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dc.contributor.advisorSpiteri, Raymond J.en_US
dc.creatorDean, Ryan Christopheren_US
dc.date.accessioned2009-02-11T12:41:58Zen_US
dc.date.accessioned2013-01-04T04:25:30Z
dc.date.available2010-04-13T08:00:00Zen_US
dc.date.available2013-01-04T04:25:30Z
dc.date.created2009en_US
dc.date.issued2009en_US
dc.date.submitted2009en_US
dc.identifier.urihttp://hdl.handle.net/10388/etd-02112009-124158en_US
dc.description.abstractMathematical models of electric activity in cardiac tissue are becoming increasingly powerful tools in the study of cardiac arrhythmias. Considered here are mathematical models based on ordinary differential equations (ODEs) and partial differential equations (PDEs) that describe the behaviour of this electrical activity. Generating an efficient numerical solution of these models is a challenging task, and in fact the physiological accuracy of tissue-scale models is often limited by the efficiency of the numerical solution process. In this thesis, we discuss two sets of experiments that test ideas for making the numerical solution process more efficient. In the first set of experiments, we examine the numerical solution of four single cell cardiac electrophysiological models, which consist solely of ODEs. We study the efficiency of using implicit-explicit Runge-Kutta (IMEX-RK) splitting methods to solve these models. We find that variable step-size implementations of IMEX-RK methods (ARK3 and ARK5) that take advantage of Jacobian structure clearly outperform most methods commonly used in practice for two of the models, and they outperform all methods commonly used in practice for the remaining models. In the second set of experiments, we examine the solution of the bidomain model, a model consisting of both ODEs and PDEs that are typically solved separately. We focus these experiments on numerical methods for the solution of the two PDEs in the bidomain model. The most popular method for this task, the Crank-Nicolson method, produces unphysical oscillations; we propose a method based on a second-order L-stable singly diagonally implicit Runge-Kutta (SDIRK) method to eliminate these oscillations. We find that although the SDIRK method is able to eliminate these unphysical oscillations, it is only more efficient for crude error tolerances.en_US
dc.language.isoen_USen_US
dc.subjectbidomain modelen_US
dc.subjectcardiac electrophysiologyen_US
dc.subjectSDIRK methoden_US
dc.subjectimplicit-explicit Runge-Kutta methodsen_US
dc.subjectnumerical methodsen_US
dc.titleNumerical methods for simulation of electrical activity in the myocardial tissueen_US
thesis.degree.departmentComputer Scienceen_US
thesis.degree.disciplineComputer Scienceen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Science (M.Sc.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US
dc.contributor.committeeMemberPatrick, George W.en_US
dc.contributor.committeeMemberOsgood, Nathanielen_US
dc.contributor.committeeMemberEramian, Mark G.en_US


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