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

Aaron Gobeyn1,2, Desmond Kabus1,3, Elena G Tolkacheva4

  • 1KU Leuven Campus Kortrijk (KULAK), Department of Mathematics, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium.

Chaos (Woodbury, N.Y.)
|December 2, 2025
PubMed
Summary

New algorithms identify "heads" and "tails" in excitation patterns, crucial for understanding conduction blocks in complex systems like cardiac tissue. This aids in automated analysis and classification of arrhythmias.

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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.