Simulated sinoatrial exit blocks explained by circle map analysis

In an accompanying study, it was seen that most cardiac arrhythmias that were simulated during poor intercellular coupling in the sinus node, were the same as those obtained in a two-element system in which one element suffered from a strong leakage current. This element corresponds to the sinus node periphery and is thus the one which feeds the atrium. In this paper, the interior element was replaced by a periodic stimulator. The dynamics of the peripheral element is then determined by its phase response curve. Phase response curves for sinus node elements subject to leakage were simulated for many different amplitudes of depolarizing stimuli. Simulations with circle maps based on these curves produced the same sequence of progressing levels of exit block as stimulus strength decreased, as did the two-element system when coupling strength was reduced. The bifurcations of the circle maps leading to the observed rhythms were identified. We found that the essential qualities of the phase response curves were determined by generally accepted properties of membrane currents. This suggests that the observed rhythms and bifurcations are generic.