Phase transitions towards frequency entrainment in large oscillator lattices

We investigate phase transitions towards frequency entrainment in large, locally coupled networks of limit cycle oscillators. Specifically, we simulate two-dimensional lattices of pulse-coupled oscillators with random natural frequencies, resembling pacemaker cells in the heart. As coupling increases, the system seems to undergo two phasetransitions in the thermodynamic limit. At the first, the largest cluster of frequency entrained oscillators becomes macroscopic. At the second, global entrainment settles. Between the two transitions, the system has features indicating self-organized criticality.Comment: 4 pages, 5 figures, submitted to PR

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

Arrhythmia as a result of poor intercellular coupling in the sinus node: A simulation study

The effects of reduced intercellular coupling in the sinus node were investigated by means of simulations. Coupling was reduced both uniformly, and by introducing localized interaction blocks. In either case, model sinus node element networks typically splitted into frequency domains. These were defined as groups of neighbour elements which all attained the same mean firing frequency. In systems, simulating the vicinity of an impulse outlet to the atrium, the sinus node elements often splitted into two domains, one slowly firing just inside the outlet, and one normally firing large domain in the sinus node interior. This two-domain situation was analysed using a two-element system. Wenckebach conduction and advanced (m:1) exit blocks were seen, together with more odd block patterns and slow chaotic rhythms. The two-domain situation appeared also when two discrete outlets were considered. The slow domains around each outlet synchronized via the atrium. However, if there were some degree of exit block through one of the outlets only, brady-tachy like rhythms could be simulated due to a re-entrant circuit including both sinus node and atrial tissue. In conclusion, poor coupling in the sinus node seems to be sufficient to produce most arrhythmias in the sick sinus syndrome