Complex-Periodic Spiral Waves Induced by Linearly Polarized Electric Field in the Excitable Medium

Complex-periodic spiral waves are investigated extensively in the oscillatory medium. In this paper, the linearly polarized electric field (LPEF) is employed to induce complex-periodic spiral waves in the excitable medium with abnormal dispersion. As the amplitude of LPEF is increased beyond a threshold, the simple-periodic spiral wave converts into an irregularly complex-periodic one, in which, the local dynamics exhibit several regular spikes followed by one missed spiking period. Furthermore, with the increase of the LPEF amplitude, the missed spiking period follows different numbers of regular spikes [so-called period-1 (P-1), period-2 (P-2), etc.], even a mix of different periods. Meanwhile, the wavelength of the spiral wave transits from a short to a longer one. The pure-periodic (from P-6 to P-2) spirals generally contain defect lines, across which the phase of local oscillation changes by [Formula: see text]. In contrast, there is no defect line in the mixed-periodic spiral waves. This finding indicates that the defect line is not a necessary feature for complex-periodic spiral waves. Moreover, three types of tip trajectories of pure-periodic spiral waves are identified depending on the periods. That is, the outward-petal meandering, the outward-petal meandering with slow modulation, and drifting tip motion, and the tip trajectories could be used to distinguish them from the complex-oscillatory spiral waves.

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DEFECT-LINE DYNAMICS IN OSCILLATORY SPIRAL WAVES

Fluctuation and Noise Letters ◽

10.1142/s0219477506003537 ◽

2006 ◽

Vol 06 (04) ◽

pp. L379-L386

Author(s):

STEVEN WU

Keyword(s):

Critical Point ◽

Period Doubling ◽

Spiral Wave ◽

Chaotic Regime ◽

Spiral Waves ◽

Bifurcation Parameter ◽

Local Dynamics ◽

Total Length ◽

Defect Line ◽

Large Fluctuations

We study defect-line dynamics in a 2-D spiral-wave pair in the Rössler model for its underlying local dynamics in period-N and chaotic regimes with a single bifurcation parameter κ. We find that a spiral wave pair is always stable across the period-doubling cascade and in the chaotic regime. When N ≥ 2 defect lines appear spontaneously and a loop exchange occurs across the defect line. There exists a "critical point" κ c below and above which the time-averaged total length of defect lines L converges to almost constant but different values L1 and L2. When κ > κ c defect lines show large fluctuations due to creation and annihilation processes.

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EXCITABLE SPIRAL WAVES IN NEMATIC LIQUID CRYSTALS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127494000873 ◽

1994 ◽

Vol 04 (05) ◽

pp. 1173-1182 ◽

Cited By ~ 12

Author(s):

P. COULLET ◽

F. PLAZA

Keyword(s):

Liquid Crystals ◽

Electric Field ◽

Nematic Liquid Crystals ◽

Spiral Wave ◽

Spiral Waves ◽

Excitable Medium ◽

Ginzburg Landau ◽

Landau Model ◽

Excitable System ◽

Mechanical Analog

A mechanical analog of the chemical and biological excitable medium is proposed. In nematic liquid crystals, the Freedericksz transition induced by a rotating tilted electric field provides a simple example of such a mechanical excitable system. We study this transition, derive a Ginzburg-Landau model for it, and show that the excitable spiral wave can be produced from a retractable finger-like soliton in this context.

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Spiral wave unpinning facilitated by wave emitting sites in cardiac monolayers

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0420 ◽

2019 ◽

Vol 475 (2230) ◽

pp. 20190420

Author(s):

Shreyas Punacha ◽

Sebastian Berg ◽

Anupama Sebastian ◽

Valentin I. Krinski ◽

Stefan Luther ◽

...

