Algoritmos paralelos e adaptativos no tempo e no espaço para simulação numérica da eletrofisiologia do coração

Abstract

Computational models have become valuable tools for the study of the electrical behavior of the heart. However, the high complexity of thebiophysical processes translates into expensive computational models. In this work we propose, implement and combine strategies using parallel computing and graphical processing unit (GPU), adaptive meshes in space and time adaptive methods in order to reduce the execution time of cardiac electrophysiology simulations.In our first approach different GPU implementations are compared, OpenGL, NVIDIA CUDA and OpenCL, to a CPU multicore implementation that uses OpenMP. The OpenGL approach showed to be the fastest with a speedup of 446 (compared to the multicore implementation) for the solution of the nonlinear system of ordinary differential equations (ODEs) associated to the solution of the cardiac model, whereas CUDA was the fastest for the numerical solution of the parabolic partial differential equation with a speedup of 8. Although we achieved a significant improvement in the execution time of the cardiac electrophysiology simulations, we are far from real-time simulations.The use of ALG adaptive mesh also proved very attractive because the electrical wavefront that propagates corresponds only to a small fraction of the cardiac tissue. Usually, the numerical solution of the partial differential equations that model the phenomenon requires fine enough space discretizations to follow the wave front, which is about 0.25 mm. The use of uniform meshes leads to a high computational cost, as it requires a large number of mesh points. In this sense, the tests reported in this work show that the bi-dimensional heart tissue model simulations were accelerated up to 20 times by using the adaptive mesh algorithm, with no loss in accuracy of numerical solution obtained.Furthermore, the combination of adaptive meshes techniques together with numerical methods with adaptive time step and parallel computing using both multicore computers and GPUs proved extremely effective achieving speedups larger than 1000x using only one machine equipped with eight cores and a GPU.