Relating Structure and Function in the Human Brain: Relative Contributions of Anatomy, Stationary Dynamics, and Non-stationarities

Investigating the relationship between brain structure and function is a central endeavor for neuroscience research. Yet, the mechanisms shaping this relationship largely remain to be elucidated and are highly debated. In particular, the existence and relative contributions of anatomical constraints and dynamical physiological mechanisms of different types remain to be established. We addressed this issue by systematically comparing functional connectivity (FC) from resting-state functional magnetic resonance imaging data with simulations from increasingly complex computational models, and by manipulating anatomical connectivity obtained from fiber tractography based on diffusion-weighted imaging. We hypothesized that FC reflects the interplay of at least three types of components: (i) a backbone of anatomical connectivity, (ii) a stationary dynamical regime directly driven by the underlying anatomy, and (iii) other stationary and non-stationary dynamics not directly related to the anatomy. We showed that anatomical connectivity alone accounts for up to 15% of FC variance; that there is a stationary regime accounting for up to an additional 20% of variance and that this regime can be associated to a stationary FC; that a simple stationary model of FC better explains FC than more complex models; and that there is a large remaining variance (around 65%), which must contain the non-stationarities of FC evidenced in the literature. We also show that homotopic connections across cerebral hemispheres, which are typically improperly estimated, play a strong role in shaping all aspects of FC, notably indirect connections and the topographic organization of brain networks.Author Summary: By analogy with the road network, the human brain is defined both by its anatomy (the ‘roads’), that is, the way neurons are shaped, clustered together and connected to each others and its dynamics (the ‘traffic’): electrical and chemical signals of various types, shapes and strength constantly propagate through the brain to support its sensorimotor and cognitive functions, its capacity to learn and adapt to disease, and to create consciousness. While anatomy and dynamics are organically intertwined (anatomy contributes to shape dynamics), the nature and strength of this relation remain largely mysterious. Various hypotheses have been proposed and tested using modern neuroimaging techniques combined with mathematical models of brain activity. In this study, we demonstrate the existence (and quantify the contribution) of a dynamical regime in the brain, coined ‘stationary’, that appears to be largely induced and shaped by the underlying anatomy. We also reveal the critical importance of specific anatomical connections in shaping the global anatomo-functional structure of this dynamical regime, notably connections between hemispheres.