Optimal control for nonlocal reaction-diffusion system describing calcium dynamics in cardiac cell
BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Language
en
Article de revue
This item was published in
Mathematical Methods in the Applied Sciences. 2021-04, vol. 44, n° 6, p. 4802-4834
Wiley
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Optimal control
calcium model
nonlocal diffusion
weak solution
finite element method
first order optimality conditions
numerical simulation
Origin
Hal imported