Spectral properties of the temporal evolution of brain network structure

Abstract

The temporal evolution properties of the brain network are crucial for complex brain processes. In this paper, we investigate the differences in the dynamic brain network during resting and visual stimulation states in a task-positive subnetwork, task-negative subnetwork, and whole-brain network. The dynamic brain network is first constructed from human functional magnetic resonance imaging data based on the sliding window method, and then the eigenvalues corresponding to the network are calculated. We use eigenvalue analysis to analyze the global properties of eigenvalues and the random matrix theory (RMT) method to measure the local properties. For global properties, the shifting of the eigenvalue distribution and the decrease in the largest eigenvalue are linked to visual stimulation in all networks. For local properties, the short-range correlation in eigenvalues as measured by the nearest neighbor spacing distribution is not always sensitive to visual stimulation. However, the long-range correlation in eigenvalues as evaluated by spectral rigidity and number variance not only predicts the universal behavior of the dynamic brain network but also suggests non-consistent changes in different networks. These results demonstrate that the dynamic brain network is more random for the task-positive subnetwork and whole-brain network under visual stimulation but is more regular for the task-negative subnetwork. Our findings provide deeper insight into the importance of spectral properties in the functional brain network, especially the incomparable role of RMT in revealing the intrinsic properties of complex systems. The temporal evolution of brain network structure is crucial to revealing brain functions at different brain states, such as learning, memory, and visual stimulation. The sliding window method is effective for the construction of a dynamic brain network, and complex network analysis has been widely used to characterize these networks. Recently, the spectral property analysis of complex networks has attracted increasing attention based on its ability to measure more intrinsic properties of networks than complex network analysis. In particular, the dynamic brain network constructed from human electroencephalogram (EEG) data has been successfully studied by applying random matrix theory (RMT), which aims to identify the spectral fluctuation properties of networks. However, little is known about the spectral properties of the dynamic brain network based on human functional magnetic resonance imaging (fMRI) data at different brain states, and how spectral properties reflect changes in the dynamic brain network must be explained in greater detail. Here, we addressed these issues and investigated the spectral properties of a dynamic brain network constructed from human fMRI data. We show that the global and local properties of the eigenvalue of the brain network are effective for evaluating the changes in the dynamic brain network caused by visual stimulation. However, the differences between global properties...

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