Marreiros André C, Kiebel Stefan J, Daunizeau Jean, Harrison Lee M, Friston Karl J
The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, UK.
Neuroimage. 2009 Feb 1;44(3):701-14. doi: 10.1016/j.neuroimage.2008.10.008. Epub 2008 Oct 25.
In this paper, we describe a generic approach to modelling dynamics in neuronal populations. This approach models a full density on the states of neuronal populations but finesses this high-dimensional problem by re-formulating density dynamics in terms of ordinary differential equations on the sufficient statistics of the densities considered (c.f., the method of moments). The particular form for the population density we adopt is a Gaussian density (c.f., the Laplace assumption). This means population dynamics are described by equations governing the evolution of the population's mean and covariance. We derive these equations from the Fokker-Planck formalism and illustrate their application to a conductance-based model of neuronal exchanges. One interesting aspect of this formulation is that we can uncouple the mean and covariance to furnish a neural-mass model, which rests only on the populations mean. This enables us to compare equivalent mean-field and neural-mass models of the same populations and evaluate, quantitatively, the contribution of population variance to the expected dynamics. The mean-field model presented here will form the basis of a dynamic causal model of observed electromagnetic signals in future work.
在本文中，我们描述了一种用于对神经元群体动力学进行建模的通用方法。这种方法对神经元群体状态的完整密度进行建模，但通过根据所考虑密度的充分统计量用常微分方程重新表述密度动力学来巧妙处理这个高维问题（参见矩量法）。我们采用的群体密度的特定形式是高斯密度（参见拉普拉斯假设）。这意味着群体动力学由控制群体均值和协方差演化的方程来描述。我们从福克 - 普朗克形式体系推导出这些方程，并说明它们在基于电导的神经元交换模型中的应用。这种表述的一个有趣方面是，我们可以将均值和协方差解耦，以构建一个仅基于群体均值的神经质量模型。这使我们能够比较相同群体的等效平均场模型和神经质量模型，并定量评估群体方差对预期动力学的贡献。这里提出的平均场模型将在未来的工作中构成观测电磁信号动态因果模型的基础。
