Effects of local feedback on dispersion of electrical waves in the cerebral cortex

Abstract

This paper generalizes an existing continuum model of the large-scale electrical activity of the brain by incorporating local feedback. The model is first reformulated by parametrizing neuronal function in more detail and we then show that only four broad classes of local feedback are consistent with general physiological constraints. The corresponding linear dispersion relations are found to contain additional modes as a result of feedback. It is shown that each feedback class can produce lightly damped or undamped oscillatory modes at frequencies similar to those seen in electroencephalography, although not all combinations of type and speed of feedback result in oscillatory behavior. Three kinds of lightly damped resonances are found, each with distinctive frequency characteristics. The effect of feedback on other roots is also described.