Isogeometric Analysis of Electrophysiological Models on Surfaces

In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-UniformRational B-Splines) basis functions in the approximation of the traveling waves of the action potential. As application, we consider the numerical simulations on the human left atrium modeled as a surface. Firstly in our analysis, we consider a benchmark time dependent diffusion-reaction problem describing a traveling front in a two dimensional domain, for which we aim at understanding the role of NURBS basis functions in the approximation of the conduction velocity. Then, we extend the analysis to more complex electrophysiological models, in particular to the numerical approximation of the monodomain equation. The latter is a Partial Differential Equation and a system of Ordinary Differential Equations. We consider the Aliev-Panfilov model and we analyze the different aspects related to its numerical approximation, including the role of high order continuous NURBS basis functions in the simulation of cardiac excitation models. Then, we consider realistic simulations of the Mitchell-Schaeffer model on the human left atrium represented as a surface for which the strong anisotropic behavior of the action potential, due to the fiber orientation of the cardiac tissue, is taken into account