The past decade has witnessed a renewed interest in cortical local field potentials (LFPs) — that is, extracellularly recorded potentials with frequencies of up to about 500 Hz.
Key reasons for this resurgence are that LFPs offer a unique window into key integrative synaptic processes and their potential use in neural prosthetics.
Multiple neural signal processes contribute to the LFP, and computational methods are needed to tease apart these contributions and to properly interpret the signal in terms of its underlying neural activity.
The biophysical origin of LFPs is well understood, and accurate LFP modelling schemes based on detailed neuron models have been established.
Computational models explain how LFPs generated by cortical neural populations depend on electrode position, the dendritic morphologies of synaptically activated neurons, and on the spatial distribution and temporal correlations of synaptic inputs.
New methods for current source density (CSD) analysis are better able to identify the three-dimensional position of neural sources.
Advanced spectral and information-theoretical methods allow separation of independent contributions to the LFP in time and frequency.
Spike–field relationships probe additional aspects of functional connectivity.
Fitting the predictions of biophysical models to extracellular potentials allows the estimation of key network parameters.
Simultaneous measurements of LFPs and other large-scale measures of neural activity (for example, functional MRI) can progress our understanding of how macroscopic and microscopic networks interact.
The past decade has witnessed a renewed interest in cortical local field potentials (LFPs) — that is, extracellularly recorded potentials with frequencies of up to ∼500 Hz. This is due to both the advent of multielectrodes, which has enabled recording of LFPs at tens to hundreds of sites simultaneously, and the insight that LFPs offer a unique window into key integrative synaptic processes in cortical populations. However, owing to its numerous potential neural sources, the LFP is more difficult to interpret than are spikes. Careful mathematical modelling and analysis are needed to take full advantage of the opportunities that this signal offers in understanding signal processing in cortical circuits and, ultimately, the neural basis of perception and cognition.
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We thank H. Lindén, K. H. Pettersen, C. Magri, F. Szymanski and J. Schnupp for help with the figures, and J. Assad, M. Diamond, N. Brunel, A. Mazzoni and A. Marreiros for precious comments on the manuscript. This work was supported by the Research Council of Norway (eVita, NOTUR, NevroNor and ISP-Fysikk), the Max Planck Society in Germany, the Compagnia di San Paolo in Italy, the SI-CODE (FET-Open, FP7-284533) and BrainScaleS (FP7-269921) projects within the Seventh Framework for Research, and the People Programme (Marie Curie Actions) ABC (FP7-290011) project of the European Union's Seventh Framework Programme FP7 2007-2013 under grant agreement PITN-GA-2011-290011. In addition, this work was part of the research programme of the Bernstein Center for Computational Neuroscience, Tübingen, funded by the German Federal Ministry of Education and Research (BMBF; FKZ: 01GQ1002).
The authors declare no competing financial interests.
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- Current source density
The net volume density of transmembrane currents (including the capacitive membrane currents) entering the extracellular domain in a small volume of neural tissue.
- Forward-modelling scheme
A scheme in which models are used to compute physical quantities (such as the extracellular potentials from synaptic neural activity) measured in experiments. Forward models are also known as 'generative models'.
- Inverse modelling
Inversion of models refers to the selection of the best model (given some empirical data) and making probabilistic estimations of the parameters of that model. Models obtained with an inversion process are called 'inverse models'.
- Multicompartmental neuron models
Neuron models in which dendrites and/or axons are divided into several compartments so that the membrane potential throughout each compartment can be assumed to be the same.
- Current sinks
Transmembrane currents that leave the extracellular domain and enter cells (including capacitive membrane currents).
- Current sources
Transmembrane currents that enter the extracellular domain from the interior of cells (including capacitive membrane currents).
- Open-field structure
A geometrical arrangement of synaptic inputs onto neurons in which, on average, there is a substantial spatial distance between synaptic currents and the bulk of the return currents, allowing for the generation of a large dipolar local field potential contribution (for example, apical inputs onto a population of large pyramidal neurons).
- Closed-field configuration
A geometrical arrangement of synaptic inputs onto neurons in which, on average, there is no preferred orientation of spatial patterns of synaptic input currents and return current, giving a very small dipolar local field potential contribution.
- Single-compartment integrate-and-fire neuron models
Neuron models in which the membrane potential is assumed to be the same across the soma and dendrites.
