时空调制引起的漫游螺旋波与旅行螺旋波共存现象

以Barkley模型为研究对象, 研究了在时空调制作用下螺旋波时空动力学行为特性. 发现在适当的调制参数的作用下, 能够在同一系统中同时观察到漫游螺旋波与旅行螺旋波. 通过数值模拟研究分析, 给出了能产生漫游螺旋波与旅行螺旋波共存现象的潜在机理, 并详细讨论了在Barkley 模型中要产生这种共存现象的两个必要条件. 关键词： 时空调制 漫游螺旋波 旅行螺旋波     

Controlling spiral wave with target wave in oscillatory systems

Spiral waves have been controlled by generating target waves with a localized inhomogeneity in the oscillatory medium. The competition between the spiral waves and target waves is discussed. The effect of the localized inhomogeneity size has also been studied.     

The inverse excitation-induced abnormal spiral wave

The effects of a local constant forcing on spiral waves in two-dimensional excitable media described by Bär model are investigated. A constant external forcing is imposed on the core of spiral wave, leading to parameter variability of a medium. It is found that the forcing can significantly alter the shape and rotation period of spiral wave when the values of related parameters are properly chosen. The change of wave structure is attributed to the transition from normal excitation to inverse excitation in the forced medium. An abnormal spiral wave with a very thick spiral arm has been observed. The physical mechanism underlying these phenomena is theoretically analyzed.     

通过抑制波头旋转消除心脏中的螺旋波和时空混沌

本文采用Luo-Rudy相I模型研究如何通过调控心肌细胞钠电流变化来控制心脏中的螺旋波和时空混沌,提出了这样的钠电流调控方案:当细胞将被激发时启动钠电流调节,若由模型方程得到的钠电流的绝对值小于钠电流控制阈值的绝对值,就让钠电流等于钠电流控制阈值,其他情况下则限制钠电流的绝对值不能高于一个给定的最大值;当膜电位上升超过-5 mV时,让钠电流自然演化.这种调节钠电流的方式保证了所有细胞几乎具有相同的钠电流幅值,从而使所有细胞具有相同的激发性,数值模拟结果表明,只要钠电流控制阈值达到一定临界值,就可以有效抑制螺旋波波头的旋转,导致螺旋波运动出系统边界而消失,以及时空混沌演化为螺旋波后消失,如果钠电流控制阈值足够大,螺旋波和时空混沌还可通过传导障碍而消失.这些结果能够为抗心律失常治疗提供新的思路.     

Autapse-induced target wave,spiral wave in regular network of neurons

Autapse is a type of synapse that connects axon and dendrites of the same neuron, and the effect is often detected by close-loop feedback in axonal action potentials to the owned dendritic tree. An artificial autapse was introduced into the Hindmarsh-Rose neuron model, and a regular network was designed to detect the regular pattern formation induced by autapse. It was found that target wave emerged in the network even when only a single autapse was considered. By increasing the(autapse density) number of neurons with autapse, for example, a regular area(2×2, 3×3, 4×4, 5×5 neurons) under autapse induced target wave by selecting the feedback gain and time-delay in autapse. Spiral waves were also observed under optimized feedback gain and time delay in autapses because of coherence-like resonance in the network induced by some electric autapses connected to some neurons. This confirmed that the electric autapse has a critical role in exciting and regulating the collective behaviors of neurons by generating stable regular waves(target waves, spiral waves) in the network. The wave length of the induced travelling wave(target wave, spiral wave), because of local effect of autapse, was also calculated to understand the waveprofile in the network of neurons.     

小世界网络上螺旋波失稳的研究

利用数值计算和分析,研究了螺旋波失稳与重联概率p之间的关系.通过对基于FitzHugh-Nagumo神经元模型的小世界网络的计算和分析,发现螺旋波的小世界效应失稳具有全局性作用和失稳后再激发作用等特点,是不同于爱克豪斯(Eckhaus)失稳和多普勒(Doppler)失稳的又一种新的重要失稳方式. 关键词： 螺旋波 失稳 小世界网络 重联概率     

A primary mechanism for spiral wave meandering

The stability and dynamics of spiral wave meandering were studied by examining the behavior of small perturbations to a steadily rotating action potential wave. The disturbances responsible for meandering were found to be generated through an interaction between the unstable local linear dynamics characteristic of the action potential trailing edge near the core and perturbations existing in the region immediately behind this edge. Significantly, for the cases studied, neither wavefront curvature nor head-tail interactions were involved in this process. Study of the generation mechanism using a series of representative mathematical models and computer experiments led to the prediction that the following features of rotating action potentials render them more susceptible to meandering: (1) proximity of the wave tip to the center of rotation, (2) wider action potential leading and trailing edges, and (3) slower wave rotation speeds. Variation of basic tissue properties, including firing threshold potentials and excitability above threshold, affected these properties, and those of the perturbation dynamics, in several ways, producing both stabilizing and destabilizing effects. The nature of the involvement of various tissue and membrane electrical properties is therefore complex, affecting several factors relevant to meandering at once. (c) 2002 American Institute of Physics.     

