Artefactual origin of biphasic cortical spike-LFP correlation
Artefactual origin of biphasic cortical spike-LFP correlation
l Okun 0 1 2 3 4
0 Institute of Neurology, University College London, WC1N 3BG , London , UK
1 Centre for Systems Neuroscience, University of Leicester , Leicester LE1 7QR , UK
2 Department of Neuroscience , Psychology and Behaviour , University of Leicester , Leicester LE1 9HN , UK
3 Institute of Ophthalmology, University College London, EC1V 9EL , London , UK
4 Department of Neuroscience, Physiology and Pharmacology, University College London, WC1E 6DE , London , UK
Electrophysiological data acquisition systems introduce various distortions into the signals they record. While such distortions were discussed previously, their effects are often not appreciated. Here I show that the biphasic shape of cortical spike-triggered LFP average (stLFP), reported in multiple studies, is likely an artefact introduced by high-pass filter of the neural data acquisition system when the actual stLFP has a single trough around the zero lag. Action Editor: Alain Destexhe
Phase distortion; Extracellular amplifier; Neural probes; Silicon probes; Neural data acquisition
Cortical local field potential (LFP) is a readily measurable
signal that provides a wealth of information on neuronal
activity in the vicinity of the recording electrode. In particular,
the relationship between LFP and the spiking of nearby
neurons can lead to important insights into the cortical function,
(Gray and Singer 1989; Arieli et al. 1995; Destexhe et al.
1999; Fries et al. 2001; Montemurro et al. 2008; Nauhaus et al.
2009; Martin and Schroeder 2016; Cui et al. 2016)
, and can be
utilized in the design of brain-machine interfaces (BMIs)
(Gulati et al. 2014; Hall et al. 2014)
. The simplest quantitative
measure of the relationship between spiking activity and LFP
is the spike-LFP cross-correlation, also known as
spiketriggered LFP average (stLFP). stLFP can be computed for
spike trains of individual neurons as well as for multi-unit
spiking activity (MUA). In the former case, the shape and
magnitude of stLFP are inherited from the cross-correlation
between the membrane potential (Vm) of the neuron and the
(Okun et al. 2010)
In multiple previous studies, including our own, the stLFP
often had a characteristic biphasic shape, whereby a trough
around the 0 time lag is followed by a slower positivity, with a
peak offset by several hundred milliseconds from 0, see Fig. 1
(Arieli et al. 1995; Destexhe et al. 1999; Rasch et al. 2008;
Rasch et al. 2009; Okun et al. 2010; Taub et al. 2015; Martin
and Schroeder 2016)
. This positive peak of stLFP was thought
to have a biophysical origin, and several possible explanations
(Rasch et al. 2009; Ray 2014)
. Here, I show
that in our data the positive peak of stLFP is a by-product of
high-pass filtering of the actual LFP by the neural data
acquisition system. Since passing the acquired signal through a
high-pass filter with a cutoff frequency in the 0.1–1 Hz range
is a standard feature of extracellular recording systems, it
would only be natural to presume that the same explanation
applies to other similar reports in the literature. Such
interpretation also explains why in some studies, most notably when
LFP was measured with an intracellular amplifier (i.e.
effectively recording LFP in DC mode, which lets through all
frequencies), a biphasic correlation between the LFP and the Vm
of nearby neurons was not observed, e.g.,
(Poulet and Petersen
2008; Haider et al. 2016)
All experimental procedures were conducted according to the
UK Animals (Scientific Procedures) Act 1986 (Amendment
Regulations 2012). Experiments were performed at University
College London under personal and project licenses released
by the Home Office following institutional ethics review.
The data analysed here originates from recordings of
spontaneous activity made as part of previously published studies
(Okun et al. 2015, 2016)
. Briefly, acute and chronic recordings
were performed in the infragranular layers of primary visual
cortex in C57BL/6 J mice. In both cases recordings were
performed in head fixed animals, after the mice underwent
several sessions of acclimatisation to head fixation. Acute
recordi n g s w e r e p e r f o r m e d u s i n g C e r e b u s ( B l a c k r o c k
Microsystems, Salt Lake City, UT) neural acquisition system
with Buzsaki32 probes (NeuroNexus, Ann Arbor, MI). The
Cerebus system was used in the basic setting, where no digital
filtering followed the initial high-pass at 0.3 Hz and low-pass
at 7.5 kHz analog filtering in the amplifier. The impedance
of the recording sites was ~1 MΩ at 1 kHz. Chronic
recordings were performed using the OpenEphys system (Siegle
et al. 2015) and Intan RHD2132 16-channel amplifier board
(Intan Technologies, Los Angeles, CA) with CM16
NeuroNexus probes with 2 tetrodes on each shank. The
recordings were performed with the default filtering settings of
OpenEphys software (1 Hz high-pass, 7.5 kHz low-pass).
