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BRIEF

Communicated by Eric Halgren

Effect of Reference Scheme on Power and Phase
of the Local Field Potential

Vinay Shirhatti
vinay@cns.iisc.ernet.in
Ayon Borthakur
borthakur.ayon@gmail.com
Supratim Ray
sray@cns.iisc.ernet.in
Centre for Neuroscience, Indian Institute of Science, Bangalore, Indien, 560012

Brain signals are often analyzed in the spectral domain, where the power
spectral density (PSD) and phase differences and consistency can reveal
important information about the network. Jedoch, for proper inter-
pretation, it is important to know whether these measures depend on
stimulus/behavioral conditions or the reference scheme used to analyze
Daten. We recorded local ﬁeld potential (LFP) from an array of micro-
electrodes chronically implanted in area V1 of monkeys under different
stimulus/behavioral conditions and computed PSD slopes, coherence,
and phase difference between LFPs as a function of frequency and in-
terelectrode distance while using four reference schemes: single wire,
average, bipolar, and current source density. PSD slopes were dependent
on reference scheme at low frequencies (below 200 Hz) but became in-
variant at higher frequencies. Average phase differences between sites
also depended critically on referencing, switching from 0 degrees for
single-wire to 180 degrees for average reference. Results were consistent
across different stimulus/behavioral conditions. We were able to account
for these results based on the coherence proﬁle across sites and properties
of the spectral estimator. Our results show that using different reference
schemes can have drastic effects on phase differences and PSD slopes and
therefore must be interpreted carefully to gain insights about network
properties.

1 Einführung

Local ﬁeld potential (LFP) recorded using microelectrodes implanted in-
side the brain is thought to reﬂect mainly the overall synaptic activity of the
neuronal population (Buzs´aki, Anastassiou, & Koch, 2012; Einevoll, Kayser,
Logothetis, & Panzeri, 2013; Logothetis, 2003; Mitzdorf, 1985; Nunez &

V.S. and A.B. contributed equally.

Neural Computation 28, 882–913 (2016)
doi:10.1162/NECO_a_00827

C(cid:2) 2016 Massachusetts Institute of Technology.
Veröffentlicht unter Creative Commons
Namensnennung 3.0 Unportiert (CC BY 3.0) Lizenz.

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Effect of Reference on LFP

883

Srinivasan, 2006) and provides clues about the properties of the neuronal
network around the microelectrode. LFPs are usually studied in spectral
domain by computing the Fourier transform of its autocorrelation function,
called the power spectral density (PSD), in which brain rhythms associated
with different behavioral states (Buzsaki, 2006; Buzs´aki & Draguhn, 2004)
are captured as band-limited peaks. Zusätzlich, PSDs of brain signals have
a typical 1/f form, whose slope reveals important information about the
neuronal network, such as the nature of noise. Zum Beispiel, while white
noise produces a slope of zero, a slope of 2 can be generated by shot (Brow-
nian) noise, whose origin might be due to up-down states of slow-wave
sleep just as a telegraphic process or from an exponential relaxation pro-
cess of synaptic currents that is driven by random spiking (Baranauskas
et al., 2012; B´edard, Kr ¨oger, & Hand, 2006A; Müller, Sorensen, Ojemann,
& Nijs, 2009; Milstein, Mormann, Fried, & Koch, 2009). Zusätzlich, ﬁlter-
ing properties of the network, such as capacitive coupling or ﬁltering by
active conductances, are captured in the slope (B´edard et al., 2006A; B´edard
& Hand, 2009; Lind´en, Pettersen, & Einevoll, 2010; Logothetis, Kayser,
& Oeltermann, 2007). Weiter, while earlier studies mainly focused on the
power of the signal at different frequencies (captured using the PSD), Re-
cent theories have proposed a potential role of phase in cortical processing.
Zum Beispiel, communication between two brain areas can be facilitated
by aligning their relative phases appropriately (communication through
coherence hypothesis; Fries, 2005; Womelsdorf et al., 2007). Testing these
hypotheses require an accurate estimation of the power and phase of the
LFP at multiple sites.

Potential recorded at the microelectrode tip is relative to some reference
voltage, the choice of which can potentially change the properties of the
signal (Nunez & Srinivasan, 2006). LFPs are usually measured relative to
a single electrode or wire placed far away from the microelectrode (called
a single-wire reference here). Jedoch, a critical issue with this scheme is
that if the reference wire itself picks up some neural activity, all microelec-
trodes show that activity as well (because the reference signal is subtracted
from the potential obtained from each microelectrode). Weiter, Manchmal
all the electrodes pick up some common noise, and it is desirable to re-
move this common component and focus only on the local neural activity
speciﬁc to the location near the electrode. This is achieved by constructing
another reference signal that represents the common noise and subtract-
ing it from the recording signal of interest. Some of the common referenc-
ing schemes (proposed mainly for EEG data analysis, but the same extends
to LFP analysis as well) are average reference (the reference signal is the
average of all electrodes), bipolar reference (each electrode is referenced to
a nearby electrode), and current source density (CSD: the reference signal
for a 2D grid is the average of four nearest neighbors). The reference signal
comes progressively closer to the recording signal as we move from average
Referenz, bipolar to CSD, highlighting progressively localized neural

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884

V. Shirhatti, A. Borthakur, and S. Ray

Aktivität. Note that we use the term reference for bipolar and CSD schemes
Auch, even though they involve a single or up to four electrodes only (in diesem
letter, we only use a 2-dimensional CSD reference because we do not have
recordings along the depth of the cortical tissue; see equation 2.1).

There is no gold standard when it comes to the choice of a referencing
scheme (Nunez & Srinivasan, 2006; Schiff, 2005). Instead the choice is of-
ten arbitrary, depending on the preference of the experimenter, the level of
common noise, and the speciﬁc question of interest. Previous studies using
EEG or electrocorticogram (ECoG) signals have shown that phase consis-
tency between electrode pairs when single-wire reference is used depends
on the amplitude of the reference signal itself (Fein, Raz, Braun, & Merrin,
1988; Hu, Stead, Gardner, & Worrell, 2007; Hu, Stead, Dai, & Worrell, 2010;
Nunez & Srinivasan, 2006; Schiff, 2005). Jedoch, the effect of different ref-
erence schemes on PSD slopes and phase differences or consistency has not
been well studied, especially in LFP data. We therefore recorded LFP from
chronically implanted 10 × 10 microelectrode arrays in monkeys and com-
pared PSD slopes and phase relationships under the referencing schemes
mentioned above. Weiter, we tested whether PSD slopes and phase rela-
tionships depended on stimulus conditions or the attentional state of the
Tiere.

