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.
Miri Rekavandi, A., Jbabdi, S., Smith, S. M.
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