Symmetry groups and spiral wave solution of a wave propagation equation

We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.     

耦合复金兹堡-朗道(Ginzburg-Landau)方程中的模螺旋波

以双层耦合复金兹堡-朗道(Ginzburg-Landau)方程系统为时空模型, 研究了其中的模螺旋波, 讨论了这种特殊波动现象的稳定条件和相关影响因素. 模螺旋波与该类时空系统中常见的相螺旋波相比, 其中心不存在缺陷点, 同时仅在其变量的振幅部分(而非相位部分) 表现为螺旋结构. 本文通过数值方法研究了耦合复金兹堡-朗道方程中产生模螺旋波所需要的初始和参数条件.研究表明, 当双层耦合系统的初始斑图之间的差距较大时, 才能够产生模螺旋波; 同时观察到系统在参数不匹配的条件下会发生相螺旋波向模螺旋波的转变.通过对同步函数的计算, 发现该转变过程具有非连续性.     

Complexity in spiral wave dynamics(a))

In closed systems of the Belousov-Zhabotinsky reaction a large number of dynamic states found in open systems is sampled as they evolve in time. During such slow aging processes of thin solution layers, prepared under appropriately chosen chemical conditions, an unexpectedly rich variety of spiral tip behavior was observed experimentally. Within a (concentration, time) parameter plane, the movement of free ends of waves was classified as follows: (a) in a stable domain-periodic rigid rotation with cores of small (200 &mgr;m) or very large (2 mm) diameter; quasiperiodic compound motion along a hypocycle, a straight loopy line or an epicycle; complex meandering composed of possibly more than two components; (b) rectilinear tip motion indicating the boundary of spiral wave stability; and (c) in an unstable domain-shrinking of open ends of wave fronts during propagation. The main properties of these parameters are compared with recently published computer calculations.     

Breakup of spiral wave under different boundary conditions

In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter \varepsilon is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave (AOMSW), we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of \varepsilon.     

A dynamical systems approach to spiral wave dynamics

A simple system of five nonlinear ordinary differential equations is shown to reproduce many dynamical features of spiral waves in two-dimensional excitable media.     

复Ginzburg-Landau方程中模螺旋波的稳定性研究

研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域:在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.     

Electrical alternans and spiral wave breakup in cardiac tissue

This paper reports the results of a theoretical investigation of spiral wave breakup in model equations of action potential propagation in cardiac tissue. A general formulation of these equations is described in which arbitrary experimentally determined restitution and dispersion curves can in principle be fitted. Spiral wave behavior is studied in two-dimension as a function of a parameter Re which controls the steepness of the restitution curve at short diastolic intervals. Spiral breakup is found to occur when the minimum period T(min), below which a periodically stimulated tissue exhibits alternans in action potential duration, exceeds by a finite amount the spiral rotation period T(S). At this point, oscillations in action potential duration are of sufficiently large amplitude to cause a spontaneous conduction block to form along the wavefront. The latter occurs closer to the initiation point of reentry (spiral tip) with increasing steepness and, hence, in smaller tissue sizes. Spiral breakup leads to a spatially disorganized wave activity which is always transient, except for tissues larger than some minimum size and within a very narrow range of Re which increases with dispersion.     

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.     

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.     

Patterns of spiral wave attenuation by low-frequency periodic planar fronts

There is evidence that spiral waves and their breakup underlie mechanisms related to a wide spectrum of phenomena ranging from spatially extended chemical reactions to fatal cardiac arrhythmias [A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 2001); J. Schutze, O. Steinbock, and S. C. Muller, Nature 356, 45 (1992); S. Sawai, P. A. Thomason, and E. C. Cox, Nature 433, 323 (2005); L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988); R. A. Gray et al., Science 270, 1222 (1995); F. X. Witkowski et al., Nature 392, 78 (1998)]. Once initiated, spiral waves cannot be suppressed by periodic planar fronts, since the domains of the spiral waves grow at the expense of the fronts [A. N. Zaikin and A. M. Zhabotinsky, Nature 225, 535 (1970); A. T. Stamp, G. V. Osipov, and J. J. Collins, Chaos 12, 931 (2002); I. Aranson, H. Levine, and L. Tsimring, Phys. Rev. Lett. 76, 1170 (1996); K. J. Lee, Phys. Rev. Lett. 79, 2907 (1997); F. Xie, Z. Qu, J. N. Weiss, and A. Garfinkel, Phys. Rev. E 59, 2203 (1999)]. Here, we show that introducing periodic planar waves with long excitation duration and a period longer than the rotational period of the spiral can lead to spiral attenuation. The attenuation is not due to spiral drift and occurs periodically over cycles of several fronts, forming a variety of complex spatiotemporal patterns, which fall into two distinct general classes. Further, we find that these attenuation patterns only occur at specific phases of the descending fronts relative to the rotational phase of the spiral. We demonstrate these dynamics of phase-dependent spiral attenuation by performing numerical simulations of wave propagation in the excitable medium of myocardial cells. The effect of phase-dependent spiral attenuation we observe can lead to a general approach to spiral control in physical and biological systems with relevance for medical applications.