Topological Network Analysis of Beta‐Amyloid and Tau in Alzheimer’s Disease Using PET Imaging Data

Abstract

AbstractBackgroundAlzheimer’s disease (AD) is characterized by the presence of beta‐amyloid (Aβ) and tau in the brain. Understanding the interplay between these proteins and their spatial distribution may provide insights into disease progression. This study aims to investigate the topological features of Aβ and tau networks in AD, mild cognitive impairment (MCI), and normal cognition (NC) groups using PET images from the ADNI dataset.MethodPartial correlation matrices between the standardized uptake value ratio of 68 regions of interest (ROI’s) were used to generate networks for the AD, MCI, and NC groups, with nodes representing ROI’s and edges representing correlation coefficients. Topological features, including H0 features (connected components), H1 features (loops), and landscape functions of H1 features, were calculated for each sample’s persistent homology. For each group, 100 bootstrapping samples were used to generate the 95% confidence intervals for landscape functions. The connected components were further studied by representing the samples as hierarchical tree structures. In the tree space, the first few generated connections, representing the most consistent pairs of regions positive for Aβ and tau, were compared across groups. Clustering performances were compared using Wasserstein distance of H0 features, Wasserstein distance of H1 features, landscape function distance, and geodesic distance in tree space respectively.ResultThe geodesic distance in tree space showed the best clustering accuracy in both Aβ and tau analyses. Compared with Aβ, H1 features and the corresponding landscape functions performed better for tau. Unique connections in AD and MCI groups were identified, with AD showing more unique connections than MCI compared to NC samples. Dominant unique connections in the AD group included left‐right isthmus cingulate and left fusiform‐left inferior temporal for Aβ, and left‐right paracentral and left cuneus‐left pericalcarine for tau. These connections indicate region pairs with related concentrations of Aβ and tau in AD.ConclusionTopological network analysis can reveal complex underlying structures in PET images and identify consistent patterns in ROI’s associated with Aβ and tau localization. Tau aggregation exhibits more complex behavior than Aβ and is more strongly associated with AD. The identified unique connections in the AD group may serve as potential biomarkers for disease progression.