Computation of the electroencephalogram (EEG) from network models of point neurons.

Pablo Martínez-Cañada,Tommaso Fellin,Stefano Panzeri,Torbjørn V Ness,Gaute T Einevoll,Daniele Marinazzo

doi:10.1371/journal.pcbi.1008893

Abstract

The electroencephalogram (EEG) is a major tool for non-invasively studying brain function and dysfunction. Comparing experimentally recorded EEGs with neural network models is important to better interpret EEGs in terms of neural mechanisms. Most current neural network models use networks of simple point neurons. They capture important properties of cortical dynamics, and are numerically or analytically tractable. However, point neurons cannot generate an EEG, as EEG generation requires spatially separated transmembrane currents. Here, we explored how to compute an accurate approximation of a rodent's EEG with quantities defined in point-neuron network models. We constructed different approximations (or proxies) of the EEG signal that can be computed from networks of leaky integrate-and-fire (LIF) point neurons, such as firing rates, membrane potentials, and combinations of synaptic currents. We then evaluated how well each proxy reconstructed a ground-truth EEG obtained when the synaptic currents of the LIF model network were fed into a three-dimensional network model of multicompartmental neurons with realistic morphologies. Proxies based on linear combinations of AMPA and GABA currents performed better than proxies based on firing rates or membrane potentials. A new class of proxies, based on an optimized linear combination of time-shifted AMPA and GABA currents, provided the most accurate estimate of the EEG over a wide range of network states. The new linear proxies explained 85-95% of the variance of the ground-truth EEG for a wide range of network configurations including different cell morphologies, distributions of presynaptic inputs, positions of the recording electrode, and spatial extensions of the network. Non-linear EEG proxies using a convolutional neural network (CNN) on synaptic currents increased proxy performance by a further 2-8%. Our proxies can be used to easily calculate a biologically realistic EEG signal directly from point-neuron simulations thus facilitating a quantitative comparison between computational models and experimental EEG recordings.

Highlights

Electroencephalography is a powerful and widely used technique for non-invasively measuring neural activity, with important applications both in scientific research and in the clinic [1]
To allow a direct integration between neural network theory and empirical EEG data, here we derived a new mathematical expression, termed EEG proxy, which estimates with high accuracy the EEG based on the variables available from simulations of point-neuron network models
Our work provides important mathematical tools that allow a better interpretation of experimentally measured EEGs in terms of neural models of brain function

Summary

Introduction

Electroencephalography is a powerful and widely used technique for non-invasively measuring neural activity, with important applications both in scientific research and in the clinic [1]. These models reduce the morphology of neurons to a single point in space and describe the neuron dynamics by a tractable set of coupled differential equations These models are sufficiently simple to be understood thoroughly, either with simulations that are relatively light to implement, or by analytical approaches [12,13]. Despite their simplicity, they generate a wide range of network states and dynamics that resemble those observed in cortical recordings. It remains an open question how to compute realistically EEGs from such widely used network models of simple point neurons

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Discussion

Conclusion