Tuned solutions in dynamic neural fields as building blocks for extended EEG models

The most prominent functional property of cortical neurons in sensory areas are their tuned receptive fields which provide specific responses of the neurons to external stimuli. Tuned neural firing indeed reflects the most basic and best worked out level of cognitive representations. Tuning properties can be dynamic on a short time-scale of fractions of a second. Such dynamic effects have been modeled by localised solutions (also called "bumps" or "peaks") in dynamic neural fields. In the present work we develop an approximation method to reduce the dynamics of localised activation peaks in systems of n coupled nonlinear d-dimensional neural fields with transmission delays to a small set of delay differential equations for the peak amplitudes and widths only. The method considerably simplifies the analysis of peaked solutions as demonstrated for a two-dimensional example model of neural feature selectivity in the brain. The reduced equations describe the effective interaction between pools of local neurons of several (n) classes that participate in shaping the dynamic receptive field responses. To lowest order they resemble neural mass models as they often form the base of EEG-models. Thereby they provide a link between functional small-scale receptive field models and more coarse-grained EEG-models. More specifically, they connect the dynamics in feature-selective cortical microcircuits to the more abstract local elements used in coarse-grained models. However, beside amplitudes the reduced equations also reflect the sharpness of tuning of the activity in a d-dimensional feature space in response to localised stimuli.