Applied Mathematics Seminar

A recently developed neurophysical model of the generation of brain electrical activity is outlined and applied to electroencephalograms (EEGs) and evoked response potentials to stimuli (ERPs) in normal subjects, and in subjects suffering from disorders including epilepsy. The model incorporates both single-neuron physiology and the large-scale anatomy of corticocortical and corticothalamic pathways, including synaptic strengths, dendritic propagation, nonlinear firing responses, and axonal conduction. Under this model, small perturbations around steady-state conditions account for the spatial and temporal observed EEGs as functions of state of arousal, and can be analyzed using wave equations. Similarly for evoked response potentials, which arise as impulse response functions of the system. It is found that feedback via the thalamus is critical in determining the forms of the EEG and evoked potentials, the transition between sleep and waking, and the stability of the brain against seizures. A number of common disorders correspond to significant changes in EEGs, which can be quantified in terms of underlying physiology using inverse modeling techniques within the framework of our theory. In the nonlinear regime, limit-cycle and chaotic behavior are seen. In particular, when negative feedback via the thalamus falls below a threshold relative to positive feedback, limit cycle oscillations develop with the characteristic 3 Hz spike-and-wave form of petit mal epilepsy.