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Mathematical Modelling of the Neurochemical Processes in Schizophrenia

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Noori, H. (2008). Mathematical Modelling of the Neurochemical Processes in Schizophrenia. PhD Thesis, Universität Heidelberg, Heidelberg, Germany.

Cite as: https://hdl.handle.net/21.11116/0000-0003-93BA-5
Schizophrenia is an endogenous psychosis with a 1 \% prevalence in world population. Several pharmacological studies suggest that alterations in the function of different neurotransmitter systems such as dopamine or glutamate are related to schizophrenic symptoms. This thesis represents mathematical models that are constructed to investigate the dynamical behaviour of the neurochemical systems in the human brain. These models formulate the anatomical properties and physiological processes of synapses, single brain compartments and large neurochemical pathways involved in the regulation of behaviour such as the basal ganglia and the limbic system. The interaction between the neurochemical systems and the electrophysiological activities are considered by modelling in different scales. In the synaptic scale, it has been shown that the transport of neurotransmitters in the synaptic cleft is merely governed by electrical forces than diffusion. The intra-synaptic concentration of neurotransmitters is modelled using partial differential equations and is coupled to the Hodgkin-Huxley equation (neurochemical modification) to model the effect of neurotransmitter-receptor binding in the generation of post-synaptic potentials. Considering the morphological and ultra-morphological studies of brain compartments, the averaged electrophysiological activity is modelled by integral equations respecting these internal structures. A system comprised by nonlinear delay differential equations is constructed to simulate the dynamical behaviour of neurochemical concentrations, coupled to the local electrophysiological activity of the compartments, on the brain pathways. By parameter sensitivity analysis, we have also investigated qualitatively the influence of certain anti-psychotic agents. Synchronized oscillations are experienced in electrophysiological systems. The neurotransmitter concentrations also demonstrate an oscillatory behaviour. The resulting oscillatory dynamics of these processes reveals a profound view on the relation between the dynamical behaviour of the neurochemical systems and the occurrence of psychotic states. These facts led us to establish a hypothesis on this relation, called the oscillation hypothesis of psychosis. Because of the general formulation of the models, these are not only useful for schizophrenia, but also for the investigations of other neurological diseases.