Current researches on default mode network (DMN) in normal elderly have mainly focused on finding some dysfunctional areas with decreased or increased connectivity. The global network dynamics of apolipoprotein E (APOE) e4 allele group is rarely studied. In our previous brain network study, we have demonstrated the advantage of persistent homology. It can distinguish robust and noisy topological features over multiscale nested networks, and the derived properties are more stable. In this study, for the first time we applied persistent homology to analyze APOE-related effects on whole-brain functional network. In our experiments, the risk allele group exhibited lower network radius and modularity in whole brain DMN based on graph theory, suggesting the abnormal organization structure. Moreover, two suggested measures from persistent homology detected significant differences between groups within the left hemisphere and in the whole brain in two datasets. They were more statistically sensitive to APOE genotypic differences than standard graph-based measures. In summary, we provide evidence that the e4 genotype leads to distinct DMN functional alterations in the early phases of Alzheimer’s disease using persistent homology approach. Our study offers a novel insight to explore potential biomarkers in healthy elderly populations carrying APOE e4 allele.

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.