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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 734070, 14 pages
http://dx.doi.org/10.1155/2012/734070
Research Article

Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Malaysia

Received 28 August 2012; Accepted 5 December 2012

Academic Editor: Rafael Martinez-Guerra

Copyright © 2012 Kin Wei Ng and Ahmad Rohanin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY) method and the Liu-Storey-Conjugate-Descent (LS-CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.