Selection of spiral waves in excitable media with a phase wave at the wave back

Universal relationships between the medium excitability and the angular velocity and the core radius of rigidly rotating spiral waves in excitable media are derived for situations where the wave front is a trigger wave and the wave back is a phase wave. Two universal limits restricting the region of existence of spiral waves in the parameter space are demonstrated. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the Kessler-Levine model.     

External forcing of spiral waves

The effect of an external rhythm on rotating spiral waves in excitable media is investigated. Parameters of the unperturbed medium were chosen, such that the organizing spiral tip describes meandering (hypocyclic) trajectories, which are the most general shape for the experimentally observed systems. Periodical modulation of excitability in a model of the Belousov-Zhabotinsky (BZ) reaction forces meandering spiral tips to describe trajectories that are not found at corresponding stationary conditions. For different modulation periods, two types of resonance drift, phase-locked tip motion, a spectrum of hypocyclic trajectories, and complex multifrequency patterns were computed. The computational results are complemented by experimental data obtained for periodically changing illumination of the photosensitive BZ reaction. The observed drastic deformation of the tip trajectory is considered as an efficient means to study and to control wave processes in excitable media.     

Motion of spiral waves induced by local pacing

The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.      

Kinetic Monte Carlo simulations of travelling pulses and spiral waves in the lattice Lotka-Volterra model

Kinetic Monte Carlo simulations are used to study the stochastic two-species Lotka-Volterra model on a square lattice. For certain values of the model parameters, the system constitutes an excitable medium: travelling pulses and rotating spiral waves can be excited. Stable solitary pulses travel with constant (modulo stochastic fluctuations) shape and speed along a periodic lattice. The spiral waves observed persist sometimes for hundreds of rotations, but they are ultimately unstable and break-up (because of fluctuations and interactions between neighboring fronts) giving rise to complex dynamic behavior in which numerous small spiral waves rotate and interact with each other. It is interesting that travelling pulses and spiral waves can be exhibited by the model even for completely immobile species, due to the non-local reaction kinetics.     

Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media

Spiral waves in diverse excitable media exhibit strikingly variegated behavior. Mechanistic interpretations of excitability in laboratory systems are commonly tested by comparing the wavelength, period, and meander patterns of the model's spiral waves with laboratory observations, but models seem seldom to be rejected by such tests. The reason may be that almost any excitable medium behaves in many respects like almost any other, if its parameters are properly adjusted within a reasonable range. What generalizations can be made about "excitable media" in the absence of more specifications? It would be useful to distinguish such generic features from idiosyncrasies of specific models. The range of behavioral flexibility of the FitzHugh-Nagumo excitable medium is explored by varying two of its parameters and comparing the results with other excitable media to suggest a generic pattern of parameter dependence. The results exhibit the remarkable diversity of rotor behavior in a single model and provide a database for quantitative testing of mathematical generalizations.     

Negative filament tension at high excitability in a model of cardiac tissue

One of the fundamental mechanisms for the onset of turbulence in 3D excitable media is negative filament tension. Thus far, negative tension has always been obtained in media under low excitability. For this reason, its application to normal (nonischemic) cardiac tissue has been questionable, as such cardiac turbulence typically occurs at high excitability. Here, we report expansion of scroll rings (low curvature negative filament tension) in a medium with high excitability by numerical integration of the Luo-Rudy model of cardiac tissue. We discuss the relation between negative tension and the meandering of 2D spiral waves and the possible applications to cardiac modeling.     

多可激性障碍下的螺旋波动力学

在许多实际可激系统中局部不均匀是广泛存在的, 它们是螺旋波形成以及动力学行为改变的重要因素. 本文研究了可激性障碍对螺旋波动力学行为的影响. 研究表明, 在障碍区域内可激性参数大于区域外情况下障碍会对其附近的螺旋波波头有吸引作用, 多局部障碍共存时吸引行为不仅依赖障碍分布, 而且依赖障碍的大小以及区域内可激性参数的具体取值. 通过抑制变量小值区域的变化分析了这些行为发生的原因. 在障碍区域内可激性参数小于区域外情况下障碍对其近邻的螺旋波波头有排斥作用, 排斥后波头的运动依赖初始螺旋波是刚性旋转的还是漫游的. 多局部障碍共存时排斥作用对螺旋波动力学行为的改变依赖障碍的分布、大小与区域内可激性参数的具体取值以及初始螺旋波的类型. 关键词： 螺旋波 时空混沌 可激性障碍     

