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Solvability analysis and numerical approximation of linearized cardiac electromechanics

hal.structure.identifierLaboratoire de Mathématiques et Physique Théorique [LMPT]
hal.structure.identifierLaboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
dc.contributor.authorANDREIANOV, Boris
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierChair of Modelling and Scientific Computing [CMCS]
hal.structure.identifierModeling and Scientific Computing [Milano] [MOX]
dc.contributor.authorQUARTERONI, Alfio
hal.structure.identifierChair of Modelling and Scientific Computing [CMCS]
hal.structure.identifierInstitut des sciences de la terre [Lausanne] [ISTE]
dc.contributor.authorRUIZ BAIER, Ricardo
dc.date.accessioned2024-04-04T03:17:30Z
dc.date.available2024-04-04T03:17:30Z
dc.date.created2015-03-01
dc.date.issued2015
dc.identifier.issn0218-2025
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194310
dc.description.abstractEnThis paper is concerned with the mathematical analysis of a coupled elliptic-parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction-diffusion system governing the dynamics of ionic quantities, intra and extra-cellular potentials, and the linearized elasticity equations are adopted to describe the motion of an incompressible material. The coupling between muscle contraction, biochemical reactions and electric activity is introduced with a so-called active strain decomposition framework, where the material gradient of deformation is split into an active (electrophysiology-dependent) part and an elastic (passive) one. Under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffusivities, we prove existence of weak solutions to the underlying coupled reaction-diffusion system and uniqueness of regular solutions. The proof of existence is based on a combination of parabolic regularization, the Faedo-Galerkin method, and the monotonicity-compactness method of J.L. Lions. A finite element formulation is also introduced, for which we establish existence of discrete solutions and show convergence to a weak solution of the original problem. We close with a numerical example illustrating the convergence of the method and some features of the model.
dc.language.isoen
dc.publisherWorld Scientific Publishing
dc.rights.urihttp://creativecommons.org/licenses/by-nc/
dc.subject.enFinite element approximation
dc.subject.enWeak compactness method
dc.subject.enWeak-strong uniqueness
dc.subject.enElectro--mechanical coupling
dc.subject.enBidomain equations
dc.subject.enActive deformation
dc.subject.enWeak solutions
dc.subject.enConvergence of approximations
dc.title.enSolvability analysis and numerical approximation of linearized cardiac electromechanics
dc.typeArticle de revue
dc.identifier.doi10.1142/S0218202515500244
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halInformatique [cs]/Analyse numérique [cs.NA]
dc.description.sponsorshipEuropeERC-2008-AdG 227058, MATHCARD: Mathematical Modelling and Simulation of the Cardiovascular System
bordeaux.journalMathematical Models and Methods in Applied Sciences
bordeaux.page959-993
bordeaux.volume25
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00865585
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00865585v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Models%20and%20Methods%20in%20Applied%20Sciences&rft.date=2015&rft.volume=25&rft.spage=959-993&rft.epage=959-993&rft.eissn=0218-2025&rft.issn=0218-2025&rft.au=ANDREIANOV,%20Boris&BENDAHMANE,%20Mostafa&QUARTERONI,%20Alfio&RUIZ%20BAIER,%20Ricardo&rft.genre=article


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