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This article is part of the supplement: Nineteenth Annual Computational Neuroscience Meeting: CNS*2010

Open Access Poster Presentation

The perturbation response and power spectrum of a mean-field of IF neurons with inhomogeneous inputs

Andre DH Peterson12*, Hamish Meffin4, Anthony N Burkitt12, Iven MY Mareels1, David B Grayden12, Levin Kuhlmann1 and Mark J Cook23

Author Affiliations

1 Department of Electrical & Electronic Engineering, The University of Melbourne, Victoria, 3010, Australia

2 The Bionic Ear Institute, 384-388 Albert St, East Melbourne, VIC 3002, Australia

3 Department of Clinical Neurosciences, St. Vincent’s Hospital, Melbourne, VIC, 3065, Australia

4 NICTA VRL, c/- Dept of Electrical & Electronic Engineering, University of Melbourne, VIC 3010, Australia

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BMC Neuroscience 2010, 11(Suppl 1):P44  doi:10.1186/1471-2202-11-S1-P44

The electronic version of this article is the complete one and can be found online at:

Published:20 July 2010

© 2010 DHPeterson et al; licensee BioMed Central Ltd.

Poster Presentation

The aim of this study is to construct a bottom-up model of cortical dynamics that is capable of describing the same types of neural phenomena as top-down continuum models, namely the power spectrum, frequency response to perturbation and EEG time-series. The key difference between the two approaches is that the bottom-up approach preserves more of the intrinsic physiological details than the top-down models [1]. A stochastic Fokker-Planck modelling approach is used to describe a network of leak integrate-and-fire (IF) neurons with temporally inhomogeneous inputs. Previous work either calculated the response of a single neuron with conductance-based synapses, or the network with current-based synapses [2]. In this study we use and extend a recently published Fokker-Planck approach [3] within an analytical framework to calculate the dynamical firing-rate of a network with conductance-based synapses receiving temporally inhomogeneous synaptic input. In particular, the network has fully recurrent connectivity with both the steady-state and the dynamic perturbation response of the background activity fed back into the inputs. This is done in a self-consistent formalism [4] for a network of excitatory and inhibitory neurons.

The Fokker-Planck formalism enables the calculation of the linear response of the firing-rate to perturbation with recurrent connections. The power spectrum and EEG time-series of the network are calculated by treating the synaptic inputs as an inhomogeneous Poisson process. From this we determine the auto-correlation function, which is identified as a cyclo-stationary process. The signal is then phase-averaged over its period and the Wiener-Khinchin theorem is used to determine the power spectrum from the autocorrelation function. The power spectrum is convolved with a filter to approximate the local field potential propagation through the extra-cellular fluid [5].

The analytical results of the frequency response of the dynamical firing rate and its power spectra are compared with numerical simulation results for a recurrently connected network with conductance-based synapses and temporally inhomogeneous inputs. Results are obtained using parameter values that represent typical cortical in vivo neurons [4]. This work is the first stage necessary for constructing a physiologically plausible mathematical model of a mesoscopic network of cortical columns.


This work was funded by the Australian Research Council (ARC Linkage Project #LP0560684).


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