Filament Tension and Phase Locking of Meandering Scroll Waves

Abstract

Meandering spiral waves are often observed in excitable media such as the Belousov-Zhabotinsky reaction and cardiac tissue. We derive a theory for drift dynamics of meandering rotors in general reaction-diffusion systems and apply it to two types of external disturbances: an external field and curvature-induced drift in three dimensions. We find two distinct regimes: with small filament curvature, meandering scroll waves exhibit filament tension, whose sign determines the stability and drift direction. In the regimes of strong external fields or meandering motion close to resonance, however, phase locking of the meander pattern is predicted and observed.

Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves

“…In several previous works, a moving frame was chosen in which the solution was either stationary [18,32,34,61,65] or periodic [16]. This comes down to expressing the derivative in Eq.…”

“…We mainly follow the derivation for rigidly rotating spiral waves [36] but extend it to the case of meander. In comparison to [16], we offer more flexibility in the frame of reference, such that also meandering spirals close to resonance can be treated.…”

A quantitative theory for phase-locking of meandering spiral waves in a rotating external field

“…The underlying reasoning is the following. The meandering spiral in Barkley's model undergoes biperiodic motion and therefore has two phases: rotation phase Φ, which governs the spatial orientation of the spiral and temporal phase Ψ, describing the periodic deformation of the wave in a co-moving frame [45]. Now, suppose that under the applied field only one of the phases is locked.…”

“…However, such previous theoretical works using RFs are only limited to rigidly rotating spiral waves rather than meandering spiral waves [40][41][42]. Only very recently, the RF approach was extended such that it is accessible to the case of meandering spiral waves [44,45]. For instance, a drift law of meandering spiral waves was derived and applied to different external perturbations [45].…”

“…Only very recently, the RF approach was extended such that it is accessible to the case of meandering spiral waves [44,45]. For instance, a drift law of meandering spiral waves was derived and applied to different external perturbations [45]. Note, however, that for the present application, we will use RFs of a circular-core spiral only.…”