Volo Matteo di, Romagnoni Alberto, Capone Cristiano, Destexhe Alain
Unité de Neuroscience, Information et Complexité, CNRS FRE 3693, 91198 Gif sur Yvette, France
Centre de Recherche sur l'inflammation UMR 1149, Inserm-Université Paris Diderot, 75018 Paris, France, and Data Team, Departement d'informatique de l'Ecole normale supérieure, CNRS, PSL Research University, 75005 Paris, France, and European Institute for Theoretical Neuroscience, 75012 Paris, France
Neural Comput. 2019 Apr;31(4):653-680. doi: 10.1162/neco_a_01173. Epub 2019 Feb 14.
Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.
构建超大规模神经模型需要精确的群体模型，但对于实际的神经元网络来说，推导这样的模型很困难，尤其是当涉及非线性特性时，如基于电导的相互作用和脉冲频率适应。在此，我们考虑基于自适应指数积分发放兴奋性和抑制性神经元网络的此类模型。使用主方程形式，我们推导了此类网络的平均场模型，并将其与完整网络动力学进行比较。平均场模型能够正确预测与体内活动相似的异步不规则状态下的平均自发活动水平。它还捕捉了网络对复杂外部输入的瞬态时间响应。最后，平均场模型还能够定量描述高活动状态和低活动状态交替出现的状态（上下状态动力学），从而导致缓慢振荡。我们得出结论，此类平均场模型在生物学上是现实的，因为它们可以捕捉自发活动和诱发活动，并且自然地成为构建涉及多个脑区的超大规模模型的候选者。
