PROPAGATION AND STABILITY OF WAVES OF ELECTRICAL-ACTIVITY IN THE CEREBRAL-CORTEX

Nonlinear equations are introduced to model the behavior of the waves of cortical electrical activity that are responsible for signals obser ved in electroencephalography. These equations incorporate nonlinearit ies, axonal and dendritic lags, excitatory and inhibitory neuronal pop ulations, and the two-dimensional nature of the cortex, while renderin g nonlinear features far more tractable than previous formulations, bo th analytically and numerically. The model equations are first used to calculate steady-state levels of cortical activity for various levels of stimulation. Dispersion equations for linear waves are then derive d analytically and an analytic expression is found for the linear stab ility boundary beyond which a seizure will occur. The effects of bound ary conditions in determining global eigenmodes are also studied in va rious geometries and the corresponding eigenfrequencies are found. Num erical results confirm the analytic ones, which are also found to repr oduce existing results in the relevant limits, thereby elucidating the limits of validity of previous approximations.