Observable Atrial and Ventricular Fibrillation Episode Durations Are Conformant With a Power Law Based on System Size and Spatial Synchronization

Abstract

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 (R 2 , 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 R 2 : 0.90, P <0.001; Courtemanche R 2 : 0.91, P <0.001; Luo-Rudy R 2 : 0.61, P <0.001). Observable clinical AF/VF durations were also conformant with a power law relationship (VF R 2 : 0.86, P <0.001; AF basket R 2 : 0.91, P <0.001; AF grid R 2 : 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.