Wilson-Cowan Equations for Neocortical Dynamics.
Wilson-Cowan Equations for Neocortical Dynamics.
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DOI：
10.1186/s13408-015-0034-5
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发表时间：
2016-12
影响因子：
2.3
通讯作者：
van Drongelen W
中科院分区：
文献类型：
--
作者：
Cowan JD;Neuman J;van Drongelen W
1972-1973年，威尔逊和考恩提出了一个新皮质中突触耦合的兴奋性和抑制性神经元种群动力学的数学模型。该模型只处理了激活和静止的兴奋性和抑制性神经元的平均数量，而没有讨论这种活动的波动和相关性。然而，在1997年，Ohira和Cowan，然后在2007-2009年，Buice和Cowan引入了这种活动的马尔可夫模型，其中包括波动和关联效应。在这里，我们展示了如何使用这两个模型来提供新皮质活动的种群动态的定量描述。我们首先描述马尔可夫模型如何解释最近对大脑皮层静息或自发活动的许多测量。特别地，我们证明了大尺度新皮质活动的功率谱具有布朗运动基线，并且在休眠状态附近发现的尖峰活动的随机爆发的统计结构表明，这种状态可以表示为随机图上的渗流过程，称为有向渗流。其他数据表明，静息的大脑皮层在相邻的细胞群体之间表现出成对的相关性，其幅度随着距离的增加而缓慢衰减，而受刺激的皮质表现出成对的相关性，随着距离的增加而迅速衰减。在这里，我们展示了马尔可夫模型如何解释成对关联的行为。最后，我们展示了1972-1973年的威尔逊-考恩方程如何解释最近的数据，这表明至少存在两种不同的皮层对刺激的反应模式。在模式1中，一个低强度的刺激会触发一个波，该波以大约0.3m/S的速度传播，其幅度呈指数衰减。在模式2中，高强度刺激会触发更大的反应，这种反应保持在局部，不会传播到邻近区域。
In 1972–1973 Wilson and Cowan introduced a mathematical model of the population dynamics of synaptically coupled excitatory and inhibitory neurons in the neocortex. The model dealt only with the mean numbers of activated and quiescent excitatory and inhibitory neurons, and said nothing about fluctuations and correlations of such activity. However, in 1997 Ohira and Cowan, and then in 2007–2009 Buice and Cowan introduced Markov models of such activity that included fluctuation and correlation effects. Here we show how both models can be used to provide a quantitative account of the population dynamics of neocortical activity. We first describe how the Markov models account for many recent measurements of the resting or spontaneous activity of the neocortex. In particular we show that the power spectrum of large-scale neocortical activity has a Brownian motion baseline, and that the statistical structure of the random bursts of spiking activity found near the resting state indicates that such a state can be represented as a percolation process on a random graph, called directed percolation. Other data indicate that resting cortex exhibits pair correlations between neighboring populations of cells, the amplitudes of which decay slowly with distance, whereas stimulated cortex exhibits pair correlations which decay rapidly with distance. Here we show how the Markov model can account for the behavior of the pair correlations. Finally we show how the 1972–1973 Wilson–Cowan equations can account for recent data which indicates that there are at least two distinct modes of cortical responses to stimuli. In mode 1 a low intensity stimulus triggers a wave that propagates at a velocity of about 0.3 m/s, with an amplitude that decays exponentially. In mode 2 a high intensity stimulus triggers a larger response that remains local and does not propagate to neighboring regions.