The Everything and Everywhere of Neural Field Theory

Neural field theories (NFT) model the waves of activity that sweep across the cortical surface. This talk will trace the formal derivation of "classic NFT" from the physiological and anatomical properties of the brain, including synaptic filtering of inputs, somatic summation, nonlinear gain, signal propagation and time-delayed feedback in loops and circuits. Under broad assumptions, NFT can be written as a damped wave equation, whose behaviour predicts the abrupt transitions observed in sleep-wake cycles and epilepsy; the spatial and temporal spectra of healthy cortical and hippocampal activity; and the impact of electrical and pharmacological neuromodulation. The damped wave equation comprises temporal and spatial components: The former captures the temporal power spectrum of neural activity, as seen in EEG. The spatial component can be expressed as a sum of weighted "geometric eigenmodes" that provide a parsimonious description of task- and resting state EEG. This talk will walk through these principles and derivations, providing the neuroimaging community with new tools and concepts to study functional neuroimaging data.