Spiral-wave dynamics in excitable media: Insights from dynamic mode decomposition

Abstract

Spiral waves are ubiquitous spatiotemporal patterns that occur in various excitable systems. In cardiac tissue, the formation of these spiral waves is associated with life-threatening arrhythmias, and, therefore, it is important to study the dynamics of these waves. Tracking the trajectory of a spiral-wave tip can reveal important dynamical features of a spiral wave, such as its periodicity, and its vulnerability to instabilities. We show how to employ the data-driven spectral-decomposition method, called dynamic mode decomposition (DMD), to detect the profile a spiral tip trajectory (TT) in three settings: (1) a homogeneous medium; (2) a heterogeneous medium; and (3) with external noise. We demonstrate that the performance of DMD-based TT (DMDTT) is either comparable to or better than the conventional tip-tracking methods, such as the isopotential-intersection method (IIM) and the integral method, in the cases (1)-(3): (1) Both IIM and DMDTT capture TT patterns at small values of the image-sampling interval τ; however, IIM is more sensitive than DMDTT to the changes in τ. (2) In a heterogeneous medium, IIM yields TT patterns, but with a background of scattered noisy points, which are suppressed in DMDTT. (3) DMDTT is more robust to external noise than IIM and is comparable in performance to the integral method. We also show that the DMDTT can detect non-trivial dynamics of spiral waves, such as their drift and the meandering; we show that DMDTT is comparable with the integral method in these cases and outperforms it if there is external noise. We show, finally, that DMD can be used to reconstruct, and hence predict, the spatiotemporal evolution of spiral waves in the models we study.