Poster Presentation | Open | Published:
The perturbation response and power spectrum of a mean-field of IF neurons with inhomogeneous inputs
BMC Neurosciencevolume 11, Article number: P44 (2010)
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 . 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 . In this study we use and extend a recently published Fokker-Planck approach  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  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 .
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 . This work is the first stage necessary for constructing a physiologically plausible mathematical model of a mesoscopic network of cortical columns.
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.
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.
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.
Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci. 2000, 8: 183-208. 10.1023/A:1008925309027.
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.
This work was funded by the Australian Research Council (ARC Linkage Project #LP0560684).