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Fast Simulations of Models of Cardiac Electrophysiology

Date

2022-04-13

Journal Title

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Type

Thesis

Degree Level

Masters

Abstract

Cardiac electrophysiology studies the electrical activity of the heart. Researchers from different fields are working together to model and simulate the electrical activity in the heart. Such simulations may lead to help cardiologists to treat a patient's heart condition with better techniques and diagnoses. Mathematical models of cardiac electrophysiology are described by a system of partial differential equations~(PDEs) and a non-linear system of ordinary differential equations~(ODEs). One way to reach real-time simulation of the electrical activity of the heart is through more efficient time integration of these ODEs. Larger time steps lead to more efficient computations provided the solutions remain accurate enough. Producing the largest stable time step for solving these ODEs is a daunting task. Usually, trial and error is used to get the largest stable time step, but it is time consuming. In this thesis, we propose a new efficient method to find the largest stable time step to solve these ODEs efficiently. In this thesis, we present thirty-seven cardiac cell models. We compare, the forward Euler method, the explicit midpoint method, the four-stage, fourth-order Runge--Kutta method, the two-stage, first-order Runge--Kutta--Chebyshev method, the three-stage, first-order Runge--Kutta--Chebyshev method, the three-stage, third-order strong-stability-preserving Runge--Kutta method, and the four-stage, third-order strong-stability-preserving Runge--Kutta method based on their largest stepsize, mixed root mean square errors, and CPU time to solve the cardiac cell models. From the theoretical largest stepsize results, the forward Euler method outperforms all the other methods considered on all thirty-seven cardiac cell models. Next to the forward Euler method, the two-stage, first-order Runge--Kutta--Chebyshev method outperforms all the other methods considered on thirty-seven cardiac cell models. From the experimental largest stepsize results, the forward Euler method outperforms all the other methods considered on all thirty-seven cardiac cell models. Next to the forward Euler method, the two-stage, first-order Runge--Kutta--Chebyshev and the explicit midpoint methods outperform all the other methods considered on thirty-six cardiac cell models and one cardiac cell model, respectively. Also, we solve the monodomain problem coupled with FitzHugh--Nagumo model using the forward Euler, the two-stage, first-order Runge--Kutta--Chebyshev method, and the three-stage, first-order Runge--Kutta--Chebyshev method in one, two, and three dimensions. We compare these methods based on their theoretical largest stepsize, experimental largest stepsize, CPU time, and mixed root mean square errors. From these results, the three-stage, first-order Runge--Kutta--Chebyshev method outperforms all the other methods over a one-dimensional problem, a two-dimensional problem, and a three-dimensional problem.

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Keywords

Electrophysiology, Cardiac cell models, Monodomain model, Time integration methods, Fast simulation

Citation

Degree

Master of Science (M.Sc.)

Department

Computer Science

Program

Computer Science

Advisor

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