Unstable Spiral Waves and Local Euclidean Symmetry in a Model of Cardiac Tissue

Abstract

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.

17 pages, 14 figures

References in corpus (4)

• Exact Coherent Structures and Chaotic Dynamics in a Model of Cardiac Tissue
• Non-specular reflections in a macroscopic system with wave-particle duality: spiral waves in bounded media
• Asymptotic dynamics of reflecting spiral waves
• Damping filter method for obtaining spatially localized solutions

Cited by in corpus (7)

• Dynamical mechanism of atrial fibrillation: a topological approach
• Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation
• Exact Coherent Structures and Chaotic Dynamics in a Model of Cardiac Tissue
• Exact Coherent Structures in Fully Developed Two-Dimensional Turbulence
• A response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves
• Filament tension and phase-locked drift of meandering scroll waves
• Memory effects, transient growth, and wave breakup in a model of paced atrium