ZEUS: Numerical methods to detect quasi-particles describing excitable media

Area of Science:

• Computational Biology
• Complex Systems Theory
• Cardiovascular Physiology

Background:

• Excitable media, such as cardiac tissue, are prone to conduction blocks causing arrhythmias.
• A topological theory identifies 'heads' and 'tails' as key points connecting wave fronts/backs to conduction blocks.
• These points are topologically preserved features within excitation patterns.

Purpose of the Study:

• To introduce robust algorithms for automatically localizing heads and tails in excitation patterns on triangle meshes.
• To provide methods for visualizing conduction blocks and their associated topological features.
• To enable automated analysis and classification of complex excitation phenomena.

Main Methods:

• Development of algorithms to detect heads and tails based on topological properties.
• Implementation of two variants depending on the co-dimension of the forbidden zone.
• Utilizing a bitwise OR operation on vertex states (ZEUS methods) for partitioning into forbidden (Z), excited (E), and unexcited (U) zones.

Main Results:

• Successful localization of heads and tails in simulated data and rabbit heart recordings of ventricular tachycardia.
• Visualization of conduction blocks as lines or extended regions.
• Comparison of ZEUS methods with classical phase singularity analysis.

Conclusions:

• The presented ZEUS methods offer robust, automated identification of topologically preserved points in excitation patterns.
• These algorithms enhance the analysis of conduction blocks in excitable media.
• The publicly available methods facilitate automated analysis and classification in various complex systems.