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  • Open Access

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

  • 1, 2Email author,
  • 4,
  • 1, 2,
  • 1,
  • 1, 2,
  • 1 and
  • 2, 3
BMC Neuroscience201011 (Suppl 1) :P44

  • Published:


  • Power Spectrum
  • Synaptic Input
  • Cortical Column
  • Recurrent Connection
  • Inhomogeneous Poisson Process

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).

Authors’ Affiliations

Department of Electrical & Electronic Engineering, The University of Melbourne, Victoria, 3010, Australia
The Bionic Ear Institute, 384-388 Albert St, East Melbourne, VIC, 3002, Australia
Department of Clinical Neurosciences, St. Vincent’s Hospital, Melbourne, VIC, 3065, Australia
NICTA VRL, c/- Dept of Electrical & Electronic Engineering, University of Melbourne, VIC, 3010, Australia


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© DHPeterson et al; licensee BioMed Central Ltd. 2010

This article is published under license to BioMed Central Ltd.