Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.
Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.
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DOI：
10.1371/journal.pcbi.1005507
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发表时间：
2017-04
影响因子：
4.3
通讯作者：
Gerstner W
中科院分区：
文献类型：
--
作者：
Schwalger T;Deger M;Gerstner W
神经群体方程（例如神经质量或场模型）被广泛用于大规模研究大脑活动。然而，这些模型与单个神经元特性的关系尚不清楚。在这里，我们从随机连接的广义积分激发神经元模型的微观模型开始，推导出介观尺度上几个相互作用群体的方程。每个群体由 50-2000 个相同类型的神经元组成，但不同的群体代表不同的神经元类型。我们发现的随机群体方程揭示了单神经元动力学中的尖峰历史效应（例如不应性和适应）如何与群体水平上的有限大小波动相互作用。随机介观方程的有效积分再现了从完整尖峰神经网络模型的微观模拟中获得的群体活动的统计行为。该理论描述了非线性涌现动力学，例如多稳态网络中有限尺寸引起的随机转变以及兴奋性和抑制性神经元平衡网络中的同步。介观方程用于快速集成由八种神经元类型组成的皮质微电路模型，这使我们能够预测自发群体活动以及对丘脑输入的诱发反应。我们的理论建立了一个基于单细胞和突触参数的有限大小神经群体动力学建模的通用框架，并提供了分析皮层电路和计算的有效方法。了解大脑需要不同空间尺度的数学模型。在神经细胞的“微观”水平上，现象学尖峰神经元模型可以很好地预测神经尖峰序列。在粗略的尺度上，神经活动可以通过现象学方程来建模，该方程总结了数千个神经元的总活动。这种群体模型广泛用于对脑电图、脑磁图或功能磁共振成像数据等神经影像数据进行建模。然而，人们很大程度上不知道大型模型如何与底层的微型模型连接。连接尺度对于正确描述群体活动的快速变化和波动至关重要，对于多尺度大脑模型也至关重要。挑战在于处理真实的尖峰动力学以及有限数量的神经元引起的波动。我们通过从底层微观模型中推导出 100-1000 个神经元介观尺度上的随机总体方程，获得了这样的联系。这些方程可以有效地积分并重现微观模拟的结果，同时实现高加速因子。我们期望我们在介观尺度上的新颖群体理论将有助于理解大脑信息处理的实验数据，并最终将微观和宏观活动模式联系起来。
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. Understanding the brain requires mathematical models on different spatial scales. On the “microscopic” level of nerve cells, neural spike trains can be well predicted by phenomenological spiking neuron models. On a coarse scale, neural activity can be modeled by phenomenological equations that summarize the total activity of many thousands of neurons. Such population models are widely used to model neuroimaging data such as EEG, MEG or fMRI data. However, it is largely unknown how large-scale models are connected to an underlying microscale model. Linking the scales is vital for a correct description of rapid changes and fluctuations of the population activity, and is crucial for multiscale brain models. The challenge is to treat realistic spiking dynamics as well as fluctuations arising from the finite number of neurons. We obtained such a link by deriving stochastic population equations on the mesoscopic scale of 100–1000 neurons from an underlying microscopic model. These equations can be efficiently integrated and reproduce results of a microscopic simulation while achieving a high speed-up factor. We expect that our novel population theory on the mesoscopic scale will be instrumental for understanding experimental data on information processing in the brain, and ultimately link microscopic and macroscopic activity patterns.