Percolation theory as a conceptual framework to explain spontaneous atrial fibrillation termination: a pilot study

Atrial fibrillation (AF) strikingly possesses the ability to abruptly transition into more organized electrical activity and spontaneously terminate, even after persisting for long periods. Despite being central to the clinical behavior and treatment of AF, these phenomena remain incompletely understood. In this paper, we hypothesized that the spontaneous termination of AF may represent a type of percolation phase transition, which is more likely to occur when a domain spanning cluster of refractory sites in the atrium are connected (called a 'percolation cluster'). This was assessed in n=50 computational simulations of AF developed using the Aliev-Panfilov (APV) 2-dimensional cell model. In self-terminating simulations of AF, it was found that the average refractory cluster size, χ(p) (median: 647.7), and the largest refractory cluster size, M1 (median: 1702.3), abruptly increased just prior to AF spontaneously terminating, indicating the onset of the formation of a domain spanning percolation cluster. In contrast, simulations of sustained AF did not demonstrate an increase in χ(p) (median: 463.0) and M1 (median: 1448.2). Self-terminating AF simulations also demonstrated hallmark properties characteristic of a percolation phase transition, such as an abrupt increase in χ(p) at the critical occupation probability pc. The cluster size distribution was also shown to obey a power law for various occupation probabilities p, also indicative of a percolation phase transition. Collectively, these properties suggests that the spontaneous termination of AF could be a form of percolation phase transition, which could provide new insights for AF treatment.