Line-defect patterns of unstable spiral waves in cardiac tissue

Spiral wave propagation in period-2 excitable media is 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 3 for a freely rotating spiral, with and without meander, but 1 for a spiral anchored around a fixed heterogeneity. We interpret this finding analytically 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.