A cellular automation model of excitable media: IV. untwisted scroll rings

Abstract We study the motion of untwisted circular scroll rings in an excitable medium modeled by a cellular automation that includes the effects of curvature and dispersion on wave propagation. We find that scroll rings either shrink or expand, with a velocity that is a function of the curvature of the ring, and they drift along their axis of symmetry.

[1]  J. Tyson,et al.  A cellular automation model of excitable media including curvature and dispersion. , 1990, Science.

[2]  A. Winfree,et al.  Scroll-Shaped Waves of Chemical Activity in Three Dimensions , 1973, Science.

[3]  A. T. Winfree,et al.  Stable Particle-Like Solutions to the Nonlinear Wave Equations of Three-Dimensional Excitable Media , 1990, SIAM Rev..

[4]  J. Tyson,et al.  A cellular automaton model of excitable media. II: curvature, dispersion, rotating waves and meandering waves , 1990 .

[5]  Arthur T. Winfree,et al.  Helical organizing centers in excitable media , 1990 .

[6]  Marc Courtemanche,et al.  Stable three-dimensional action potential circulation in the FitzHugh-Nagumo model , 1990 .

[7]  Twisted scroll waves in active three-dimensional media , 1985 .

[8]  A ROSENBLUETH,et al.  The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. , 1946, Archivos del Instituto de Cardiologia de Mexico.

[9]  A. Pertsov,et al.  [Vortex ring in a 3-dimensional active medium described by reaction-diffusion equations]. , 1984, Doklady Akademii nauk SSSR.

[10]  J. Keener,et al.  Helical and circular scroll wave filaments , 1990 .

[11]  Wolfgang Jahnke,et al.  Three-dimensional scroll ring dynamics in the Belousov-Zhabotinskii reagent and in the two-variable Oregonator model , 1989 .

[12]  Brian J. Welsh,et al.  Three-dimensional chemical waves in the Belousov–Zhabotinskii reaction , 1983, Nature.

[13]  James P. Keener,et al.  The dynamics of three-dimensional scroll waves in excitable media , 1988 .

[14]  J. Keener,et al.  The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent , 1988, Science.

[15]  A. Winfree,et al.  Dynamical stability of untwisted scroll rings in excitable media , 1989 .

[16]  A. Winfree.  When time breaks down , 1987 .

[17]  Arthur T. Winfree,et al.  Rotating Chemical Reactions , 1974 .

[18]  J. Keener.  Knotted scroll wave filaments in excitable media , 1989 .

[19]  W. Rheinboldt,et al.  A COMPUTER MODEL OF ATRIAL FIBRILLATION. , 1964, American heart journal.

[20]  A. Winfree.  Two kinds of wave in an oscillating chemical solution , 1974 .

[21]  R. Cohen,et al.  Simple finite-element model accounts for wide range of cardiac dysrhythmias. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[22]  A. V. Panfilopv.  Two regimes of the scroll ring drift in the three-dimensional active media , 1987 .

[23]  An integral invariant for scroll rings in a reaction-diffusion system , 1989 .

[24]  Alexander V. Panfilov,et al.  Dynamical simulations of twisted scroll rings in three-dimensional excitable media , 1985 .

[25]  A. Winfree.  The geometry of biological time , 1991 .

[26]  Ding Da-fu.  A plausible mechanism for the motion of untwisted scroll rings in excitable media , 1988 .

[27]  S. Hastings,et al.  Spatial Patterns for Discrete Models of Diffusion in Excitable Media , 1978 .

[28]  J. Tyson,et al.  A cellular automaton model of excitable media. III: fitting the Belousov-Zhabotinskiic reaction , 1990 .

[29]  Arthur T. Winfree,et al.  A computational study of twisted linked scroll waves in excitable media , 1987 .

[30]  Alexander V. Panfilov,et al.  Turbulent rings in 3-dimensional active media with diffusion by 2 components , 1986 .

[31]  E. Winfree,et al.  Organizing centers in a cellular excitable medium , 1985 .