Epileptiform activity in a neocortical network: a mathematical model

A simple mathematical model describing the generation and propagation of ep ileptiform activity in a cerebral cortical network is presented. The model consists of a system of nonlinear delay differential equations. Physiologic al properties are taken into account as nonlinear transmission of signals a t the synapse, temporal and spatial summation of incoming signals at the so ma, active membrane characteristics, and dendritic and axonal propagation t imes. The influence of the connectivity and the temporal parameters on the oscillatory properties of the model is studied. The computer simulations ar e in agreement with experimental observations in cortical networks: whereas a weak excitatory or strong inhibitory synaptic connection strength produc es a stationary status with short-lasting responses to external stimuli, in creases in excitation or decreases in inhibition induce spontaneous and sti mulus-evoked rhythmic discharges. Synaptic burst-like activity is observed only for an intermediate range of excitatory and inhibitory connection stre ngths and external inputs. The form and duration of the bursts can also be controlled by the temporal parameters. The results demonstrate that relativ ely simple mathematical equations are sufficient to model some of the netwo rk properties underlying the generation and propagation of epileptiform act ivity.