Brain Connectivity Modelling Through Joint Estimation of Parcels and Gradients

This paper presents a framework for modelling the topography of whole-brain connectivity in resting-state functional MRI. The aim is to disentangle functional segregation, which manifests as abrupt changes in connectivity, from so-called gradients, i.e., smooth variations in connectivity across the brain. Our core assumption is that functional segregation leads to low-rank structure in the dense (point-to-point) connectome, whereas connectivity gradients imply a sparse and non-low-rank structure in the dense connectome. Our method thus decomposes the connectome into low-rank and sparse components, enabling the integration of local-nonlinear and global-linear embedding strategies. We show that this hybrid model approximates the empirical dense connectome more effectively than purely low-rank or purely gradient approaches. We also find that connectivity gradients derived from this model exhibit strong correspondence with task-based topographic maps. We hope that this approach can provide insight into the organisational principles of brain regions where gradients remain poorly characterised.