A parallel accelerated adaptive mesh algorithm for the solution of electrical models of the heart

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 parallel numerical algorithm based on mesh adaptivity and finite volume method aiming to accelerate these simulations. This is a very attractive approach since the spreading electrical wavefront corresponds only to a small fraction of the cardiac tissue. Usually, the numerical solution of the partial differential equations that model the phenomenon requires very fine spatial discretisation 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 two-dimensional models of cardiac tissue have been accelerated by more than 340 times using the adaptive mesh algorithm and parallel computing, with no significant loss in accuracy.