Three dimensional reconstruction of organizing centers in excitable chemical media

Abstract Excitable media support nonlinear waves that propagate as pulses, e.g. the action potential in nerve fibers and heart muscle, and concentration waves in autocatalytic chemical reactions. In two and three dimensions, these waves may self-organize into persistent vortex-like patterns of activity, described in terms of a singularity point (in 2D) or line (in 3D). Experimental studies have been limited by the absence of a direct method to observe the dynamics of the singularity. Here we present a method of singularity localization based on a time-space plot analysis, and apply it to filament dynamics in a 3D Belousov-Zhabotinsky (BZ) reaction. For the first time, the phenomenon of shrinking of a 3D non-planar filament is observed directly.

[1]  A. M. Pertsov,et al.  Autowave Approaches to Cessation of Reentrant Arrhythmias , 1990, Annals of the New York Academy of Sciences.

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

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

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

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

[6]  W. Baxter,et al.  Stationary and drifting spiral waves of excitation in isolated cardiac muscle , 1992, Nature.

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

[8]  R. Aliev,et al.  Three-dimensional twisted vortices in an excitable chemical medium , 1990, Nature.

[9]  W. Jahnke,et al.  Chemical vortex dynamics in three-dimensional excitable media , 1988, Nature.

[10]  E. A. Ermakova,et al.  On the interaction of vortices in two-dimensional active media , 1989 .

[11]  Steven H. Strogatz,et al.  Organizing centres for three-dimensional chemical waves , 1984, Nature.

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

[13]  Front geometries of chemical waves under anisotropic conditions , 1991 .

[14]  B. Hess,et al.  Isotropic cellular automaton for modelling excitable media , 1990, Nature.

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

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

[17]  A. Winfree.  Electrical instability in cardiac muscle: phase singularities and rotors. , 1989, Journal of theoretical biology.

[18]  M. Menzinger,et al.  Measurement of the velocity of chemical waves by magnetic resonance imaging , 1992 .

[19]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

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

[21]  V. Krinsky.  Self-Organization Autowaves and Structures Far from Equilibrium , 1984 .

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

[23]  M. Menzinger,et al.  Detection of Chemical Waves by Magnetic Resonance Imaging , 1990 .

[24]  B. Hess,et al.  The Structure of the Core of the Spiral Wave in the Belousov-Zhabotinskii Reaction , 1985, Science.

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

[26]  E. Ding,et al.  Winding numbers for the supercritical sine circle map , 1988 .

[27]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

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