Abstract
We study theoretical and numerical propagation of autowave fronts in excitable two-variable (activator-inhibitor) systems with anisotropic diffusion. A general curvature-velocity relation is derived for the case that the inhibitor diffusion is neglected. This relation predicts the break of an activation front when the front curvature exceeds a critical value, which is corroborated by computer simulations of a particular reaction-diffusion model. Some qualitative effects associated with the inhibitor diffusion are studied numerically. It is found that the critical value of curvature decreases with an increase in the inhibitor diffusion coefficient. The core of a spiral wave increases in size and turns through an angle which depends on the inhibitor diffusion coefficient. PACS Numbers: 05.50. +q, 05.70. Ln., 82.40. -g, 87.10. +e
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Glass, L., et al.: Theory of heart, Springer, New York, 1991.
Winfree, A.T.: On measuring curvature and electrical diffusion coefficients in anisotropic myocardium, IEEE Trans. Biomed. Eng. 43 (1996), 1200–1203.
Zykov, V.S.: Simulation of wave processes in excitable media, Manchester Univ. Press, Manchester, 1987.
Davydov, V.A., Zykov, V.S. and Mikhailov, A.S.: Kinematics of autowave patterns in excitable media, Usp. Fiz. Nauk 161 (1991), 45–85.
Davydov, V.A. and Morozov, V.G.: Galilean transformations and the evolution of autowave fronts in external fields, Usp. Fiz. Nauk 166 (1996), 327–333.
Wellner, M., Pertsov, A.M. and Jalife, J.: Spatial Doppler anomaly in an excitable medium, Phys. Rev. E 54 (1996), 1120–1126.
Gómez-Gesteira, M., Mosquera, J., Davydov, V.A, Pérez-Muñuzuri, V., Muñuzuri, A.P., Morozov, V.G. and Pérez-Villar, V.: Link between the effect of an electric field on wave propagation and the curvature-velocity relation, Phys. Lett. A 231 (1997), 389–394.
Davydov, V.A. and Zykov, V.S.: Spiral waves in anisotropic excitable media, Zh. Eksp. Teor. Fiz. 95 (1989), 139–148.
Zykov, V.S.: Analytical estimation of dependence of excitation wave velocity in two-dimensional excitable medium on curvature of its front, Biofizika 25 (1980), 888–892.
Mikhailov, A.S., Davydov, V.A. and Zykov, V.S.: Complex dynamics of spiral waves and motion of curves, Physica D 70 (1994), 1–39.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Morozov, V., Davydov, N. & Davydov, V. Propagation of Curved Activation Fronts in Anisotropic Excitable Media. Journal of Biological Physics 25, 87–100 (1999). https://doi.org/10.1023/A:1005131729982
Issue Date:
DOI: https://doi.org/10.1023/A:1005131729982