Skip to main content

Advertisement

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

Article metrics

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.

References

  1. 1.

    Suffczynski P, Wendling F, Bellanger JJ, Da Silva FHL: Some insights into computational models of (patho) physiological brain activity. Proceedings of the IEEE. 2006, 94 (4): 784-804. 10.1109/JPROC.2006.871773.

  2. 2.

    Burkitt AN: A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties. Biol Cybern. 2006, 95: 97-112. 10.1007/s00422-006-0082-8.

  3. 3.

    Richardson MJE: Spike-train spectra and network response functions for non-linear integrate-and-fire neurons. Biological Cybernetics. 2008, 99 (4): 381-392. 10.1007/s00422-008-0244-y.

  4. 4.

    Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci. 2000, 8: 183-208. 10.1023/A:1008925309027.

  5. 5.

    Bedard C, Destexhe A: Macroscopic models of local field potentials and the apparent 1/f noise in brain activity. Biophys J. 2009, 96: 2589-2603. 10.1016/j.bpj.2008.12.3951.

Download references

Acknowledgments

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

Author information

Correspondence to Andre DH Peterson.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Peterson, A.D., Meffin, H., Burkitt, A.N. et al. The perturbation response and power spectrum of a mean-field of IF neurons with inhomogeneous inputs. BMC Neurosci 11, P44 (2010) doi:10.1186/1471-2202-11-S1-P44

Download citation

Keywords

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