Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology

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 wavefron...

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Main Author:	Ng, Kin Wei
Format:	Thesis
Language:	English
Published:	2013
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/33813/5/NgKinWeiPFS2013.pdf
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spelling	my-utm-ep.338132017-07-23T01:17:19Z Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology 2013-04 Ng, Kin Wei QA Mathematics 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. 2013-04 Thesis http://eprints.utm.my/id/eprint/33813/ http://eprints.utm.my/id/eprint/33813/5/NgKinWeiPFS2013.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:69820?site_name=Restricted Repository phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ng, Kin Wei Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology
description	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.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Ng, Kin Wei
author_facet	Ng, Kin Wei
author_sort	Ng, Kin Wei
title	Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology
title_short	Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology
title_full	Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology
title_fullStr	Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology
title_full_unstemmed	Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology
title_sort	optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/33813/5/NgKinWeiPFS2013.pdf
_version_	1747816191415549952

Optimal control based on nonlinear conjugate gradient method in cardiac electrophysiology

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