Non-uniform dispersion of the source-sink relationship alters wavefront curvature

The distribution of cellular source-sink relationships plays an important role in cardiac propagation. It can lead to conduction slowing and block as well as wave fractionation. It is of great interest to unravel the mechanisms underlying evolution in wavefront geometry. Our goal is to investigate the role of the source-sink relationship on wavefront geometry using computer simulations. We analyzed the role of variability in the microscopic source-sink relationship in driving changes in wavefront geometry. The electrophysiological activity of a homogeneous isotropic tissue was simulated using the ten Tusscher and Panfilov 2006 action potential model and the source-sink relationship was characterized using an improved version of the Romero et al. safety factor formulation (SFm2). Our simulations reveal that non-uniform dispersion of the cellular source-sink relationship (dispersion along the wavefront) leads to alterations in curvature. To better understand the role of the source-sink relationship in the process of wave formation, the electrophysiological activity at the initiation of excitation waves in a 1D strand was examined and the source-sink relationship was characterized using the two recently updated safety factor formulations: the SFm2 and the Boyle-Vigmond (SFVB) definitions. The electrophysiological activity at the initiation of excitation waves was intimately related to the SFm2 profiles, while the SFVB led to several counterintuitive observations. Importantly, with the SFm2 characterization, a critical source-sink relationship for initiation of excitation waves was identified, which was independent of the size of the electrode of excitation, membrane excitability, or tissue conductivity. In conclusion, our work suggests that non-uniform dispersion of the source-sink relationship alters wavefront curvature and a critical source-sink relationship profile separates wave expansion from collapse. Our study reinforces the idea that the safety factor represents a powerful tool to study the mechanisms of cardiac propagation in silico, providing a better understanding of cardiac arrhythmias and their therapy.