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

TL;DR

This paper demonstrates how dynamic mode decomposition (DMD) can effectively detect and analyze spiral wave tip trajectories in excitable media, outperforming traditional methods especially under noise and heterogeneity, and can also predict wave evolution.

Contribution

It introduces a data-driven spectral decomposition method, DMD, for robust spiral tip tracking and prediction in complex excitable media, improving over existing techniques.

Findings

DMD-based tip tracking outperforms isopotential-intersection method in noisy and heterogeneous media.

DMD is more robust to external noise than traditional methods.

DMD can reconstruct and predict spiral wave dynamics effectively.

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 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 method called the isopotential-intersection method (IIM) in the cases (1)-(3): (1) Both IIM and DMDTT capture TT patterns at small values of the image-sampling interval $\tau$; however, IIM is more sensitive than DMDTT to the changes in $\tau$. (2) In a heterogeneous medium, IIM yields TT patterns, but with a background of scattered noisy points, which is suppresed in DMDTT. (3) DMDTT is more robust to external noise than IIM. We show, finally, that DMD can be used to reconstruct, and hence predict, the spatiotemporal evolution of spiral waves in the models we study.