Vortices with linear cores in excitable media

Most naturally occurring excitable media exhibit vortex waves with circular cores. It has been reported that the spiral wave activity in cardiac muscle may revolve around longitudinal or elliptical cores. Here we demonstrate that spiral wave vortices with cores resembling a long line may result from decreasing a small parameter which affects the recovery time in an isotropic and homogeneous excitable reaction-diffusion model. The model results compare well with experimental data in cardiac muscle.

[1]  O. Selfridge,et al.  Studies on flutter and fibrillation; some notes on the theory of flutter. , 1948, Archivos del Instituto de Cardiologia de Mexico.

[2]  W. Skaggs,et al.  Chemical vortex dynamics in the Belousov-Zhabotinskii reaction and in the two-variable oregonator model , 1989 .

[3]  José Jalife.  Mathematical approaches to cardiac arrhythmias. , 1990, Annals of the New York Academy of Sciences.

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

[5]  J. Keener.  A geometrical theory for spiral waves in excitable media , 1986 .

[6]  V. I. Krinsky,et al.  Multi-armed vortices in an active chemical medium , 1982, Nature.

[7]  J. Sommer,et al.  Geometry of cell and bundle appositions in cardiac muscle: light microscopy. , 1985, American Journal of Physiology.

[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]  James E. Lough,et al.  NEW YORK ACADEMY OF SCIENCE. , 1903, Science.

[10]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[11]  T. Cochrane,et al.  When Time Breaks Down : The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias , 1987 .

[12]  Tuckerman,et al.  Spiral-wave dynamics in a simple model of excitable media: The transition from simple to compound rotation. , 1990, Physical review. A, Atomic, molecular, and optical physics.

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

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

[15]  D. Geselowitz,et al.  The Discontinuous Nature of Propagation in Normal Canine Cardiac Muscle: Evidence for Recurrent Discontinuities of Intracellular Resistance that Affect the Membrane Currents , 1981, Circulation research.

[16]  G. W. Beeler,et al.  Reconstruction of the action potential of ventricular myocardial fibres , 1977, The Journal of physiology.

[17]  Mathematical approaches to cardiac arrhythmias: Preface , 1990 .

[18]  John J. Tyson,et al.  Spiral waves in a model of myocardium , 1987 .

[19]  Gul'ko Fb,et al.  Mechanism of formation of closed propagation pathways in excitable media , 1972 .

[20]  A. Zhabotinsky,et al.  Autowave processes in a distributed chemical system. , 1973, Journal of theoretical biology.

[21]  F B Gul'ko,et al.  [Mechanism of formation of closed propagation pathways in excitable media]. , 1972, Biofizika.

[22]  Allessie,et al.  Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The "leading circle" concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle. , 1977, Circulation research.

[23]  D. Clapham,et al.  Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. , 1991, Science.

[24]  Igor R. Efimov,et al.  Transition from circular to linear rotation of a vortex in an excitable cellular medium , 1990 .

[25]  H. Swinney,et al.  Spacial patterns in a uniformly fed membrane reactor , 1991 .

[26]  医療政策委員会.  Concentration wave propagation in two-dimensional liquid-phase self-oscillating system , 1970 .

[27]  G. Ertl,et al.  Imaging of spatio-temporal pattern evolution during carbon monoxide oxidation on platinum , 1990, Nature.

[28]  José Jalife,et al.  Spiral waves in normal isolated ventricular muscle , 1991 .

[29]  P. Wolf,et al.  Stimulus-induced critical point. Mechanism for electrical initiation of reentry in normal canine myocardium. , 1989, The Journal of clinical investigation.

[30]  Balth van der Pol Jun Docts. Sc.,et al.  LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart , 1928 .

[31]  Dante R. Chialvo,et al.  Sustained vortex-like waves in normal isolated ventricular muscle. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[32]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[33]  J Bures,et al.  Spiral waves of spreading depression in the isolated chicken retina. , 1983, Journal of neurobiology.

[34]  V. Krinsky,et al.  Chaos in the non-stirred Belousov–Zhabotinsky reaction is induced by interaction of waves and stationary dissipative structures , 1984, Nature.