Wave front interaction model of stabilized propagating wave segments

A wave front interaction model is developed to describe the relationship between excitability and the size and shape of stabilized wave segments in a broad class of weakly excitable media. These wave segments of finite size are unstable but can be stabilized by feedback to the medium excitability; they define a separatrix between spiral wave behavior and contracting wave segments. Unbounded wave segments (critical fingers) lie on the asymptote of this separatrix, defining the boundary between excitable and subexcitable media. The model predictions are compared with results from numerical simulations.     

非均匀可激介质中的螺旋波

以Barkley模型为对象,研究了可激介质的非均匀性对螺旋波斑图形成的影响.该模型中各参数与可激介质的属性密切相关,通过参数涨落的正态分布来刻画非均匀性,数值研究了单参数以及多参数涨落的正态分布情形下螺旋波斑图的形成.研究表明,可激介质的非均匀性对于螺旋波波纹的粗细及疏密程度有较大影响.参数涨落分布的方差越大,形成的螺旋波波纹越粗糙.对于两参数均匀分布的极端情形,当参数分布大于某一范围,无法形成螺旋波.这些都与螺旋波旋转的角频率密切相关.螺旋波旋转的角频率越大,螺旋波波纹越粗,同时波纹越密集;反之,螺旋波 关键词： 螺旋波 非均匀介质 Barkley模型     

无扩散功能的缺陷对螺旋波动力学行为的影响

采用Br 模型,在二维激发介质中引入无扩散功能的缺陷,研究了均匀分布的缺陷对螺旋波动力学行为的影响.研究发现,缺陷导致介质的激发性降低、波传播速度减少,在一定数量的缺陷均匀分布下,缺陷可以使原来稳定的螺旋波发生漫游或破碎,缺陷使原来不稳定的螺旋波稳定或漫游,首次在激发介质中观察到螺旋波因Doppler效应破碎形成小螺旋波和时空混沌共存现象.对产生这些现象的物理机理做了简要的讨论. 关键词： 激发介质 螺旋波 缺陷     

Rotating spiral waves in a modified Fitz-Hugh-Nagumo model

A modified Fitz-Hugh-Nagumo model (a two-variable reaction-diffusion system with an excitable kinetics and a diffusing fast variable) was used to study numerically the rotating waves in a circular domain and in a two-dimensional ring. Large deviations from a Wiener type of behaviour of rotating spiral waves were revealed. We have shown that there are conditions under which: (i) vortices can appear in a medium with a hole but do not exist in a disk; (ii) two kinds of vortices with considerably differing periods can occur in the same ring; (iii) there is a non-monotonic dependence of vortex period on the hole size. These phenomena are believed to take place in myocardial tissue and in chemical active media. The conditions under which they could be observed experimentally are discussed.     

Spiral breakup induced by an electric current in a Belousov-Zhabotinsky medium

Sprial breakup in the Belousov-Zhabotinsky reaction has been observed under the influence of an externally applied alternating electric current. The dynamic mechanism of this breakup is explained in the framework of this reaction. The dependence of the critical electric current amplitude on the period of the wave and on the excitability of the medium is analyzed. Spiral breakup is shown to provide a limit of validity of electric-field-induced drift of vortices in excitable media. Experimental results are complemented with numerical simulations provided by two- and three-variable Oregonator models.     

Light induced annihilation and shift of spiral waves

The light-induced collapse of a pair of spiral waves was studied in a chemically active medium based on the photosensitive Ru(bpy)(3)-catalyzed Belousov-Zhabotinsky reaction. Spiral waves annihilate only if the light intensity is increased in proper phase relative to the spiral waves' rotation. Otherwise, the distance between spiral wave cores increases and the pair survives. Computer simulations reveal the mechanism which forces the spiral waves to collide and annihilate. It is based on the shift of a single spiral wave upon an instantaneous decrease of excitability of the medium. (c) 1996 American Institute of Physics.     