2 Materials and Methods

All the experiments carried out were in adherence to the protocols approved
by the Institutional Animal Care and Use Committee of Harvard Medical
School. Behavioral task, data collection procedure, and electrode selection
criteria are the same as in previous studies (Ray & Maunsell, 2010, 2011B)
and some details are omitted here. Brieﬂy, LFP signals were recorded from
two male rhesus monkeys (Macaca mulatta) using a 10 × 10 microelectrode
array (Blackrock Microsystems, 96 active electrodes) implanted in area V1
of the right cerebral hemisphere (um 15 mm anterior from the occipital
ridge and 15 mm from the midline; the corresponding receptive ﬁelds were
in the lower left quadrant spanning about 2 × 2 degrees of visual angle at
an eccentricity of about 4 degrees). Raw data were ﬁltered between 0.3 Hz
(Butterworth ﬁlter, ﬁrst order, analog; integrated in the recording hardware)
Und 500 Hz (Butterworth, fourth order, digital) and digitized at 2 kHz (16
bit resolution). The LFP signals were originally referenced with respect to a
single wire placed on the dura near the electrode grid (this is an insulated
wire that is typically stripped by 1 Zu 2 cm to expose the metal and placed
under or on the dura within a few centimeters of the recording array). Nur
electrodes conforming to reliable estimation of the receptive ﬁeld center
(SD less than 0.1 degree across days, mapped by ﬂashing small Gabor
stimuli on a rectangular grid that spanned the receptive ﬁelds of all the
Elektroden) wurden benutzt, yielding 27 Und 62 electrodes from monkeys 1 Und 2,
jeweils (one region of the array implanted in monkey 1 did not yield
usable signals). The monkeys performed an orientation-change detection

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Effect of Reference on LFP

885

Aufgabe (Affe 1, 10 sessions, and monkey 2, 17 sessions). They maintained
ﬁxation within 1 degree of a small central dot located at the center of a CRT
video display (100 Hz refresh rate, 1280 × 768 pixels, gamma corrected),
while two achromatic, odd-symmetric Gabor stimuli were synchronously
ﬂashed for 400 ms with an average interstimulus period of 600 MS. Eins
of the Gabors was centered on the receptive ﬁeld of one of the recording
sites (new location for each session), while the other was on the opposite
side of the ﬁxation point at an equal eccentricity. The monkey was cued
to attend to one of them in blocks of trials and rewarded for detecting
a change in the orientation (von 90 degrees) in one of the presentations.
Both the stimuli were static with an SD of 0.5 Grad, spatial frequency of 4
cycles per degree (CPD) and at the preferred orientation of the recording site
(different for each session). The contrasts of the two stimuli were matched
on each presentation and could take one of eight values—0%, 1.6%, 3.1%,
6.2%, 12.5%, 25%, 50%, and 100%—chosen pseudo-randomly. On average,
each contrast was repeated 79 mal (range, 55–101) for monkey 1 Und
74 mal (range, 47–120) for monkey 2, for each attentional condition. Except
Figure 2B, all results are shown for the attend-out condition (when the
monkey was not attending to the stimulus inside the receptive ﬁeld).

√

2.1 Reference Schemes. The recordings were initially referenced to a
single wire placed on the dura near the microelectrode grid (single-wire ref-
erence). For average reference, we took the average of 27 Und 62 Elektroden
for the two monkeys as the reference signal. For computing bipolar refer-
enz, we took all pairs of the selected electrodes, yielding 702 (27 × 26) Und
3782 (62 × 61) pairs of electrodes with varying interelectrode differences,
out of which 351 Und 1888 pairs were unique (only one of the two pairs with
the same set of electrodes ((X, j) Und (j, X)) was used; electrode distances
mehr als 4 mm (0 Und 3 pairs for the two monkeys) were discarded). Solch
a bipolar referenced signal was assumed to be recorded from a virtual elec-
trode located at the middle of the two contributing electrodes. daher,
for bipolar reference, the nearest electrodes were separated by a distance
von 0.2
2 mm (assume three real electrodes at (0, 0), (0, 0.4), Und (0.4, 0)
mm; the virtual bipolar electrodes would be at (0, 0.2) Und (0.2, 0) with a
separation of 0.2
2 mm). To avoid any directional bias, bipolar referenc-
ing was done using a center-out scheme in which the signal recorded from
an electrode farther from the center of the recording array was subtracted
from the signal from the nearer one; other schemes (such as subtraction of
lateral and dorsal electrodes from medial and ventral ones) yielded similar
results for all bipolar pairs that did not share a common electrode. Auch,
to test whether the inclusion of a single single-wire referenced electrode in
the estimation of multiple bipolar electrodes could inﬂuence our results,
we also constructed a set of bipolar electrodes in which each single-wire
electrode was used at most once. The PSDs estimated using this restricted
set of bipolar electrodes were indistinguishable from the PSDs obtained
from the full set (as shown in Figure 3B).

√

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886

V. Shirhatti, A. Borthakur, and S. Ray

For a 2D microelectrode array, we deﬁned the CSD referenced voltage at

coordinate (X, j) of a particular electrode as

CSD(X, j) = V (X, j)

− V (x − 1, j) + V (X + 1, j) + V (X, y − 1) + V (X, j + 1)
4

(2.1)

das ist, the CSDs were computed by subtracting the mean of four neighbor-
ing electrodes 400 μm apart. This analysis was limited to electrodes that had
four good neighbors (electrodes at the edge of the array or electrodes for
which any one neighboring electrode was broken were excluded), yielding
16 Und 29 electrodes for monkeys 1 Und 2.