Prior to implantation, the probes were electroplated with the
polymer PEDOT:PSS resulting in the recording sites’
impedance <100 kΩ at 1 kHz. For both acute and chronic recordings
the signal was digitised at 30 kHz and stored for offline
analysis. Spikes were detected using klusta software suite
(Rossant et al. 2016)
. Here, only multiunit activity (MUA)
comprised from all spikes detected on a shank or a tetrode
was considered, hence spike sorting was not required. For
stLFP computations, to reduce the contamination of the LFP
with the spiking, I used MUA and LFP from different shanks
of the probe, 150–200 μm apart.
Mathematically, high-pass filtering operation is a
convolution of the original signal with the transfer function of the
filter: vout(t) = h * vin(t), where vin(t) is the original signal,
vout(t) is the recorded signal and h is the transfer function of
the filter. According to the convolution theorem, in the
frequency domain it holds that Vout(ω) = H(ω)Vin(ω), where
capital letters denote the Fourier transforms of the original
functions. H(ω) is a complex number, i.e., H(ω) = |H(ω)|eiargH(ω),
which is to say that in frequency ω the filter scales the
amplitude of the original signal by |H(ω)| and shifts its phase by
argH(ω). In particular, for a high-pass filter with cutoff at ω0,
H(ω) ≈ 1 for frequencies ω ≫ ω0, and H(ω) ≈ 0 for ω ≪ ω0.
Furthermore, if the transfer function H of the filter is known,
it is possible to correct vout(t) offline, so that the phase shift
introduced by the filter in frequencies around ω0 is undone,
while the decrease in the power of these frequencies is
retained. This is easily achieved by computing in the frequency
domain a corrected signal Vcorr(ω) from Vout(ω) in the following
manner: Vcorr(ω)= e−iargH(ω)Vout(ω). A Matlab function that uses
this approach for correcting OpenEphys recordings is now
publicly available at
To examine the effect that high-pass filtering has on
crosscorrelation between signals, in addition to experimental
spiking and LFP data, I used pairs of synthetic signals x(t), y(t)
with pre-specified power spectrum P(ω) and coherence C(ω)
(both are positive real valued functions, with C(ω) ≤ 1). x(t)
and y(t) were constructed in the frequency domain in the
following manner. X(ω) = P1/2(ω)eiφ(ω), where for each frequency
ω, φ(ω) was drawn randomly and uniformly from the ½0; 2πÞ
interval. Y(ω) = − C(ω)X(ω) + Y2(ω), where Y2(ω) is an
additional signal with a power spectral density of (1 − C2(ω))P(ω).
Y2(ω) was generated similarly to X(ω), however the phases of
X(ω) and Y2(ω) were drawn independently, thus the two
signals were uncorrelated (and incoherent) with each other.
Finally, the time domain signals x(t), y(t) were obtained by
taking the inverse Fourier transform of X(ω) and Y(ω). The
result of applying a high-pass filter h to y(t) was also computed
in the frequency domain, by taking the inverse Fourier
transform of H(ω)Y(ω).
The way low frequency signals are processed by the neural
data acquisition system is central to the understanding of the
stLFP waveform. To measure the transfer function of an
acquisition system, I connected a function generator (TG310,
Thurlby Thandar Instruments, UK) to the head-stage of the
amplifier, and delivered sine waves of equal amplitude
(~5 mV) spanning frequencies between 30 Hz and 0.03 Hz.
The signal generator also emitted a TTL signal, which marked
the extrema of the input sine wave. Comparing the TTL signal
to the output of the amplifier allowed estimating the phase
shift introduced by its filters, while comparing the amplitude
of the output across frequencies provided an estimate of the
gain (Fig. 2a,b). In this manner I obtained the transfer function
for Cerebus and OpenEphys systems. The Cerebus system
was tested in the basic setting (also used for recordings),
where no digital filtering followed the initial analog filtering
in the amplifier. The OpenEphys system was tested with 1 Hz
cutoff frequency of the high-pass filter, which is the default of
its data acquisition software, and with 0.1 Hz cutoff, which is
the lowest possible value in this system. The results of these
measurements show that amplifier filtering substantially shifts
phases even in frequencies >1 Hz (Fig. 2c,d). Surprisingly, the
phase shift was larger for OpenEphys with a nominal 0.1 Hz
cutoff frequency than for Cerebus with a nominal 0.3 Hz
cutoff frequency (Fig. 2d), demonstrating that the cutoff
frequency on its own (without a full specification of the type and order
of the filter) does not provide a complete characterisation of
the high-pass filtering properties of the amplifier.
To understand the effect such high-pass filtering has on the
LFP and its correlation with spikes or Vm of nearby neurons, I
Fig. 2 Amplifier transfer function. a Measuring the amplifier transfer
function. Output of the function generator (red sine wave) was fed into
the head-stage of the amplifier, and the TTL signal (overlaid, black) was
stored for offline analysis. The output of the amplifier (black sine wave)
was also stored for offline analysis. b As in a, for a sinusoidal input of
lower frequency. A clear phase shift between the input (red) and output
(black) sine waves is seen, with the output leading the input. A small
reduction in amplitude (cf. a) is also apparent. c,d The gain and the
phase shift introduced by the amplifier, measured across a range of
frequencies as demonstrated in a-b, for OpenEphys (OE) system with
1 Hz and 0.1 Hz cutoffs, and for the Cerebus system
started by considering pairs of synthetic signals x(t), y(t)
constructed (see Methods) to have a symmetric correlation on the
same timescale as empirical stLFPs (Fig. 3a,b). In this
analysis, x(t) represents spikes or membrane potential, while y(t)
represents the LFP. After the transfer functions of the
amplifiers were applied to y(t), its correlation with x(t) became
biphasic, similar to the observed cortical stLFP (Fig. 3c, cf.
