On the validity of electric brain signal predictions based on population firing rates

Neural activity at the population level is commonly studied experimentally through measurements of electric brain signals like local field potentials (LFPs), or electroencephalography (EEG) signals. To allow for comparison between observed and simulated neural activity it is therefore important that simulations of neural activity can accurately predict these brain signals. Simulations of neural activity at the population level often rely on point-neuron network models or firing-rate models. While these simplified representations of neural activity are computationally efficient, they lack the explicit spatial information needed for calculating LFP/EEG signals. Different heuristic approaches have been suggested for overcoming this limitation, but the accuracy of these approaches has not fully been assessed. One such heuristic approach, the so-called kernel method, has previously been applied with promising results and has the additional advantage of being well-grounded in the biophysics underlying electric brain signal generation. It is based on calculating rate-to-LFP/EEG kernels for each synaptic pathway in a network model, after which LFP/EEG signals can be obtained directly from population firing rates. This amounts to a massive reduction in the computational effort of calculating brain signals because the brain signals are calculated for each population instead of for each neuron. Here, we investigate how and when the kernel method can be expected to work, and present a theoretical framework for predicting its accuracy. We show that the relative error of the brain signal predictions is a function of the single-cell kernel heterogeneity and the spike-train correlations. Finally, we demonstrate that the kernel method is most accurate for contributions which are also dominating the brain signals: spatially clustered and correlated synaptic input to large populations of pyramidal cells. We thereby further establish the kernel method as a promising approach for calculating electric brain signals from large-scale neural simulations.