Mean-field reduction of a layered macroscopic network model

The emergence of slow oscillations, i.e. resting state activity, was studied theoretically over the last years in case of simple network models [1]. Our goal is to extend these studies to a biological more realistic regime considering a layered macroscopic model of the macaque visual cortex, currently developed in our group [2]. As a first step, the mean activity in the model is determined theoretically, based on a mean-field approach [3]. The fixed point solution is challenged by the high dimensionality of the system. Here we show that the fixed point can be found by integrating a first order exponentially relaxing quasi dynamics [4] and the predicted firing rates are in good agreement with the rates found in the full spiking simulation (Fig.1A). The results indicate a linear input-output relationship for individual populations. This raises hope that the model can be mapped to a simple system of linear equations, which will allow a stability analysis and will expose the mechanisms that lead to slow resting-state oscillations. In order to study fast oscillations (gamma band), the local feedback loops of the macroscopic model have to be considered. We aim to identify the responsible loops that shape the power spectra of population signals. The high dimensionality of the macroscopic model requires a reduction to a simpler system. Recently we have developed a suitable method that maps a spiking network to an effective linear rate model [5]. For this purpose the transfer function has to be determined, quantifying how single neurons transfer synaptic input to spiking output (Fig.1B). The results indicate that the rate relaxes with two different time constants. The reduced rate model will enable us to determine correlations in the system [5] and to identify the mechanisms and recurrent loops controlling fast oscillations. [1] Deco, G., Jirsa, V. (2012), Journal of Neuroscience, 32, 3366--3375. [2] Schmidt, M., van Albada, S., Bakker, R., Diesmann, M. (2013), 10th meeting of the German Neuroscience Society, T26 10D. [3] Fourcaud, N., Brunel, N. (2002), Neural Computation, 14, 2057--2110. [4] Wong, K., Wang, X. (2006), Journal of Neuroscience, 26, 1314--1328. [5] Helias, M., Tetzlaff, T., Diesmann, M. (2013), New J Physics, 15, 023002