Topological data analysis reveals altered brain connectivity in Alzheimer’s disease

This study analyzed brain network topology by using persistent homology (PH) on resting-state functional magnetic resonance imaging data from the Alzheimer’s Disease Neuroimaging Initiative. The analysis encompassed a total of 386 imaging samples with Alzheimer’s disease (AD), early mild cognitive impairment (EMCI), mild cognitive impairment (MCI), and normal controls (NC). Functional connectivity among 46 regions of interest within the default mode network (DMN), salience network, and executive control network was constructed and transformed into multi-scale Vietoris–Rips complexes, from which topological invariants such as Betti numbers were extracted to characterize network integration and cyclic structures. Statistical analysis revealed significant global differences in the distributions of 0- and 1-dimensional Betti numbers between the AD and NC groups (p < 0.001). At the regional level, the AD group showed significantly reduced loop counts in the Frontal_Sup_L, Frontal_Sup_Orb_R, Frontal_Inf_Orb_R, Frontal_Sup_Medial_L, and Caudate_R (Mann–Whitney U test, FDR-corrected q < 0.05). Furthermore, comparisons across the NC, EMCI, and MCI groups identified significant progressive changes in loop counts in the Frontal_Sup_L, Frontal_Sup_Medial_L, Frontal_Sup_Medial_R, Parietal_Inf_L, Angular_R, and Caudate_L (Kruskal–Wallis test, FDR-corrected q < 0.05). Notably, the Frontal_Sup_Medial exhibited early degradation at the EMCI stage, whereas alterations in the parietal-angular network persisted into the MCI stage. These findings demonstrate distinct spatiotemporal patterns of topological disruption across the AD continuum. PH provides a novel computational framework for detecting early network dysfunction in AD.