Drift Of Spiral Waves Research Articles

Resonant drift of autowave vortices in two dimensions and the effects of boundaries and inhomogeneities

The effect on autowave vortices in R 2 of a non-localized, periodic external forcing with a near-resonant frequency is investigated, and the effects of boundaries and inhomogeneities in the medium and mutual interaction between vortices is explored. We adopt an asymptotic approach which results in a phenomenological description of the resonant drift in terms of ODE's for the location of the vortex core and its rotation phase. We compare the results predicted by the theory with numerical simulations. The behaviour of the vortex is more complicated than the resonant drift described by Davydov et al. [V. A. Davydov, A. S. Mikhailov and P. K. Brazhnik, “Kinetica i gorenie”, p. 39, Institute of Chemical Physics, Chernogolovka (1986) (in Russian); V. A. Davydov, V. S. Zykov, A. S. Mikhailov and P. K. Brazhnik, Drift and resonance of spiral waves in distributed media, Izv. Vuzov-Radiofizika 31, 547–582 (1988)] and Agladze et al. [K. I. Agladze, V. A. Davydov and A. S. Mikhailov, An observation of resonance of spiral waves in distributed excitable medium, Pis'ma v ZETP 45, 601–603 (1987)]. In particular, a resonantly drifting vortex can be repelled from a boundary (phenomenon of ‘resonant repulsion’). Possible applications of resonant drift in the control of cardiac arrhythmias are studied. In particular, an approach for overcoming the resonant repulsion is proposed, which involves a feed-back from the medium to the stimulation device. We show that with this technique, the voltage needed for extinguishing vortices can be an order of magnitude less than that needed for the traditional single-pulse defibrillation.

MECHANISM OF PARAMETRIC RESONANCE OF VORTICES IN EXCITABLE MEDIA

An alternating electric current induces a drift of spiral waves (vortices) in the Belousov-Zhabotinsky reaction. When the electric current frequency is twice the frequency of the vortex rotation, the vortex drifts with a velocity about 1/5 of the vortex drift in a constant electric current or 1/20 of the wave front velocity. The dependence of parametric resonance on the chirality of the vortex, excitability of the medium, phase shift between electric current and vortex rotation, frequency and amplitude of the alternating electric current is analyzed and used to control the direction and velocity of the drift. A kinematical model, based on the asymmetric effect of the current on the normal and tangential velocities of the vortex tip, is formulated and recovers the most important aspects of parametric resonance.

Nonuniform Muscle Fiber Orientation Causes Spiral Wave Drift in a Finite Element Model of Cardiac Action Potential Propagation

Reentrant tachyarrhythmias are thought to involve spiral waves of excitation and recovery that may be nonstationary. The effect of muscle fiber curvature on spiral and planar wave propagation was studied using a computational model. Two-dimensional anisotropic cardiac propagation was modeled using a finite element method to solve a modification of the FitzHugh-Nagumo equations. Spiral waves that propagated stably about a fixed core in tissue with a uniform fiber orientation were found to drift at an oblique angle to the fibers when the fibers curved. The drift velocity was linearly related to the fiber angle gradient and was 10% of the longitudinal propagation velocity with a gradient of 4 degree/cm. Planar wavefronts were also affected by fiber curvature. The maximal upstroke rate, propagation velocity, and the action potential amplitude all increased when the fibers curved toward the wavefront and decreased when they curved away. For example, when the fibers curved toward the wavefront with a moderate gradient of 15 degree/cm, maximal upstroke rate increased 74%, transverse propagation velocity increased 65%, and action potential amplitude increased 9%. This phenomenon caused the spiral wave drift: As a spiral wave traverses a cycle, the angle between the wavefront at the wavetip and the fibers changes periodically, thus altering the propagation parameters. These periodic changes affect the instantaneous radius of curvature of the wavetip path, which results in drift. Spiral and planar waves are affected by muscle fiber curvature. The resulting dynamics may be important in determining the lifetime and stability of reentrant arrhythmias.

Phototaxis of Spiral Waves

The drift of spiral waves toward regions of higher light intensity was observed experimentally in the ruthenium-catalyzed Belousov-Zhabotinsky reaction. A light gradient can thus be used to manipulate optical information in new computational systems based on photochemical media. The drift of a gradient that is rotationally invariant in space is three to four times as fast as that of a translationally invariant gradient. Simulations based on the use of a cellular automaton, which is made isotropic by a semirandom distribution of cells, are in agreement with the experimental results.

Influence of electric field on rotating spiral waves in the Belousov-Zhabotinskii reaction

Wave propagation in the Belousov-Zhabotinsky (BZ) reaction is very sensitive to an external electric field because of the ionic nature of reacting species, such as bromide and catalyst. We show that the anisotropy of wave propagation, induced by an electric field, leads to a drift of spiral waves. The rate of drift of the spiral wave core depends on the intensity of the applied electric field. The drift vector is characterized by two components

Electric-field-induced drift and deformation of spiral waves in an excitable medium.

The dynamic behavior of spiral-shaped excitation patterns in the Belousov-Zhabotinskii reaction was investigated under the influence of externally applied direct current. Spiral centers drift towards the anode. The chirality of the spirals determines the direction of an additional perpendicular drift. A deformation of the Archimedian spiral shape was observed. Both effects were studied quantitatively and were reproduced in simulations with a simple reaction-diffusion model

Interaction of rotating waves in an active chemical medium

The interaction of autowave sources is experimentally studied in an active chemical medium with excitable kinetics. Three types of vortices are considered: 1) A spiral wave (S) rotating in a simply-connected medium, 2) A spiral wave rotating around a hole (SH); and 3) A spiral wave (S N ) with topological charge N. It is found that S synchronizes SH (except very small holes), and spiral waves with lower topological charge synchronize those with higher topological charge. It is also found that the interaction of autowave sources displays some unique properties because of their ability to appear on inhomogeities, to vanish and to move in the medium. A new phenomen of induced drift of spiral waves is demonstrated. The drift was induced by high-frequency concentrational waves propagating in the medium. A similar drift is observed upon interaction of vortices. The mechanism of the induced drift is explained in terms of wave-break translocation from one wave to another. Using this effect, one can control the location of wave sources in an active medium.