Numerical Analysis of a Finite Element Method for an Optimal Control of Bidomain-bath Model
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| dc.contributor.author | BENDAHMANE, Mostafa | |
| hal.structure.identifier | Johann Radon Institute for Computational and Applied Mathematics [RICAM] | |
| dc.contributor.author | CHAMAKURI, Nagaiah | |
| dc.date.accessioned | 2024-04-04T03:15:57Z | |
| dc.date.available | 2024-04-04T03:15:57Z | |
| dc.date.issued | 2017-07-18 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194172 | |
| dc.description.abstractEn | This work is concerned with the study of the convergence analysis for an optimal control of bidomain-bath model by using the finite element scheme. The bidomain-bath model equations describe the cardiac bioelectric activity at the tissue and bath volumes where the control acts at the boundary of the tissue domain. We establish the existence of the finite element scheme, and convergence of the unique weak solution of the direct bidomain-bath model. The convergence proof is based on deriving a series of a priori estimates and using a general L 2-compactness criterion. Moreover, the well-posedness of the adjoint problem and the first order necessary optimality conditions are shown. Comparing to the direct problem, the convergence proof of the adjoint problem is based on using a general L 1-compactness criterion. The numerical tests are demonstrated which achieve the successful cardiac defibrillation by utilizing less total current. Finally, the robustness of the Newton optimization algorithm is presented for different finer mesh geometries. 1. Introduction. The electrical behavior of the cardiac tissue surrounded by a nonconductive bath is described by a coupled partial and ordinary differential equations which are so called bidomain model equations [17, 22, 24]. The bidomain model equations consist of two parabolic partial differential equations (PDEs) which describe the dynamics of the intra and the extracellular potentials. The PDEs coupled with an ordinary differential equations which model the ionic currents associated with the reaction terms. Furthermore , an additional Poisson problem has to be solved when the cardiac tissue is immersed in a conductive fluid, e.g. tissue bath in an experimental context or a surrounding torso to model in vivo scenarios. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Optimal control | |
| dc.subject.en | Bidomain model | |
| dc.subject.en | Weak solution | |
| dc.subject.en | Finite Element Method | |
| dc.subject.en | First order optimality conditions | |
| dc.subject.en | Cardiac electrophysiology | |
| dc.title.en | Numerical Analysis of a Finite Element Method for an Optimal Control of Bidomain-bath Model | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jde.2017.04.001 | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.subject.hal | Sciences du Vivant [q-bio]/Médecine humaine et pathologie/Cardiologie et système cardiovasculaire | |
| bordeaux.journal | Journal of Differential Equations | |
| bordeaux.page | 2419–2456 | |
| bordeaux.volume | 263 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01259773 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01259773v1 | |
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