Driving neural oscillations with correlated spatial input and topographic feedback

Axel Hutt, Connie Sutherland, and André Longtin

Phys. Rev. E 78, 021911 – Published 26 August 2008

Abstract

We consider how oscillatory activity in networks of excitable systems depends on spatial correlations of random inputs and the spatial range of feedback coupling. Analysis of a neural field model with topographic delayed recurrent feedback reveals how oscillations in certain frequency bands, including the gamma band, are enhanced by increases in the input correlation length. Further, the enhancement is maximal when this length exceeds the feedback coupling range. Suppression of oscillatory power occurs concomitantly in other bands. These effects depend solely on the ratio of input and feedback length scales. The precise positions of these bands are determined by the synaptic constants and the delays. The results agree with numerical simulations of the model and of a network of stochastic spiking neurons, and are expected for any noise-driven excitable element networks.

Received 10 January 2008

DOI:https://doi.org/10.1103/PhysRevE.78.021911

Authors & Affiliations

Axel Hutt^1,2,*, Connie Sutherland², and André Longtin²

¹INRIA CR Nancy—Grand Est, CS20101, 54603 Villers-ls-Nancy Cedex, France
²Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, Canada K1N 6N5

^*axel.hutt@loria.fr

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Vol. 78, Iss. 2 — August 2008

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Images

Figure 1
Topography of the feedback model under study. The plus and minus signs indicate the excitatory and inhibitory connections, respectively. The bell-shaped distributions $K_{e n} (x)$ and $K_{n e} (x)$ represent the spatial connectivity functions, while the distribution $I (x, t)$ denotes the spatial correlation function of the external input.Reuse & Permissions
Figure 2
Power spectrum of the membrane potential $E$ about the stationary state $E_{0}$ for different ratios $η$ of the feedback and the input correlation range. For the numerical simulations, a temporal time step of $0.1 ms$ and a spatial discretization step of $5 μ m$ with $10^{5}$ grid points guaranteed good resolutions in the time domain, the location space, and the $k$ space. Further parameters are $τ_{ex} = 1 ms$ , $τ_{in} = 8 ms$ , $τ_{d} = 6 ms$ , $g = 1.2$ , $Q = 0.05 {mV}^{2} ∕ s$ , and $σ_{f} = 5 mm$ , $σ_{i} = 200 mm$ for $η = 0.025$ , $σ_{f} = σ_{i} = 5 mm$ for $η = 1$ , and $σ_{f} = 200 mm$ , $σ_{i} = 5 mm$ for $η = 40$ . The abbreviations after the $η$ values denote analytical results based on Eq. (6) (analyt.) and numerical results based on Eq. (3) (num.).Reuse & Permissions
Figure 3
Frequency bands where the spectral power changes as a function of the ratio $η$ . The dashed vertical lines denote the band borders with frequencies $ν_{0}$ and $ν_{1}$ defined by Eq. (9) while the shaded (nonshaded) area represents the bands of frequencies which exhibit enhanced (attenuated) power upon decreasing $η$ . Further, the solid lines represent the frequency borders obtained numerically from Eq. (6) for $d P ∕ d η = 0$ . Other parameters are taken from Fig. 2.Reuse & Permissions
Figure 4
Response function of the system in Fourier space $R (ν, l)$ and the integrand $R (ν, l) \tilde{C} (l)$ in Eq. (6) for two values of $η = (a)$ , (b) $1 ∕ 40$ , and (c), (d) 40. Other parameters are taken from Fig. 2.Reuse & Permissions
Figure 5
Comparison of spectral power in neural fields and spiking neuron networks. (a) Power spectra of the neural field for a small $(1 ∕ η = 1 ∕ 40)$ and large $(1 ∕ η = 40)$ stimulus correlation length relative to the feedback spread. (b) Power spectra of the spike train from a single stochastic neuron embedded in a network of 100 spiking neurons with topographic delayed feedback for small $(1 ∕ η = 0)$ and large $(η = 100)$ stimulus correlation length. Each neuron is governed by Eq. (10). (c) Integrated power $Γ$ in the gamma range $(30, 50) Hz$ as a function of $1 ∕ η$ for the neural field model [Eq. (6)]. (d) Same as (c) except for the spiking neuron network with the power measured in the range $(20, 40) Hz$ . The parameters of (a) and (c) are the same as in Fig. 2. The parameters in (b) and (d) are $μ = 0.5$ (subthreshold regime), $g = - 0.6$ , $D = 0.08$ , $α = 3$ , $τ_{d} = 1$ , $τ_{r} = 0.1$ , the spiking threshold is 1, the voltage reset is 0, and all times are in units of the membrane constant, assumed to be $6 ms$ .Reuse & Permissions

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