Comparing average network signals and neural mass signals in systems with low-synchrony

Abstract

1Neural mass models are accepted as efficient modelling techniques to model empirical observations such as disturbed oscillations or neuronal synchronization. Neural mass models are based on the mean-field assumption, i.e. they capture the mean-activity of a neuronal population. However, it is unclear if neural mass models still describe the mean activity of a neuronal population when the underlying neural network topology is not homogenous. Here, we test whether the mean activity of a neuronal population can be described by neural mass models when there is neuronal loss and when the connections in the network become sparse. To this end, we derive two neural mass models from a conductance based leaky integrate-and-firing (LIF) model. We then compared the power spectral densities of the mean activity of a network of inhibitory and excitatory LIF neurons with that of neural mass models by computing the Kolmogorov-Smirnov test statistic. Firstly, we found that when the number of neurons in a fully connected LIF-network is larger than 300, the neural mass model is a good description of the mean activity. Secondly, if the connection density in the LIF-network does not exceed a crtical value, this leads to desynchronization of neurons within the LIF-network and to failure of neural mass description. Therefore we conclude that neural mass models can be used for analysing empirical observations if the neuronal network of interest is large enough and when neurons in this system synchronize.