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Spiral drift and core properties.

M Wellner¹, A M Pertsov, J Jalife

¹Department of Pharmacology, SUNY Health Science Center at Syracuse, Syracuse, New York 13210, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|April 24, 2002

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This study explains the drift of rotating spiral waves in a FitzHugh-Nagumo medium. A new semi-empirical solution accurately predicts drift using spiral rotation period and fast variable values.

Area of Science:

Computational neuroscience
Theoretical biophysics
Nonlinear dynamics

Background:

Spiral waves are crucial in biological systems, but their drift complicates modeling.
Understanding drift mechanisms in reaction-diffusion systems like FitzHugh-Nagumo is essential.

Purpose of the Study:

To mathematically model and predict the drift of stable, nonmeandering rotating spiral waves.
To establish a semi-empirical solution for spiral wave drift prediction.

Main Methods:

Analysis of a singly diffusive FitzHugh-Nagumo medium with generic reaction functions.
Perturbation theory to first order for weak diffusivity gradients or convection.
Numerical simulations to generate reference data for drift theories.

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Main Results:

Mathematical equivalence established between diffusivity gradients and convective perturbations.
Numerical examples provided for validating drift theories.
A semi-empirical solution proposed, requiring only spiral period and fast variable center value.

Conclusions:

The proposed semi-empirical solution shows good agreement with numerical simulations for moderately sparse spirals.
This work offers a practical method for predicting spiral wave drift in biological and physical systems.