Research on Alzheimer’s Disease Based on Topological Data Analysis

For Alzheimer's disease (AD), the predominant neurodegenerative disorder, early diagnosis is paramount to decelerate its disease course. While resting-state functional MRI (rs-fMRI) enables the visualization of brain connectivity patterns, conventional analytical methods suffer from inherent limitations. To address this, we constructed Vietoris-Rips complexes and functional brain networks from rs-fMRI data of 146 participants (73 AD patients and 73 normal controls), focusing on the Default Mode Network (DMN), Salience Network (SN), and Executive Control Network (ECN). Topological features such as the 0-dimensional and 1-dimensional Betti numbers were extracted to quantify connected components and loop structures. Statistical comparisons between AD and normal control (NC) groups involved analyzing the distributions of Betti curves and conducting Mann–Whitney U tests to identify regions with altered neural loop lengths. Significant between-group differences (p < 0.001) were observed in the distributions of both 0-dimensional and 1-dimensional Betti numbers. Regions with altered neural loop lengths included the Frontal_Sup_Orb_L, Olfactory_R, Frontal_Mid_Orb_R, Cingulum_Ant_R, and Caudate_R. This persistent homology-based framework serves as a computer-aided diagnosis tool that quantifies AD-related topological disruptions independently of predefined thresholds. It not only overcomes key limitations of graph-theoretical methods but also demonstrates strong potential for clinical translation by suggesting robust topological biomarkers for early AD detection.