# Patterns of spiral wave attenuation by low-frequency periodic planar fronts

Journal Article

Download PDF**Published:**Friday, March 30, 2007

**Citation:**Chaos, Volume 17, Pages 015109

**Authors (1 total):** P. C. Ivanov

**Abstract:** There is evidence that spiral waves and their breakup underlie mechanisms related to a wide spectrum of phenomena ranging from spatially extended chemical reactions to fatal cardiac arrhythmias [A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, Year: 2001);J. Schutze, O. Steinbock, and S. C. Muller, Nature356, 45 (Year: 1992);S. Sawai, P. A. Thomason, and E. C. Cox, Nature433, 323 (Year: 2005);L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, Year: 1988);R. A. Gray et al. , Science270, 1222 (Year: 1995);F. X. Witkowski et al. , Nature392, 78 (Year: 1998)]. Once initiated, spiral waves cannot be suppressed by periodic planar fronts, since the domains of the spiral waves grow at the expense of the fronts [A. N. Zaikin and A. M. Zhabotinsky, Nature225, 535 (Year: 1970);A. T. Stamp, G. V. Osipov, and J. J. Collins, Chaos12, 931 (Year: 2002);I. Aranson, H. Levine, and L. Tsimring, Phys. Rev. Lett.76, 1170 (Year: 1996);K. J. Lee, Phys. Rev. Lett.79, 2907 (Year: 1997);F. Xie, Z. Qu, J. N. Weiss, and A. Garfinkel, Phys. Rev. E59, 2203 (Year: 1999)]. Here, we show that introducing periodic planar waves with long excitation duration and a period longer than the rotational period of the spiral can lead to spiral attenuation. The attenuation is not due to spiral drift and occurs periodically over cycles of several fronts, forming a variety of complex spatiotemporal patterns, which fall into two distinct general classes. Further, we find that these attenuation patterns only occur at specific phases of the descending fronts relative to the rotational phase of the spiral. We demonstrate these dynamics of phase-dependent spiral attenuation by performing numerical simulations of wave propagation in the excitable medium of myocardial cells. The effect of phase-dependent spiral attenuation we observe can lead to a general approach to spiral control in physical and biological systems with relevance for medical applications.