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Derivation of a new macroscopic bidomain model including three scales for the electrical activity of cardiac tissue

hal.structure.identifierMathématiques, Image et Applications - EA 3165 [MIA]
dc.contributor.authorBADER, Fakhrielddine
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierInria Bordeaux - Sud-Ouest
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierLaboratoire de Mathématiques Jean Leray [LMJL]
dc.contributor.authorSAAD, Mazen
hal.structure.identifierEcole Doctorale des Sciences et de la Technologie [EDST]
dc.contributor.authorTALHOUK, Raafat
dc.date.accessioned2024-04-04T02:42:54Z
dc.date.available2024-04-04T02:42:54Z
dc.date.issued2021-12
dc.identifier.issn0022-0833
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191287
dc.description.abstractEnIn 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. The second level is associated with the microscopic structure in such a way the intracellular medium can only be viewed as a periodical layout of unit cells (mitochondria). Then, we define two kinds of local cells that are obtained by upscaling methods. The homogenization method is based on a power series expansion which allows determining the macroscopic (homogenized) bidomain model from the microscopic bidomain problem at each structural level. First, we use the two-scale asymptotic expansion to homogenize the extracellular problem. Then, we apply a three-scale asymptotic expansion in the intracellular problem to obtain its homogenized equation at two levels. The first upscaling level of the intracellular structure yields the mesoscopic equation and the second step of the homogenization leads to obtain the intracellular homogenized equation. Both the mesoscopic and microscopic information is obtained by homogenization to capture local characteristics inside the cardiac tissue structure. Finally, we obtain the macroscopic bidomain model and the heart domain coincides with the intracellular medium and extracellular one, which are two inter-penetrating and superimposed continua connected at each point by the cardiac cellular membrane. The interest of the proposed method comes from the fact that it combines microscopic and mesoscopic characteristics to obtain a macroscopic description of the electrical behavior of the heart.
dc.description.sponsorshipCentre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enDerivation of a new macroscopic bidomain model including three scales for the electrical activity of cardiac tissue
dc.typeArticle de revue
dc.identifier.doi10.1007/s10665-021-10174-8
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv2201.03412
bordeaux.journalJournal of Engineering Mathematics
bordeaux.page3
bordeaux.volume131
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03517663
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03517663v1
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