Alternative Stable Scroll Waves and Conversion of Autowave Turbulence

TL;DR

This paper studies bistable scroll waves in the FitzHugh-Nagumo model, predicting their stability and transitions, and relates these findings to phenomena like ventricular fibrillation and tachycardia.

Contribution

It introduces a bistability analysis of scroll waves with distinct periods and predicts filament tension behavior using Response Functions, confirmed by simulations.

Findings

Slow-period scrolls exhibit negative filament tension and resemble delayed after-depolarisation.

Fast-period scrolls have positive filament tension and can stabilize or collapse.

Perturbations can convert vortex types, modeling transitions from fibrillation to tachycardia.

Abstract

Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh-Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods. Response Functions are used to predict the filament tension of the alternative scrolls and it is shown that the slow-period scroll has negative filament tension, while the filament tension of the fast-period scroll changes sign within a hysteresis loop. The predictions are confirmed by direct simulations. Further investigations show that the slow-period scrolls display features similar to delayed after-depolarisation (DAD) and tend to develop into turbulence similar to Ventricular Fibrillation (VF). Scrolls with positive filament tension collapse or stabilize, similar to monomorphic Ventricular Tachycardia (VT). Perturbations, such as boundary interaction or shock stimulus, can convert the vortex with negative filament tension into the vortex with positive filament tension. This may correspond to transition from VF to VT unrelated to pinning.