Research

Critical scale of propagation influences dynamics of waves in a model of excitable medium

Joseph M Starobin^1,2 , Christopher P Danford² , Vivek Varadarajan² , Andrei J Starobin² and Vladimir N Polotski²

¹  Department of Physics and Astronomy, University of North Carolina at Greensboro, Greensboro, NC, USA

²  Mediwave Star Technology, Inc, Greensboro, NC, USA

author email corresponding author email

Nonlinear Biomedical Physics 2009, 3:4doi:10.1186/1753-4631-3-4

Published:	9 July 2009

Abstract

Background

Duration and speed of propagation of the pulse are essential factors for stability of excitation waves. We explore the propagation of excitation waves resulting from periodic stimulation of an excitable cable to determine the minimal stable pulse duration in a rate-dependent modification of a Chernyak-Starobin-Cohen reaction-diffusion model.

Results

Various pacing rate dependent features of wave propagation were studied computationally and analytically. We demonstrated that the complexity of responses to stimulation and evolution of these responses from stable propagation to propagation block and alternans was determined by the proximity between the minimal level of the recovery variable and the critical excitation threshold for a stable solitary pulse.

Conclusion

These results suggest that critical propagation of excitation waves determines conditions for transition to unstable rhythms in a way similar to unstable cardiac rhythms. Established conditions were suitably accurate regardless of rate dependent features and the magnitude of the slopes of restitution curves.