Parallel simulation of the synchronization of heterogeneous cells in the sinoatrial node

Abstract

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.

β-Adrenergic Stimulation Synchronizes a Broad Spectrum of Action Potential Firing Rates of Cardiac Pacemaker Cells toward a Higher Population Average

“…Multicellular numerical models of SAN function have been developed in 1 dimension (as a linear chain of consecutive SAN cells) [49][50][51][52][53][54], in 2 dimensions [55][56][57], and even in 3 dimensions [58]. Those models have provided new insights about the importance of cell interactions; however, they have not tested the importance of dormant cells (with their subthreshold signaling) [10][11][12], cells operating at low rates found in intact SAN [8], and autonomic modulation.…”

Assembly of the Cardiac Pacemaking Complex: Electrogenic Principles of Sinoatrial Node Morphogenesis

“…It should be emphasized that synchronization denotes that the system of cells becomes entrained to a stable periodicity, not necessarily that all cells match the rate of any individual cell’s activity. Multiple studies have indicated that the rate at which systems of pacemaker cells synchronize is a complex function of the independent activities of the coupled cells and not merely a convergence to the cycle length of the fastest cell in the system [ 37 , 38 , 39 , 40 , 41 , 42 , 43 ]. For example, Mata et al showed that the more heterogeneous cardiac pacemaker cells (CPCs), the shorter the cycle length at which they synchronize [ 43 ].…”

“…Furthermore, the influence of the coupled atrial tissue is not typically considered when examining the process of synchronization. As described below, computational treatments of sinoatrial node function are continually adding increased complexity to our view of heterogeneity, including variations in gap junctional conductivities, ion channel conductance [ 45 ], cellular make up [ 46 , 47 ] and cell-to-cell connectivity [ 43 ]. In particular, recent models introduced by Gratz et al, Ly and Weinberg, Mata et al, and Sehgal et al may be able to account for all these features in future analysis of synchronization [ 43 , 45 , 46 , 48 ].…”

β-Adrenergic Stimulation Synchronizes a Broad Spectrum of Action Potential Firing Rates of Cardiac Pacemaker Cells towards a Higher Population Average

“…Testing new ideas and establishing exact mechanisms require new theoretical modeling. Multicellular numerical models of SAN function have been developed in 1 dimension (as a linear chain of consecutive SAN cells) [49][50][51][52][53][54], in 2 dimensions [55][56][57] and even in 3 dimensions [58]. Those models have provided new insights about the importance of cell interactions, but they have not tested importance of dormant cells (with their subthreshold signaling) [10][11][12], cells operating at low rates found in intact SAN [8], and autonomic modulation.…”