Computational and Mathematical Methods in Medicine
Volume 10 (2009), Issue 4, Pages 273-285
doi:10.1080/17486700802616526
Original Article

Mathematical Identification of a Neuronal Network Consisting of GABA and DA in Striatal Slices of the Rat Brain

L. Ramrath,1 J. Levering,2 M. Conrad,3 A. Thuemen,2 H. Fuellgraf,2 and A. Moser2

1Institute for Robotics und Cognitive Systems, University of Luebeck, Luebeck D-23538, Germany
2Neurochemical Research Group, Department of Neurology, University of Luebeck, Luebeck D-23538, Germany
3Institute of Mathematics, University of Luebeck, Luebeck D-23538, Germany

Received 9 May 2008; Accepted 11 November 2008

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

High frequency stimulation (HFS) has been used to treat various neurological and psychiatric diseases. Although further disorders are under investigation to extend the clinical application of HFS, the complex effect of HFS within a neuronal network is still unknown. Thus, it would be desirable to find a theoretical model that allows an estimation of the expected effect of applied HFS. Based on the neurochemical analysis of effects of the γ-aminobutyric acid (GABA)A receptor antagonist bicuculline, the D2-like receptor antagonist sulpiride and the D1-like receptor antagonist SCH-23390 on HFS evoked GABA and dopamine (DA) release from striatal slices of the rat brain, a mathematical network model is proposed including the neurotransmitters GABA, DA and glutamate (GLU). The model reflects inhibitory and excitatory interactions of the neurotransmitters outflow in the presence of HFS. Under the assumption of linear interactions and static measurements, the model is expressed analytically. Numerical identification of inhibition and excitation is performed on a basis of real outflow levels of GABA and DA in the rat striatum. Results validate the nature of the proposed model. Therefore, this leads to an analytical model of the interactions within distinct neural network components of the rat striatum.