Imagine the human brain as a vast network of interconnected roads, where information travels from one region to another. Scientists have discovered a way to measure the changes that occur in this complex network as we age. By using geometry-inspired mathematical concepts called Forman-Ricci curvature and Ollivier-Ricci curvature, researchers applied these tools to functional connectivity networks in the brains of healthy young and older subjects. The results were fascinating! They found that these curvatures could accurately capture the differences in connectivity between age groups, revealing patterns associated with cognitive functions such as movement, affective processing, and somatosensory processing. Amazingly, some brain regions with age-related curvature differences were also linked to behavioral scores of affective processing. Furthermore, there was an intriguing overlap between brain regions showing curvature differences and areas that demonstrated improved movement in older adults when stimulated non-invasively. These findings highlight the potential of geometry-inspired curvatures in understanding changes in brain organization and function throughout aging. To dive into the fascinating details of this research, read the full article!

IntroductionGeometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is unexplored.MethodsWe apply Forman-Ricci curvature and Ollivier-Ricci curvature to compare functional connectivity networks of healthy young and older subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset (N = 225).ResultsWe found that both Forman-Ricci curvature and Ollivier-Ricci curvature can capture whole-brain and region-level age-related differences in functional connectivity. Meta-analysis decoding demonstrated that those brain regions with age-related curvature differences were associated with cognitive domains known to manifest age-related changes—movement, affective processing, and somatosensory processing. Moreover, the curvature values of some brain regions showing age-related differences exhibited correlations with behavioral scores of affective processing. Finally, we found an overlap between brain regions showing age-related curvature differences and those brain regions whose non-invasive stimulation resulted in improved movement performance in older adults.DiscussionOur results suggest that both Forman-Ricci curvature and Ollivier-Ricci curvature correctly identify brain regions that are known to be functionally or clinically relevant. Our results add to a growing body of evidence demonstrating the sensitivity of discrete Ricci curvature measures to changes in the organization of functional connectivity networks, both in health and disease.

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