Functional harmonics reveal multi-dimensional basis functions underlying cortical organization

ABSTRACT The human brain consists of functionally specialized areas, which flexibly interact and integrate forming a multitude of complex functional networks. However, the nature and governing principles of these specialized areas remain controversial: a distinct modular architecture versus a smooth continuum across the whole cortex. Here, we demonstrate a candidate governing principle ubiquitous in nature, that resolves this controversy for the brain at rest, during perception, cognition and action: functional harmonic modes. We calculated the harmonic modes of the brain’s functional connectivity, called “functional harmonics”, from functional magnetic resonance imaging (fMRI) data in resting state of 812 participants. Each functional harmonic provides an elementary pattern of brain activity with a different spatial frequency. The set of all functional harmonics - ordered according to their spatial frequencies - can reconstruct any pattern of brain activity. The activity patterns elicited by 7 different tasks from the Human Connectome Project can be reconstructed from a very small subset of functional harmonics, suggesting a novel relationship between task and resting state brain activity. Further, the isolines of the continuous functional harmonic patterns delineate the borders of specialized cortical areas as well as somatotopic and retinotopic organization. Our results demonstrate a candidate scalable governing principle for functional brain organization, resolving the controversy between modular versus gradiental views, and demonstrate that a universal principle in nature also underlies human brain cortical organization.