The structure of the brain network exhibits modularity at multiple spatial scales. The effect of the modular structure on the brain dynamics has been the focus of several studies in recent years but many aspects remain to be explored. For example, it is not well-known how the delays in the transmission of signals between the neurons and the brain regions interact with the modular structure to determine the brain dynamics. In this paper, we show an important impact of the delays on the collective dynamics of brain networks with modular structure; that is, the degree of the synchrony between different brain regions depends on the oscillating frequency. In particular, we show that when increasing the frequency of the nodes the network transits from a global synchrony state to an asynchronous state, through a transition region over which the local synchrony inside the modules is stronger than the global synchrony. When the delays depend on the distance between the nodes, the modular structure of different spatial scales appears in the correlation matrix over different specific frequency bands, so that, finer spatial modular structures reveal in higher frequency bands. The results are corroborated by a simple theoretical argument and elaborated by simulations on several simplified modular networks and the connectome with different spatial resolutions.

脑网络的结构在多个空间尺度上表现出模块化。近年来，模块化结构对大脑动力学的影响一直是数项研究的重点，但许多方面仍有待探索。例如，在神经元和大脑区域之间的信号传输中的延迟如何与模块化结构相互作用以确定大脑动力学是未知的。在本文中，我们显示了延迟对具有模块化结构的大脑网络的集体动力学的重要影响；也就是说，不同大脑区域之间的同步程度取决于振荡频率。特别是，我们表明，当增加节点的频率时，网络将从全局同步状态转换为异步状态，通过过渡区域，模块内部的本地同步性强于全局同步性。当延迟取决于节点之间的距离时，在不同的特定频段上，相关矩阵中会出现不同空间比例的模块化结构，因此，在较高频段上会显示出更精细的空间模块化结构。一个简单的理论论据证实了这一结果，并通过对几种简化的模块化网络和具有不同空间分辨率的连接组的模拟进行了详细阐述。精细的空间模块化结构可在更高的频段显示。一个简单的理论论据证实了这一结果，并通过对几种简化的模块化网络和具有不同空间分辨率的连接组的模拟进行了详细阐述。精细的空间模块化结构可在更高的频段显示。一个简单的理论论据证实了这一结果，并通过对几种简化的模块化网络和具有不同空间分辨率的连接组的模拟进行了详细阐述。