Algebraic Connectivity Reveals Modulated High-Order Functional Networks in Alzheimer's Disease

TL;DR

This study introduces a hypergraph-based framework to model high-order functional connectivity in the Alzheimer's disease (AD) spectrum and weights hyperedges using the algebraic connectivity $a(\mathcal{G})$ of the subgraphs formed by each hyperedge. A common HC-derived hypergraph backbone is constructed, and the approach demonstrates superior sensitivity to group differences and stronger discriminative power in HC vs AD, MCI vs AD, and HC vs MCI classifications compared with baseline methods. Mediation analyses indicate that high-order functional information captured by selective hyperedges (notably hyperedges 60 and 75) partially mediates the relationship between entorhinal tau burden and cognitive scores, supporting a mechanistic link between molecular pathology and cognition. External validation on higher-resolution atlases and an independent ADNI cohort confirms robustness and highlights network-level disruptions in salience/ventral attention, default-mode, somatomotor, and visual systems in AD. Overall, the work provides a principled, scalable way to extract meaningful, high-order functional features that connect brain network architecture to AD pathology and clinical outcomes.

Abstract

Functional MRI is a neuroimaging technique that analyzes the functional activity of the brain by measuring blood-oxygen-level-dependent signals throughout the brain. The derived functional features can be used for investigating brain alterations in neurological and psychiatric disorders. In this work, we employed a hypergraph to model high-order functional relations across brain regions, introducing algebraic connectivity (a(G)) for estimating the hyperedge weights. The hypergraph structure was derived from healthy controls to build a common topology across individuals. The considered cohort for subsequent analyses included subjects covering the Alzheimer's disease (AD) continuum, encompassing both mild cognitive impairment and AD patients. Statistical analysis and three classification tasks: HC vs AD, MCI vs AD, and HC vs MCI, were performed to assess differences across the three groups and the potential of the hyperedge weights as functional features. Furthermore, a mediation analysis was performed to evaluate the reliability of the a(G) values, representing functional information as the mediator between tau-PET levels, a key biomarker of AD, and cognitive scores. The proposed approach identified a larger number of hyperedges statistically different across groups compared to state-of-the-art methods. The a(G) hyperedge weights also demonstrated a higher discriminative power in all three binary classifications. Finally, two hyperedges belonging to salience/ventral attention and somatomotor networks showed a partial mediation effect between the tau biomarker and cognitive decline. These results suggested that a(G) can be an effective approach for extracting the hyperedge weights, including important functional information that resides in the brain areas forming the hyperedges.

Figures (5)

• Figure 1: Pipeline of this work. Initially, the mean time series are extracted from the fMRI volumes for each region of the Schaefer atlas. Then, the LASSO regression is computed between the intra-subject time series to extract the coefficients' matrix, subsequently binarized in the incidence matrix $\mathbf{H}$. After that, the hyperedge weights (matrix $\mathbf{W}$) are computed. Finally, a post-hoc analysis is performed.
• Figure 2: Incidence matrix H of the hypergraph. H is composed of 96 hyperedges, with a maximum of 7 regions per hyperedge, a minimum of 3, and an average of 4.66 regions.
• Figure 3: Schematic representation of the mediation analysis of this work.
• Figure 4: Hyperedges found statistically relevant in the proposed analysis with their FDR-corrected p-values for the four different approaches (FDR level of 0.05). The highlighted regions were mainly part of salience/ventral attention, somatomotor, dorsal attention, default-mode, and visual FNs.
• Figure 5: Boxplots representing the distribution of the weights of the three groups for the statistically significant hyperedges and FNs. In the figure, the hyperedges are denoted by the letter "e" followed by the corresponding hyperedge number used in this study. For each hyperedge, the Kruskal-Wallis FDR-corrected p-value ($\mathrm{p}<0.05$) and corresponding effect size (ES) are annotated.