A topological hypothesis for atrial fibrilllation, atrial flutter and focal atrial tachycardia: comparison and contrast with Kosterlitz-Thouless physics.

While the role of topology is established in active matter systems, its importance in cardiac electrophysiology, particularly concerning common arrhythmias, warrants further emphasis. Atrial fibrillation (AF), atrial flutter (AFL), and focal atrial tachycardia (FAT) are the most prevalent arrhythmias impacting human health. This article proposes a framework conceptualizing these atrial rhythm disturbances through the lens of topological states and phase transitions, drawing inspiration from the Kosterlitz-Thouless (KT) transition. Central to this framework is the hypothesis that distinct arrhythmia patterns emerge as discrete topological states constrained by the fundamental requirement that the net topological charge (associated with electrical phase singularities or vortices) must sum to zero across the atrial tissue. Within this constrained topological perspective, AF, characterised by disorganised activity, is likened to the KT unbound vortex state, dominated by disorder with repetitive vortex regeneration and an exponential decay in spatial correlation. In contrast, AFL, with its organized regularity, resembles the KT bound vortex state, where vortex-antivortex pairs result in ordered activity. Finally, FAT and Sinus Rhythm are characterized as topologically vortex-free states exhibiting ordered planar wave conduction. Importantly, while the resulting topological states show clear analogies, the specific biophysical mechanisms driving vortex defect formation, interaction, and unbinding in cardiac tissue likely differ significantly from the thermal free-energy considerations governing the classic KT transition. This viewpoint frames the transition between arrhythmias as a change in the topological organization of atrial electrical activity, governed by charge conservation principles and cardiac-specific dynamics. This perspective may offer novel diagnostic and therapeutic avenues applicable to human cardiac mapping procedures.