Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology

Abstract

Sudden cardiac death is often attributed to cardiac arrhythmia, the situation when normal heart rhythm is disordered. In the context of optimal control of cardiac arrhythmia, it is essential to determine the optimal current required to be injected to the patient for dampening the excitation wavefront propagation resulting from cardiac arrhythmia, in which this process is known as defibrillation. Consequently, this leads to an optimization problem arising from cardiac electrophysiology, namely Optimal Control Problem of Monodomain Model (OCPMM). The OCPMM is a nonlinear programming problem that is constrained by parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which turned out to be computationally demanding. The main aim of this research is on discovering more efficient optimization methods for solving OCPMM. First, the original complex problem is decomposed into sub-problems through the operator splitting technique for reducing the complexity of OCPMM. Next, the classical, modified and hybrid nonlinear conjugate gradient methods are employed to solve the split and discretized OCPMM. Numerical results prove that the modified method, namely the variant of the Dai-Yuan (VDY) method as well as the new developed hybrid method, namely the hybrid Ng-Rohanin (hNR) method are very efficient in solving OCPMM. Besides that, this research also studies the effects of control domain on OCPMM using two recognized factors, which are the position and the size. Numerical findings indicate that the control domains should consist of small size domains and located near to the excitation domain, for achieving better defibrillation performance. Lastly, based on the observed effects, an ideal control domain is proposed. Numerical results show that lowest current as well as shortest time are required by the ideal control domain during the defibrillation process. As a conclusion, the ideal control domain is capable of ensuring an efficient and successful defibrillation process.