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Stability analysis of decoupled time-stepping schemes for the specialized conduction system/myocardium coupled problem in cardiology

hal.structure.identifierFaculté des Sciences Mathématiques, Physiques et Naturelles de Tunis [FST]
dc.contributor.authorAOUADI, Salwa
hal.structure.identifierFaculté des Sciences Mathématiques, Physiques et Naturelles de Tunis [FST]
dc.contributor.authorMBARKI, W
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorZEMZEMI, Nejib
dc.date.accessioned2024-04-04T03:07:52Z
dc.date.available2024-04-04T03:07:52Z
dc.date.issued2017-10-13
dc.identifier.issn0973-5348
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193482
dc.description.abstractEnThe Purkinje network is the rapid conduction system in the heart. It ensures the physiological spread of the electrical wave in the ventricles. In this work, we consider a problem that models the coupling between the Purkinje network and the myocardium. We first prove the stability of the space semi-discretized problem. Then we present four different strategies for solving the Purkinje/ myocardium coupling. The strategies are based on different time discretization of the coupling terms. The first scheme is fully coupled, where the coupling terms are considered implicit. The second and the third schemes are based on Gauss-Seidel time-splitting schemes where one coupling term is considered explicit and the other is implicit. The last is a Jacobi-like time-splitting scheme where both coupling terms are considered explicit. Our main result is the proof of the stability of the three considered schemes under the same restriction on the time step. Moreover, we show that the energy of the problem is slightly affected by the time-splitting schemes. We illustrate the theoretical result by different numerical simulations in 2D. We also conduct 3D simulations using physiologically detailed ionic models.
dc.language.isoen
dc.publisherEDP Sciences
dc.title.enStability analysis of decoupled time-stepping schemes for the specialized conduction system/myocardium coupled problem in cardiology
dc.typeArticle de revue
dc.identifier.doi10.1051/mmnp/201712513
dc.subject.halInformatique [cs]/Modélisation et simulation
bordeaux.journalMathematical Modelling of Natural Phenomena
bordeaux.page208-239
bordeaux.volume12
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue5
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01655411
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01655411v1
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