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Anesthetic-Induced Transitions by Propofol Modeled by Nonlocal Neural Populations Involving Two Neuron Types

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Abstract

The present work derives the spatiotemporal field equation of neural populations considering two types of neurons. The model considers pyramidal cells, which may excite or inhibit other neurons, and GABAergic interneurons inhibiting terminal neurons. Additionally, taking into account excitatory and inhibitory synapses, the neural population obeys a vector-field equation involving nonlocal spatial interactions. The work studies the effect of the anesthetic agent propofol, which increases the decay time of inhibitory synapses. In addition, it explains the bifurcation mechanism in some detail and finds a saddle–node bifurcation subject to the propofol concentration. This bifurcation may model the transition between consciousness and nonconsciousness and vice versa during the administration of general anesthetics in medicine.

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Acknowledgements

The authors would like to thank Michael Zaks for valuable discussions and acknowledge the financial support by the Deutsche Forschungsgemeinschaft (SfB-555).

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Authors and Affiliations

  1. INRIA CR Nancy – Grand Est, CS20101 54603, Villers-Les-Nancy Cedex, France

    Axel Hutt

  2. Humboldt University at Berlin, 12489, Berlin, Germany

    Lutz Schimansky-Geier

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  1. Axel Hutt
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  2. Lutz Schimansky-Geier
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Correspondence to Lutz Schimansky-Geier.

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Hutt, A., Schimansky-Geier, L. Anesthetic-Induced Transitions by Propofol Modeled by Nonlocal Neural Populations Involving Two Neuron Types. J Biol Phys 34, 433–440 (2008). https://doi.org/10.1007/s10867-008-9065-4

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  • DOI: https://doi.org/10.1007/s10867-008-9065-4

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