Simulations of cardiac electrophysiology combining GPU and adaptive mesh refinement algorithms

Abstract

Computer models have become valuable tools for the study and comprehension of the complex phenomena of cardiac electrophysiology. However, the high complexity of the biophysical processes translates into complex mathematical and computational models. In this paper we evaluate a hybrid multicore and graphics processing unit numerical algorithm based on mesh adaptivity and on the finite volume method to cope with the complexity and to accelerate these simulations. This is a very attractive approach since the electrical wavefront corresponds to only a small fraction of the cardiac tissue. Usually, the numerical solution of the partial differential equations that model the phenomenon requires very fine spatial discretization to follow the wavefront, which is approximately 0.2 mm. The use of uniform meshes leads to high computational cost as it requires a large number of mesh points. In this sense, the tests reported in this work show that simulations of three-dimensional models of cardiac tissue have been accelerated by more than 626 times using the adaptive mesh algorithm together with its parallelization, with no significant loss in accuracy.