2.2 Phase Coherence and PSD. If the Fourier coefﬁcients of two signals
( F )e jθ
are expressed as Ak
, (where f is the frequency and
k is the trial number, which varies from 1 to N), phase coherence or phase
locking value is calculated by (Lachaux, Rodriguez, Martinerie, & Varela,
1999)

( F )e jφ

and Bk

( F )

Cphase

( F ) = 1
N

e j(Phi

( F )−θ

( F ))

(cid:2)
(cid:2)
(cid:2)
(cid:2)
(cid:2)

(cid:3)

Given N phase angles, the angular deviation is deﬁned as

Phase

(cid:4)

2(1 − R),

(2.2)

(2.3)

where R is the length of the mean resultant vector (same as Cphase in equation
2.2 if phase angles correspond to phase differences across trials). Das ist ein
measure of the circular spread about the mean resultant vector. Weil
√
the angular deviation varies over [0,
2], it is preferred over the standard
deviation, which is unbounded for directional statistics (Berens, 2009; Zar,
2010). Circular statistics were performed using CircStat (Berens, 2009).

PSDs, phases, and phase coherence were computed using the multita-
per method (Thomson, 1982), implemented in Chronux 2.0 (Mitra & Bokil,
2007), an open source, data analysis toolbox available at http://chronux
.org. Brieﬂy, the multitaper method reduces the variance of spectral esti-
mates by premultiplying the data with several orthogonal tapers known as
Slepian functions (Jarvis & Mitra, 2001; Mitra & Pesaran, 1999). We used a
single taper to maximize the frequency resolution. For baseline analyses (alle
ﬁgures except Figure 2), data for all eight contrasts were pooled to compute
the PSD, and PSDs across sessions (10 Und 17 for the two monkeys) war
averaged to get one PSD per electrode. For stimulus period and attention

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Effect of Reference on LFP

887

Analyse (siehe Abbildung 2), for each session, we chose only electrodes whose
receptive ﬁelds were within 0.2 degree of the stimulus center, which yielded
63 Und 89 electrodes for the two monkeys across all sessions, out of which
23 Und 53 electrodes were unique. As for the baseline case, we averaged
PSDs for a unique electrode across sessions to get a single estimate of PSD
per electrode.

We corrected the PSDs for the ampliﬁer roll-off, which was experi-
mentally determined by passing a sinusoidal signal at various frequencies
through the data recording system and measuring the output (see online
supplementary Figure 1). This experimentally determined transfer func-
tion was very similar to the theoretical transfer function up to about 500 Hz
(calculated based on the properties of the Butterworth ﬁlters used in the
Blackrock data acquisition system), although at higher frequencies (über
um 500 Hz), the experimentally determined function had higher power
indicating ampliﬁer or measurement or digitization noise. To avoid any
possible inﬂuence of the ﬁlter roll-off on our results, the slopes are reported
only up to 400 Hz. The Blackrock ampliﬁer has an input impedance above
1 T(cid:5), and therefore the ampliﬁer-induced distortion in the phase and am-
plitude in this frequency range is negligible (Stacey, Kellis, Patel, Greger, &
Butson, 2012).

2.2.1 Curve Fitting. We ﬁtted the PSDs with the following function

(Müller, Sorensen, Ojemann, & Nijs, 2009):

P = A. F

−α + B,

(2.4)

where P is the PSD and f is the frequency, while A (scaling function), B (noise
Boden), and α (slope) are free parameters. The parameters were obtained
using least square minimization using the program fminsearch in Matlab.
Data corresponding to the frequencies of Monitor refresh rate (100 Hz),
line noise, and its harmonics were not included in the analysis. Slopes were
computed in steps of 10 Hz between 20 Und 400 Hz by taking PSD segments
of ±15 Hz around each frequency point. Larger ﬁt lengths (±25 or ±50 Hz)
resulted in smoothing the slope function (see supplementary Figure 2A),
but otherwise the results remained unchanged.

3 Ergebnisse

Figure 1A shows the mean PSD of the single-wire referenced LFP signals
across electrodes after ampliﬁer roll-off correction (see supplementary Fig-
ure 1 for details) for the baseline period (500 ms to 0 ms before the stimulus
onset; attend-out condition) for monkeys 1 Und 2. The PSD slopes obtained
by ﬁtting equation 2.4 on ±15 Hz segments around each frequency are
shown in Figure 1B. LFP power did not decrease with a constant slope with

