Line-Defect Patterns of Unstable Spiral Waves in Cardiac Tissue

TL;DR

This study investigates line-defects in spiral waves within cardiac tissue, revealing how their number varies with spiral anchoring and providing an analytical framework to understand their behavior and dynamics.

Contribution

It introduces a theoretical model explaining the quantization of line-defects in spiral waves and characterizes their slow inward rotation in different regimes.

Findings

Number of line-defects is three for freely rotating spirals.

Number of line-defects is one for anchored spirals.

Analytical model based on Helmholtz equation explains defect quantization.

Abstract

Spiral wave propagation in period-2 excitable media is often accompanied by line-defects, the locus of points with period-1 oscillations. Here we investigate spiral line-defects in cardiac tissue where period-2 behavior has a known arrhythmogenic role. We find that the number of line defects, which is constrained to be an odd integer, is three for a freely rotating spiral, with and without meander, but one for a spiral anchored around a fixed heterogeneity. We interpret analytically this finding using a simple theory where spiral wave unstable modes with different numbers of line-defects correspond to quantized solutions of a Helmholtz equation. Furthermore, the slow inward rotation of spiral line-defects is described in different regimes.