The cells of the sinoatrial node (SAN) are self-excitable entities that show a coupled electrical pattern that consists of the synchronized activation of action potentials that determine the heart rate. To accurately describe the behavior of cell membrane proteins, theoretical biophysicists have devoted themselves to the study of the electrical activity of individual cells, which involves solving a large number of coupled differential equations. This computational limitation makes the modeling of a large number of cells unattainable, since the intracellular distribution of Ca 2+ must be considered and this fact increases in grand extent the number of differential equations involved. In this work, we explore different parallel architectures (using OpenMP, MPI, and CUDA libraries) to show advances in the computational modeling and simulation of the SAN using a multicellular array in which the cells are endowed of heterogeneous conductances and are electrically coupled, considering a variable connectivity among them.
With an aperiodic, self-similar distribution of two-dimensional arrangement of atrial cells, it is possible to simulate such phenomena as Fibrillation, Fluttering, and a sequence of Fibrillation-Fluttering. The topology of a network of cells may facilitate the initiation and development of arrhythmias such as Fluttering and Fibrillation. Using a GPU parallel architecture, two basic cell topologies were considered in this simulation, an aperiodic, fractal distribution of connections among 462 cells, and a chessboard-like geometry of 60×60 and 600×600 cells. With a complex set of initial conditions, it is possible to produce tissue behavior that may be identified with arrhythmias. Finally, we found several sets of initial conditions that show how a mesh of cells may exhibit Fibrillation that evolves into Fluttering.
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