Search

This work is dedicated to study the cardiac defibrillation problem by using an optimal thoracic electroshock treatment. The problem is formulated as an optimal control problem in a 3D domain surrounded by the bath and including the heart. The control corresponds to the thoracic electroshock and the model describing the electrical activity in the heart is the bidomain model. The bidomain model is coupled with the quasi-static Maxwell's equation to consider the effect of an external bathing medium. The existence and uniqueness of a weak solution for the direct problem is assessed as well as the existence of a weak solution for the adjoint problem. The numerical discretization is realized using a finite element method for the spatial discretization and linearly implicit Runge–Kutta methods for the temporal discretization of the partial differential equations. The numerical results are demonstrated for the termination of re-entry waves. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]