Optimal control for nonlocal reaction‐diffusion system describing calcium dynamics in cardiac cell
| Autor: | Mostafa Bendahmane, Fahd Karami, Elmahdi Erraji |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Ecole Supérieure de Technologie d'Essaouira, Université Cadi Ayyad [Marrakech] (UCA), the research program PPR supported by CNRST (Morocco), project 'Modèles Mathématiques appliquées l’environnement, à l’imagerie médicale et aux biosystèmes' |
| Rok vydání: | 2020 |
| Předmět: |
calcium model
Computer simulation [SDV]Life Sciences [q-bio] General Mathematics Weak solution finite element method General Engineering nonlocal diffusion weak solution Mechanics Optimal control first order optimality conditions Cardiac cell Finite element method Calcium dynamics numerical simulation Reaction–diffusion system [MATH]Mathematics [math] Mathematics |
| Zdroj: | Mathematical Methods in the Applied Sciences Mathematical Methods in the Applied Sciences, 2021, 44 (6), pp.4802-4834. ⟨10.1002/mma.7071⟩ |
| ISSN: | 1099-1476 0170-4214 |
| Popis: | International audience; The purpose of this paper is to introduce an optimal control for a nonlocal calcium dynamic model in a cardiac cell acting on ryanodine receptors. The optimal control problem is considered as a coupled nonlocal reaction-diffusion system with a transmission boundary condition covering the sarcoplasmic reticulum and cytosolic domain. We establish the well-posedness result of the adjoint problem using Faedo-Galerkin approximation, a priori estimates and compactness arguments. The numerical discretization of direct and adjoint problems is realized by using the implicit Euler method in time and the finite element for spatial discretization. Moreover, we obtain the stability result in the 2-norm for the direct and the adjoint discrete problems. Finally, in order to illustrate the control of our calcium dynamic model, we present some numerical experiments devoted to constant and nonlocal diffusions using the proposed numerical scheme. |
| Databáze: | OpenAIRE |
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