Scale-invariant structures of spiral waves

Daniel Sohn, Konstantinos Aronis, Hiroshi Ashikaga

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Background: Spiral waves are considered to be one of the potential mechanisms that maintain 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. Method: 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 the finite-time Lyapunov exponent between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. Results: 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. Conclusions: Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.

Original languageEnglish (US)
Pages (from-to)291-298
Number of pages8
JournalComputers in Biology and Medicine
StatePublished - Jan 2019


  • Coherent structures
  • Fibrillation
  • Pattern formation
  • Renormalization
  • Spiral waves
  • information theory

ASJC Scopus subject areas

  • Computer Science Applications
  • Health Informatics


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