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

Danuta Makowiec1 and Zbigniew Struzik2
1University of Gdansk, 2Graduate Scool of Education,Tokyo University


Aim: There are evidences that the human right atrium and sinoatrial node (SAN) are functionally separated except at discrete SAN-atrial electrical junctions, called SAN-exit-pathways. We hypothesize that this type anatomy is a source of re-entry around the SAN.

Methods: A computationally efficient model was developed to reconstruct human right atrium electrophysiology. Activity of a myocyte was simulated by a timed automaton with continuous and discrete transitions reproducing stages of cellular membrane. A stochastic 2D-network of timed automata was designed to model the right atrium architecture: SAN, atria-ventricular node (AVN), SAN-exit-pathways and heterogeneous atrial tissue. Simulations were performed to measure effects of quantity of SAN-exit-pathways: all-, half-, few-cells connections, on development and propagation of normal versus arrhythmic excitations: SAN re-entry or fibrillation. Additionally, two parameters were controlled to measure an influence of (1) atrial tissue fibrosis: p_trans - probability for transversal intercellular network connections, and (2) impairment of individual cells: p_refuse - probability of a cell to refuse to excite. 100 simulations for wide range of studied parameters were performed.

Results: In case of normal density of intercellular connections (p_trans = 0.60), in large interval of p_refuse (0 <= p_refuse < 0.45), probability to observe normal rhythm/SAN re-entry/fibrillation changed from 0.33/0.66/0.00 for all-cells connections, to 0.96/0.04/0.00 for few-cells connections between SAN and atrium. Then at p_refuse > 0.45, all simulations led to stabilization with fibrillation. In case of high fibrosis (p_trans = 0.30), again systems with few-cells connections provided the highest ratio of normal states when p_refuse <= 0.20, which then switched rapidly to fibrillation.

Conclusion: The simulations provided a critical relationship between atrial anatomy and rhythm of heart excitations. A discrete model of cells and intercellular connections was found as efficient method for quantifying this relationship.