Is the brain macroscopically linear? A system identification of resting state dynamics

A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal functioning. An implicit assumption has thus formed that an accurate computational model of whole-brain dynamics must also be highly nonlinear, whereas linear models may provide a first-order approximation. Here, we provide a rigorous and data-driven investigation of this hypothesis at the level of whole-brain blood-oxygen-level-dependent (BOLD) and macroscopic field potential dynamics by leveraging the theory of system identification. Using functional MRI (fMRI) and intracranial EEG (iEEG), we model the resting state activity of 700 subjects in the Human Connectome Project (HCP) and 122 subjects from the Restoring Active Memory (RAM) project using state-of-the-art linear and nonlinear model families. We assess relative model fit using predictive power, computational complexity, and the extent of residual dynamics unexplained by the model. Contrary to our expectations, linear auto-regressive models achieve the best measures across all three metrics, eliminating the trade-off between accuracy and simplicity. To understand and explain this linearity, we highlight four properties of macroscopic neurodynamics which can counteract or mask microscopic nonlinear dynamics: averaging over space, averaging over time, observation noise, and limited data samples. Whereas the latter two are technological limitations and can improve in the future, the former two are inherent to aggregated macroscopic brain activity. Our results, together with the unparalleled interpretability of linear models, can greatly facilitate our understanding of macroscopic neural dynamics and the principled design of model-based interventions for the treatment of neuropsychiatric disorders.