Understanding sustained spiral chaos using non-chaotic solutions of a simple model of atrial excitation

Abstract

Coherent relaxation and contraction of the heart muscle is essential for efficiently pumping blood through the circulatory system. This coordinated behavior can be disrupted by the dynamics of the electrical waves controlling the contraction, leading to arrhythmic behaviors in which the efficiency of the pumping is drastically reduced. Atrial fibrillation – an example of sustained spiral chaos – is one such arrhythmia featuring multiple interacting spiral waves where the spatial and temporal coherence of the contracting cardiac tissue is lost. This regime is dominated by slow recurrent evolution intermittently punctuated by fast transitions between distinct multi-spiral configurations through the creation or annihilation of spiral cores. Both recurrent and transitional dynamics can be understood in terms of the constituent features of the state – the excitation waves themselves – through the persistence of local Euclidean symmetry. I discuss the computation of relative periodic orbits in a simple model of cardiac excitation dynamics, and the properties of these solutions, especially as relates to boundary interactions and fibrillation-like patterns.