Modal Analysis of Corticothalamic Dynamics, Electroencephalographic Spectra, and Evoked Potentials

The effects of cortical boundary conditions and resulting modal aspects of continuum corticothalamic electrodynamics are explored, including feedbacks. Dispersion relations, electroencephalographic spectra, and stimulus response functions are calculated from the underlying physiology, and the effects of discrete mode structure are determined. Conditions under which modal effects are important are obtained, along with estimates of the point at which modal series can be truncated, and the limit in which only a single globally uniform mode need be retained. It is found that for physiologically plausible parameters only the lowest cortical spatial eigenmode together with the set of next-lowest modes can produce distinct modal structure in spectra and response functions, and then only at frequencies where corticothalamic resonances reduce dissipation to the point where the spatial eigenmodes are weakly damped. The continuum limit is found to be a good approximation, except at very low frequencies and, under some circumstances, near the alpha resonance. It is argued that the major electroencephalographic rhythms result from corticothalamic feedback resonances, but that cortical modal effects can contribute to weak substructure in the alpha resonance. This mechanism is compared and contrasted with purely cortical and pacemaker-based alternatives and testable predictions are formulated to enable experimental discrimination between these possibilities.