Second order numerical solution for optimal control of opt e � monodomain model in cardiac electrophysiology

Abstract. In this article, second order numerical methods for optimal control of the mon-odomain equations in cardiac electrophysiology are presented. The mono- and bidomain equations are well established as a major building block for describing the the wave propagation of the action potential in the human heart. The mathematical model equations consist of a non-linear parabolic partial differential equation of reaction-diffusion type, coupled with ordinary differential equations describing the interaction with the ionic current variables. Optimal control problems suggest them-selves quite naturally for this important class of modeling problems. Specifically we present an optimal control formulation for the monodomain equations with an extra-cellular current as the con-trol variable which must be determined in such a way that excitations of the transmembrane voltage are damped in an optimal manner. A nonlinear conjugate gradient method and a Newton method are compared for solving the optimization problem. Key words. Reaction-diffusion systems, optimal control problems, constrained PDE’s. AMS subject classifications. 35J55, 35K57, 49J20, 74S05 1. Introduction. Modelin