Instability and Death of Spiral Wave in a Two-Dimensional Array of Hindmarsh–Rose Neurons
Instability and Death of Spiral Wave in a Two-Dimensional Array of Hindmarsh–Rose Neurons
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DOI：
10.1088/0253-6102/53/2/32
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发表时间：
2010-02
影响因子：
3.1
通讯作者：
Wang Chunni;Ma Jun;Tang Jun;Li Yan-long
中科院分区：
文献类型：
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作者：
Wang Chunni;Ma Jun;Tang Jun;Li Yan-long
在可兴奋介质中可以观察到螺旋波，在适当的参数下神经元往往是可兴奋的。心脏组织内螺旋波的出现和形成与单纯性室性心动过速有关，单纯性心动过速可去神经转化为多形性心动过速和室性颤动。神经系统通常由大量具有复杂连接的神经元组成。本文从理论上研究了具有完全最近邻连接的Hindmarsh-Rose神经元二维阵列从螺旋波到螺旋湍流和均匀状态（螺旋波死亡）的转变。在数值研究中，我们先建立一个稳定的旋转螺旋波作为初始状态，然后改变分岔参数，分别观察螺旋波向均匀状态的转变、螺旋波的破碎和螺旋波的微弱变化。利用平均场理论定义了同步的统计因子来分析螺旋波向其他空间状态的转变，并绘制了所有神经元的膜电位快照和所有神经元的平均膜电位时间序列来讨论螺旋波的变化。发现同步因子与分岔参数曲线上的急变点表示螺旋波向其他状态的突然转变。结果与我们使用的神经元数量无关。
Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriate parameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventricular tachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system often consists of a large number of neurons with complex connections. In this paper, we theoretically study the transition from spiral wave to spiral turbulence and homogeneous state (death of spiral wave) in two-dimensional array of the Hindmarsh–Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiral wave is developed and selected as the initial state, then the bifurcation parameters are changed to different values to observe the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave, respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition from spiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of mean membrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharp changing points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition from spiral wave to other states. And the results are independent of the number of neurons we used.