Keyword(s):

Electric Field ◽

Electrical Activity ◽

Spiral Wave ◽

Electrical Stimulus ◽

Spiral Waves ◽

Time Interval ◽

Field Pulse ◽

The Core ◽

Rotating Wave ◽

Multiple Obstacles

Rotating spiral waves of electrical activity in the heart can anchor to unexcitable tissue (an obstacle) and become stable pinned waves. A pinned rotating wave can be unpinned either by a local electrical stimulus applied close to the spiral core, or by an electric field pulse that excites the core of a pinned wave independently of its localization. The wave will be unpinned only when the pulse is delivered inside a narrow time interval called the unpinning window (UW) of the spiral. In experiments with cardiac monolayers, we found that other obstacles situated near the pinning centre of the spiral can facilitate unpinning. In numerical simulations, we found increasing or decreasing of the UW depending on the location, orientation and distance between the pinning centre and an obstacle. Our study indicates that multiple obstacles could contribute to unpinning in experiments with intact hearts.

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

Physical Review Letters ◽

10.1103/physrevlett.68.248 ◽

1992 ◽

Vol 68 (2) ◽

pp. 248-251 ◽

Cited By ~ 160

Author(s):

O. Steinbock ◽

J. Schütze ◽

S. C. Müller

Keyword(s):

Electric Field ◽

Spiral Waves ◽

Excitable Medium

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Spiral waves within a bistability parameter region of an excitable medium

New Journal of Physics ◽

10.1088/1367-2630/ac47ca ◽

2022 ◽

Author(s):

Vladimir Zykov ◽

Eberhard Bodenschatz

Keyword(s):

Initial Conditions ◽

Three Dimensional ◽

Spiral Wave ◽

Gradient Flow ◽

Spiral Waves ◽

Excitable Medium ◽

Excitable Media ◽

Circular Trajectory ◽

Parameter Region ◽

Scroll Wave

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

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Fast propagation regions cause self-sustained reentry in excitable media

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1611475114 ◽

2017 ◽

Vol 114 (6) ◽

pp. 1281-1286 ◽

Cited By ~ 19

Author(s):

Vladimir Zykov ◽

Alexei Krekhov ◽

Eberhard Bodenschatz

Keyword(s):

Spiral Wave ◽

Spiral Waves ◽

Excitable Medium ◽

Excitable Media ◽

Control Parameters ◽

Ablation Procedure ◽

Electrophysiological Activity ◽

Weakly Conducting ◽

Rotating Wave ◽

Theoretical Results

Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core. This is puzzling because the tissue at the anatomically defined spiral core would already be weakly conducting, and a further decrease should not improve the situation. In the case of a functionally determined core, an ablation procedure should even further stabilize the rotating wave. The efficacy of the procedure thus needs explanation. Here, we show theoretically that fundamentally in any excitable medium a region with a propagation velocity faster than its surrounding can act as a nucleation center for reentry and can anchor an induced spiral wave. Our findings demonstrate a mechanistic underpinning for the recently developed ablation procedure. Our theoretical results are based on a very general and widely used two-component model of an excitable medium. Moreover, the important control parameters used to realize conditions for the discovered phenomena are applicable to quite different multicomponent models.

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A SURVEY OF SPIRAL-WAVE BEHAVIORS IN THE OREGONATOR MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127491000348 ◽

1991 ◽

Vol 01 (02) ◽

pp. 445-466 ◽

Cited By ~ 143

Author(s):

WOLFGANG JAHNKE ◽

ARTHUR T. WINFREE

Keyword(s):

Spiral Wave ◽

Spiral Waves ◽

Excitable Medium ◽

Parameter Plane ◽

Complex Behavior ◽

Excitation Rate ◽

Numerical Exploration ◽

Oregonator Model ◽

Two Parameters ◽

Boundary Curves

We carried out a numerical exploration of spiral waves in a typical excitable medium, emphasizing the variety of behaviors encountered while changing two parameters of local excitability: the threshold for starting an excitation and the excitation rate at the wavefront. Within this parameter plane we found domains in which: 1) propagation is impossible, 2) propagation succeeds but there are no spiral waves, 3) spiral waves are stable and strictly periodic, 4) spiral waves exhibit two-period quasiperiodicity, and 5) spiral waves exhibit complex behavior that might be associated with the well-known instability of three-period flows on the three-torus. The boundary curves (bifurcation loci) separating these domains run parallel to the propagation boundary over much of their extent.

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