Strings, branes and twistons: topological analysis of phase defects in excitable media such as the heart

TL;DR

This paper introduces a topological framework for analyzing phase defects in 2D and 3D excitable media like the heart, revealing new structures such as branes and twistons that explain complex wave patterns.

Contribution

It extends the topological analysis of phase defects from 2D to 3D media, identifying new defect structures and mechanisms for complex pattern formation.

Findings

Identification of phase defect surfaces (branes) in 3D media

Discovery of twistons as crossing points of defect curves

Prediction of splitting and branching of defect surfaces

Abstract

Several excitable systems, such as the heart, self-organize into complex spatio-temporal patterns that involve wave collisions, wave breaks, and rotating vortices, of which the dynamics are incompletely understood. Recently, conduction block lines in two-dimensional media were recognized as phase defects, on which quasi-particles can be defined. These particles also form bound states, one of which corresponds to the classical phase singularity. Here, we relate the quasi-particles to the structure of the dynamical attractor in state space and extend the framework to three spatial dimensions. We reveal that 3D excitable media are governed by phase defect surfaces, i.e. branes, and three flavors of topologically preserved curves, i.e. strings: heads, tails, and pivot curves. We identify previously coined twistons as points of co-dimension three at the crossing of a head curve and a pivot curve. Our framework predicts splitting and branching phase defect surfaces that can connect multiple classical filaments, thereby proposing a new mechanism for the origin, perpetuation, and control of complex excitation patterns, including cardiac fibrillation.