Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Ainseba, Bedr'Eddine²  Bendahmane, Mostafa²  Ruiz-Baier, Ricardo¹ 

[1] Ecole Polytech Fed Lausanne, MATHICSE, CH-1015 Lausanne, Switzerland

[2] Univ Bordeaux 2, CNRS, UMR 5251, Inst Math Bordeaux, F-33076 Bordeaux, France

关键词: Optimal control;    Finite volume approximation;    Convergence;    Cardiac electrophysiology;    Tridomain model;   

DOI  :  10.1016/j.jmaa.2011.11.069

来源: Elsevier

【 摘 要 】

In the present paper, an optimal control problem constrained by the tridomain equations in electrocardiology is investigated. The state equations consisting in a coupled reaction-diffusion system modeling the propagation of the intracellular and extracellular electrical potentials, and ionic currents, are extended to further consider the effect of an external bathing medium. The existence and uniqueness of solution for the tridomain problem and the related control problem is assessed, and the primal and dual problems are discretized using a finite volume method which is proved to converge to the corresponding weak solution. In order to illustrate the control of the electrophysiological dynamics, we present some preliminary numerical experiments using an efficient implementation of the proposed scheme. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free