Ageing conserves and redistributes local geometry in the human structural connectome: an Ollivier-Ricci curvature analysis across the adult lifespan

Network measures of the ageing connectome are dominated by magnitude: connection strength and density decline, and the topological summaries built on them decline with them. Whether the geometry of the network follows the same course is not known, because the quantities in common use do not separate how strong a connection is from how it sits among the connections around it. We computed the Ollivier-Ricci curvature of every edge in structural connectomes from 307 participants spanning the adult lifespan, a quantity defined by optimal transport between the neighbourhoods of connected regions, and asked how it changes with age. The total geometric separation between within-network and between-network connections did not change across seven decades. Underneath that constancy, individual network pairs moved substantially and in opposite directions, gaining curvature around the salience and ventral attention system and losing it between the control and default mode networks. Curvature and connection strength reached half of their age-related variation almost four decades apart, and a small set of prefrontal nodes moved against the global trend. Ageing appears to conserve the local redundancy of the structural connectome in total while relocating it, on a timescale distinct from that of connection strength.