Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two set-ups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both set-ups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms always display phase amplitude coupling. However, two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behavior; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING set-up. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing intensity and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in our model, only by incrementing, at the same time, also the stimulation power. An effect achieved by increasing the amplitude either of the noise or of the forcing term proportionally to the theta frequency. On the basis of our analysis both the PING and the ING mechanism give rise to theta-nested gamma oscillations with almost identical features.

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下一代神经质量模型中的 Theta 嵌套伽马振荡

已经在大脑的许多区域报告了 Theta 嵌套伽马振荡，并且被认为代表了跨空间和时间尺度传输信息的基本机制。在最近的一系列体外实验中，可以通过光遗传学 theta 频率刺激复制在行为动物中观察到的 theta 和 gamma 节律之间的交叉频率耦合 (CFC) 的几个特征。为了重现这些实验的主要发现，我们考虑了一类新的神经质量模型，能够准确重现尖峰神经网络的宏观动力学。在这个框架中，我们研究了两种能够支持集体伽马振荡的设置：即金字塔神经元网络伽马 (PING) 和神经元网络伽马 (ING)。在这两种设置中，我们通过在 Hopf 分岔附近用正弦 theta 强迫驱动系统来观察 theta 嵌套伽马振荡的出现。这些混合节奏总是显示相位幅度耦合。然而，可以识别两种不同类型的嵌套振荡：一种以θ和伽马节律之间的完美锁相为特征，对应于整体周期性行为；另一种情况是锁定不完美，动力学是准周期性的，甚至是混沌的。从我们的分析中可以看出，在 ING 设置中，锁定状态更为频繁。与实验一致，我们发现在 [1:10] Hz 范围内的强迫频率的 theta 嵌套伽马振荡，其振幅与强迫强度成比例增长，并且显然由 theta 相位调制。此外，与实验类似，伽马功率和伽马功率峰值的频率随着强迫幅度的增加而增加。与实验结果不同，伽马功率峰值不会通过增加 theta 频率而转移到更高的频率。在我们的模型中，只能通过同时增加刺激功率来获得这种效果。通过与 theta 频率成比例地增加噪声或强制项的幅度来实现的效果。根据我们的分析，PING 和 ING 机制都产生了具有几乎相同特征的 theta 嵌套伽马振荡。通过增加 theta 频率，伽马功率峰值不会转移到更高的频率。在我们的模型中，只能通过同时增加刺激功率来获得这种效果。通过与 theta 频率成比例地增加噪声或强制项的幅度来实现的效果。根据我们的分析，PING 和 ING 机制都产生了具有几乎相同特征的 theta 嵌套伽马振荡。通过增加 theta 频率，伽马功率峰值不会转移到更高的频率。在我们的模型中，只能通过同时增加刺激功率来获得这种效果。通过与 theta 频率成比例地增加噪声或强制项的幅度来实现的效果。根据我们的分析，PING 和 ING 机制都产生了具有几乎相同特征的 theta 嵌套伽马振荡。