Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation

Abstract

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (electroencephalograms, magnetoencephalograms, electrocorticograms and local field potentials) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide recommendations for interpreting the data using forward and inverse models. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems.

Fig. 1 |. Field potential recording modalities.

a, EEG and MEG signals are measured noninvasively. EEG involves electrodes ~10 mm in size placed at the scalp across the head. MEG is measured using sensitive sensors (superconducting quantum interference devices, or SQUIDS) placed just outside the head. ECoG is measured invasively and involves placing electrodes either epidurally, on the dura that protects the brain, or subdurally, directly on the pia at the surface of the brain. ECoG can be performed in humans in the relatively rare case of epilepsy surgery and is otherwise mainly used in animal models. ECoG electrodes are smaller than EEG electrodes and range in size from 1 to several millimeters in size. All dimensions are in millimeters. b, Invasive recordings can also be made at finer spatial scales. Micro-ECoG involves 20–200 μm contacts placed on the pia^,. Coverage can extend to many square centimeters at sites across the brain. LFP is the most invasive procedure and involves inserting electrodes into the brain. As a result, LFP recordings are made with even smaller recording contacts than ECoG, extending to microelectrodes and thin-film electrodes that can also record the activity of individual neurons. All dimensions are in micrometers.

Fig. 2 |. Forward models.

a, The biophysical forward model predicts that the amplitude of field potentials generated by populations of neurons will depend on the dendritic morphology of local neurons, as well as the somato-dendritic location of the incoming synaptic inputs, and will not depend on the axonal morphology of local neurons. Box 1 discusses other contributions. Left: layer (L) 4 stellate neurons have restricted and symmetric dendritic arbors (blue) with extended axonal distributions that ramify locally (red). L5 pyramidal neurons have the most extended dendritic arbors and relatively sparse axonal distributions. Image adapted with permission from Shepherd et al., Springer Nature. Synaptic input to a population of neurons generates a current dipole that gives rise to the extracellular field potential signal according to the biophysical forward model. Center: populations of L5 pyramidal neurons can receive synaptic input to the apical or basal dendrites and generate large-amplitude field potentials in each case. Right: populations of L4 stellate neurons can receive synaptic input near the cell body and generate relatively small amplitude field potentials. Note that this is a simplification. The size of the generated potentials will depend on how displaced the return currents are from the synaptic input currents and spatial distribution of the return currents. The return currents depend on several other factors, including the thickness and branching of the dendrites. For example, in some cases about half of the current injected into the apical dendrite of a L5 neuron will return through the soma, and even less in neurons with a thinner apical dendrite. Density and strength of synaptic inputs, membrane potential, and membrane conductance of the postsynaptic population will also contribute to the magnitude of the generated potentials. b, Functional variant of the biophysical forward model. The functional variant predicts that information can be decoded from field potentials depending on the measurement projection given by the biophysical forward model and the spatiotemporal distribution of source selectivity in the brain. Left: the measurement projection underlying a field potential recording pools information across a volume (shaded). Spatial aspects are illustrated here, but note that the measurement projection also depends on temporal correlations (see Box 1). The selectivity of the underlying neuronal sources can be expressed as a directional arrow. Center: field potentials will exhibit strong selectivity if the spatial distribution of the underlying source selectivity is organized so that the measurement projection pools one or several sources with similar selectivity. Right: field potentials will exhibit weak or no selectivity if the spatial distribution of the underlying source selectivity is disordered and if the measurement projection pools several or many sources. Note that even if the spatial distribution of the underlying source selectivity is organized, weak selectivity can arise if the measurement projection pools over a much larger spatial extent.

Fig. 3 |. Time series and spectral estimation.

a, Left: the sampling rate of a time series, F_s, is inversely related to the sampling interval, df. The maximum frequency that can be resolved in a time series, called the Nyquist frequency, is determined by the sampling interval and equals F_s/2. The bandwidth W is the lowest frequency that can be resolved in a time series, also called the Rayleigh resolution. It is inversely related to the duration of the observation window and equals 1/T. Right: time-frequency plane. The Rayleigh resolution is an example of the time-frequency uncertainty principle, which states that the product of the resolution in time, T, and resolution in frequency, 2W, must be equal or greater than 1; i.e., 2 WT ≥ 1. We can increase the time × bandwidth product by increasing the analysis interval T, and hence smoothing more in time, or by increasing bandwidth W, and hence smoothing more in frequency. In each case, we effectively assume that the properties of neuronal activity are constant within the chosen time and frequency resolution that leads to a smoother, less variable estimate. Image reproduced with permission from Pesaran (2008), copyright 2008, Society for Neuroscience. b, Spectrum of LFP activity in macaque posterior parietal cortex. Left, single-trial, 500-ms periodogram spectrum estimate. Right, single-trial, 500-ms, 10-Hz multitaper spectrum estimate. Image reproduced with permission from Pesaran (2008), copyright 2008, Society for Neuroscience. c, Spectrogram of LFP activity in macaque posterior parietal cortex averaged across nine trials. Each trial is aligned to the presentation of a spatial cue, which occurs at 0 s. Saccade and reach are made at around 1.2 s. Left: multitaper estimate with duration of 500 ms and bandwidth of 10 Hz. Right: multitaper estimate with duration of 200 ms and bandwidth 25 Hz. White rectangle shows the time-frequency resolution of each spectrogram. The color bar shows the spectral power on a log scale in arbitrary units. Image reproduced with permission from Pesaran (2008), copyright 2008, Society for Neuroscience.

Fig. 4 |. Current source density analysis.

a, A cylindrical model in infinite medium, showing the relationship between current source density (CSD), current flow and field potential for the simple case of a columnar geometry receiving input at a particular layer. The geometry is a cylinder having a diameter-to-length ratio of 0.5 and embedded within an infinite medium of finite conductivity. Because there is circular symmetry, only the points on the z axis along the cylinder are shown. The CSD (transmembrane current l_m; left) gives rise to a current flow (J_z; center). Current flow establishes the field potentials (V_z; right). Current density enters the cylinder and returns below. This generates a downward current flow above and below the source and sink and an upward current flow between the source and sink. The resulting field potentials extend beyond the generating current source. Thus, CSD has higher spatial resolution than field potentials. Adapted with permission from Nicholson and Freeman, The American Physiological Society. b, Laminar patterns of auditory responses in the auditory cortex. Line plots show the LFP responses recorded using a linear array multielectrode with 100-μm intercontact spacing (schematic on left). Color plot (center) shows the corresponding laminar LFP profile, with negative deflections in red and positive deflections in blue. CSD profile (right) is estimated using the second spatial derivative of the field potential profile. Red depicts extracellular current sinks associated with net local inward transmembrane current flow. Blue depicts extracellular current sources associated with net local outward transmembrane current flow. Selected multiunit activity (MUA) responses are superimposed on the CSD plot. Vertical thin lines indicate stimulus onset. Here, the peak of multiunit activity corresponds to the peak negativity of the LFP and the current sink (CSD) at the response onset in layer 4. Asterisk indicates a superficial sink that produced the N50 feature in the LFP measured in superficial sites. Image adapted with permission from Kajikawa and Schroeder, Elsevier. c, Limitations of traditional CSD estimation method. Simulated one-dimensional recordings for simplified CSD profile in a. Estimated (est.) CSDs for increasing diameter-to-height ratios, as indicated by the number and inset in the lower left of each panel. Diameter refers to the diameter of the source. All estimates are based on the second spatial derivative formula of the traditional CSD method. Arbitrary units, negative values to the left and positive to the right. Spurious sources and sinks are inferred for small diameter activity. Estimation error stems from the incorrect assumption of an infinite activity diameter perpendicular to the laminar electrode. To avoid spurious source and sink inferences, a full three-dimensional CSD analysis is needed. Such an analysis can be achieved by making measurements of field potentials in all three spatial directions and using second spatial derivative methods. Alternatively, spurious source and sink inferences can also be avoided by using prior constraints or assumptions as is done in the iCSD and kCSD methods. Image reproduced with permission from Pettersen et al., Cambridge University Press.

Fig. 5 |. Granger-causal inferences.

a, Schema of multivariate autoregressive models. Each time series is modeled as a linear combination of its own past, the past of the other time series, and an innovation term. These signals are corrupted by measurement noise that can be either correlated or uncorrelated. b, Cross-correlation function example, showing that cross-correlation methods are not appropriate for detecting causal relationships. In this case, the cross-correlation function tells us that future (lagging) but not past (leading) values of y(t) are strongly correlated with x(t). Despite this, the Granger-causal influence from y(t) to x(t) is stronger than the influence from x(t) to y(t). c, Application of reversed GC testing to LFP data from monkey primary visual cortex (V1) and V4. Interaction in the gamma band shows full reversal with time series reversal and is therefore robust. This behavior is shown across V1-V4 pairs. In the beta range, GC causality does not reverse with time series reversal, indicating a potential influence of correlated noise.

Fig. 6 |. Phase-dependent neuronal coding.

a, Place information encoded by the phase of hippocampal LFP activity. Left panels: feature-tuned field potentials (FFPs) recorded from the hippocampus during running on a linear track (top). FFPs uniformly tile the length of a linear track. The spatial extent and spacing of different FFPs is largely homogeneous across the track (middle). FFPs exhibit phase precession with respect to the first principal component of LFP activity (bottom). Place-field hues are assigned based on location of maximal activation. Right panels: activation of FFPs during running in a T-maze. Waiting area is enclosed in a red box. Far right shows close-up of activations in waiting area, separated by direction of entry. Asterisks mark activations that are entry-direction selective. Each point represents a time bin where FFP activation exceeded a threshold, its size indicating the magnitude of activation. Hues are assigned to distinguish neighbors. Image reproduced with permission from Agarwal et al., AAAS. b, Object information in PFC spiking during a working memory task depends on LFP phase. PFC neuron spiking encodes the identity of two sequentially presented objects during a delay interval. Spikes carry the most information about the memorized objects at specific phases of the local 32-Hz LFP. Left: optimal encoding of the first presented object is significantly earlier on the falling flank of the 32-Hz cycle. Right: encoding of the second presented object occurs later (permutation test, P = 0.007). Error bars denote s.e.m. Phase dependence induced by stimulus-locked responses was discounted. Image reproduced with permission from Siegel et al.. c, Choice information in PPC spiking depends on beta and gamma LFP phases. Top left: average phase-dependent histogram of spike count for the beta frequency range. Coloring of the phase bins in all histograms corresponds to the schematic phase binning shown in the center. The spike-preferred phase (dark green) is depicted as a trough in the schematic to capture the tendency of spiking to occur at or near the troughs of LFP activity. The green bin at 0° corresponds to the average spike-preferred phase in the 200–1,000 ms epoch after target onset, when the choice can be made. The radial distance for each phase bin indicates the difference in spike count from random phases. Error bars depict 95% confidence intervals. The radial black line depicts the trigonometric moment of the histogram, with its 95% confidence interval indicated at the end of the line. Top right: as before but for mutual information about choice (choice-MI). Same data as before at each phase bin. Fully colored circles indicate choice-MI significantly different from the average choice-MI across all phase bins (permutation test, P < 0.05). Bottom row: as in the top row but for the gamma frequency range. Image reproduced with permission from Hawellek et al.. d, Orientation information in V1 spiking depends on gamma LFP phases. Match between stimulus orientation and neuronal orientation preference determines spike phase in the gamma cycle. Data from one example V1 neuron. Left: firing rate as a function of stimulus orientation. Right: the black sine wave at the top and the sinusoidal gray shading in the background illustrate the LFP gamma phase. The colored lines show spike densities as a function of phase in the gamma cycle. The colors correspond to those in the panel at left. All spike density curves are probability densities, normalized such that the mean value of each curve is 1/2 (bottom left calibration bar applies to all curves, and curves are offset along the y axis to correspond to the panel at left). Reproduced with permission from Vinck et al., Society for Neuroscience.

Extracellular potential biophysics.

