Fractal basin boundaries in coupled map lattices

Critical phase transitions during ablation of atrial fibrillation

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia with significant morbidity and mortality. Pharmacological agents are not very effective in the management of AF. Therefore, ablation procedures have become the mainstay of AF management. The irregular and seemingly chaotic atrial activity in AF is caused by one or more meandering spiral waves. Previously, we have shown the presence of sudden rhythm organization during ablation of persistent AF. We hypothesize that the observed transitions from a disorganized to an organized rhythm is a critical phase transition. Here, we explore this hypothesis by simulating ablation in an anatomically-correct 3D AF model. In 722 out of 2160 simulated ablation, at least one sudden transition from AF to an organized rhythm (flutter) was noted (33%). They were marked by a sudden decrease in the cycle length entropy and increase in the mean cycle length. At the same time, the number of reentrant wavelets decreased from 2.99 ± 0.06 in AF to 1.76 ± 0.05 during flutter, and the correlation length scale increased from 13.3 ± 1.0 mm to 196.5 ± 86.6 mm (both P < 0.0001). These findings are consistent with the hypothesis that transitions from AF to an anatomical flutter behave as phase transitions in complex non-equilibrium dynamical systems with flutter acting as an absorbing state. Clinically, the facilitation of phase transition should be considered a novel mechanism of ablation and may help to design effective ablation strategies.

Spiral-wave dynamics depend sensitively on inhomogeneities in mathematical models of ventricular tissue

Every sixth death in industrialized countries occurs because of cardiac arrhythmias such as ventricular tachycardia (VT) and ventricular fibrillation (VF). There is growing consensus that VT is associated with an unbroken spiral wave of electrical activation on cardiac tissue but VF with broken waves, spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus spiral-wave activity in cardiac tissue has been studied extensively. Nevertheless, many aspects of such spiral dynamics remain elusive because of the intrinsically high-dimensional nature of the cardiac-dynamical system. In particular, the role of tissue heterogeneities in the stability of cardiac spiral waves is still being investigated. Experiments with conduction inhomogeneities in cardiac tissue yield a variety of results: some suggest that conduction inhomogeneities can eliminate VF partially or completely, leading to VT or quiescence, but others show that VF is unaffected by obstacles. We propose theoretically that this variety of results is a natural manifestation of a complex, fractal-like boundary that must separate the basins of the attractors associated, respectively, with spiral breakup and single spiral wave. We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy I models, where we show that the suppression of spiral breakup depends sensitively on the position, size, and nature of the inhomogeneity.