Figure 1.

Power law scaling in atrial fibrillation (AF) and ventricular fibrillation (VF) termination. A, Depicts a power law relationship associated with the average lifetime of transient disorder (chaos). The power law exhibits scale-invariance, revealing that alterations in 1 quantity produces proportional changes in another across multiple scales. This suggests that the same simple principles govern behavior across a wide range of scales and is what makes power laws applicable to diverse phenomena (a property known as universality). B, Outlines the hypothesis motivating this study, which reasons that there should be a power law scaling relationship between the number of independent regions (given by $\mathrm{L}/\mathrm{\xi }$) and time until termination ($\mathrm{\tau }\left(\mathrm{L}\right)$) in episodes of spontaneously terminating AF and VF. C, Provides a numerical example demonstrating why a greater number of independent regions ($\mathrm{L}/\mathrm{\xi }$) associates with longer lasting transient disorder, where P represents the probability of an independent region collapsing (here equal to 0.1). In the context of AF and VF, this can be related to electrical dynamics in the heart. More organized electrical activity (left) is associated with larger islands of coordinated activity, leading to a fewer number of independent regions. This is thus reasoned to associate with shorter durations of spatiotemporal disorder, hence shorter AF/VF episodes. The converse is true for less-organized electrical activity (right).