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

Author summary Networks of point neurons are widely used to model neural dynamics. Their output, however, cannot be directly compared to the electroencephalogram (EEG), which is one of the most used tools to non-invasively measure brain activity. 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 simply on the variables available from simulations of point-neuron network models. To compare and validate these EEG proxies, we computed a realistic ground-truth EEG produced by a network of simulated neurons with realistic 3D morphologies that receive the same synaptic input of the simpler network of point neurons. The new obtained EEG proxies outperformed previous approaches and worked well under a wide range of network configurations with different cell morphologies, distribution of presynaptic inputs, position of the recording electrode and spatial extension of the network. The new proxies approximated well both EEG spectra and EEG evoked potentials. Our work provides important mathematical tools that allow a better interpretation of experimentally measured EEGs in terms of neural models of brain function. 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.

Automated summary

This study derived a new mathematical expression called EEG proxy, which can accurately estimate EEG signals based on simulations of point-neuron network models. The new proxies outperformed previous approaches and provided a better approximation of EEG spectra and evoked potentials. This work offers important mathematical tools for interpreting experimentally measured EEGs within neural models of brain function.