at the intersection of mathematical modeling, mathematics PDEs, homogenization theory, multiscale mathematical modeling and analysis, cardiac electrophysiology, reaction-diffusion system, and numerical simulation.
Additional affiliations
September 2022 - August 2023
September 2021 - August 2022
Education
December 2018 - November 2021
December 2018 - November 2021
September 2017 - August 2018
Publications
Publications (9)
![(A) Periodic heterogeneous domain Ω\documentclass[12pt]{minimal}...](publication/356888737/figure/fig3/AS:11431281119462753@1676085008534/A-Periodic-heterogeneous-domain-Odocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The sets Ωˆiε,δ\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/356888737/figure/fig4/AS:11431281119447386@1676085008582/The-sets-Oie-ddocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
In this paper, we are dealing with a rigorous homogenization result at two different levels for the bidomain model of cardiac electro-physiology. The first level associated with the mesoscopic structure such that the cardiac tissue consists of extracellular and intracellular domains separated by an interface (the sarcolemma). The second one related...
![A Periodic heterogeneous domain Ω\documentclass[12pt]{minimal}...](publication/355182697/figure/fig2/AS:11431281118646161@1675825798889/A-Periodic-heterogeneous-domain-Odocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
In the present paper, a new three-scale asymptotic homogenization method is proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities at two different levels. The first level is associated with the mesoscopic structure such that the cardiac tissue is composed of extracellular and intracellular domains....
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 (Acta Appl.Math. 179 (2022) 1--35), we detail this model in which gap junctions are considered as the connections between adjacent cells in cardiac m...
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 (Acta Appl.Math. 179 (2022) 1–35), we detail this model in which gap junctions are considered as the connections between adjacent cells in cardiac mu...
![(Left) Periodic heterogeneous domain Ω\documentclass[12pt]{minimal}...](publication/360907933/figure/fig2/AS:1169230582038534@1655777702650/Left-Periodic-heterogeneous-domain-Odocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
We present a novel microscopic tridomain model describing the electrical activity in cardiac tissue with dynamical gap junctions. The microscopic tridomain system consists of three PDEs modeling the tissue electrical conduction in the intra- and extra-cellular domains, supplemented by a nonlinear ODE system for the dynamics of the ion channels and...
We present a novel microscopic tridomain model describing the electrical activity in cardiac tissue with dynamical gap junctions. The microscopic tridomain system consists of three PDEs modeling the tissue electrical conduction in the intra-and extra-cellular domains, supplemented by a nonlinear ODE system for the dynamics of the ion channels and t...
In this paper, we are dealing with a rigorous homogenization result at two different levels for the bidomain model of cardiac electro-physiology. The first level associated with the mesoscopic structure such that the cardiac tissue consists of extracellular and intracellular domains separated by an interface (the sarcolemma). The second one related...
In the present paper, a new three-scale asymptotic homogenization method is proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities at two different levels. The first level is associated with the mesoscopic structure such that the cardiac tissue is composed of extracellular and intracellular domains....
This thesis is mainly devoted to the modeling and multi-scale analysis of bidomain and tridomain electro-cardiology systems. Cardiac electro-physiology describes and models the chemical and electrical phenomena that occur in cardiac tissue. At the microscopic level, cardiac tissue is very complex and it is therefore very difficult to understand and...
