1 research outputs found
Scale-Invariant Structures of Spiral Waves
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.Comment: 13 pages, 4 figure