Mechanism of defibrillation of cardiac tissue by periodic low-energy pacing

Rotating excitation waves and electrical turbulence in excitable cardiac tissue are associated with arrhythmias such as life-threatening ventricular fibrillation. Experimental studies (S. Luther et al., Nature 475, 235-239 (2011)). have shown that a time-periodic sequence of low-energy electrical far-field pulses is able to terminate fibrillation more gently than a single high-energy pulse. During this so called low-energy antifibrillation pacing (LEAP), only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. Based on extensive simulations and simple theoretical reasoning, we present a comprehensive unified mechanism for successful LEAP in two spatial dimensional systems, which is able to explain both the termination of stable spirals and of spatiotemporal chaos. We carried out extensive simulations (more than 500000 runs for each considered model) varying pacing periods, pacing field strength and initial conditions using a model of cardiac tissue perforated by blood vessels, which was found earlier to reproduce the behavior seen in the LEAP experiments for different dynamical regimes and different cellular models (P. Buran et al., Chaos 27, 113110 (2017) and New J. Phys. 24 083024 (2022)). We studied altogether three different cellular models to capture qualitatively different kinds of fibrillatory states like stable spirals and spatiotemporal chaos. To achieve a mechanistic understanding of the simulation results, we have investigated a variety of macroscopic observables characterizing an excitable medium with respect to their correlation with the success of an individual low-energy pulse during LEAP. We found in all considered cases that the refractory boundary length LRB, the total length of the borders between refractory and excitable parts of the tissue, displays the strongest correlation with the success of the pacing and thus predicts best the success of an individual LEAP pulse. Furthermore, we found the success probability PL decays exponentially with this length according to PL = exp(- k(E)LRB), where E is the strength of the electrical field in pacing and k(E) is a monotonically decreasing function of E. A closer look at the spatiotemporal dynamics in the simulations reveals that actually each pulse during LEAP annihilates practically all defects and excitation fronts, however, also induces new pairs of defects and associated excitation fronts at the refractory boundaries. The success probability of each individual pulse can thus be simply interpreted as the probability that no new rotor pair gets created by the shock, while all existing defects get annihilated. This assumption allows to derive the observed exponential dependence of the success probability on the refractory boundary length, where the prefactor k(E) in the exponent is equal (for stable spirals) or proportional (for spatiotemporal chaos) to the probability{lambda} (E) that a new rotor pairs is created by the shock along a segment of unit length along the refractory boundary. Our findings are in conformity with the upper limit of vulnerability (ULV) hypothesis, which states that the single pulse defibrillation threshold is simply given by the lowest field strength, where no new rotor pairs arise as a result of the shock. LEAP operates at field strengths (and energies) below this ULV limit. Successful LEAP protocols are characterized by a coordinated interplay between the pulses, that gradually decreases the refractory boundary length and therefore simultaneously increases the success probability until complete defibrillation is achieved.