H-VIP: Quantifying regional topological contributions from the brain network towards cognition

Sumita Garai¹Sandra Vo²Lucy Blank¹Frederick Xu¹Jiong Chen¹DUY DUONG-TRAN³Yize Zhao⁴Brielin C. Brown⁵Li Shen^5*

• ¹University of Pennsylvania, Philadelphia, United States
• ²Regis University, Denver, United States
• ³Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, United States
• ⁴Yale University, New Haven, United States
• ⁵Radiology and Imaging Sciences, Perelman School of Medicine, University of Pennsylvania, Philadelphia, IN, United States

Introduction: Understanding the role of various brain regions of interest (ROIs) in various cognitive functions or tasks, in healthy or neurodegenerative conditions across 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, Homological Vertex Importance Profile (H-VIP), designed to assess the relevance of vertices that participate in persistent topological structures (e.g., connected components, cavities or voids) 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: Levering homological constructs of brain connectomes, we extends two of our previously defined network-level measures: average persistence and persistence entropy to ROI-level measure, i.e., H-VIP. We then applied 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. H-VIP scores were used for prediction of multiple cognitive measures. Results: In both anatomical and functional brain networks, H-VIP values demonstrate predictive power for various cognitive measures. 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 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, H-VIP can be used for practically other types of complex networks where topological features are of utmost importance such as financial, social or bio-ecological networks.