Jacobian-determinant vector method of identifying filaments in a three-dimensional medium

Area of Science:

• * Computational physics
• * Biophysics
• * Mathematical modeling

Background:

• * Scroll waves in 3D excitable media feature singular filaments, acting as topological defects.
• * Accurate filament localization is crucial for studying dynamics and understanding cardiac arrhythmias.
• * Existing methods face challenges in complex or noisy environments.

Purpose of the Study:

• * To introduce a novel Jacobian-determinant vector method for precise scroll wave filament identification.
• * To validate the method's performance against existing techniques.
• * To provide a robust tool for analyzing scroll wave dynamics.

Main Methods:

• * Development of a Jacobian-determinant vector field based on topological current theory.
• * Defining a vector field where magnitude indicates filament presence and direction indicates orientation.
• * Validation using the Aliev-Panfilov model with complex filament configurations (Hopf links, trefoil knots).

Main Results:

• * The Jacobian-determinant vector method accurately identifies filament locations.
• * Demonstrated superior performance compared to convolution-based and zero-normal-velocity methods.
• * Showed enhanced robustness in noisy and slightly fibrotic simulated cardiac tissue.

Conclusions:

• * The Jacobian-determinant vector method offers a significant advancement in scroll wave filament localization.
• * This technique is valuable for theoretical studies and practical applications, including cardiac electrophysiology.
• * Provides a reliable tool for investigating complex 3D scroll wave dynamics.