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Efficient Cardiac Cell Solvers and Simulating Temperature Dependence in the Myocardium Open Access


Other title
ODE Solvers
Spiral Waves
Bidomain and Monodomain Models
Cardiac Cell Models
Numerical Methods for Cardiac Models
Transmembrane Potential
Type of item
Degree grantor
University of Alberta
Author or creator
Grenier, Justin G
Supervisor and department
Youssef Belhamadia (Biomedical Engineering, Mathematical and Statistical Sciences, Campus St Jean)
Examining committee member and department
Richard Thompson (Biomedical Engineering)
Stevan Dubljevic (Chemical and Material Engineering)
Department of Biomedical Engineering

Date accepted
Graduation date
Master of Science
Degree level
The modelling of the electrical activity in cardiac tissue can enable researchers to study heart phenomena such as arrhythmias which are difficult to observe in vivo. However, the nature of the mathematical equations used to represent these behaviors present multiple numerical difficulties which limit their large scale usage. In this thesis, we have suggested the application of a nested implicit Runge-Kutta method of order 4 (NIRK4) as a means of efficiently solving the stiff cardiac cell models. By comparing its performance to multiple common implicit and explicit solvers, we have established the advantages of using NIRK4 when solving multiple cell models of varying complexities. Due to recent experimental and modelling results, it was deemed advantageous to investigate the effects of the temperature on the transmembrane potential. Therefore, we developed a mathematical model by coupling Pennes' bioheat equation to the bidomain model to simulate the induced heat caused by cardiac action potential. The influence of the temperature on ionic conductances in the Aliev-Panfilov and Luo-Rudy cardiac cell models was also investigated. Furthermore, the induced heat caused by the transmembrane potential's propagation was studied as a potential method for detecting spiral-waves.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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