Fig. 1). Next, I examined the effect that the power spectrum
of y(t) has on the shape of the cross-correlation with x(t) before
and after the distortion by high-pass filtering. When y(t)
contains more power in frequencies <10 Hz, its correlation with
x(t) increases in magnitude (Fig. 3d,e). In these cases, the
distortion introduced by high-pass filtering of y(t) is much
more prominent and is manifested in two features of the
x(t)y(t) cross-correlation. First, the artefactual positive peak can
grow to be of almost equal magnitude to the central negative
trough around 0 time lag (Fig. 3f). Second, the correlation
at 0 time lag differs prominently from its true value
(cf. Fig. 3e,f).
When the above simulations were repeated using a spike
train derived from x(t) instead of the continuous signal x(t)
itself (spikes corresponded to x(t) going above its 99th
percentile value), the results were identical up to a scaling factor of
the ordinate (data not shown). This result is consistent with the
mathematical theory of triggered cross-correlations
The knowledge of the transfer function of the amplifier
allows to reverse, via offline processing, the phase distortion
the amplifier introduces into the LFP recording, as described
in the Methods section. Here I applied such a correction to
recordings previously acquired in the mouse primary visual
cortex. Examples of LFP traces before and after the phase
correction are shown in Fig. 4a,b. As expected, the difference
between the recorded and the corrected signals is in low
frequencies, and at first glance might appear rather small.
However, after the phase correction, the correlation with the
spiking activity was no longer biphasic (Fig. 4c,d).
A comprehensive overview of the distortions caused by
recording electrodes and amplifier filtering was provided in
(Nelson et al. 2008)
. Here I did not consider distortions
introduced by the silicon probe because according to their
measurements such a distortion is relatively small (< 0.33 rad) for
amplifiers with input impedance >1 GΩ (which, according to
the specifications, is the case for both Cerebus and Intan
amplifier head-stages). The methodological approach to
measuring and correcting the distortion used here is virtually identical
to the approach proposed in
(Nelson et al. 2008)
Nelson et al. do not provide any concrete examples, beyond a
passing mention of numerous publications where LFP
where the power spectrum of x(t) and the coherence were as in a, while
the power spectrum of y(t) varied as shown (the middle spectrum is as in
a). e The cross-correlation between x(t) and y(t), for the different cases of
y(t)’s power spectrum shown in d (colours match). f The
crosscorrelations after y(t) was filtered with the 0.1 Hz cutoff OpenEphys
high-pass transfer function (colours match to d-e)
Fig. 4 Offline correction of phase distortion. a Example of LFP in mouse
primary visual cortex, recorded with the OpenEphys system with 1 Hz
cutoff high-pass filter, before and after the phase correction. b As in a, for
LFP exhibiting a rather different dynamics, recording performed with the
Cerebus system. c,d stLFP for recordings shown in a,b, computed using
LFP signal as it was recorded by the data acquisition system and after
phase correction. Scale bars: 50 μV
distortion might not have been accounted for. The present
work therefore is, to the best of my knowledge, the first to
provide a concrete example of a well-documented feature of
spike-LFP dynamics that appears to be produced by amplifier
filtering rather than genuine biophysical mechanisms. That
being said, this explanation does not fully exclude the
possibility that under some experimental conditions cortical stLFP
can have a biphasic shape. More generally, the present work
demonstrates that low frequency filtering, which is employed
by the vast majority of neural data acquisition systems in use
today, has important confounding implications for the study of
LFP. In particular, the distortion is not limited to stLFP, but is a
general property of cross-correlations involving the LFP
signal. In other words, the second signal can be neural or external
events other than spikes, e.g., onsets of UP states
et al. 2012)
The distortion of the low frequencies of the LFP can be
corrected offline. This requires measuring the transfer function
of the amplifier system and reversing its effect, as demonstrated
here and in
(Nelson et al. 2008)
. An example Matlab code to
perform this correction is provided in supplementary material
(Nelson et al. 2008)
, and some vendors might already have a
special utility for their neural data acquisition systems (e.g.,
FPAlign of Plexon Inc., Dallas, TX). A Matlab function for
correcting OpenEphys recordings (which was used to generate
Fig. 4a,c) is publicly available at
Acknowledgments I would like to thank Sylvia Schroeder and
Nicholas Steinmetz for commenting on the manuscript and Kenneth
Harris and Matteo Carandini for supporting this work (via Wellcome
Trust grants 95668 and 95669).
Compliance with ethical standards
Conflict of interest The author declares that he has no conflict of
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