Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models.

Alberto Mazzoni,Henrik Lindén,Gaute T Einevoll,Stefano Panzeri,Anders Lansner,Hermann Cuntz,Arnd Roth

doi:10.1371/journal.pcbi.1004584

Abstract

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.

Highlights

Models of recurrently connected networks of leaky integrate-and-fire (LIF) neurons are well established tools for studying brain function [1,2]
Leaky integrate-and-fire (LIF) networks are often used to model neural network activity. The spike trains they produce, cannot be directly compared to the local field potentials (LFPs) that are measured by low-pass filtering the potential recorded from extracellular electrodes. This is because LFPs are generated by neurons with spatial extensions, while LIF networks typically consist of point neurons
Predictions from the various LFP proxies were compared with “ground-truth” LFPs computed by means of well-established volume conduction theory where synaptic currents corresponding to the LIF network simulation were injected into populations of multi-compartmental neurons with realistic morphologies

Summary

Introduction

Models of recurrently connected networks of leaky integrate-and-fire (LIF) neurons are well established tools for studying brain function [1,2]. The equations describing the single LIF neuron are simple and can be adapted to generate complex dynamics [3,4] Despite their simplicity, LIF network models have proved able to describe a wide spectrum of different cortical dynamics and cortical functions, from the emergence of up and down states [5,6,7], working memory [8,9,10], attention [11,12], decision making [13], rhythmogenesis [14], and sensory information coding [11,15,16]. The recording of LFPs has a prominent role in systems neuroscience, and such recordings have been used extensively to investigate cortical network mechanisms involved in sensory processing [26], motor planning [27], and higher cognitive processes [28]

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