  Brain regions are often topographically connected: nearby locations within
one brain area connect with nearby locations in another area. Mapping these
connection topographies, or 'connectopies' in short, is crucial for
understanding how information is processed in the brain. Here, we propose
principled, fully data-driven methods for mapping connectopies using functional
magnetic resonance imaging (fMRI) data acquired at rest by combining spectral
embedding of voxel-wise connectivity 'fingerprints' with a novel approach to
spatial statistical inference. We applied the approach in human primary motor
and visual cortex, and show that it can trace biologically plausible,
overlapping connectopies in individual subjects that follow these regions'
somatotopic and retinotopic maps. As a generic mechanism to perform inference
over connectopies, the new spatial statistics approach enables rigorous
statistical testing of hypotheses regarding the fine-grained spatial profile of
functional connectivity and whether that profile is different between subjects
or between experimental conditions. The combined framework offers a fundamental
alternative to existing approaches to investigating functional connectivity in
the brain, from voxel- or seed-pair wise characterizations of functional
association, towards a full, multivariate characterization of spatial
topography.
