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      Theoretical Investigation of NMDA Effect on the Cerebral Cortex

      AL Saidi, Waleed Hamdan Khalfan
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      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 https://hdl.handle.net/10289/2465
      Permanent Research Commons link: https://hdl.handle.net/10289/2465
      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.
      Date
      2008
      Type
      Thesis
      Degree Name
      Master of Science (MSc)
      Publisher
      The University of Waikato
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      All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
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