Computationally efficient approaches to integrated cardiac electrophysiology

Paşaoğlu, Özgür
This work is concerned with the development of numerically efficient approaches for cardiac electrophysiology within the bidomain setting. In this approach, nonlinear cardiac tissue is embedded into a linear conductor, called the torso. While the excitation of cardiac tissue involves two field variables, the transmembrane potential and the extracellular potential, the electrical activity of the torso involve the extracellular potential filed only. The electrophysiological behavior of cardiac tissue is governed by a set of two partial differential equations. One of these equations contains a highly non-linear ionic current term that is modeled by the celebrated ten Tusscher model. The linear and time-independent nature of the differential equations describing the electrical behavior of torso enables us to propose computationally efficient approaches. These include the condensation of the stiffness matrix for an entirely Finite Element-based approach and the hybrid Finite Element Method - Boundary Element Method (FEM-BEM) approach. In the former, owing to the linear behavior of the torso, the conductivity matrix of the surrounding tissue is constant and can be assembled once and for all. Consequently, we can rearrange the overall coefficient matrix to decrease the total number of degrees of freedom. In the latter approach, we exploit the linear differential equation of the torso and solve it by using the BEM. The coupling between the nonlinear equations of cardiac tissue and the equations of the torso is achieved on the surface of the heart by the FEM-BEM approach. The efficiency of the proposed approaches is demonstrated through the representative numerical examples. 
Citation Formats
Ö. Paşaoğlu, “Computationally efficient approaches to integrated cardiac electrophysiology,” M.S. - Master of Science, Middle East Technical University, 2017.