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888

V. Shirhatti, A. Borthakur, and S. Ray

Figur 1: Power spectral density (PSD) slope analysis. (A) Mean PSD across
Elektroden (denoted by N in the legend) during the baseline period (500 ms to
0 ms interval before stimulus onset) for the two monkeys. Power at frequencies
around the monitor refresh rate (100 Hz) and noise harmonics (120, 240, Und
360 Hz) has been masked for visual clarity. (B) Mean PSD slope as a function
of frequency, computed between 20 Und 400 Hz in steps of 10 Hz. The shaded
region denotes the SEM of the slope. Black markings on the frequency axis de-
note frequencies at which the difference in the slopes was statistically signiﬁcant
(ANOVA, P < 0.05 with Bonferroni correction). frequency, suggesting that LFPs did not follow a universal power law that extended to a large frequency range. At frequencies below approximately 250 Hz, PSD slopes varied considerably with frequency and also across animals. However, at higher frequencies, the slopes settled to a value of approximately 1.4 for both monkeys. Results were similar when different ﬁt lengths were used (supplementary Figure 2A) or when the PSD was computed over a different time period (supplementary Figures 2B and 2C). 3.1 Effect of Stimulus Contrast on PSD Slopes. We next checked whether the PSD slopes depended on stimulus conditions or the behavioral state of the animals. Figure 2A shows the mean PSDs when a Gabor stim- ulus of varying contrasts was presented and the corresponding slopes. For this analysis, PSDs (of single-wire referenced LFP signals) were computed between 200 and 400 ms after stimulus onset (this time period was chosen to avoid strong stimulus related transients; see Figure 1B of Ray & Maun- sell, 2010, for time-frequency power spectrum), and only electrodes that were well stimulated by the stimulus (receptive ﬁeld centers were within 0.2 degree of the stimulus center; see section 2) were used, yielding 23 and 53 electrodes for the two monkeys. Note that due to the shorter analysis interval of 200 ms, the slopes were noisier (see supplementary Figure 2C). Stimulus onset led to a decrease in power around the alpha band (< 20 Hz) l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Effect of Reference on LFP 889 Figure 2: Effect of stimulus contrast and attention on PSDs and slopes. (A) Mean PSD (left) and mean PSD slopes (right) during the stimulus period (200 ms– 400 ms after stimulus onset) for different stimulus contrasts (indicated in the second column). The traces corresponding to the lowest (0%; black) and highest contrast (100%, lightest gray) are plotted thicker for clarity. The insets in the ﬁrst and third columns show the change in power (in decibels) from the baseline period (300–100 ms before stimulus onset) for the different contrast conditions to highlight the suppression of alpha power at about 10 Hz and increase in gamma power above 30 Hz. The black markings over the frequency axis denote the frequencies at which the difference in the slopes is statistically signiﬁcant (p < 0.05; Bonferroni corrected; ANOVA). SEMs are omitted for clarity. (B) Mean PSD and corresponding slopes during the baseline period (300–100 ms before stimulus onset) and stimulus period (200–400 ms after stimulus onset; only 100% contrast condition is shown) when attention was directed inside (Attention IN) or outside (Attention OUT) the receptive ﬁeld. The insets in the ﬁrst and third columns show the change in power (in decibels) from the Attention OUT baseline condition. and an increase in the gamma band (about 30–80 Hz) (highlighted in the insets), whose center frequency increased with stimulus contrast (Jia, Xing, & Kohn, 2013; Ray & Maunsell, 2010). These stimulus-dependent changes in the PSD resulted in occasional differences in slopes across contrasts at low frequencies (< 100 Hz). However, in spite of a clear elevation in power, the slopes remained unchanged with contrast at higher frequencies. One possible explanation for the invariance of slopes at high frequencies is that the instrument noise ﬂoor was higher than physiological neural noise at these frequencies, so the PSD slopes were essentially determined by the statistics of the ampliﬁer or ﬁlter noise. However, the absolute power at high frequencies was much higher during the stimulus period than base- line (this increase in high-gamma power is due to the increase in ﬁring rate during the stimulus period; see Ray & Maunsell, 2011a, for a detailed l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 890 V. Shirhatti, A. Borthakur, and S. Ray study on the relationship between high-gamma power and multiunit ﬁring rates using data from the same monkeys), and yet the slopes were similar during stimulus and baseline periods, which rules out the possibility of instrumentation noise biasing our results. 3.2 Effect of Attention on PSD Slopes. Figure 2B shows the PSDs during baseline (300–100 ms before stimulus onset to match the stimulus analysis period; thin lines) and during the presentation of a stimulus of 100% contrast (200–400 ms after onset) when attention was directed outside (black) or inside (gray) the receptive ﬁeld. Attention led to well-studied changes in alpha and gamma bands (see the inset), but not at other fre- quencies. In the alpha range, we observed a signiﬁcant reduction in power due to attention (monkey 1: reduction of 14.3% and 16.7% for baseline and stimulus periods, p < 10−5 for both; monkey 2: reduction of 12.9%, p < 10−6 for baseline period, and 1.2%, p = 0.62 for stimulus period, paired t-test; note that monkey 2 had very weak alpha, so the effect was not observed at the stimulus period). We also observed a signiﬁcant increase in gamma center frequency with attention (monkey 1: mean shift of 1.74 Hz, p = 0.05; monkey 2: mean shift of 1.60 Hz, p < 10−2, paired Wilcoxon signed rank test; note that for both monkeys, the analysis interval of 200 ms duration (spectral resolution of 5 Hz) led to noisy estimates of peak frequencies), consistent with prior studies (Bosman et al., 2012). Similar results were obtained for lower-contrast stimuli also (data not shown). Importantly, in spite of clear changes in alpha and gamma bands, there was no change in the slope of the PSD at any frequency range, suggesting that the effect of attention was spectrally localized. 3.3 Effect of Reference Scheme on PSD Slopes. Figure 3A represents the mean PSD across electrodes of LFP signals for the baseline period (500 ms–0 ms before the stimulus onset) of monkeys 1 and 2 using four referencing schemes: single-wire reference (red trace), average reference (green trace), bipolar reference (obtained by subtracting the signal from an- other electrode 400 μm away; blue trace), and CSD (orange trace), and the corresponding slopes. At low frequencies (< 200 Hz), the slope depended on the reference type: it was signiﬁcantly larger for single-wire and average references com- pared to bipolar and CSD references (for which the reference signal was constructed from electrodes that were close to the recording electrode). In contrast, slopes at frequencies beyond 200 Hz varied much less with the referencing scheme. Similar results were obtained when slopes were determined using different frequency ﬁt ranges or when PSDs were com- puted for a different time period (as in supplementary Figure 2; data not shown). To study the effect of bipolar referencing in more detail, we chose the reference electrode from progressively larger distances. Figure 3B shows l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Effect of Reference on LFP 891 Figure 3: Effect of referencing on PSDs and slopes. (A) Mean PSDs (computed between 500 and 0 ms before stimulus onset; left plot) and the corresponding slopes (right plot) calculated for the single-wire reference (red), average refer- ence (green), bipolar reference (blue), and CSD (orange) for monkeys 1 and 2. The number of electrodes averaged is given in the inset in the ﬁrst and third columns. (B) Mean PSDs (left plot) and slopes (right plot) using bipolar refer- ence where the reference electrode was taken from varying distances from the recording electrode (distance ranges in μm and the number of electrode pairs are shown in the inset in the ﬁrst and third columns). The insets in the ﬁrst and third columns show the PSDs between 0 and 100 Hz, the typical range used in most LFP studies. the average PSDs and slopes when the reference electrode was selected from four different distance ranges (shown in the legend along with the number of electrode pairs in each category). Moving the reference electrode away increased the slope at low frequencies for both monkeys but had a negligible effect at frequencies beyond approximately 200 Hz. 3.4 Phase Coherence across Electrodes. To explain the changes in PSD slopes with referencing, we ﬁrst computed the PSDs of the reference signals themselves (see supplementary Figure 3; note that for the bipolar reference, the reference signal is simply the single-wire referenced signal recorded from a neighboring electrode). We found that at low frequencies, the power of all the reference signals was comparable to the single-wire referenced signal, but at higher frequencies, the power of the reference signals was much smaller than the power of the single-wire referenced signal (see Sup- plementary Figure 3). Because the average reference and the CSD signals are computed by averaging signals from several electrodes, power of this reference signal at a particular frequency depends on the phase relationship l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 892 V. Shirhatti, A. Borthakur, and S. Ray l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 between electrodes. Of particular importance is the consistency in the phase difference across time (here, computed for time intervals at a particular