Abstract
Neural field theories successfully describe normal, awake mesoscale to macroscale brain activity using linearized partial differential equations that involve a Laplacian operator. These neural field theories therefore predict spatial brain activity patterns that are simple, smooth eigenfunctions of the Laplacian operator that satisfy the Helmholtz equation and extend across the entire cortex. However, complex, localized spatial patterns such as resting-state networks have been proposed from data analysis of brain activity measurements, primarily fMRI. Using Human Connectome Project data, the Helmholtz eigenmode prediction of neural field theory is shown to be consistent with eigenvectors of both fMRI and MEG covariance matrices. It is explained why these Helmholtz equation eigenmodes have been difficult to observe due to their similar spectra, effects of covariant input stimuli to the brain, and measurement noise. This implies that complex spatial patterns like resting-state networks may be the result of complex input to the brain but simple intrinsic brain dynamics, rather than simple stimuli and complex brain dynamics, as assumed in many existing models.