Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). The extended theory offers an approximate mean-field dynamics for the synaptic input currents arising from populations of spiking neurons and synapses undergoing Tsodyks–Markram STP. The approximate mean-field dynamics accounts for both finite number of synapses and correlation between the two synaptic variables of the model (utilization and available resources) and its numerical implementation is simple. Comparisons with Monte Carlo simulations of the microscopic model show that in both feedforward and recurrent networks, the mesoscopic mean-field model accurately reproduces the first- and second-order statistics of the total synaptic input into a postsynaptic neuron and accounts for stochastic switches between Up and Down states and for population spikes. The extended mesoscopic population theory of spiking neural networks with STP may be useful for a systematic reduction of detailed biophysical models of cortical microcircuits to numerically efficient and mathematically tractable mean-field models.

中文翻译：

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具有突触短期可塑性的尖峰神经网络的介观种群方程

获得神经活动的介观模型的生物神经网络的粗粒度微观模型是迈向大脑多尺度模型的重要步骤。在这里，我们将具有静态突触的介观种群动态的最新理论扩展到具有短期可塑性（STP）的动态突触的情况。扩展的理论为突触神经元和突触经历Tsodyks–Markram STP产生的突触输入电流提供了近似的平均场动力学。近似平均场动力学说明了有限数量的突触和模型的两个突触变量（利用和可用资源）之间的相关性，其数值实现很简单。与微观模型的蒙特卡洛模拟的比较表明，在前馈网络和递归网络中，介观均值场模型都能准确地将突触后神经元总突触输入的一阶和二阶统计信息重现，并解释了Up之间的随机切换。和Down州以及人口激增。带有STP的尖峰神经网络的介观种群理论的扩展对于将皮层微电路的详细生物物理模型系统地简化为数值有效且数学上易处理的均场模型可能有用。