po- sition relative to the onset of a stimulus) typically measured using coherence or phase coherence. We have reported phase consistency using several dif- ferent measures in a previous study (Srinath & Ray, 2014); the results are summarized below and in Figure 4. Effect of Reference on LFP 893 We observed that while we were using single-wire reference, the phase coherence between electrodes was high at low frequencies but decreased with increasing frequency and ﬁnally approached a constant baseline value above about 100 Hz (see Figure 4A). This baseline value was greater than zero only because of a positive bias in the coherence estimator that depends on the number of trials: using an unbiased estimator such as pairwise phase consistency (Vinck, van Wingerden, Womelsdorf, Fries, & Pennartz, 2010) showed that the true coherence was zero above about 100 Hz (Srinath & Ray, 2014). When other reference schemes were used, phase coherence was reduced to baseline levels at almost all frequencies, which suggested that most of the observed coherence could simply be due to volume conduction effects (see Figures 4B to 4D). Similar results were obtained during the stimulus period; the only exception was the gamma band for which the coherence peak remained for all reference schemes (see supplementary Figure 4; refer to Srinath & Ray, 2014, for a more detailed discussion). Phase coherence was also high for some distance ranges such as 0.2 2 and 0.4 mm for bipolar reference and 0.4 mm for CSD, but this was simply an artifact of having part of the same signal during referencing. For example, if the single- wire referenced signals for two electrodes separated by 0.4 mm are V1 and V2, CSD1 will have a V1-V2/4 term while CSD2 will have a V2-V1/4 term, and this common component will lead to a spuriously high coherence and a phase difference of π. This effect is best illustrated by considering bipolar pairs separated by 0.4 mm, for which some pairs receive a contribution from a shared electrode (e.g., for three consecutive electrodes V1, V2, and V3 in a line, the bipolar pair V1-V2 and V2-V3) while others do not (for four electrodes V1 to V4 at vertices of a 0.4 mm × 0.4 mm square, bipolar pair V1-V2 and V3-V4). Phase coherence was high only for bipolar pairs with a shared electrode (see Figure 4C). √ Figure 4: Phase coherence after the signals are referenced using different schemes. The insets show the interelectrode distance ranges and the number of electrode pairs in each range. We chose the baseline period between 300 ms and 100 ms interval before stimulus onset such that the analysis durations were the same for baseline and stimulus conditions (200–400 ms after onset; results are shown in supplementary Figure 4); similar results were obtained if the baseline period was chosen between 500 ms and 0 ms instead. (A) Single-wire reference. (B) Average reference. (C) Bipolar reference. (D) CSD reference. For bipolar and CSD reference schemes, we show some additional ranges (0.2 2 for 2 and 0.8 mm for CSD) at which the computed referenced signals bipolar, 0.4 share a common component, which largely determines the coherence and phase differences. For the bipolar reference scheme, we also split the 0.4 mm distance range into two cases—one where the bipolar pairs share a common component and other where they do not. √ √ l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 894 V. Shirhatti, A. Borthakur, and S. Ray Coherence is a measure of phase consistency across time epochs, but it does not depend on the actual phase difference between the two signals. However, while averaging signals to compute the reference, the magnitude of the phase difference across electrode pairs is an important factor. For example, two signals that are perfectly out of phase have a coherence of 1 but will cancel each other out perfectly. We therefore studied the mean and variability of phase differences across electrodes as a function of frequency and interelectrode distance. For the single-wire reference, the mean phase difference (across elec- trodes) was close to zero and was invariant of frequency or interelectrode distance (see Figure 5A), while the circular standard deviation (see Fig- ure 6A) increased with frequency as well as interelectrode distance. Between 0 to 200 Hz, where the PSD slopes (see Figure 3A) and coherence (see Fig- ure 4A) fell drastically, the circular standard deviation across electrodes was reasonably low (< 0.25 for nearby electrodes), so the signals from two electrodes were approximately in phase. Note that even at high frequencies, the mean phase difference remained zero throughout (instead of taking ran- dom values between −π and π), and the circular standard deviation was 2, suggesting that the phases were not completely random not close to across electrodes. Similar results were obtained by taking the mean of the absolute value of phase differences (not shown here), which is sometimes used to remove the ambiguity regarding the choice of the electrode posi- tion in a pair while computing the difference (i.e., given two electrodes, we could either use ϕ 1 as the phase difference). 2 or ϕ − ϕ − ϕ √ 1 2 These phase relationships provide a simple explanation of the effect of referencing. At low frequencies, signals from different electrodes that are av- eraged to get the reference signal have approximately the same phase and therefore do not cancel out with averaging, such that the low-frequency component of the reference signal is almost as large as the recording signal (see supplementary Figure 3) and subtracting the reference signal decreases the power at low frequencies appreciably and makes the slopes ﬂatter as compared to the single-wire referenced signal. This effect is stronger for monkey 1 (see Figure 3A) because of higher phase coherence at low frequen- cies compared to monkey 2 (see Figure 4A), which resulted in a larger ref- erence signal. The similarity between the reference signal and the recorded signal increases in the order of average reference, bipolar reference, and CSD, leading to more reduction in power and more ﬂattening of the slope in the same order. At high frequencies beyond 200 Hz, all signals used for referencing have almost random phase, and therefore the reference signal is much weaker than the original single-wire signal (see supplementary Figure 3), so subtracting this reference does not affect the power or the slope. The upward shift in the PSD at high frequencies for the bipolar reference (the blue trace is above the red and green traces in Figure 3A) can similarly be explained based on the phase relationships described above. When two l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Effect of Reference on LFP 895 2 √ 1 and θ sinusoids of the same frequency (ω) but different amplitudes (A1 and A2) and phases (θ ) are added, the resulting signal is a sinusoid of frequency ω and amplitude )). So when 2 + 2A1A2 cos(θ amplitudes are equal and phases are random, the expected value of cos(θ − 1 θ 2 times the original amplitude (whether 2 two signals are added or subtracted does not make any difference because the phases are random). This explains why the power at higher frequencies increases by a factor of two with respect to the original signal (upward shift of the log PSD by log 10(2), or about 0.3; blue trace in Figure 3A). ) is zero and the amplitude is ∼ (A1 2 + A2 √ − θ 1 2 3.5 Effect of Referencing Scheme on Phase Differences. If the phase differences across electrodes for the single-wire reference are shown in a circular histogram, the distribution is skewed toward zero degrees at all fre- quencies (see, for example, Figure 7A; the degree of skewness might depend on the neural activity picked up by the reference wire and its proximity to the microelectrode grid), although the skewness decreases with increasing frequency as the circular standard deviation increases (see Figure 8A; the distribution becomes more spherical). Because all three referencing schemes essentially remove part of the common component present in the single- wire referenced signals, we expected the phase difference distributions to be more circular at all frequencies, with a mean phase difference of either zero (if the distribution is not perfectly circular) or random (if the distribu- tion became completely circular) and an increase in the circular standard deviation in all cases. This was indeed observed for both bipolar and CSD references (see Figures 5C, 5D, 6C, and 6D)—apart from the distances for which there was a deterministic common component in the referenced sig- 2 and 0.4 mm, with nals that largely determined the phase difference (0.2 √ 2, and 0.8 for CSD), the phase differ- a shared electrode, for bipolar; 0.4, 0.4 ences were distributed randomly, and the CSD was close to 2. However, the results obtained for the average reference signal were counterintuitive. While the mean phase differences remained close to zero at 0.4 mm (which was expected, because the coherence did not decrease to baseline levels for this distance range—see Figure 4B—suggesting that some of the common component in the signals remained even after referencing), the mean phase differences shifted to π at high frequencies for the distance range between 0.4 mm and 1.2 mm and all frequencies for larger distances (see Figure 5B). In terms of the polar plot, this suggests that although the reference signal was much smaller than the original signal (especially at high frequencies; see supplementary Figure 3), subtracting this small signal and again com- puting the phase differences caused the skew to shift from zero to π (see Figures 7B and 8B). The CSD also showed a nonintuitive trend: as a whole, it increased as compared to the single-wire reference (see Figure 6B versus 6A), but it was higher for intermediate distances (0.4–1.2 mm) and reduced at higher distance ranges (>1.2 mm).

