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Time resolution for wavefront and phase singularity tracking using activation maps in cardiac propagation models.

Samuel Gagné¹, Vincent Jacquemet¹

¹Institut de Génie Biomédical, Département de Pharmacologie et Physiologie, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, Quebec H3C 3J7, Canada.

Chaos (Woodbury, N.Y.)

|April 3, 2020

Summary

Accurate tracking of cardiac phase singularities (PSs) is crucial for understanding fibrillation dynamics. This study introduces a novel mathematical method using the Hungarian algorithm for precise PS tracking, improving accuracy in complex cardiac tissue models.

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Area of Science:

Computational Biology
Cardiac Electrophysiology
Mathematical Modeling

Background:

Cardiac fibrillation dynamics are characterized by phase singularities (PSs).
Accurate tracking of PSs is challenging in heterogeneous cardiac tissues with fibrosis and anisotropy.
Existing methods struggle with complex spatio-temporal dynamics.

Purpose of the Study:

To develop a robust mathematical formulation for tracking phase singularities (PSs) in two-dimensional reaction-diffusion models of cardiac fibrillation.
To improve the accuracy and reliability of PS tracking in complex cardiac substrates.

Main Methods:

Developed a novel PS tracking method based on activation maps at full spatiotemporal resolution.
Formulated PS tracking as a linear assignment problem solved using the Hungarian algorithm.

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Last Updated: Dec 25, 2025

Multiparametric Optical Mapping of the Langendorff-perfused Rabbit Heart

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Incorporated distances, chirality, and wavefront information into the cost matrix for tracking.

Main Results:

The method successfully tracks wavefronts and PSs simultaneously.
Graph-based analysis of PS trajectories simplifies descriptions at longer time scales.
Improved time resolution (0.1 ms) significantly reduced tracking error rates by an order of magnitude.
Identified macroscopically stable rotors despite wavefront fragmentation by fibrosis.

Conclusions:

The developed mathematical formulation provides accurate and robust phase singularity tracking in complex cardiac models.
The graph-based analysis aids in understanding fibrillation dynamics and identifying stable rotors.
Enhanced temporal resolution is critical for minimizing tracking errors in simulating cardiac fibrillation.