Theoretical Investigation of NMDA Effect on the Cerebral Cortex
AL Saidi, W. H. K. (2008). Theoretical Investigation of NMDA Effect on the Cerebral Cortex (Thesis, Master of Science (MSc)). The University of Waikato, Hamilton, New Zealand. Retrieved from http://hdl.handle.net/10289/2465
Permanent Research Commons link: http://hdl.handle.net/10289/2465
This thesis examines the dynamical behaviour of incorporating NMDA (an excitatoryneurotransmitter) for the electrodynamic model of the cerebral cortex. Themodel used is the mean-field model developed by Steyn-Ross et al. (2005) whichdescribes the behaviour of the cortex in terms of parameters averaged over spatiallylocalised populations. The behaviour of the model is determined by the four controlparameters: inhibitory effect li, subcortical drive s, and NMDA neurotransmittere ect set by an excitatory factor le and the magnesium concentration C. Adoptingthis model could give a better understanding of the cortex functionality and theanaesthetic mechanism.The model predicts that there are either one or three stationary states available tothe cortex. We identify two of these with highly activated state and a quiescentstate and focus on the transition between the two. Theoretical stability predictions(eigenvalue analysis) verified by a numerical simulation show that the system isunstable between the two Hopf bifurcations. In addition, in the stable region thesteady states remains stable under a small perturbation, while in the unstable regioneither a transition between states or a limit cycle (oscillation) occurs depending onthe position of the steady state.
The University of Waikato
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