Model study of transitions in cardiac reentry dynamics following a two-stimulations protocol

Reentry was induced in a 1-dimensional ring model of cardiac myocytes using a modified Beeler-Reuter representation. In this setting, reentry, with one activation front, traveling around the ring, is periodic when the length (L) of the ring is longer than a critical value L_crit, and quasiperiodic for L_crit>L≥L_min, the minimal length with sustained reentry. When L>2L_min, sustained reentries with two activation fronts traveling simultaneously around the ring also exist. These are quasiperiodic if 2L_crit>L>2L_min, and periodic if L>2L_crit. We have studied the conditions under which a pair of coupled stimuli can induce either a resetting or an annihilation of the one-front reentry, or a transition from one-front to two-fronts reentry. We show how the outcome of the stimulations depends on the relative timing of the pulses and on the length of the circuit by providing a global description of the dynamics as a function of these parameters. We also show that it can be understood by the interaction of the dynamics of repolarisation and of the speed of propagation, since a simplified integral delay model based on these properties reproduces the behavior of the ionic model.