Andre DH Peterson

Anthony N Burkitt

David B Grayden

H Meffin

Hamish Meffin

Iven MY Mareels

J Milton

Mark J Cook

PA Robinson

BMC Neuroscience

English

PubMed

Springer - Publisher Connector

POSTER PRESENTATION Open Access
A bifurcation analysis of a modified neural field
model: conductance-based synapses act as an
anti-epileptic regulatory mechanism
Andre DH Peterson1,2,3*, Iven MY Mareels1, Hamish Meffin1,4, David B Grayden1,2,4, Mark J Cook2,3,
Anthony N Burkitt1,2
From Twentieth Annual Computational Neuroscience Meeting: CNS*2011
Stockholm, Sweden. 23-28 July 2011
The spread of seizure-like behaviour through the cortex
is facilitated not only by hyper-excitable, hyper-synchro-
nous neuronal population firing, but by overcoming the
regulatory mechanisms of the brain, such as feedback
and feed-forward inhibition. These control mechanisms
normally stabilise such pathological behaviour [1]. We
suggest an additional network regulatory mechanism in
the form of a ‘shunting’ effect based on the properties of
conductance-based synapses, an important neurophysio-
logical structure whose mechanism is often overlooked
in macroscopic models of brain dynamics.
A mathematical neural field model [2] is modified to
include conductance-based synapses as opposed to cur-
rent-based synapses. This is a more realistic description
of synaptic dynamics that has a significant effect on the
network behaviour [3]. A nonlinear summation of the
synaptic currents is introduced that incorporates local
feedback from the membrane potential and an ‘effective’
time constant that varies inversely with the amount of
input. The result is a more physiologically detailed
description of the synaptic current produced by post-
synaptic potentials. The fixed-points of the new system
are found and a perturbation analysis is performed. The
stability of the system is determined and a bifurcation
diagram is generated using the external input and net-
work balance as bifurcation parameters. These results
are then compared to that of the original model with
current-based synapses and the differences interpreted
physiologically. The fixed points, dynamics and oscilla-
tory properties of the conductance-based model differ
significantly from the current-based model. This is
largely due to the ‘shunting’ effect of the synapses, which
acts as a network regulatory mechanism. In particular,
oscillatory behaviour in the conductance-based model is
suppressed. Hence, conductance-based synapses are an
important physiological structure whose mechanism of
synaptic transmission should not be neglected in mean-
field models, particularly when applied to epilepsy.
Acknowledgments
This work was funded by the Australian Research Council (ARC Linkage
Project #LP0560684).
Author details
1University of Melbourne, Victoria 3010, Australia. 2The Bionic Ear Institute,
East Melbourne, Victoria 3002, Australia. 3St. Vincent’s Hospital Melbourne,
Victoria 3065, Australia. 4NICTA Victoria Research Laboratory, Victoria 3010,
Australia.
Published: 18 July 2011
References
1. Milton J, Jung P: Epilepsy as a Dynamic Disease. Springer; 2003.
2. Robinson PA, Rennie CJ, Rowe D: Dynamics of large-scale brain activity in
normal arousal states and epileptic seizures. Phys Rev E 2002, 65:041924.
3. Meffin H, Burkitt AN, Grayden DB: An analytical model for the ‘large,
fluctuating synaptic conductance state’ typical of neocortical neurons in
vivo. J Comput Neurosci 2004, 16:159-175.
doi:10.1186/1471-2202-12-S1-P24
Cite this article as: Peterson et al.: A bifurcation analysis of a modified
neural field model: conductance-based synapses act as an anti-epileptic
regulatory mechanism. BMC Neuroscience 2011 12(Suppl 1):P24.
* Correspondence: peterson@unimelb.edu.au
1University of Melbourne, Victoria 3010, Australia
Full list of author information is available at the end of the article
Peterson et al. BMC Neuroscience 2011, 12(Suppl 1):P24
http://www.biomedcentral.com/1471-2202/12/S1/P24
© 2011 Peterson et al; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.


A bifurcation analysis of a modified neural field model: conductance-based synapses act as an anti-epileptic regulatory mechanism

Crossref

An analytical model for the ‘large, fluctuating synaptic conductance state’ typical of neocortical neurons in vivo.

Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E

Epilepsy as a Dynamic Disease.

http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3240345

A bifurcation analysis of a modified neural field model: conductance-based synapses act as an anti-epileptic regulatory mechanism

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