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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

hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorBADER, Fakhrielddine
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierLaboratoire de Mathématiques Jean Leray [LMJL]
dc.contributor.authorSAAD, Mazen
hal.structure.identifierÉcole Supérieure d'Ingénierie Léonard de Vinci [ESILV]
hal.structure.identifierEcole Doctorale des Sciences et de la Technologie [EDST]
dc.contributor.authorTALHOUK, Raafat
dc.date.accessioned2024-04-04T02:40:32Z
dc.date.available2024-04-04T02:40:32Z
dc.date.issued2022-09-08
dc.identifier.issn0921-7134
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191070
dc.description.abstractEnWe 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 muscle and could serve as alternative or supporting pathways for cell-to-cell electrical signal propagation. Departing from this microscopic cellular model, we apply the periodic unfolding method to derive the macroscopic tridomain model. Several difficulties prevent the application of unfolding homogenization results, including the degenerate temporal structure of the tridomain equations and a nonlinear dynamic boundary condition on the cellular membrane. To prove the convergence of the nonlinear terms, especially those defined on the microscopic interface, we use the boundary unfolding operator and a Kolmogorov–Riesz compactness’s result.
dc.description.sponsorshipCentre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
dc.language.isoen
dc.publisherIOS Press
dc.subject.enTridomain model
dc.subject.enreaction-diffusion system
dc.subject.enhomogenization theory
dc.subject.entime-periodic unfolding method
dc.subject.engap junctions
dc.subject.encardiac electric field
dc.title.enMicroscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 – Derivation of the macroscopic tridomain model by unfolding homogenization method
dc.typeArticle de revue
dc.identifier.doi10.3233/ASY-221804
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv2209.07169
bordeaux.journalAsymptotic Analysis
bordeaux.page1-32
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03776998
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03776998v1
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