Roberts J A, Robinson P A
School of Physics, University of Sydney, and Brain Dynamics Centre, Westmead Millenium Institute, Westmead Hospital, Westmead, New South Wales 2145, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Nov;78(5 Pt 1):051901. doi: 10.1103/PhysRevE.78.051901. Epub 2008 Nov 3.
The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.
相连神经元群体之间的传导延迟范围通常被建模为单个离散延迟，假定为所有纤维速度的有效平均值。本文展示了分布式延迟对信号传播的影响。分布起到线性滤波器的作用，施加一个与延迟宽度成反比的高频截止。将分布式丘脑皮质和皮质丘脑延迟纳入基于生理学的皮质和丘脑平均场模型，以说明它们对脑电图（EEG）的影响。功率谱对丘脑皮质延迟分布的宽度极为敏感，比对皮质丘脑分布的敏感性更强，因为所有输入信号都必须沿着丘脑皮质通路传播。这会强加一个截止频率，高于该频率频谱会过度衰减。静息EEG中频谱峰值的位置主要取决于分布均值，对分布宽度的依赖性较弱。增加分布宽度会增加定点解的稳定性。只要适度调整其他模型参数，单个离散延迟就能成功近似低于与延迟宽度成反比的截止频率的频率下的分布。一对离散延迟共同具有与分布相同的均值、方差和偏度，在相同频率范围内近似该分布，而无需参数调整。具有大分数宽度的延迟分布可由低阶微分方程很好地近似。
