Unfolding homogenization method applied to physiological and phenomenological bidomain models in electrocardiology
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| dc.contributor.author | BENDAHMANE, Mostafa | |
| hal.structure.identifier | Département de Mathématiques et Informatique - Université de Nantes | |
| dc.contributor.author | MROUE, Fatima | |
| hal.structure.identifier | Laboratoire de Mathématiques Jean Leray [LMJL] | |
| dc.contributor.author | SAAD, Mazen | |
| hal.structure.identifier | الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth] [LU / ULB] | |
| dc.contributor.author | TALHOUK, Raafat | |
| dc.date.accessioned | 2024-04-04T02:44:33Z | |
| dc.date.available | 2024-04-04T02:44:33Z | |
| dc.date.issued | 2019-12 | |
| dc.identifier.issn | 1468-1218 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191417 | |
| dc.description.abstractEn | In this paper, we apply a rigorous homogenization method based on unfolding operators to a microscopic bidomain model representing the electrical activity of the heart at a cellular level. The heart is represented by an arbitrary open bounded connected domain with smooth boundary and the cardiac cells’ (myocytes) domain is viewed as a periodic region. We start by proving the well posedness of the microscopic problem by using Faedo–Galerkin method and -compactness argument on the membrane surface without any restrictive assumptions on the conductivity matrices. Using the unfolding method in homogenization, we show that the sequence of solutions constructed in the microscopic model converges to the solution of the macroscopic bidomain model. Because of the nonlinear ionic function, the proof is based on the surface unfolding method and Kolmogorov compactness argument. | |
| dc.description.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/ | |
| dc.subject.en | Bidomain model | |
| dc.subject.en | Reaction–diffusion system | |
| dc.subject.en | Homogenization theory | |
| dc.subject.en | Unfolding method | |
| dc.subject.en | Convergence | |
| dc.title.en | Unfolding homogenization method applied to physiological and phenomenological bidomain models in electrocardiology | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.nonrwa.2019.05.006 | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| bordeaux.journal | Nonlinear Analysis: Real World Applications | |
| bordeaux.page | 413-447 | |
| bordeaux.volume | 50 | |
| 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-02142028 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02142028v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Nonlinear%20Analysis:%20Real%20World%20Applications&rft.date=2019-12&rft.volume=50&rft.spage=413-447&rft.epage=413-447&rft.eissn=1468-1218&rft.issn=1468-1218&rft.au=BENDAHMANE,%20Mostafa&MROUE,%20Fatima&SAAD,%20Mazen&TALHOUK,%20Raafat&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||