√

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896

V. Shirhatti, A. Borthakur, and S. Ray

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To explain this effect, we took a representative pair of electrodes sep-
√
(1.62 + 0.42)) and studied how the
arated by approximately 1.65 mm (
phase differences changed once the signals were average referenced. Feige-
ures 7A and 7B show the circular histogram of the mean phase difference
for frequencies between 5 Hz and 25 Hz (the results were similar when
a different low-frequency range was selected) for single-wire and average

Effect of Reference on LFP

897

reference schemes. Consistent with the results shown in Figure 5, der Mittelwert
phase difference shifted from approximately 0 degrees for single-wire ref-
erence to approximately 180 degrees for average reference. A similar trend
was observed at high frequencies (200–300 Hz; results remain the same for
a different frequency range; see Figures 8A and 8B). This was counterin-
tuitive because the amplitude of the average reference signal (obtained by
averaging the single-wire referenced electrodes) was smaller than any of
the electrodes, especially at high frequencies (see the green trace in Figure
7C), and therefore subtraction of this small average reference signal from
individual electrode was not expected to change the phases substantially.

There are two reasons that average referencing produces the observed
phase shift. The ﬁrst reason, which is more applicable at low frequencies,
is related to the high variability of the spectral estimator used to calculate
the amplitude spectrum (see Jarvis & Mitra, 2001; Srinath & Ray, 2014). In
our data, because we used a single taper to estimate the PSD, the power
followed an exponential distribution across trials, while the amplitude fol-
lowed a Rayleigh distribution (see Srinath & Ray, 2014). Rayleigh distri-
bution has a signiﬁcant proportion of values that are very small, so for a
given trial, no matter how small the average reference signal was, Dort
were always some electrodes for which the signal amplitude fell below the
average reference amplitude, especially at low frequencies. To demonstrate
Das, we plotted the fraction of trials for which the signal amplitude was
a smaller-than-average reference amplitude (see Figure 7E). The fraction

√

Figur 5: Mean phase difference between electrode pairs, averaged across all
the electrode pairs within a distance range. Same format and analysis interval
as Figure 4. For the bipolar reference scheme, the distance ranges for which the
referenced signals share a common component (0.2
2 Und 0.4 mm) are shown
in dashed and dashed-dotted blue lines. Distance range 0.4 mm with no shared
common component is shown as a thicker solid blue line. For the CSD reference
scheme, the distance ranges for which the referenced signals share a common
2 Und 0.8 mm) are shown in thicker lines. For the bipolar
component (0.4, 0.4
Referenz, the phase difference due to the deterministic component could be
entweder 0 or π depending on how the signal is referenced (z.B., if the voltages
recorded from three nearby electrodes are V1, V2, and V3, the bipolar referenced
signals could be BP1 = V1-V2 and BP2 = V2-V3, which would produce a phase
difference of π ; or it could be BP1 = V1-V2 and BP2 = V3-V2, which would
produce a phase difference of 0). For CSD, the phase difference at 0.4 mm is π
because CSD at electrode 1 has a V1-V2/4 term while CSD at electrode 2 hat
a V2-V1/4 term. Electrodes separated by 0.4
2 Und 0.8 mm share two or one
neighbors, jeweils, so their CSDs have a common component that leads
to a phase difference of 0. If we ignore these special cases, phase differences
for the remaining electrode pairs show a random value (thin lines in C and D)
and high circular standard deviation (Figures 6C and D), suggesting that phase
differences are random.

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898

V. Shirhatti, A. Borthakur, and S. Ray

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Figur 6: Circular standard deviation of phase differences across electrodes for
different reference schemes. This measure has a range of 0 Zu
2. It uses the
same format and analysis interval as Figure 5.

√

expectedly decreased with increasing frequency, but even at high frequency,
when the mean amplitude (across trials) of either electrode was larger
than the mean amplitude of the average reference signal by an order of

Effect of Reference on LFP

899

magnitude (Figure 7C), in about 10% of the trials, the average reference am-
plitude was larger than the signal amplitude. This proportion was almost
40% at low frequencies because the coherence was high and the average
reference signal was relatively much larger.

