Introduction: Understanding the role of various brain regions of interest (ROIs) in various cognitive functions or tasks, across healthy or neurodegenerative conditions and multiple degrees of separation, remains a key challenge in neuroscience. Conventional network measures can only capture localized or quasi-localized features of brain ROIs. Topological data analysis (TDA), particularly persistent homology, provides a threshold-free, mathematically rigorous framework for identifying topologically salient features in complex networks. In this paper, we introduce a new metric, the Homological Vertex Importance Profile (H-VIP), designed to assess the relevance of vertices that participate in persistent topological structures (e.g., connected components, cycles or cavities) in brain networks. The H-VIP quantifies the topological features of the network at the ROI (node) level by compressing its higher-order connectivity profile using homological constructs.
Methods: Leveraging homological constructs of brain connectomes, we extend two of our previously defined network-level measures-average persistence and persistence entropy-to an ROI-level measure, i.e., the H-VIP. We then applied the H-VIP to two independent datasets: structural connectomes from the Human Connectome Project and functional connectomes from the Alzheimer's Disease Neuroimaging Initiative. Persistent homology was computed for each network, and H-VIP scores were derived to evaluate vertex-level contributions. Finally, H-VIP scores were used for the prediction of multiple cognitive measures.
Results: In both anatomical and functional brain networks, H-VIP values demonstrate predictive power for various cognitive measures. Notably, the connectivity of the frontal lobe exhibited stronger correlations with cognitive performance than the whole-brain network.
Discussion: H-VIP offers a robust and interpretable means to locate, quantify, and visualize region-specific contributions to network's topological, higher-order landscape. Its ability to detect potentially impaired connectivity at the individual level suggests possible applications in personalized medicine for neurological diseases and disorders. Beyond brain connectomics, the H-VIP can be used for other types of complex networks where topological features are of importance, such as financial, social, or ecological networks.
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