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BACKGROUND: Atrial fibrillation (AF) and ventricular fibrillation (VF) episodes exhibit varying durations, with some spontaneously ending quickly while others persist. A quantitative framework to explain episode durations remains elusive. We hypothesized that observable self-terminating AF and VF episode lengths, whereby durations are known, would conform with a power law based on the ratio of system size and correlation length (L/ξ). METHODS: Using data from computer simulations (2-dimensional sheet and 3-dimensional left-atrial), human ischemic VF recordings (256-electrode sock, n=12 patients), and human AF recordings (64-electrode basket-catheter, n=9 patients; 16-electrode high definition-grid catheter, n=42 patients), conformance with a power law was assessed using the Akaike information criterion, Bayesian information criterion, coefficient of determination (R², significance=P<0.05) and maximum likelihood estimation. We analyzed fibrillatory episode durations and L/ξ, computed by taking the ratio between system size (L, chamber/simulation size) and correlation length (xi, estimated from pairwise correlation coefficients over electrode/node distance). RESULTS: In all computer models, the relationship between episode durations and L/ξ was conformant with a power law (Aliev-Panfilov R²: 0.90, P<0.001; Courtemanche R²: 0.91, P<0.001; Luo-Rudy R²: 0.61, P<0.001). Observable clinical AF/ VF durations were also conformant with a power law relationship (VF R²: 0.86, P<0.001; AF basket R²: 0.91, P<0.001; AF grid R²: 0.92, P<0.001). L/ξ also differentiated between self-terminating and sustained episodes of AF and VF (P<0.001; all systems), as well as paroxysmal versus persistent AF (P<0.001). In comparison, other electrogram metrics showed no statistically significant differences (dominant frequency, Shannon Entropy, mean voltage, peak-peak voltage; P>0.05). CONCLUSIONS: Observable fibrillation episode durations are conformant with a power law based on system size and correlation length. [ABSTRACT FROM AUTHOR]

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, M 1 (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 M 1 (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 p c . 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.

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions., (© 2023 Crown.)

The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with conservative system dynamics. Renewal theory has recently been suggested as a statistical formulation with governing equations to quantify the formation and destruction of wavelets and rotors in fibrillatory dynamics. In this perspective Review, we aim to explain the origin of the renewal theory paradigm in spatiotemporal chaos. The ergodic nature of pattern formation in spatiotemporal chaos is demonstrated through the use of three chaotic systems: two classical systems and a simulation of cardiac fibrillation. The logistic map and the baker's transformation are used to demonstrate how the apparently random appearance of patterns in classical chaotic systems has macroscopic parameters that are predictable in a statistical sense. We demonstrate that the renewal theory approach developed for cardiac fibrillation statistically predicts pattern formation in these classical chaotic systems. Renewal theory provides governing equations to describe the apparently random formation and destruction of wavelets and rotors in atrial fibrillation (AF) and ventricular fibrillation (VF). This statistical framework for fibrillatory dynamics provides a holistic understanding of observed rotor and wavelet dynamics and is of conceptual significance in informing the clinical and mechanistic research of the rotor and multiple-wavelet mechanisms of AF and VF.