At low frequencies, phase differences were small across electrode pairs
in a single-wire reference scheme, so if we represent the amplitudes and
phases of individual electrodes as vectors, all signal vectors, sowie
the vector corresponding to the average reference signal, would point in
approximately the same direction. Subtracting this average reference signal
would keep the phase approximately the same if the signal amplitude was
larger than the average reference amplitude; otherwise the vector should
show a shift of π. daher, assuming the original phase difference to
be zero, the ﬁnal phase difference would be π if exactly one of the two
electrodes had an amplitude greater than the average reference amplitude.
To illustrate this, we plotted the absolute phase difference in the single-
wire scheme versus the absolute phase difference after average referencing
(see Figure 7D). We separated the trials into three categories: when both
(orange), exactly one of the two (Grün), or neither of the two (black) signal
amplitudes was larger than the average reference amplitude. For trials in
which either both amplitudes (orange) oder keines von beiden (black) were larger, Die
mean phase difference remained close to zero degrees even after average
referencing, although the distribution was much less skewed (larger circular
Standardabweichung). Jedoch, when only one amplitude was larger than
the average reference (Grün), the mean phase difference indeed shifted to π.
Gesamt, the mean circular distribution became more spherical (increase in
Standardabweichung) after average referencing (see Figure 7B), but the large
shift of π in the phase difference of selected trials caused the overall phase
difference to have a slight skew toward π. This effect was further illustrated
by plotting the mean absolute shift in phase difference due to referencing
as a function of the amplitudes of the two signals after subtracting the
average reference amplitude (see Figure 7F). In this plot, the ﬁrst quadrant
corresponds to the trials shown in orange in Figure 7D, the third quadrant
corresponds to black, and the remaining quadrants correspond to green
Versuche. In der Tat, the mean absolute phase shift was about 0 for orange and
black trials and π for the green trials.

At high frequencies (200–300 Hz), the overall phase differences were
much more scattered (see Figure 8A). Even for this case, there was a large
shift in the mean phase after average referencing (see Figure 8B). The reason
described for the low-frequency case is insufﬁcient to explain this result
because now the average reference signal was very small, and consequently,
there were fewer trials for which either one or both electrodes had amplitude
less than the average reference. Jedoch, we noticed another trend in this
Fall: even for the trials for which both electrodes had amplitude greater
than the average reference, the distribution shifted toward π, wenngleich

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900

V. Shirhatti, A. Borthakur, and S. Ray

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none of the trials showed a large change in phase difference when average
referenced (see Figure 8C, orange dots).

This behavior can be explained based on vector algebra. Erste, without
loss of generality, assume that the phase of the average reference signal
Ist 0 degrees, such that average referencing involves adding a small vector
pointing toward π. Auch, assume that the magnitude of the signal is larger
than the average reference. Applying average reference to a signal shifts
the phase toward π, but the magnitude of the shift depends on the signal
Phase. If an electrode has a phase close to zero, it would not change by much
after average referencing (it would shift by π for a small fraction of trials
for which the signal amplitude is less than the average reference amplitude,
as discussed in Figure 7). But if the signal phase is close to π/2, the signal
vector would move substantially toward π after average referencing. Das

Effect of Reference on LFP

901

explains why the scatter in phase difference after average reference in-
creases with increasing phase difference for the single-wire reference: Wenn
two electrodes have a very small phase difference in the single-wire refer-
enz (phase difference close to zero), both phases shift by approximately the
same amount, and therefore the phase difference would remain small after
average referencing. Jedoch, if the phase difference is large, the phase
would shift by dissimilar amounts after average referencing, and the re-
sulting phase difference would be more scattered around the single-wire
phase difference values.

Now consider the case when the phase difference between electrodes
is close to π/2. This could happen if the ﬁrst phase is anywhere between
zero and π/2, while the second is shifted further by π/2. When the ﬁrst
phase is close to zero and second is close to π/2, applying average reference
would leave the ﬁrst phase unchanged, but the second one would move
toward π, and therefore the overall phase difference would increase. Das
would happen as long as the ﬁrst phase is less than π/4. The opposite
would be observed if the ﬁrst phase is near π/2 and the second near π;
now the ﬁrst one would shift towards π and the second would not change
viel, and therefore the phase difference would decrease after applying the
average reference. Jedoch, the percentage of trials for which this happens
would be fewer than the earlier case, because these signal vectors (along
with other electrodes) are averaged to get the average reference vector and
therefore are more likely to be pointing toward the average reference vector.
Gesamt, this would cause an asymmetric shift in the phase differences, mit
an overall upward shift in the orange dots in the middle portion of the plot.
In der Tat, we observed that more dots were above the diagonal than below,

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Figur 7: Effect of average referencing on the phase difference between a pair
of electrodes separated by approximately 1.65 mm, recorded from the baseline
period of monkey 1 (300–100 ms interval before stimulus onset). (A) Distribu-
tion of single-wire referenced phase differences in the 5–25 Hz frequency range.
(B) Distribution of phase differences for the same two electrodes but after the sig-
nals are average referenced. (C) Amplitude spectrum of individual electrodes
(light gray), electrode pair selected for analysis (dark gray), the average am-
plitude spectrum of all the electrodes (black), and the average reference signal
(Grün). (D) Scatter plot and the corresponding histograms of the absolute phase
differences in the 5–25 Hz frequency range, separated based on the three possi-
ble relationships between the amplitudes of two electrode amplitudes and the
average reference amplitude. The mean phase differences and the correspond-
ing percentage of trials are shown in the respective insets. (E) Fraction of trials
for which the signal amplitude was less than the average reference amplitude
for the two electrodes (gray) and the mean of the fractions of all the electrodes
(black). (F) Change in absolute phase difference after average referencing as a
function of the amplitudes for the two electrodes minus the average reference
Amplitude.

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V. Shirhatti, A. Borthakur, and S. Ray

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Figur 8: Same format and analysis interval as Figures 7A to 7C but for the
frequency range of 200 Hz to 300 Hz. The mean vectors shown in panels A (In
Rot) and B (in green) are lengthened by a factor of 10 for better clarity.

and therefore the distribution as a whole shifted toward π. Auch, as the
interelectrode distance increased, average referencing changed the skew
in the phase histogram from 0 to π. The histogram was more circular at
intermediate distances, due to which the circular standard deviation was
larger (see Figure 6B).

