Scale-Invariant Structures of Spiral Waves

TL;DR

This study investigates the scale-invariant properties of spiral waves in cardiac tissue, revealing that certain information flow structures remain consistent across multiple spatial and temporal scales, despite overall changes.

Contribution

It introduces a novel multiscale analysis of spiral wave dynamics using renormalization and LCS, identifying scale-invariant information flow structures in cardiac arrhythmias.

Findings

Some LCS are preserved across scales

Scale-invariant structures are not obvious from voltage trajectories

Spiral wave dynamics exhibit multiscale invariance

Abstract

Spiral waves are considered to be one of the potential mechanisms that maintains complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales. We simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of finite-time Lyapunov exponent (FTLE) between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. Both the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice. Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.