Second Order Numerical Solution for Optimal Control of Monodomain Model in Cardiac Electrophysiology
نویسندگان
چکیده
Abstract. In this article, second order numerical methods for optimal control of the monodomain equations in cardiac electrophysiology are presented. The monoand 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 themselves 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 control 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.
منابع مشابه
Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology
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