- Current dipole moments
Mathematical measures of spatial distribution of transmembrane currents across the neuronal membrane.
- Far-field dipole expressions
Mathematical expressions for the extracellular potential generated by a current dipole source for distances far away from the dipole. In this limit, the potential will be proportional to the current dipole moment and inversely proportional to the square of the distance.
- Ground-truth data
In its original context in remote sensing, this term refers to data recorded on location (on the ground) to validate methods for analysing remote-sensing imaging data. In the context of local field potential (LFP) data, it refers to data obtained using the detailed biophysical forward-modelling scheme in which the neural activity is fully known, allowing for validation of methods for analysis of the LFP and prediction of LFPs in cortical network simulations.
- Traditional CSD analysis
(Traditional current source density analysis). A method for estimating the depth profile of CSD across cortical laminae based on taking the 'double spatial derivative' of multielectrode local field potential (LFP) data, inherently assuming the LFP (and CSD) to be constant in the lateral directions.
- Inverse CSD
(Inverse current source density). A method for estimating CSD from multielectrode local field potential (LFP) data based on numerical inversion of the forward model, linking CSD distributions to measured LFPs.
- Band-limited power
The total power (square of the absolute value or amplitude) of a signal that can be approximated by a sum of sine waves with frequencies that are restricted to a relatively narrow range ('frequency band').
- Laminar multielectrode
(Also known as a linear multielectrode). An electrode used for making extracellular electrical recordings. It has many contacts orientated along a single shaft and is typically inserted perpendicularly into the cortex to span several cortical layers.
- Signal correlations
A measure of correlations between neural signals attributable to the external correlate. The correlations are quantified as the correlation of tuning of two neural signals to the external conditions (for example, the correlation of the trial-averaged response profile across different external conditions).
- Noise correlations
A measure of correlations between neural signals that cannot possibly be attributed to the external correlate. The correlations are quantified as the correlation between two neural signals at a fixed external stimulus or behavioural condition.
- Mutual information
A measure of the amount of knowledge about a stochastic variable (for example, an external stimulus) that can be extracted from the single-trial observation of another stochastic variable (for example, a neural signal). It is measured in bits — one bit corresponds to a reduction of uncertainty by a factor of two.
- Information maximizing band-separation method
A method that determines frequency band boundaries so that they maximize the information about external conditions (such as sensory stimuli or cognitive tasks) extracted from the resulting band-separated neural response.
- Matching pursuit
An algorithm that iteratively decomposes a signal into waveforms selected from a set of functions, including functions extended in time but narrow in frequency, and functions brief in time but broad in frequency.
- Non-negative matrix factorization
(NMF). An algorithm that learns, with an unsupervised technique, how to decompose non-negative datasets into parts or modules, the linear sum of which approximates the data. It can then be used to group data samples into clusters based on their decompositions in terms of these parts.
- Directional measures of causal interactions
Statistical techniques to evaluate the causal effect of a group of simultaneously recorded signals onto another group of simultaneously recorded signals.
- Spike-triggered average of the LFP
(Spike-triggered average of the local field potential). The value of the LFP as a function of time around the spike emission times, averaged over all observations of spikes. It is used to quantify the stereotypical values of mean fields that are measured near the observation of a spike.
- Laminar population analysis
(LPA). A method for estimating cortical laminar population profiles, time-resolved laminar population firing rates and synaptic connection patterns between laminar populations based on joint modelling of multiunit activity and local field potentials from multielectrode recordings.
- Multiunit activity
(MUA). The high-frequency part of recorded extracellular potentials (above approximately 500 Hz) used as a measure of action-potential spiking from neurons in the vicinity of electrode. MUA can be estimated by identifying individual spikes by thresholding the high-pass signal (sometimes with the additional step of convolving the resulting spike time series with a temporal kernel), or alternatively it can be estimated by first high-pass filtering the signal in the range of more than ∼700–800 Hz and then rectifying it.
- Bayesian model inversion
A statistical technique that estimates the model parameters that best fit some given empirical data.
- Neural mass models
Models of neural network dynamics in which activity of a neural ensemble is summarized with a single variable: the mean of the density of ensemble activity. They are also known as firing-rate models.
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Einevoll, G., Kayser, C., Logothetis, N. et al. Modelling and analysis of local field potentials for studying the function of cortical circuits. Nat Rev Neurosci 14, 770–785 (2013). https://doi.org/10.1038/nrn3599
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