Theoretical Investigation of NMDA Effect on the Cerebral Cortex

Abstract

This thesis examines the dynamical behaviour of incorporating NMDA (an excitatory neurotransmitter) for the electrodynamic model of the cerebral cortex. The model used is the mean-field model developed by Steyn-Ross et al. (2005) which describes the behaviour of the cortex in terms of parameters averaged over spatially localised populations. The behaviour of the model is determined by the four control parameters: inhibitory effect li, subcortical drive s, and NMDA neurotransmitter e ect set by an excitatory factor le and the magnesium concentration C. Adopting this model could give a better understanding of the cortex functionality and the anaesthetic mechanism. The model predicts that there are either one or three stationary states available to the cortex. We identify two of these with highly activated state and a quiescent state and focus on the transition between the two. Theoretical stability predictions (eigenvalue analysis) verified by a numerical simulation show that the system is unstable between the two Hopf bifurcations. In addition, in the stable region the steady states remains stable under a small perturbation, while in the unstable region either a transition between states or a limit cycle (oscillation) occurs depending on the position of the steady state.