Topological signatures of brain dynamics: persistent homology reveals individuality and brain-behavior links.

Introduction: Understanding individual differences in brain dynamics is a central goal in neuroscience. While conventional time series features capture signal properties of local brain regions, they often fail to reveal the deeper structure embedded in the brain's complex activity patterns. Methods: Resting-state fMRI data from approximately 1,000 subjects in the Human Connectome Project were analyzed. A TDA-based framework integrating time-delay embeddings and persistent homology was employed to extract global dynamic features from resting-state fMRI data. Classification models and canonical correlation analysis (CCA) were employed to examine the associations between brain topological features and individual characteristics, including gender and behavioral traits. Results: Topological features exhibited high test-retest reliability and enabled accurate individual identification across sessions. In classification tasks, these features outperformed commonly used temporal features in predicting gender. Canonical correlation analysis identified a significant brain-behavior mode that links topological brain patterns to cognitive measures and psychopathological risks. Regression analyses across behavioral domains showed that persistent homology features matched or exceeded the predictive performance of traditional features in higher-order domains such as cognition, emotion, and personality, while traditional features performed slightly better in sensory-related domains. Discussion: These findings highlight persistent homology as a robust and informative framework for modeling individual differences in brain function, offering promising avenues for personalized neuroimaging analysis.