Analysis of complex excitation patterns using Feynman-like diagrams.

Many extended chemical and biological systems self-organise into complex patterns that drive the medium behaviour in a non-linear fashion. An important class of such systems are excitable media, including neural and cardiac tissues. In extended excitable media, wave breaks can form rotating patterns and turbulence.

Scroll Waves and Filaments in Excitable Media of Higher Spatial Dimension.

Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic or electrical scroll waves in the heart. Here we show that such phenomena can be extended to a space of four or more dimensions and propose that connections of excitable elements in a network setting can be regarded as additional spatial dimensions.

Numerical methods for the detection of phase defect structures in excitable media.

Electrical waves that rotate in the heart organize dangerous cardiac arrhythmias. Finding the region around which such rotation occurs is one of the most important practical questions for arrhythmia management. For many years, the main method for finding such regions was so-called phase mapping, in which a continuous phase was assigned to points in the heart based on their excitation status and defining the rotation region as a point of phase singularity.

A Phase Defect Framework for the Analysis of Cardiac Arrhythmia Patterns.

During cardiac arrhythmias, dynamical patterns of electrical activation form and evolve, which are of interest to understand and cure heart rhythm disorders. The analysis of these patterns is commonly performed by calculating the local activation phase and searching for phase singularities (PSs), i.e.