4 Diskussion

We studied the effect of stimulus, behavior, and referencing on power and
phase of LFP signals recorded using microelectrode arrays from V1 cortex

Effect of Reference on LFP

903

of awake monkeys. The signals were originally recorded with reference to
a single wire on the dura of the monkeys (single-wire reference), and were
re-referenced using three popular schemes: average reference, bipolar, Und
CSD (siehe Sektion 2 for details). We found that the power of the LFP signal
and the slope of the PSD depended on the reference scheme at low frequen-
cies (< 200 Hz) but became invariant at higher frequencies. These results were explained based on the coherence proﬁle across electrode pairs, which was high at low frequency for the single-wire reference but decreased to baseline levels at higher frequencies. Further, the coherence decreased to baseline levels at all frequencies for other reference schemes, suggesting that the low-frequency coherence of the single-wire reference signals was due to a common source, whose contribution was removed by referencing leading to a decrease in PSD power and slope. Most important, we found that average reference caused the mean phase difference across electrodes to shift from zero to π. This was due to two reasons. First, due to the variability of the spectral estimator, a fraction of electrodes always had a magnitude less than the average reference signal on any given trial, such that a fraction of phase differences shifted from 0 to π with average refer- encing (see Figure 7; more applicable at low frequencies). Second, phases shifted by different amounts with average referencing that depended on the signal phase relative to the average reference phase (see the orange dots in Figure 8C; see section 3 for details). Varying stimulus contrast or attentional focus changed the PSDs at alpha and gamma bands, but otherwise had little effect on the PSD slopes or phase differences. 4.1 Reference Techniques and Their Uses. In EEG or ECoG record- ings, the use of single-wire reference induces biases in phase coherence across sites, which depend on the amplitude of the reference signal itself (Fein et al., 1988; Hu et al., 2007, Hu, Stead, Dai, & Worrell, 2010; Nunez & Srinivasan, 2006; Schiff, 2005). Different reference techniques have tra- ditionally been explored and used in the context of EEG recordings, each with its advantages as well as shortcomings (Bertrand, Perrin, & Pernier, 1985; Qin, Xu, & Yao, 2010; Dien, 1998; Nunez et al., 1997). With the ad- vent of microelectrode recordings, these reference techniques can be used similarly for LFP recordings as well. Average referencing is used to re- move any external noise that is common to all the sites and is believed to yield better signal-to-noise ratios (Crone, Boatman, Gordon, & Hao, 2001; Yuval-Greenberg, Tomer, Keren, Nelken, & Deouell, 2008; Ludwig et al., 2009; Sinai et al., 2009; Boatman-Reich et al., 2010; Podvalny et al., 2015). Bipolar referencing is preferred if one wants to magnify highly local events that occur near an electrode (DeCoteau et al., 2007; Hamam´e et al., 2014; Bosman et al., 2012; Brunet et al., 2014; Spaak, Bonnefond, Maier, Leopold, & Jensen, 2012; van Kerkoerle et al., 2014). For example, van Kerkoerle and colleagues (2014) showed that the interarea (V1-V4) coherence proﬁle depended on whether a global (similar to single-wire reference here) or a l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u n e c o a r t i c e - p d / l f / / / / 2 8 5 8 8 2 2 0 1 5 7 2 6 n e c o _ a _ 0 0 8 2 7 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 904 V. Shirhatti, A. Borthakur, and S. Ray local reference (similar to bipolar reference here) was chosen (see their Fig- ure 7B). In particular, the overall coherence across all frequencies dropped drastically when bipolar reference was chosen, but a frequency dependence also emerged (the gamma band showed relatively higher coherence than other frequencies), which was not seen very saliently earlier. CSD analysis has been used in the case of extracellular recordings to extract local effects in the form of current sources and sinks (Einevoll et al., 2013; Lakatos, Chen, O’Connell, Mills, & Schroeder, 2007; Lakatos, Karmos, Mehta, Ul- bert, & Schroeder, 2008; Schroeder et al., 2001). These different referencing techniques have been used across recording modalities, at varying scales of spatial resolution, to evaluate properties of signals such as the spectral char- acteristics and phase coupling (or coherency) (Bosman et al., 2012; Brunet et al., 2015; 2014; Ng, Logothetis, & Kayser, 2013; Lachaux et al., 1999) or cross-frequency phase-amplitude coupling (He, 2014; He, Zempel, Snyder, & Raichle, 2010). However, how these referencing techniques might them- selves affect the PSDs and the phase relationship between LFPs at different recording sites has not been evaluated. Here we show that these features of the signal are indeed sensitive to the reference technique. In particular, our results show that average reference should be avoided while doing phase analysis. While computing PSD slopes, it is better, wherever possi- ble, to focus on a frequency range for which different reference schemes give similar results (> 200 Hz), although most LFP analyses are typically
limited to approximately 200 Hz and PSDs in different frequency ranges
can have different well-characterized slopes (Bedard et al., 2006A). Ein anderer
possibility is to use more advanced methods to estimate the reference signal
(which is subsequently used for re-referencing), such as reference estima-
tion standardization technique (REST) or robust maximum likelihood type
estimation (see Lepage, Kramer, & Chu, 2014, for details).

4.2 Spectral Slopes and Underlying Mechanisms. Consistent with our
results, several reports have shown PSD slopes between 1 Und 3 at frequency
ranges below 100 Hz in both EEG and ECoG (Dehghani, B´edard, Cash,
Halgren, & Hand, 2010; Freeman, Holmes, Westen, & Altes Haus, 2006;
Freeman, Rogers, Holmes, & Silbergeld, 2000; He et al., 2010; Miller et al.,
2009; Podvalny et al., 2015; Pritchard, 1992) as well as LFP (B´edard et al.,
2006A; Petermann et al., 2009). Slopes in this frequency range critically
depend on the referencing scheme, so these results must be interpreted
with caution.

Although studies involving LFP and ECoG have traditionally focused on
oscillations below about 100 Hz, recent studies have shown the existence of
both fast oscillations (Buzsaki & Draguhn, 2004; