György Buzsáki, Costas A. Anastassiou, Christof Koch. The origin of extracellular fields and currents — EEG, ECoG, LFP and sp..

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Теги: Нейропсихология. EEG. ECoG. LFP
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Electric current contributions from all active cellular
processes within a volume of brain tissue superimpose
at a given location in the extracellular medium and
generate a potential, Ve (a scalar measured in Volts),
with respect to a reference potential. The difference in
Ve between two locations gives rise to an electric field
(a vector whose amplitude is measured in Volts per
distance) that is defined as the negative spatial gradient
of Ve. Electric fields can be monitored by extracellularly
placed electrodes with submillisecond time resolution
and can be used to interpret many facets of neuronal
communication and computation (FIG. 1). A major
advantage of extracellular field recording techniques is
that, in contrast to several other methods used for the
investigation of network activity, the biophysics related
to these measurements are well understood. This has
enabled the development of reliable and quantitative
mathematical models to elucidate how transmembrane
currents give rise to the recorded electric potential.
Historically, Ve has been referred to as the electro­
encephalogram (EEG) when recorded from the scalp,
as the electrocorticogram (ECoG) when recorded by
subdural grid electrodes on the cortical surface, and
as the local field potential (LFP; also known as micro ­,
depth or intracranial EEG 1) when recorded by a small ­
size electrode in the brain (BOX 1 ; FIG. 1). The term ‘local
field potential’ (meaning an electric potential ( Ve)), is
a regrettable malapropism, but we continue to use the
term LFP because it is familiar to most neuroscientists.
The magnetic field induced by the same activity is
referred to as the magnetoencephalogram (MEG) 2.
Recent advances in microelectrode technology
using silicon ­based polytrodes offer new possibilities
for estimating input–output transfer functions in vivo ,
and high ­density recordings of electric and magnetic
fields of the brain now provide unprecedented spatial
coverage and resolution of the elementary processes
involved in generating the extracellular field. In
addition, novel time ­resolved spectral methods provide
insights into the functional meaning of the information ­
rich high ­frequency bands of the Ve signal 3,4. These
new developments have led to a more in ­depth
understanding not only of the relationship between
network activity and cognitive behaviour 5 but also of
the pathomechanisms in brain diseases 6.
Several excellent but somewhat dated reviews
discuss various aspects of extracellular signals in the
brain 2,7–25. Here we provide an overview of our present
understanding of the mechanisms that underlie
the generation of extracellular currents and fields.
Although all nervous structures generate extracellular
fields, our focus is the mammalian cerebral cortex,
as most of our quantitative knowledge is the result of
studies in cortex.
Contributors to extracellular fields
Any excitable membrane — whether it is a spine,
dendrite, soma, axon or axon terminal — and any
type of transmembrane current contributes to the
extracellular field. The field is the superposition of
all ionic processes, from fast action potentials to the
slowest fluctuations in glia. All currents in the brain
1Center for Molecular and Behavioural Neuroscience, Rutgers, The State University of New Jersey, 197 University Avenue, Newark, New Jersey 07102, USA.2New York University Neuroscience Institute, New York University Langone Medical Center, New York, New York 10016, USA.3Center for Neural Science, New York University, New York, New York 10003, USA.4Division of Biology, California Institute of Technology, 1200 East California Boulevard, Pasadena, California 91125, USA.5Allen Institute for Brain Science, 551 North 34th Street, Seattle, Washington 98103, USA.Correspondence to G.B. e-mail: gyorgy.buzsaki@ nyumc.orgdoi:10.1038/nrn3241
The origin of extracellular fields and
currents — EEG, ECoG, LFP and spikes
György Buzsáki 1,2,3 , Costas A. Anastassiou 4 and Christof Koch 4,5
Abstract | Neuronal activity in the brain gives rise to transmembrane currents that can be
measured in the extracellular medium. Although the major contributor of the extracellular
signal is the synaptic transmembrane current, other sources — including Na + and Ca 2+
spikes, ionic fluxes through voltage- and ligand-gated channels, and intrinsic membrane
oscillations — can substantially shape the extracellular field. High-density recordings of
field activity in animals and subdural grid recordings in humans, combined with recently
developed data processing tools and computational modelling, can provide insight into
the cooperative behaviour of neurons, their average synaptic input and their spiking
output, and can increase our understanding of how these processes contribute to the
extracellular signal.
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a b
c
d
Strip (ECoG)
Grid (ECoG)
Scalp EEG
Depth (LFP)
Strip (ECoG)
1 s
O2
Fz
1 s
1 s
800
µV
150
µV
Am
HC
EC
SM
Cz
MEG (fT)
1000
–1000
500
–500
0
100
0
–100
iEEG (
µV)
VI
V
IV
III
II
I
20 mV
Intracellular
LFP surface
LFP depth
superimpose at any given point in space to yield Ve
at that location. Thus, any transmembrane current,
irrespective of its origin, leads to an intracellular as
well as an extracellular (that is, LFP) voltage deflection.
The characteristics of the LFP waveform, such as the
amplitude and frequency, depend on the proportional
contribution of the multiple sources and various
properties of the brain tissue. The larger the distance
of the recording electrode from the current source, the
less informative the measured LFP becomes about the
events occurring at the location(s) of the source(s). This
is mainly owing to the fact that the Ve amplitude scales
with the inverse of the distance r between the source
and the recording site, and to the inclusion of other
(interfering) signals (leading to ‘spatial averaging’). In
addition to the magnitude and sign of the individual
current sources, and their spatial density, the temporal
coordination of the respective current sources (that
is, their synchrony) shapes the extracellular field.
Thus, extracellular currents can emerge from multiple
sources, and these are described below.
Synaptic activity. In physiological situations,
synaptic activity is often the most important source
of extracellular current flow. The idea that synaptic
currents contribute to the LFP stems from the
recognition that extracellular currents from many
individual compartments must overlap in time to induce
a measurable signal, and such overlap is most easily
achieved for relatively slow events, such as synaptic
currents 7,10,23. The dendrites and soma of a neuron form
a tree ­like structure with an electrically conducting
interior that is surrounded by a relatively insulating
membrane, with hundreds to tens of thousands of
synapses located along it. Neurotransmitters acting on
synaptic AMPA and NMDA receptors mediate excitatory
currents, involving Na + or Ca 2+ ions, respectively,
which flow inwardly at the synapse. This influx of
cations from the extracellular into the intracellular
space gives rise to a local extracellular sink . To achieve
effective electroneutrality within the time constants of
relevance for systems neuroscience, the extracellular
sink needs to be ‘balanced’ by an extracellular source ,
that is , an opposing ionic flux from the intracellular to
the extracellular space, along the neuron; this flux is
termed passive current or return current . Depending on
the location of the sink current(s) and its distance from
the source current(s), a dipole or a higher ­order n ­pole
is formed (FIG. 2a) . The contribution of a monopole to
Ve scales as 1/ r, whereas the contribution of a dipole
decays faster, as 1/ r2; this steeper decay is due to the two
opposing charges that comprise the dipole cancelling
each other out to first order.
Notably, GABA subtype A (GABA A) receptor ­
mediated inhibitory currents are typically assumed
to add very little to the extracellular field as the Cl –
equilibrium potential is close to the resting membrane
potential 26,27. However, in actively spiking neurons the
membrane is depolarized, and therefore inhibitory (and
often hyperpolarizing) currents can generate substantial
transmembrane currents 28–30 (FIG. 2b,c) .
Figure 1 | Extracellular traces using different recording methods are fundamentally similar. a | Simultaneous recordings from three depth electrodes (two selected sites each) in the left amygdala and hippocampus (measuring the local field potential (LFP)); a 3 × 8 subdural grid electrode array placed over the lateral left temporal cortex (measuring the electrocorticogram (ECoG); two four -contact strips placed under the inferior temporal surface (measuring the ECoG); an eight -contact strip placed over the left orbitofrontal surface (measuring the ECoG); and scalp electroencephalo -
graphy (EEG) over both hemispheres (selected sites are the Fz and O2) in a patient with drug-resistant epilepsy. The amplitude signals are larger and the higher-frequency patterns have greater resolution at the intracerebral (LFP) and ECoG sites compared to scalp EEG. b | A 6 s epoch of slow waves recorded by scalp EEG (Cz, red), and LFP (blue) recorded by depth electrodes placed in the deep layers of the supplementary motor area (SM) and entorhinal cortex (EC), hippocampus (HC) and amygdala (Am). Also shown are multiple-unit activity (green) and spikes of isolated neurons (black ticks). c | Simultaneously recorded magnetoencephalogram (MEG; black) and anterior hippocampus depth EEG (red) from a patient with drug-resistant epilepsy. Note the similar theta oscillations recorded by the depth electrode and the trace calculated by the MEG, without any phase delay. d | Simultaneously recorded LFP traces from the superficial (‘surface’) and deep (‘depth’) layers of the motor cortex in an anaesthetized cat and an intracellular trace from a layer 5 pyramidal neuron. Note the alternation of hyperpolarization and depolarization (slow oscillation) of the layer 5 neuron and the corresponding changes in the LFP. The positive waves in the deep layer (close to the recorded neuron) are also known as delta waves. iEEG, intracranial EEG. Part a courtesy of G. Worrell, Mayo Clinic, Minneapolis, Minnesota, USA, and S. Makeig, University of California at San Diego, USA. Part b is reproduced, with permission, from REF. 157 © (2011) Cell Press. Part c courtesy of S. S. Dalal, University of Konstanz, Germany, and J.-P. Lachaux and L. Garnero, Université
de Paris, France. Part d is reproduced, with permission, from REF. 158 © (1995) Society for Neuroscience.
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Fast action potentials. Fast (Na +) action potentials gen ­
erate the strongest currents across the neuronal mem ­
brane and can be detected as ‘unit’ or ‘spike’ activity in
the extracellular medium 27. Although Na + spikes gener ­
ate large ­amplitude Ve deflections near the soma (FIG. 2d) ,
until recently they were thought not to contribute sub ­
stantially to the traditionally considered LFP band
(<100 Hz) or to the scalp ­recorded EEG 10,16, because
the strongest fields they generate are of short duration
(<2 ms) and nearby neurons rarely fire synchronously
in such short time windows under physiological con ­
ditions 31. However, synchronous action potentials from
many neurons can contribute substantially to high ­
frequency components of the LFP. Therefore, with
appropriate methods, valuable information can be
extracted from the LFP about the temporal structure of
spiking neuronal populations (see below).
Calcium spikes. Other non ­synaptic events that can
contribute prominently to the extracellular field are
the long ­lasting (10–100 ms) Ca 2+­mediated spikes 32.
Because voltage ­dependent regenerative Ca 2+ spikes are
often triggered by NMDA receptor ­mediated excitatory
postsynaptic potentials (EPSPs) 33–36, separating
them from EPSPs in extracellular recordings is not
straightforward. A potential differentiating factor is that,
in contrast to EPSPs, Ca 2+ spikes can actively propagate
within the cell and can therefore generate fields across
the laminar boundaries of afferent inputs. Ca 2+ spikes
can also be triggered by back ­propagating somatic
action potentials 37, in which case they are independent
of synaptic activity. Because dendritic Ca 2+ spikes are
large (10–50 mV) and long lasting 37–39, their share in the
measured extracellular events can be substantial under
certain circumstances (FIG. 3). Unfortunately, very little
is known about Ca 2+ spikes in vivo 40.
Intrinsic currents and resonances. Ih currents and
IT currents are prominent examples of intrinsic,
voltage ­dependent membrane responses 39.
Although synaptically induced voltage changes are a
prerequisite for the activation of voltage ­dependent
hyperpolarization ­activated cyclic nucleotide (HCN) ­
gated and T ­type calcium channels, the large membrane
and extracellular currents that these channels generate
are not synaptic events. These and other voltage ­
gated currents contribute to intrinsic resonance and
oscillation of the membrane potential. Several neuron
types possess resonant properties; that is, they respond
more effectively to inputs of a particular frequency
range 39. When intracellular depolarization is sufficiently
strong, the resonant property of the membrane can
give way to a self ­sustained oscillation of the voltage.
Voltage ­dependent resonance and oscillations at theta
frequency have been described in principal neurons of
several cortical regions 39,41–44. By contrast, perisomatic
inhibitory interneurons have a preferred resonance in
the gamma frequency (30–90 Hz) range 45,46. Because
resonance is both voltage ­ and frequency ­dependent 39,41,
its impact on the magnitude of the extracellular field can
vary in a complex manner. To contribute substantially to
the LFP, resonant membrane potential fluctuations must
occur synchronously in nearby neurons, a feature that
most often occurs in inhibitory interneurons.
Box 1 | Recordings methods of extracellular events
ElectroencephalographyElectroencephalography (EEG) is one of the oldest and most widely used methods for the investigation of the electric activity of the brain 10,16. The scalp electroencephalo - gram, recorded by a single electrode, is a spatiotemporally smoothed version of the local field potential (LFP), integrated over an area of 10 cm 2 or more. Under most conditions, it has little discernible relationship with the firing patterns of the contributing individual neurons 16, and this is largely due to the distorting and attenuating effects of the soft and hard tissues between the current source and the recording electrode. The recently introduced ‘high-density’ EEG recordings, in combination with source-modelling that can account for the gyri and sulci (as inferred from structural MRI imaging) of the subject, have substantially improved the spatial resolution of EEG 16,146,147.
MagnetoencephalographyMagnetoencephalography (MEG) uses superconducting quantum interference devices (SQUIDs) to measure tiny magnetic fields outside the skull (typically in the 10–1,000 fT range) from currents generated by the neurons 2. Because MEG is non-invasive and has a relatively high spatiotemporal resolution (~1 ms, and 2–3 mm in principle) 2, it has become a popular method for monitoring neuronal activity in the human brain. An advantage of MEG is that magnetic signals are much less dependent on the conductivity of the extracellular space than EEG. The scaling properties (that is, the frequency versus power relationship) of EEG and MEG often show differences, typically in the higher-frequency bands. These differences may be partly explained by the capacitive properties of the extracellular medium (such as skin and scalp muscles) that distort the EEG signal but not the MEG signal 148.
ElectrocorticographyElectrocorticography (ECoG) is becoming an increasingly popular tool for studying various cortical phenomena in clinical settings 149. It uses subdural platinum–iridium or stainless steel electrodes to record electric activity directly from the surface of the cerebral cortex, thereby bypassing the signal-distorting skull and intermediate tissue. The spatial resolution of the recorded electric field can be substantially improved (<5 mm 2)102 by using flexible, closely spaced subdural grid or strip electrodes (FIG. 1).
Local field potentialEEG, MEG and ECoG mainly sample electrical activity that occurs in the superficial layers of the cortex. Electrical events at deeper locations can be explored by inserting metal or glass electrodes, or silicon probes into the brain to record the LFP (also known as ‘micro-EEG’). Recording the wide-band signal (direct current to 40 kHz) — which contains both action potentials and other membrane potential-derived fluctuations in a small neuronal volume — using a microelectrode yields the most informative signal for studying cortical electrogenesis. Many observation points, with short distances between the recording sites and with minimal impact on brain tissue, are needed to achieve high spatial resolution. In principle, the spiking activity of nearly all or at least a representative fraction of the neuron population in a small volume can be monitored with a sufficiently large density of recording sites. Additional clues about the intracellular dynamics can be deduced from the waveform changes of the extracellular action potentials 99,150. Progress in this field has been accelerated by the availability of micro-machined silicon-based probes with ever-increasing numbers of recording sites 130,151,152.
Voltage-sensitive dye imagingVoltage changes can also be detected by membrane-bound voltage-sensitive dyes or by genetically expressed voltage-sensitive proteins 153–155 . Using the voltage-sensitive dye imaging (VSDI) method, the membrane voltage changes of neurons in a region of interest can be detected optically, using a high-resolution fast-speed digital camera, at the peak excitation wavelength of the dye. A major advantage of VSDI is that it directly measures localized transmembrane voltage changes, as opposed to the extracellular potential. A second advantage is that the provenance of the signal can be identified if a known promoter is used to express the voltage-sensitive protein. Limitations are inherent in all optical probe-based methods 156, and for VSDI these include interference with the physiological functions of the cell membrane, photoxicity, a low
signal-to-noise ratio and the fact that it can only measure surface events.
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1 nA
Membrane potential
Amplitude (normalized)
a d
b c
0.1 1 10 100
100
µm
50 μV
µV
Frequency (Hz) 100 101 102 103
100
10–1
10–2
10–3
10–4
Normalized power 0.1 µV
Count Vm
ms –30 –15 15 30 0
600
400
200
0
–70.5
–70.0
40 mV
10 µV
5 ms
SLM
SR
SP
SO
–0.4 0.0 0.4 0.8
–200
–100
0100
200
300
400
Distance from SP (
µm)
SinkBy convention, a site on the neuronal membrane where positive charges enter the neuron.
ElectroneutralityThe phenomenon that, owing to charge conservation, at any given point in time the total charge entering and leaving the cell across all of its membrane equals zero.
SourcesLocations along the neuronal membrane where positive charge flows out of the neuron. For negative charge, the location of sinks and sources is inverted.
Return currentA loop current that flows in the opposite direction to an active sink or source.
DipoleAn ideal electric dipole is defined by two charges of opposite polarity with infinitely small separation, such that the product of the charge times the distance r separating them remains finite. The electric potential of a dipole falls off as 1/ r2.
Equilibrium potentialThe voltage difference between intracellular and extracellular space of a neuron when the net ionic flux across the membrane equals zero.
Ih currentsCurrents flowing through hyperpolarization deinactivated cyclic nucleotide-gated channels.
IT currentsLow-threshold (hyperpolarization-induced) transient Ca 2+ currents, which often lead to burst firing.
ResonanceA property of the neuronal membrane to respond to some input frequencies more strongly than others. At the resonant frequency, even weak periodic driving can produce large-amplitude oscillations.
Silicon probesMultiple-site recording electrodes for high spatial density monitoring of the extracellular field. The recordings sites can record Ve along one, two or even three orthogonal axes.
Spike afterhyperpolarizations and ‘down’ states.
Elevation of the intracellular concentration of a certain
ion may trigger influx of other ions through activation of
ligand ­gated channels, and this will in turn contribute to
Ve. For example, bursts of fast spikes and associated den ­
dritic Ca 2+ spikes are often followed by hyperpolarization
of the membrane, owing to activation of a Ca 2+­mediated
increase of K + conductance in the somatic region 47.
As the amplitude and duration of such burst ­induced
afterhyperpolarizations (AHPs) can be as large (and last
as long as) synaptic events, AHPs also contribute to the
extracellular field 48, particularly when bursting of nearby
neurons occurs in a temporally coordinated fashion: for
example, following hippocampal sharp ­wave events 49.
In the intact brain, responses to unexpected stimuli or
movement initiation are often associated with relatively
long ­lasting (0.5–2 s) LFP shifts, which might be medi ­
ated by synchronized AHPs. This slow LFP is often
Figure 2 | Excitatory and inhibitory postsynaptic currents are the most ubiquitous contributors to Ve. a | Computer-simulated local field potential (LFP) traces (left panel; grey) in response to an excitatory synaptic current input (a sink, shown by the blue circle) injected into the distal apical dendrite of a purely passive layer 5 pyramidal model neuron. The waveform of the injected current is illustrated in the box. Red and blue contour lines correspond to positive and negative values for the LFP amplitude, respectively. The calculated double logarithmic power spectra of the transmembrane potential are also shown (right panel), following injection of current into the apical dendrite near the injection site (blue trace), mid-apical dendrite (green trace) and soma (orange trace). Note that high-frequency activity decreases with the distance from the active synaptic site (that is, the sink). b | A monosynaptic inhibitory connection between a putative layer 3 entorhinal cortical interneuron (red circle) and intracellularly recorded pyramidal cell (blue triangle). Below it, a cross-correlogram between the spikes of the reference interneuron (at time 0, red line) and the pyramidal cell and, superimposed on it, the spike-triggered average of the membrane potential (Vm) of the pyramidal cell (in blue). Note the small, short-latency hyperpolarization (the dip) superimposed on the rising phase of the intracellular theta oscillation and the corresponding decreased spike discharge of the pyramidal cell. c | Inhibition-induced LFPs. LFPs were generated in the vicinity of a pyramidal neuron (bottom cell) by intracellularly induced action potentials in a nearby basket cell (top cell), and were recorded extracellularly at six sites in multiple layers of the hippocampus. The mean LFP amplitude at each site is shown by the blue squares. Example LFP traces (blue) from six sites and the action potential of the basket cell (red trace) are shown on the right. Note that the largest positive response by inhibition-induced hyperpolarization occurs near the soma. d | Extracellular contribution of an action potential (‘spike’) to the LFP in the vicinity of the spiking pyramidal cell. The magnitude of the spike is normalized. The peak-to-peak voltage range is indicated by the colour of the traces. Note that the spike amplitude decreases rapidly with distance from the soma, without a change in polarity within the pyramidal layer (the approximate area of which is shown by the box), in contrast to the quadrupole (that is, reversed polarity signals both above and below the pyramidal layers) formed along the somatodendritic axis. The distance-dependence of the spike amplitude within the pyramidal layer is shown (bottom left panel) with voltages drawn to scale, using the same colour identity as the traces in the boxed area in d. The same traces are shown normalized to the negative peak (bottom right panel). Note the widening of the spike with distance from the soma, owing to greater contributions from dendritic currents and intrinsic filtering of high-frequency currents by the cell membrane. SLM, stratum lacunosum moleculare; SO, stratum oriens; SP, stratum pyramidale; SR, stratum radiatum. Part a is reproduced, with permission, from REF. 83 © (2010) Springer. Part b is reproduced, with permission, from REF. 137 © (2010) Society for Neuroscience. Part c is reproduced from REF. 29 © (2009) Macmillan Publishers Ltd. All rights reserved. Part d courtesy of E. W. Schomburg, California Institute of Technology, USA.
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D1
100 ms
D2 D3 D4 D E
10 ms
C
A
Vdend
Vdend
F/F
Slow potential amplitude (mV)
Ba
Bb
Bc
Bd –50 mV
–70 mV
Intra
2 s
0.2 mV
Extra
50 mV
50 ms
10 mV
10 ms50% 0 0.0
0.5
1.0
25 50
ECoG spike amplitude (mV) 5 4
2/3 1Pia
Cover-glass
ECoG Agar
473 nm; 140 µW
593 nm; 220 µW
200 µV
referred to as Bereitschaftspotential 50, readiness potential
or contingent negative variation 51.
During non ­rapid eye movement (non ­REM) sleep,
the membrane potential of cortical neurons periodically
shifts (0.5–1.5 Hz) between a hyperpolarized ‘down’
state and a more depolarized ‘up’ (that is, spiking)
state 52 (FIGS  1d,3D) . At least part of the cessation of
spiking during the down states can be explained by
AHPs of the synchronously bursting pyramidal cells
in the up state 48,53. The temporally coordinated silent
down state of nearby neurons is associated with a
positive Ve in infragranular layers and a negative Ve
in the supragranular layers (these down states are also
known as delta waves 48,54–56). Various mechanisms
contribute to these state transitions, including a
gradual decrease in extracellular Ca 2+ concentration
and a corresponding decrease in synaptic transmission,
inactivation of I h channels 53,57, and other network
effects 52. As the largest ­amplitude up–down shifts of
the membrane voltage occur in large layer 5 pyramidal
neurons 53,58, it has been suggested that the large voltage
shifts in the somata of the synchronously active –silent
neurons induce the formation of an extracellular
dipole between deep (infragranular) and superficial
(supragranular) layers 48,58. Neither interneurons nor the
thalamocortical inputs are active during the down state,
so that the down state (characterized by delta waves) is a
disfacilitatory, non ­synaptic event that can be mimicked
by synchronous hyperpolarization of nearby pyramidal
neurons (FIG. 3E) .
Gap junctions and neuron–glia interactions. Direct
electric communication between neurons through
gap junctions (also known as electrical ‘synapses’) 59–61
can enhance neuronal synchrony 49,62,63. Although gap
junctions allow ionic movement across neurons and,
therefore, do not involve any extracellular current flow,
they can affect neuronal excitability and contribute
indirectly to the extracellular field.
Membrane potential changes in non ­neuronal cells,
such as glia, may also give rise to Ve. Recent studies on
neuron –glia interactions have indicated that the glial
syncytium may contribute to slow and infraslow (<0.1 Hz)
field patterns 1,64,65. These slow LFPs may arise from glia,
glia–neuron interactions or from vascular events 66–68.
Ephaptic effects. Neurons are surrounded by a
conducting medium — the extracellular space —
and can therefore ‘sense’ the electric gradients they
generate during neuronal processing. In fact, the
effect of gradients brought about by synchronous
population activity along cable ­like dendrites can
be mimicked by appropriate intracellular current
injections 69,70. This raises the question of whether the
spatiotemporal field fluctuations in the brain are merely
an epiphenomenon of coordinated cellular activity or
whether they also have a functional ‘feedback’ (or even
amplification) role by affecting the discharge properties
of neurons 71. That is, do they serve any function for
the organism or are they like the heartbeat, a useful
diagnostic epiphenomenon? Given the resistivity of
Figure 3 | Non-synaptic contributions to the LFP. Ca2+ spikes, disfacilitation and disinhibition contribute to the local field potential (LFP). A | Voltage-dependence of a theta-frequency oscillation in a hippocampal pyramidal cell dendrite in vivo . A continuous recording of extracellular (extra) and intradendritic (intra) activity in a hippocampal CA1 pyramidal cell is shown. The holding potential was manually shifted to progressively more depolarized levels by intradendritic current injection. The recording electrode contained QX -314 to block Na + spikes. Note the large increase in the amplitude of the intradendritic theta oscillation upon depolarization. Arrows, putative high-threshold Ca 2+ spikes phase-locked to the LFP theta oscillation. Ba | Dendritic Ca 2+ spikes (shown by an arrow) have a large amplitude and are long-lasting in vivo . Bb–Bd | The response of a CA1 pyramidal cell to ventral hippocampal commissural stimulation (vertical arrows) paired with dendritic depolarization. Such inhibition can delay ( Bb), prevent ( Bc) or abort ( Bd) the dendritic Ca 2+ spike. LFPs recorded from a nearby electrode in the pyramidal layer show the timing and magnitude of the stimulation (lower traces in Bb–Bd). Note that the number of Na 2+ spikes
remains approximately the same, irrespective of the presence or absence of the Ca 2+ spike. C | Whisker stimulation-evoked dendritic Ca 2+ spikes correlate with surface cortical LFP changes. The setup for recording the electrocorticogram (ECoG), intradendritic potential (Vdend) and Ca 2+ fluorescence is shown in the left panel. The relationship between the intradendritic potential amplitude (horizontal arrows) and simultaneously measured Ca 2+ influx (∆ F/F) is shown in the middle panel. The ECoG response as a function of the Ca 2+ spike (‘slow potential’) amplitude is shown in the right panel. D | ‘Down’ states in cortical pyramidal cells during sleep produce extracellular LFP ‘delta’ waves. Shown are simultaneously recorded LFP (top) and unit activity (bottom) at three layer 5 intracortical locations (spaced approximately 1 mm apart; indicated by different colours). Note that down states (shaded areas), reflected as positive waves (delta waves) in the LFP, can be either strongly localized (in D2 and D3) or more widespread (in D1 and D4). E | Generation of extracellular potentials by depolarization or hyperpolarization of a limited number of CA1 neurons that express both channelrhodopsin 2 (ChR2) and halorhodopsin, in response to blue (top) and yellow (bottom) light in vivo . Note the depolarization-induced negative LFP (top) and the hyperpolarization-induced positive LFP (bottom) in the pyramidal layer. Part A is reproduced, with permission, from REF. 159 © (1998) Wiley. Part B is reproduced, with permission, from REF. 160 © (1996) National Academy of Sciences. Part C is reproduced from REF. 161 © (1999) Macmillan Publishers Ltd. All rights reserved. Part D is reproduced, with permission, from REF. 56 © (2005) Cambridge Journals. Part E courtesy of
E. Stark, New York University, Langone Medical Center, USA.
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Ephaptic couplingThe effect of the extracellular field on the transmembrane potential of a neuron.
Open fieldWhen the sink (or the source) is substantially spatially separated from the return currents of the dipole.
Closed fieldWhen the sink (or the source) is minimally spatially separated from the return currents of the dipole.
Power law (of LFP)The power law of LFP describes a relationship between the amplitude of the extracellular signal and its temporal frequency. A descending straight line on the log–log plot (power versus frequency) would be an indication of a power law that scales as 1/ fn.
Low-pass frequency filteringA process by which the frequency components of a signal beyond a cutoff frequency are increasingly attenuated, typically owing to a serial capacitance (for example, the bi-lipid membrane).
the extracellular medium in the mammalian brain
and the highly transient nature of spikes, it is unlikely
that spikes from individual neurons greatly affect the
excitability of nearby neurons through ephaptic coupling .
However, the situation is very different when many
neurons are simultaneously active, as such synchrony
can generate strong spatial gradients in the extracellular
voltage. Experiments have shown that small ­amplitude,
slow ­frequency application of extracranial currents
(trans ­cranial electrical stimulation) has a detectable
effect on neuronal activity 72 and cognitive function 73;
the small but effective voltage gradients brought about
in brain tissue by such external fields are comparable to
the voltage gradients produced by population patterns
in vivo under physiological conditions 70,74–76. Ephaptic
coupling has been shown to affect population activity
during hypersynchronous epileptic discharges 77,78.
Furthermore, ephaptic feedback may enhance spike–
field coherence and bias the preferred spiking phases
with respect to the LFP also under physiological
conditions 75,76,79–81; for example, during hippocampal
sharp waves or theta waves 70,76,77.
Neuronal geometry and architecture
All neuron types contribute to the extracellular field,
but their relative contribution depends in part on the
shape of the cell. Pyramidal cells are the most populous
cell type. They have long, thick apical dendrites that
can generate strong dipoles along the somatodendritic
axis. Such dipoles give rise to an open field , as there is
considerable spatial separation of the active sink (or
the source) from the return currents. This induces
substantial ionic flow in the extracellular medium
(FIG.  2). Therefore, neurons that generate open fields,
such as pyramidal cells, make a sizeable contribution
to the extracellular field. By contrast, spherically
symmetric neurons — such as thalamocortical cells
— that emanate dendrites of relatively equal size in all
directions, can give rise to a closed field 82. However, a
strictly closed field only occurs when several dendrites
are simultaneously activated. As this is rarely the case,
depolarization of a single dendrite generates a small
dipole even in spherically symmetric cells 83.
Assuming a homogeneous medium, the two most
important determinants of the extracellular field strength
are the spatial alignment of neurons and the temporal
synchrony (discussed in the next section) of the dipole
moments they generate 13,22,84. In cytoarchitecturally
regular structures, such as the cortex, the apical dendrites
of pyramidal neurons lie parallel to each other and the
afferent inputs run perpendicular to the dendritic
axis. This geometry is ideal for the superposition
of synchronously active dipoles and is the primary
reason why LFPs are largest in cortex. In the rodent
hippocampus, the somata of pyramidal cells occupy only
a few rows. By contrast, in the human hippocampus the
cell bodies are vertically shifted relative to each other
and form a wider somatic layer 85. As a result, the source
currents from the soma flow in the opposite direction
to the sink currents from the dendrites of neighbouring
neurons, effectively cancelling each other. This partly
explains why the amplitude of the LFP decreases from
rat to cat, and from cat to primate 86,87. Another reason
why brain size affects the magnitude of the extracellular
current is that mammals with smaller brains have smaller
pyramidal neurons, which are therefore more densely
packed compared to mammals with larger brains 88,
leading to a smaller conductivity σ. Indeed, all LFP
patterns have larger amplitude in the mouse brain than
in the rat brain 89.
Another important geometric factor that affects
the magnitude of the extracellular current flow is the
highly folded nature of the cortex in higher mammals 10.
When the cortical sheet bends to form a gyrus, the
apical dendrites are pushed closer to each other on
the concave side, and current density becomes higher
compared to when the apical dendrites occupy the
convex side of the curve 16. The influence of tissue
curving on the LFP is particularly striking in the dentate
gyrus–hippocampus–subiculum axis, where concave
and convex bends alternate 90. In subcortical structures,
spatial regularity of neurons and afferents is much less
prominent. Nevertheless, afferent fibres from one source
may have some asymmetric distribution on spherically
symmetric neurons (for example, cortical afferents to
the medium spiny neurons of the striatum 91), whose
temporally synchronous activity can generate spatially
distinct sinks and sources.
Temporal scaling properties
Geometric factors alone cannot fully explain the
magnitude of the extracellular current. For example,
the cerebellum is a perfectly ordered structure with
stratified inputs and a single layer of giant Purkinje
neurons, but it generates very small extracellular
fields 92. This is because cerebellar computation is
mainly local and therefore does not require the
cooperation of large numbers of neurons. However,
when synchrony is imposed on the cerebellar cortex
from the outside, large ­amplitude LFP signals can
emerge from cerebellar circuits 93. Thus, in addition to
cytoarchitecture, a second critical factor in determining
the magnitude of the extracellular current is the
temporally synchronous fluctuations of the membrane
potential in large neuronal aggregates. Synchrony,
which is often brought about through network
oscillations, explains why different brain states are
associated with dramatically different magnitudes of
LFP 9–14. A consistent quantitative feature of the LFP is
that the magnitude of LFP power (that is, the square of
the Fourier amplitude) is inversely related to temporal
frequency f, that is, there is 1/ fn scaling with n = 1–2
(the exact value of n depends on various factors) 94,95.
These features have given rise to much speculation
regarding the relationship between network features
of the brain and the extracellular signal (see below),
although a strict power law behaviour of the LFP is still
being debated 94,96–98.
The 1/ fn scaling of the LFP power can be primarily
attributed to the low-pass frequency filtering property
of dendrites 83,99,100. Simulations have shown that in
layer 5 pyramidal neurons (FIG.  2a) the effect of a
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Phase–amplitude couplingThe power of a faster oscillation is phase-modulated by a slower oscillation.
OhmicElectrical current flow through a purely resistive milieu. The extracellular cytoplasm is primarily ohmic in the 1–10,000 kHz frequency range.
Current source density(CSD). The current source density reflects the rate of current flow in a given direction through the unit surface (unit, A m –2) or volume (unit, A m –3).
AnisotropicAnsiotropic tissue can conduct electricity in a direction-dependent manner.
high ­frequency local input (100 Hz) to the distal
dendrite can be detected extracellularly near the
distal dendritic segment, whereas the signal is
attenuated approximately 100 ­fold near the soma.
Slower signals (for example, 1 Hz) are attenuated much
less. The low ­pass filtering effect of a purely passive
neuron depends on the distance between the soma and
the location of the input, and on the membrane time
constant 27. This suggests that dendritic morphology
is an important factor in frequency filtering and
that pyramidal cells, with their long dendrites, are
particularly effective low ­pass filters. However, as the
electrotonic length and input resistance of neurons can
be effectively altered by synaptically induced excitatory
and inhibitory conductance changes 26,101, the frequency
filtering performance of neurons depends not only on
the geometric characteristics of the neurons but also
on their physiological state. Another frequently cited
cause of high ­frequency attenuation of the LFP is the
capacitive nature of the extracellular medium itself 96,102,
although the capacitive and inductive properties of the
brain tissue remain a subject of debate 16,24,103.
Network mechanisms also contribute to the 1/ fn
feature of the power spectrum. In a brief time window,
only a limited number of neurons can be recruited in
a given volume, whereas in longer time windows the
activity of many more neurons can contribute to the LFP,
therefore generating larger amplitude LFP at slower
frequencies. This frequency dependence is also
reflected in the phase coherence–distance relationship,
with lower ­frequency signals having higher coherence
compared to high ­frequency signals. Provided that
neuronal recruitment occurs within the time constant
of an integrating mechanism (for example, NMDA or
GABA B receptors have a slow time constant, whereas
AMPA or GABA A receptors have a fast time constant),
the amplitude of low ­frequency LFP components will
be larger than the amplitude of high ­frequency LFP
components. Finally, the different network oscillations
generated in the cerebral cortex show a hierarchical
relationship 5,104,105, often expressed by cross ­frequency
coupling between the various rhythms 106–111. As the
phase of the slower oscillations modulates the power
of higher ­frequency events (a phenomenon known as
phase–amplitude coupling ), the duration of the faster
events is limited by the ‘allowable’ phase of the slower
event. In summary, multiple mechanisms can contribute
to the 1/ fn power scaling.
Although the phenomenological 1/ fn relationship
may capture various statistical aspects of brain dynamics
at longer timescales, it should be emphasized that
most neuronal computation takes place in short time
windows (from tens to hundreds of milliseconds).
The spectral properties of such short time windows
strongly deviate from the scale ­free frequency–power
distribution and are often dominated by oscillations or
sensory input ­triggered ‘evoked’ or ‘induced’ events.
These stimulus ­driven, transient LFP events are the
physiologically relevant time windows from which one
aims to infer neuronal computation from the mean field
behaviour of neuronal populations 13.
The role of volume conduction in Ve The electric field specifies the forces acting upon a
charged particle. The field is defined at every point
of space from which one can measure a force ‘felt’ by
an electric charge, and it can be transmitted through
volume (for example, through brain tissue); a
phenomenon known as volume conduction. The origin
of the volume ­conducted field is the return currents of
the dipoles 18,22,83. The extent of volume conduction
depends on the intricate relationships between the
current dipole and the features of the conductive
medium 84,112. Consequently, some LFP patterns can
be recorded far away from the source, whereas others
remain relatively local. The most robust demonstration
of the importance and extent of volume conduction is
that return currents from active dipoles in brain tissue
can be measured on the scalp by electric recording
methods (BOX 1) .
Assuming that conductivity in the brain is purely
ohmic , the Ve induced by a current dipole depends on
the magnitude and location of the current source, and
on the conductivity of the extracellular medium. In turn,
conductivity in the medium depends on the degree of
isotropy and homogeneity of the medium and is there ­
fore a function of a number of factors, including the
geometry of the extracellular space. The relationship
between Ve and the current source density (CSD) J (meas ­
ured in A m –2) at a particular point of brain tissue is
given by Maxwell’s equations of electromagnetism, that
in their simplified form (that is, when the magnetic con ­
tributions can be neglected) dictate ∇(σ→ Ve) = – ∇ J→,
where σ→ (amplitude measured in S m –1) is the extracel ­
lular conductivity tensor. The properties of σ→ crucially
affect the waveform and functionality of the spatiotem ­
poral Ve deflections. Assuming that the extracellular
milieu can be satisfactorily described by a purely homo ­
geneous and isotropic ohmic conductivity σ, Ve is gov ­
erned by Laplace’s equation ∇2Ve = 0, with the boundary
condition along a cable ­like source described by σ Ve = J
(with J as the transmembrane current density). For a
single point source in an unbounded isotropic volume
conductor, the solution is Ve = I/4πσr, in which I (unit,
A) is the current amplitude of the point source and r
(unit, m) is the distance from the source to the measure ­
ment. Multiple current sinks and sources then combine
linearly by the superposition principle. Conceptually,
the point ­source equation is key to computing the
extracellular potential in response to any transmem ­
brane current. It also follows that the transmembrane
voltage, often used in intracellular versus extracellular
comparisons, is a relatively poor estimator of the LFP,
whereas the transmembrane current is a more reliable
estimator 99. The above calculations assume that the
extracellular medium is homogeneous and isotropic
(that is, a constant σ). Measurements of the extracellular
medium in the relevant frequency range (<10 kHz) have
not yet fully resolved this issue, with some experiments
concluding that the extracellular medium is anisotropic
and homogeneous 24,113, and others suggesting that it is
strongly anisotropic, inhomogeneous 68,103,114 and may
even possess capacitive features 91,96,97.
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Striking examples of volume ­conducted events have
been described in hemispherectomized patients over
the missing hemisphere 115. Furthermore, auditory ­
evoked brain stem responses recorded over the scalp
are a clinically used diagnostic tool that is based on
volume conduction 116. Volume conduction clearly
poses problems for the interpretation of the functional
meaning of the relationship between signals recorded
from different brain locations. For example, two nearby
dipoles with different orientations can produce volume ­
conducted fields at distant sites. When the coherence
between signals recorded at these distant sites increases
(for example, as a function of behaviour), this may
be falsely interpreted to reflect some ‘dynamic’ or
‘functional coupling’ between the circuits residing at
the sites of the recording electrodes, even though the
coherence increase was brought about by the temporal
shifts between the two close dipoles 117. For these reasons,
verification of the local nature of the signal always
requires the demonstration of a correlation between the
LFP and local neuronal firing.
The inverse problem of LFP
Extracellular signals provide information about
the collective behaviour of aggregates of neurons,
particularly with regard to the temporal scales of their
activity. However, the same macroscopic extracellular
signal can be generated by diverse cellular events.
Thus, a seemingly similar theta oscillation in the
hippocampus and neocortex may be brought about
by different elementary mechanisms. A common
obstacle in interpreting the ‘mean field signal’ is the
‘inverse problem’ 16,118. The inverse problem arises
when attempting to infer the microscopic variables
from the macroscopic ones — in this case, inferring
the characteristics of the primary current dipoles
from the spatiotemporal profile of the volume ­
conducted field. The inverse problem is commonly
dealt with by first solving the ‘forward problem’ —
deriving macroscopic variables from their elementary,
causal constituents — and then using the established
relationships between microscopic and macroscopic
variables to gain insight into the microscopic events
from the macroscopic patterns. The first step in this
process is to identify the contribution of the suspected
synaptic and non ­synaptic mechanisms of the LFP by
correlating the macroscopic events (that is, the LFP)
and the microscopic events 119,120,122. The second step is
to experimentally recreate the LFP from its primary
constituents, such as synaptic currents and the spiking
patterns of various neuron types. The technical
means required to create such LFP patterns are now
available (FIG. 3E) . Alternatively, synthetic mean fields
can be generated in network models of neurons in
which events in the different domains of the neurons
are timed on the basis of experimentally observed
temporal patterns.
Localizing the current sinks and sources: CSD analysis.
In deciphering the location of the current sources (that
is, cations flowing from the intracellular space to the
extracellular space) and sinks (that is, cations flowing
into the cell) that give rise to the LFP, the concept of
CSD is useful. CSD is a quantity that represents the
volume density of the net current entering or leaving
the extracellular space 113,121. Consider a distant current
source relative to three linearly and equally spaced
recording sites in a homogenous volume (FIG. 4). Each
electrode will measure some contribution to the field
from the distant source, and the voltage difference
between the middle and side electrodes will be small.
As a consequence, the difference between the ‘voltage
differences per distance’ (that is, the second spatial
derivative of Ve, a vector with units of V m –2) between
the middle and side electrodes is small; an indication
that the field can be attributed to a distant source. By
contrast, if the three electrodes span the location of
the current ­generating synapse or neuron group, the
voltage at the three recording sites will be unequal
and the difference magnitude of this derivative will be
large; an indication of the local origin of the current.
The current flow between two recording sites can be
calculated from the voltage difference and resistivity
using Ohm’s law, provided that information about
the conductance (which is inversely proportional to
resistivity) of the tissue is available (0.15–0.35 Ω m
in brain tissue 68,103,113). The conductance is a factor of
both conductivity and the specific geometry of volume.
Using high ­density recording probes to monitor the
LFP, it is possible to precisely determine the maximum
CSD and therefore the exact location of the current
sink (or source).
Interpreting current density. Unfortunately, it is not
possible to conclude using CSD measurement alone
whether, for example, an outward current close to
the cell body layer is due to active inhibitory synaptic
currents or reflects the passive return current of active
excitatory currents impinging along the dendritic arbor.
The missing information may be obtained by selectively
stimulating the various anatomically identified inputs
to the recorded circuit (FIG. 4). This process helps to
attribute the sinks (and sources) to the known sources
of synaptic inputs 106,122. In addition to anatomical
knowledge, simultaneous intracellular recordings from
representative neurons within the population responsible
for the generation of the LFP may be required.
Alternatively, it is possible to record extracellularly from
identified pyramidal cells and inhibitory interneurons
in the same volume of tissue and use the spike–field
correlations to determine whether, for example, a local
current is an active hyperpolarizing current or a passive
return current from a more distant depolarizing event.
Unfortunately, ambiguity may still remain if the sinks
and sources are generated by a non ­synaptic mechanism
rather than by a synaptic mechanism.
Somatic hyperpolarization brought about by
the activity of perisomatic basket neurons 44,123 also
generates a voltage gradient between the soma
and dendrites (inhibitory dipole; FIGS 2b,c,4a,b ). As
dendritic excitation and somatic inhibition result in
the same direction of current flow, the excitatory and
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Recordings close to source
Recordings far from source
o
p
r
hf
100 ms
Source
Sink
CSD close to source
CSD far from source
100 ms
150 mV mm –2
100 ms
0.5 mV
a b
c d
2 mV
op
r
hf
CA1
CA3
inhibitory return currents will superimpose in the
extracellular space, resulting in large ­amplitude LFPs.
Although strong somatic inhibition can enhance the
magnitude of the LFP, it may at the same time ‘veto’ the
occurrence of action potentials in pyramidal cells. This
complex relationship is the reason why large ­amplitude
extracellular current flow may be associated with
strong spiking, moderate spiking or no spike output
at all from the pyramidal neurons. As a result, the
measured correlation between LFP and spiking activity
can vary substantially even within a small volume.
Such variable coupling between LFP and unit firing
may be one of the sources of the controversy regarding
the contribution of LFP versus spikes to the functional
MRI (blood oxygen level ­dependent (BOLD)) signal
because often there is a strong correlation between
LFP power in the gamma ­frequency band and spiking
activity 23,124.
Figure 4 | Identifying current sources. a | A current source–sink dipole, embedded in a homogeneous and isotropic conductive medium, that is induced by barrage-like inhibitory input (shown by the red symbol) impinging on the perisomatic region. Lines show the iso-potentials (red, positive; blue, negative). A triplet of linearly and equally spaced recording electrodes (shown in yellow) is located near the soma (top), that is, close to the current source, and another is located far from the current source. b | Ve traces (left panels) measured at the three equally spaced locations relative to an ideal infinite (reference) site. The middle trace in the top panel is from the electrode positioned closest to the soma. The voltage contribution induced by the active dipole decays in the medium as the inverse square of the distance (compare with FIG. 2a). The current source density (CSD) traces (right panels) are calculated from the voltage traces. Although dipole-induced Ve can be measured far from the source, CSD is spatially confined and can therefore help to identify the anatomical location of the dipole. c | Simultaneous recordings from 96 sites (six shanks (represented by columns in the figure) with 16 recording sites each (LFP traces shown in grey)) in a behaving rat. Simultaneously recorded evoked field responses in the CA1–dentate gyrus axis of the rat hippocampus (black lines show the outline of the layers) in response to electrical stimulation of entorhinal afferents are shown. Such trisynaptic activation of CA1 pyramidal cells is reflected as negative LFP (and sink, blue) in the apical dendritic layer (stratum radiatum, r). The black rectangle indicates missing channels. d | A CSD map of average spontaneously occurring sharp waves. Note the nearly identical distribution of sinks and sources in CA1 during the evoked responses and sharp waves, supporting the idea that sharp waves reflect CA3-induced depolarization of the apical dendrites of CA1 neurons. Selective activation of known afferents thus can be used to ‘calibrate’ the locations of sinks and sources, and relate them to the CSD distribution of spontaneously occurring LFP events. hf, stratum lacunosum-moleculare; o, stratum oriens; p, pyramidal layer. Parts c and d courtesy of J. Csicsvari, Institute of Science and Technology, Austria, and D. Sullivan, New York University, Langone Medical Center, USA.
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100 600 Frequency (Hz)
2 0
4 68
12 10
14
Time (ms)
Power decrease (%)
b
1
0
0.5
Time (ms)0 400 200 200 200 200
a
Firing rate (normalized)
Frequency (Hz) Power (dB)
0 400 0 400
200
0
100
0 400
0
10
5
15
–5
No spikes No pyramidal cellsNo interneurons
The CSD method described above is, in principle,
applicable to any other a priori identified rhythmic
or transient LFP event. However, it is important
to emphasize that conventional one ­dimensional
(typically along the somatodendritic axis) estimation
of CSD is possible only in a situation in which the
LFP varies little in the lateral direction, that is, within
the same layer. The assumption is often not satisfied
when the layers curve. In this case, two ­dimensional
estimation of the CSD, using equally spaced high ­
density electrodes in both vertical and horizontal
directions, is required 113,125. Further complications arise
when several dipoles are involved in the generation
of LFP patterns, particularly when these dipoles are
temporally disparate, as is the case in the generation
of most cortical patterns 48,126,127. Nevertheless, the
above strategies have been successfully used in the
identification of evoked and spontaneous LFP patterns
in multiple brain regions 121,122,128,129. The ever ­increasing
density of recording sites on silicon ­based recording
probes 130 in combination with optogenetic tools 131 will
help us to disentangle the contribution of multiple
dipoles.
Spike contribution to the LFP
As noted above, any transmembrane current
contributes to the LFP, including currents that are
generated by action potentials. The action potential
includes not only the ‘spike’ itself but also spike ­
induced AHPs, which have durations and magnitudes
that vary for different neuron types and that can change
as a function of brain state 132. The spike contribution
to the LFP has important implications. First, increased
spiking generates a broad ­frequency spectrum with a
power distribution that depends on the composition of
the active cell types 95,98,111,133,134. Second, both increased
spike frequency and synchrony increase spectral
power, particularly in the higher ­frequency (>100 Hz)
bands 135,136 (FIG. 5). However, when spike AHPs are
also considered, the contribution of action potentials
may be substantial in the lower ­frequency range as
well, even in the absence of synaptic transmission 119.
Thus, increased power in the higher ­frequency bands
can be regarded as an index of spiking synchrony.
Third, high ­frequency power has a restricted spatial
component: it increases in layers with a high density
of cell bodies 111,137 and axon terminals. Fourth, high ­
frequency power, which largely reflects spiking activity,
co­varies with LFP components that emanate from
postsynaptic potentials and other non ­spike ­related
membrane voltage fluctuations 18,22,23,86,98,100–112,133,136.
Fifth, the high ­frequency power can be phase ­locked
to lower ­frequency oscillations; this occurs because it is
largely the phase ­locked spiking neurons that generate
the rhythmic extracellular currents 22,23,86,111,112,133,136.
Last, the high ­frequency power of extracellular
LFP provides indirect access to the spike outputs of
neurons 4,111,124,138. Together, these aspects show that
spike ‘contamination’ of the LFP should be regarded
as good news, in that high ­frequency LFP power
can provide a ‘proxy’ for the assessment of neuronal
outputs. The ‘mesoscopic’ information provided by
the high ­frequency band of the LFP is therefore an
important link between the macroscopic ­level EEG
and the microscopic ­level spiking activity of neuronal
assemblies.
Conclusions and future directions
Electric currents from all excitable membranes
contribute to the extracellular voltage. These currents
emerge mainly from synaptic activity but often with
substantial contributions from Ca 2+ spikes and other
voltage ­dependent intrinsic events, as well as from
action potentials and spike afterpotentials. The two
most important factors contributing to the LFP are
the cellular ­synaptic architectural organization of
Figure 5 | Spike contribution to the LFP. a | Average multiunit recording of the visual cortex of a monkey during presentation of a static grating (0 to 400 ms) at six different sizes, shown in different colours (left panel). Also shown are time–frequency–power difference plots demonstrating the difference between baseline power (in dB) and power in response to increasing size stimuli (right panel). Note the increase in wide-band power (at ~50 ms) with increased firing and synchrony of units after stimulus onset. The arrow indicates sustained gamma frequency oscillation. b | The effect of local field potential (LFP) ‘de-spiking’ on spectral power. The figure shows the percentage change of power at different frequencies after de-spiking the LFP. Thick lines indicate the frequencies at which there was a significant difference between the original LFP power and the power of the LFP after removing interneuron spikes (No interneurons), pyramidal
cell spikes (No pyramidal cells) or all spikes (No spikes). Part a is reproduced from REF. 162 . Part b is reproduced, with permission, from REF. 111 © (2012) Society for Neuroscience.
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Theta SPW-R
* * CA1
CA3
ori pyr
rad
Im
mol
gc
hil
CA1
CA3
ori pyr
rad
Im
mol
gc
hil
the network and synchrony of the current sources.
The extracellular potential can be reconstructed from
simultaneous monitoring of several current source
generators across the neuronal membrane, provided
that sufficient details are known about the contributing
sources and the extracellular milieu. This forward
reconstruction is theoretically possible because the
physical processes underlying the generation of Ve are
mostly understood. The forward reconstruction of the
LFP is accelerated by advancements in microelectrode
technology and other new methods, and developments
in computational modelling. Reconstruction of the
LFP signal from the measured current sources and
sinks can, in turn, provide insights into resolving
the inverse problem, that is, the deduction of the
microscopic processes from the macroscopic LFP
measurements.
A practically important application of the forward–
inverse relationship would be the reconstruction of cell
assembly sequences from the constellation of the LFP.
Cell assemblies can be defined as a temporal coalition
of neurons — typically within gamma cycles — the
collective action of which can lead to the discharge of
a downstream ‘reader’ neuron 139. Such assemblies (or
‘neural letters’) are organized into assembly sequences
(or ‘neural words’) by the slower rhythms. Although
the temporal organization of neuronal dynamics
can be effectively inferred from the cross ­frequency
coupling of the various brain rhythms, additional
steps are required to reveal the spiking content of
the LFP patterns. In the intact brain, spiking neurons
are embedded in interconnected networks and may
be influenced by the local electric field through
ephaptic effects. Therefore, the output spikes of
the cell assemblies within and across networks are
transformed into spatially distributed transmembrane
events through synaptic activity (‘synapsembles’) 139. Of
course, these transmembane events are responsible for
the LFP. We suggest that as the composition of spiking
assemblies varies over time, the spike patterns induce
unique patterns of LFPs, which vary from moment to
moment (for example, from one gamma cycle to the
next). Recording the LFP from a sufficiently large and
representative neuronal volume with sufficiently high
spatial density may therefore provide access to the
time ­evolving synaptic currents brought about by the
spiking assemblies ( FIG. 6; Supplementary information
S1 and S2 (movies)). Such synapsembles 139, reflected
indirectly by the LFP vectors, can be as informative
about the encoded information as the spiking cell
assemblies themselves 140–142. In support of this idea, it
has been shown that during cognitive tasks, the spatial
distribution of spectral power varies in a task ­relevant
manner 98,134,143–145. We foresee that the spatially resolved,
wide ­band LFP signal, which contains information
about both afferent patterns and assembly outputs, may
turn out to be the most useful signal for understanding
neuronal computations 11,13,135.
Figure 6 | Spikes are embedded in unique synapsembles and spatially distributed LFP. Spike-triggered averages of the local field potential (LFP) in the hippocampus during exploration (left panel) and sleep (right panel). During exploration, spikes were sampled while the rat ran on a linear track for a water reward; during sleep, spikes were sampled during sharp wave-ripples (SPW-R). Recordings were made by an eight -shank (300 μm intershank distance), 256-site silicon prove (32 recording sites on each shank, linerarly spaced 50 μm apart). The LFP was smoothed both within and across shanks. The LFP was triggered by the spikes of a fast-firing putative interneuron in CA1 stratum oriens (ori; shown by a star). Both panels show a 100 μs snapshot of the LFP map at the time of the spike occurrence. Note that during exploration (left panel), the spike is associated with synaptic activity (negative wave, hot colours) mainly in the stratum lacunosum-moleculare (lm; shown by an arrow) and the dentate molecular layer (mol), indicating entorhinal cortex activation. During sleep (right panel), activity arises in CA3 and invades the CA1 stratum radiatum (rad; shown by an arrow). We propose that such LFP ‘snapshots’ reflect unique constellations of cell assemblies responsible for the discharge of the neuron. The LFP map changes characteristically with time (see Supplementary information S1 and S2 (movies)). We suggest that the time-evolving constellation of the LFP map or vector reflects a unique distribution of postsynaptic potentials (that is, synapsembles 139) brought about by the evolving spike assemblies within and upstream of the hippocampus. Sufficiently high-density LFP recordings can therefore be informative of the evolving cell assemblies that bring about the LFP changes. gc, granule cell layer; hil, hilus; pyr, pyramidal layer. Figure courtesy of A. Berényi and Z. Somogyvári, New York University, Langone Medical Center, USA.
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AcknowledgementsThe authors are supported by the National Institutes of Health (grants NS34994, MH54671 and NS074015), the Swiss National Science Foundation (grant PA00P3_131470), the G. Harold and Leila Y. Mathers Charitable Foundation, the US–Israel Binational Foundation, the Global Institute for
Scientific Thinking and the Human Frontiers Science Program (grant RGP0032/2011). Parts of this Review were written while G.B. was a visiting scholar at the Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem (2007) and at the Zukunftskolleg Program, University of Konstanz, Germany (2011). We thank G. Einevoll, E. Schomburg and J. Taxidis for their comments on the manuscript.
Competing interests statementThe authors declare no competing financial interests.
FURTHER INFORMATIONGyörgy Buzsáki’s homepage: http://www.med.nyu.edu/ buzsakilab/ Christof Koch’s homepage: http://www.klab.caltech.edu
SUPPLEMENTARY INFORMATIONSee online article: S1 (movie) | S2 (movie)
ALL LINKS ARE ACTIVE IN THE ONLINE PDF
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Biographies
György Buzsáki is the Biggs Professor of Neural Science at New
York University, New York, USA. His primary interests are brain
oscillations, sleep and memory. He sits on the editorial boards of
several leading neuroscience journals, including Science and Neuron .
He is a co ­recipient of the 2011 Brain Prize.
Costas Anastasiou studied chemical engineering at the Swiss Federal
Institute of Technology, Zurich, Switzerland, and completed his Ph.D.
in bioengineering at Imperial College London, UK, on electrochemical
sensing and data processing under the supervision of D. O’Hare and K.
Parker. After completion of a visiting fellowship at the Department of
Mathematics at the Massachusetts Institute of Technology, Cambridge,
Massachusetts, USA, he joined the laboratory of C. Koch at the
California Institute of Technology, Pasadena, California, USA. His
research focuses on the biophysics of neural computation and cognitive
processing with a particular interest in the origin and functionality of
extracellular brain activity. To do so, he uses a spectrum of theoretical,
computational and experimental techniques.
Christof Koch is a professor of biology and engineering at the
California Institute of Technology. His laboratory focuses on the
biophysics of computation, and on unravelling the computational,
physiological and psychological bases of selective visual attention
and visual consciousness. He is now also the Chief Scientific Officer
at the Allen Institute for Brain Science, Seattle, Washington, USA,
where he is leading a 10 ­year, large ­scale and high ­throughput effort
to build a series of ‘observatories’ to exhaustively catalogue, map,
probe and model the form and function of the cerebral cortex and its
constitutive elements.
Online ‘at‑a ‑glance’ summary
• All currents in the brain superimpose to yield an ‘electric field’
at any given point in space. The current sources and sinks form
dipoles or higher ­order n ­poles.
• Extracellular currents arise from many sources, including synaptic
currents, fast action potentials and their afterpotentials, calcium
spikes and voltage ­dependent intrinsic currents.
• The magnitude of extracellular currents depends critically on two
factors: the cytoarchitectural organization of a network and the
temporal synchrony of the various current sinks and sources.
• Depending on the recording method, neuroscientists distinguish
between electroencephalogram (EEG), electrocorticogram
(ECoG) and local field potential (LFP; also known as micro ­, depth
or intracranial EEG), although all of these measures refer to the
same biophysical process.
• The electric field is the force ‘felt’ by an electric charge, and can
be transmitted through brain volume. The extent of volume
conduction depends on the relationships between the current
dipole and the features of the conductive medium.
• High ­density sampling of the extracellular field with contemporary
methods enables the calculation of current source density, and
therefore the localization of current sinks and sources.
• The voltage gradients generated by highly synchronous activity
of neuronal groups can affect the transmembrane potential of
the member neurons and alter their excitability through ephaptic
coupling.
• Synchronous spiking of nearby neurons is the main source of the
high ­frequency components of the local field.
• There is a discernable relationship between the temporal evolution
of cell assemblies and the time ­dependent changes of the spatially
distributed currents. High ­density, wide ­band recordings of the
local field can therefore provide access to both afferent inputs and
the spiking output of neurons.
TOC blurb
000 The origin of extracellular fields and
currents — EEG, ECoG, LFP and spikes
György Buzsáki, Costas A. Anastassiou and Christof
Koch
Neuronal activity in the brain gives rise to
transmembrane and extracellular electromagnetic
fields that can be measured in the extracellular
medium using several approaches. In this Review,
Buzsáki and colleagues provide an overview of
the mechanisms that underlie the generation of
extracellular currents and fields.
Subject categories
Cellular Neuroscience, Computational Neuroscience, Cognition, Ion
channels, Neurophysiology
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Supplementary information legends
Supplementary information S1 (movie). Spike ­triggered average of
the LFP in the hippocampus during exploration. Recordings were
made by an 8 ­shank (300 µm intershank distance), 256 ­site silicon
probe (32 recording sites on each shank linearly spaced at 50 µm). LFP
was smoothed both within and across shanks. A fast firing putative
interneuron in CA1 stratum oriens (ori; star) was used for LFP
averaging. Spikes were sampled while the rat was running on a linear
track for water reward. Note that the spike is preceded by synaptic
activity (negative wave, hot colors) first in the stratum lacunosum ­
moleculare (lm) and the dentate molecular layer (ml), indicating
entorhinal cortex activation, followed by CA1 stratum radiatum
(rad) activity, which represents CA3 activation. The movie illustrates
that the spike is embedded into an evolving and unique stream of
two ­dimensional LFP vectors (100 µs frames). Black trace (top), LFP
recorded from the CA1 pyramidal layer (pyr). Time is shown in the
upper right corner (–20 ms to 20 ms). The horizontally wide LFP spike
(red) that appears at time zero in stratum oriens (on the second shank)
is due to spatial smoothing. Hypothesis: since different neurons have
different synapsembly/LFP signatures, the time resolved population
vectors of the LFP can reliably track the dynamic of evolving spiking
cell assemblies 1. gc, granule cell layer; hil, hilus. Courtesy of Antal
Berényi and Zoltán Somogyvári.
1. Buzsáki, G. Neural syntax: cell assemblies, synapsembles, and readers. Neuron 68, 362–385 (2010).
Supplementary information S2 (movie). Spike triggered average of the
LFP in the hippocampus during non ­REM sleep. Same arrangement
as in Video 1 but the spikes were sampled during sharp wave ripples
during sleep. Note that the activity arises from CA3 and spreads to
CA1 via the stratum radiatum. Sharp waves emerge by self ­organized
activity in the recurrent collateral system of CA3 region 1–3. Courtesy
of Antal Berényi and Zoltán Somogyvári.
1. Buzsáki, G., Traub, R. D. & Pedley, T. A. in Current Practice of Clinical Encephalography (eds Ebersole, J. S. & Pedley, T. A.) 1–11 (Lippincott-Williams and Wilkins, 2003). 2. Pettersen, K. H., Hagen, E. & Einevoll, G. T. Estimation of population firing rates and current source densities from laminar electrode recordings. J. Comput. Neurosci. 24, 291–313 (2008). 3. Csicsvari, J., Hirase, H., Mamiya, A. & Buzsáki, G. Ensemble patterns of hippocampal CA3-CA1 neurons during sharp wave-associated population events. Neuron 28, 585– 594 (2000).
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