Beyond the Kuramoto-Zel’dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon

In numerical experiments with the Fitzhugh-Nagumo set of reaction-diffusion equations describing two-dimensional excitable media, unusual solutions are found that correspond to a concave spiral wave steadily rotating round a circular obstacle in a finite-size medium. Such a wave arises in the region of parameters corresponding to the solitonlike regime (see text); it appears due to the interaction between the peripheral areas of a “seed” spiral wave with a convex front and the echo waves incoming from the outer boundaries of a medium. The solutions obtained are in contradiction with intuition and represent a numerical counterexample to the known theories that forbid steadily moving excitation waves with concave fronts. Nevertheless, a concave spiral wave is a stable object; being transformed to the usual spiral wave with a convex front by suppressing echo at the outer boundaries of the medium, it is again recovered upon restoring the echo conditions. In addition to the single-arm spiral concave wave, solutions are obtained that describe multiarm waves of this type; for this reason, the concave fronts of these waves are a coarse property.     

Dynamics of Vortex-Wave under a Travelling-Wave Modulation

The mechanism of destabilization is studied for the rotating vortices （scroll waves and spiral waves） in excitable media induced by a parameter modulation in the form of a travelling-wave. It is found that a rigid rotating spiral in the two-dimensional （2D） system undergoes a synchronized drift along a straight line, and a 3D scroll ring with its filament closed into a circle can be reoriented only if the direction of wave number of a travelling-wave perturbation is parallel to the ring plane. Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scroll ring, the approximate formulas are given to exhibit qualitative agreements with the observed results.     

随机扰动对螺旋波动力学的影响研究

心脏中的心肌组织是一种典型的可激发介质, 鉴于心肌细胞分布的离散性, 采用离散可激发介质模型研究了不应态时间随机扰动对螺旋波动力学行为的影响, 在扰动随机出现情况下, 螺旋波的稳定性与受扰元胞的数目和扰动幅度有关, 数值计算结果表明: 在适当的条件下, 可以观察到螺旋波漫游、破碎和消失现象, 并简要分析了产生这些现象的机理. 关键词： 螺旋波 激发介质 随机扰动     

两层耦合可激发介质中螺旋波转变为平面波

采用Br-Eiswirth模型研究了两层耦合可激发介质中螺旋波的动力学,两层介质通过网络连接,即在每一层介质上,每一列选一个可激发单元作为中心点,在一层介质上同一列的可激发单元只与另一层介质上对应的中心点及其8个邻居有耦合.数值模拟结果表明:通过这种局部耦合,在适当小的耦合强度下两耦合螺旋波可实现同步,增大耦合强度会导致螺旋波漫游和漂移,造成螺旋波不同步,观察到螺旋波与静息态、低频平面波和不规则斑图共存现象.在适当强的耦合强度下,还观察到两螺旋波转变成同步的平面波消失现象.对产生这些现象的物理机理做了讨论.     

Controlling Spiral Dynamics in Excitable Media by a Weakly Localized Pacing

Spiral dynamics controlled by a weakly localized pacing around the spiral tip is investigated. Numerical simulations show two distinct characteristics when the pacing is applied with the weak amplitude for suitable frequencies： for a rigidly .rotating spiral, a transition from rigid rotation to meandering motion is observed, and for unstable spiral waves, spiral breakup can be prevented. Successfully preventing spiral breakup is relevant to the modulation of the tip trajectory induced by a localized pacing.     

New approach to the defibrillation problem: Suppression of the spiral wave activity of cardiac tissue

A model of an excitable medium is considered for describing the development of fibrillation (i.e., spatiotemporal chaos) in cardiac tissue through the generation of a set of coexisting spiral waves. It is shown that a weak external point action on such a medium leads to the suppression of all spiral waves and, correspondingly, to the stabilization of the system dynamics. After reaching the regular regime, only the external source exists in the medium. The frequencies and amplitudes at which such stabilization occurs are determined. The case of the action of several point sources is considered. Analysis is performed using the Bray method to identify the number of spiral waves.