Current brain network studies based on persistent homology mainly focus on the spatial evolution over multiple spatial scales, and there is little research on the evolution of a spatiotemporal brain network of Alzheimer’s disease (AD). This paper proposed a persistent homology-based method by combining multiple temporal windows and spatial scales to study the spatiotemporal evolution of brain functional networks. Specifically, a time-sliding window method was performed to establish a spatiotemporal network, and the persistent homology-based features of such a network were obtained. We evaluated our proposed method using the resting-state functional MRI (rs-fMRI) data set from Alzheimer’s Disease Neuroimaging Initiative (ADNI) with 31 patients with AD and 37 normal controls (NCs). In the statistical analysis experiment, most network properties showed a better statistical power in spatiotemporal networks than in spatial networks. Moreover, compared to the standard graph theory properties in spatiotemporal networks, the persistent homology-based features detected more significant differences between the groups. In the clustering experiment, the brain networks on the sliding windows of all subjects were clustered into two highly structured connection states. Compared to the NC group, the AD group showed a longer residence time and a higher window ratio in a weak connection state, which may be because patients with AD have not established a firm connection. In summary, we constructed a spatiotemporal brain network containing more detailed information, and the dynamic spatiotemporal brain network analysis method based on persistent homology provides stronger adaptability and robustness in revealing the abnormalities of the functional organization of patients with AD.

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