Stationary pulses and wave front formation in an excitable medium

T. Bountis, C. F. Starmer, A. Bezerianos

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In an excitable medium, the method of phase plane analysis of ODE reductions is often used to separate suprathreshold disturbances that collapse from disturbances that expand and result in a propagating front. Following this approach, we study here pulse formation in 1-Dimensional (1-D) and 2-D media and derive closed form (1-D) and approximate (2-D) expressions for a critical pulse structure, which is stationary but unstable. This critical structure, called a stationary pulse, can be modulated by altering (e.g. adding a constant to) the reaction portion of the reaction-diffusion equation, suggesting a mechanism for extinguishing the initial expanding phase of front formation or for steering a front. We have also studied analytically and numerically the onset of "recovery", leading from a single wavefront to an ordinary action potential wave. Possible applications of these ideas to the development of practical strategies for controlling cardiac arrhythmia are discussed.

Original languageEnglish
Pages (from-to)12-33
Number of pages22
JournalProgress of Theoretical Physics Supplement
Issue number139
DOIs
Publication statusPublished - 2000

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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