a, Application of cable theory in a multicompartmental model. In cable theory, we simplify the three-dimensional complexity of the long, thin dendrites and axons to a one-dimensional core conductor along the long axis. This is the axis along which the membrane potential will vary the most. In this example, an apical dendritic branch, assumed to be purely passive with only capacitive and leak membrane currents, is divided into a set of compartments indexed by n. The circuit diagram shows the equivalent electric circuit of the compartment. The net transmembrane current l_n(t) is, in this case, the sum over the capacitive and leak membrane currents in compartment n. I_n(t) is then used in forward-modeling schemes, such as is implemented in LFPy, to calculate extracellular potentials. Two elements in the equivalent electric circuit represent intracellular resistive currents between compartment n and the neighboring compartments n + 1 and n − 1. Other elements represent currents due to capacitive properties of the cell membrane and various other membrane processes, such as passive and active intrinsic ion channels and synaptic inputs. If we assume point current sources, the extracellular potential ϕ(r,t) recorded at position r due to each of the transmembrane currents l₀(t) at position r₀ is given by ϕ(r,t) = l₀(t) / 40πσ|r − r₀|. σ is the extracellular conductivity, assumed to be real, scalar and homogeneous. Note that the simplest model producing an extracellular potential is a two-compartment model wherein a transmembrane current entering the neuron at one compartment leaves at the other compartment, forming a current dipole. Reproduced with permission from Linden et al.. b, Field potential amplitude depends on neuronal morphology. Top: simulations illustrating the dependence of population LFP on the ‘pyramidalness’ of the neurons—i.e., on the distance between cylinders containing the basal and apical dendrites (apical cylinder marked with blue shading). When the two cylinders are completely superimposed (left), the structure corresponds to a stellate cell. When the two cylinders are positioned immediately on top of each other (center), the morphology roughly corresponds to a layer 2/3 pyramidal cell. When the boundaries of the two cylinders are separated by 250 μm (right), the cell morphology resembles a layer 5 pyramidal cell. In all cases, GABA synapses were distributed only on dendrites in the lower cylinder, while AMPA synapses were distributed over the entire dendritic tree (see “Reference” distribution in c). Bottom: average absolute amplitude (s.d.) of LFP fluctuations as a function of distance between cylinders. The LFP value corresponds to the LFP amplitude averaged across depths along the axis of the cylinders. Adapted with permission from Mazzoni et al. c, Field potential amplitude depends on the distribution of synaptic inputs. Top: simulations for different synaptic distributions. Left, homogeneous: both AMPA and GABA synapse distributed over the entire surface of the cell. Center, reference: GABA synapses distributed only in the lower cylinder, with AMPA synapses distributed over the entire cell. Right, separate: GABA synapses distributed only in the lower cylinder and AMPA synapses only in the upper cylinder. Bottom: average LFP absolute amplitude versus dipole moment (s.d. over time) for the different synaptic distributions (homogeneous, black; reference, red; separate, green). Adapted with permission from Mazzoni et al..

Local and remote sources.

a, Local activity in cat visual cortex. Top: moving stimuli generate coherent gamma oscillations in cat visual area 17. Middle: the same stimuli generate higher frequency oscillations in lateral geniculate nucleus (LGN). Bottom: visual cortex and LGN oscillations are not coherent with each other (n.s., not significant). Adapted with permission from Castelo-Branco et al., Society for Neuroscience. b, Gamma oscillations in developing rodent cortex due to thalamic input. Top: experimental setup for simultaneous recordings of single-whisker evoked responses in the thalamic ventroposterior medial nucleus (VPM) whisker C5 barreloid and corresponding cortical barrel column in the postnatal day 6 rat. Bottom: responses averaged across 100 whisker deflections in the matching barreloid of VPM thalamus, showing multiunit (MU) poststimulus time histogram (black) in the VPM and evoked LFP (red) in the granular layer of the corresponding cortical barrel. Cortical LFP gamma activity is present at a stage of development during which cortical circuits do not generate gamma activity. Thalamic multiunit activity preceding cortical gamma implies that cortical LFP is due to incoming thalamic spiking and not local cortical spiking. Adapted with permission from Minlebaev et al., AAAS. c, LFP activity in rabbit cortex due to thalamic input. Top: experimental setup. Two thalamic electrodes recorded from neurons in neighboring ventrobasal (VB) barreloids (labeled a and b) and cortical electrodes recorded spike-triggered averages in the topographically aligned (and neighboring) primary somatosensory cortex (S1) barrels (labeled A and B). Spike-triggered averages were generated by two neurons in barreloid a (a1 and a2) and by one neuron in barreloid b. Bottom: spike-triggered averages elicited in barrel A by barreloid neurons a1, a2, and b are shown at left. Spike-triggered averages elicited in barrel B by the same three VB neurons is shown at right. Reproduced with permission from Swadlow and Gusev, The American Physiological Society.