# Dynamical mechanism of atrial fibrillation: a topological approach

## TL;DR

This paper investigates the mechanisms sustaining atrial fibrillation using a topological approach, revealing a balance between wave coalescence and collapse, challenging the traditional view of wave breakup as the main factor.

## Contribution

It introduces a novel topological framework to explain atrial fibrillation maintenance, emphasizing wave coalescence and collapse over wave breakup.

## Key findings

- Spatiotemporal chaos maintained by wave coalescence and collapse.
- Wave breakup does not sustain atrial fibrillation.
- Topological processes explain the dynamics of wavelet number changes.

## Abstract

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead this complexity is maintained as a dynamical balance between wave coalescence -- a unique, previously unidentified, topological process that increases the number of wavelets -- and wave collapse -- a different topological process that decreases their number.