Solvability analysis and numerical approximation of linearized cardiac electromechanics
| hal.structure.identifier | Laboratoire de Mathématiques et Physique Théorique [LMPT] | |
| hal.structure.identifier | Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB] | |
| dc.contributor.author | ANDREIANOV, Boris | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BENDAHMANE, Mostafa | |
| hal.structure.identifier | Chair of Modelling and Scientific Computing [CMCS] | |
| hal.structure.identifier | Modeling and Scientific Computing [Milano] [MOX] | |
| dc.contributor.author | QUARTERONI, Alfio | |
| hal.structure.identifier | Chair of Modelling and Scientific Computing [CMCS] | |
| hal.structure.identifier | Institut des sciences de la terre [Lausanne] [ISTE] | |
| dc.contributor.author | RUIZ BAIER, Ricardo | |
| dc.date.accessioned | 2024-04-04T03:17:30Z | |
| dc.date.available | 2024-04-04T03:17:30Z | |
| dc.date.created | 2015-03-01 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0218-2025 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194310 | |
| dc.description.abstractEn | This 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.iso | en | |
| dc.publisher | World Scientific Publishing | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/ | |
| dc.subject.en | Finite element approximation | |
| dc.subject.en | Weak compactness method | |
| dc.subject.en | Weak-strong uniqueness | |
| dc.subject.en | Electro--mechanical coupling | |
| dc.subject.en | Bidomain equations | |
| dc.subject.en | Active deformation | |
| dc.subject.en | Weak solutions | |
| dc.subject.en | Convergence of approximations | |
| dc.title.en | Solvability analysis and numerical approximation of linearized cardiac electromechanics | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1142/S0218202515500244 | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Informatique [cs]/Analyse numérique [cs.NA] | |
| dc.description.sponsorshipEurope | ERC-2008-AdG 227058, MATHCARD: Mathematical Modelling and Simulation of the Cardiovascular System | |
| bordeaux.journal | Mathematical Models and Methods in Applied Sciences | |
| bordeaux.page | 959-993 | |
| bordeaux.volume | 25 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00865585 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00865585v1 | |
| bordeaux.COinS | ctx_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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