Analysis of electrically induced reentrant circuits in a sheet of myocardium

Understanding the complex spatiotemporal dynamics of action potential propagation in the heart during arrhythmia is exceedingly difficult. This study applies nonlinear dynamics tools to simplify this task. Using the results of a simulation of an electrical induction of reentry in a sheet of myocardium represented as a bidomain, transmembrane voltage maps are processed to obtain: (i) spatial maps of phase angle and phase singularity trajectories, (ii) state scatter plots, and (iii) spatial maps of even phase resetting, wave fronts and wave tails. Tracking the phase singularities allows us to identify the "seeds" of reentry before the reentrant circuit is formed and to characterize the spatiotemporal evolution of the organizing center of the reentrant circuit. The state scatter plots demonstrate the effect of the shock on the instantaneous state of the system. The spatial maps of even phase resetting allow us to identify the shock-induced excitable gaps (regions of regenerative repolarization) as well as the regions directly activated by the shock. These nontraditional approaches to the analysis of electrophysiological phenomena greatly enhance our ability to conceptualize the dynamics of arrhythmias.