Impact of Limits in Pathways Between Sinoatrial Node and Atrium on Heart Rhythm by Timed Automata Model

There are evidences that the human right atrium and sinoatrial node (SAN) are functionally separated except at discrete SAN-atrial electrical junctions.We hypothesize that such anatomy could be a source of re-entry around the SAN.A model was developed which reconstructs the human right atrium anatomy.The activity of a myocyte was simulated by a timed automaton with continuous and discrete transitions reproducing the known stages of the action potential of the cellular membrane.A stochastic 2D network of timed automata was designed to model the grid of the right atrium.Discrete modeling allowed us to specify directly the rate of SAN to atrium pathways.Also, the influence of (1) atrial tissue fibrosis, via probability for transversal intercellular network connections, and of (2) impairment of individual cells via probability of a cell to excite, were controlled.The simulations provided a critical relationship between atrial anatomy and the rhythm of heart excitations.It occurred that at probability of 1/8 of SAN-atrium pathways (randomly chosen), the occurrence of the normal rhythm attained the highest probability -close to 1, in large intervals for the density of transversal intercellular connections, and for the levels of cellular impairment.