神经元网络中局部同步引发的各种效应

Various effects induced by local synchronization in neural networks

在大脑皮层中,神经元大范围的同步放电可以引发癫痫,而癫痫发作期间可以自发出现螺旋波,大量神经元的同步放电与螺旋波自发产生之间的关系目前仍不清楚.本文通过增加水平长程连接构造了具有局域长程耦合区的二维神经元网络,采用Morris-Lecar神经元模型研究了具有多个长方形长程耦合区的神经元网络中波的传播,数值模拟结果表明:传播方向与长程耦合朝向平行的平面波和靶波经过长程耦合区会导致长程耦合区内的神经元同步激发,这种同步激发伴随一部分神经元延迟激发,而另一部分提前激发;当长程耦合区宽度超过临界宽度时,长程耦合区所有神经元延迟激发;当长程耦合区宽度超过最大导通宽度时,波将不能通过长程耦合区.当适当选择长方形长程耦合区的尺寸时,神经元同步激发可使网络出现波回传效应和具有波传播方向的选择性,而且这种波传播方向的选择性对神经元是否处于定态和耦合强度变化很敏感,以致高频平面波列可以部分通过宽度超过最大导通宽度的长程耦合区,因此可以通过对长程耦合区内的神经元施加微扰来控制低频波是否可以通过一定宽度的长程耦合区.对于适当选取的神经元网络结构,当平面波或靶波经过长程耦合区时,网络可自发出现自维持平面波、螺旋波和靶波等现象.本文对产生这些现象的物理机制作了分析.

In the cerebral cortex,the large-scale synchronous firing of neurons can cause epilepsy,during which spiral waves can spontaneously occur.The relationship between the synchronous firing of a large number of neurons and the spontaneous generation of spiral waves is still unclear.In this paper,a two-dimensional neuronal network with the long-range coupling regions generated by adding long-range horizontal connections is constructed.The Morris-Lecar neuron model is used to study the propagation of waves in the two-dimensional neuronal network with the rectangular longrange coupling regions.Numerical simulation results show that the plan and target waves whose propagation directions are both parallel to that of the long-range coupling can lead the neurons to be excited synchronously in the long-range coupling region.This synchronous firing is accompanied by delayed firing of some neurons and premature firing of others.When the width of the long-range coupling region exceeds the critical width,all the neurons in the long-range coupling region delay firing.When the width of the long-range coupling region exceeds a maximum conduction width,the waves will not pass through the long-range coupling region.When the size of the rectangular region of the long-range coupling is selected appropriately,the synchronous excitation of neurons can cause network to present the backfiring effect and to have the selectivity of wave propagation direction.Furthermore,the selectivity of wave propagation direction is very sensitive to whether the neuron is in the stationary state and also to the change of coupling strength,so that the high frequency plane wave train can partially pass through the long-range coupling region whose width exceeds the maximum conduction width.So we can control whether the wave can pass through the long-range coupling region of a certain width by giving the neurons in the long-range coupling region a tiny perturbation.When one or two long-range coupling regions are constructed in the neural network and the size of the long-range coupling regions is selected appropriately,the self-sustaining plane wave,spiral wave and target wave can appear spontaneously in the network when the wave passes through the long-range coupling regions.The physical mechanisms behind those phenomena are also analyzed.