Efficient Cardiac Cell Solvers and Simulating Temperature Dependence in the Myocardium

  • Author / Creator
    Grenier, Justin G
  • 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.

  • Subjects / Keywords
  • Graduation date
    Fall 2014
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.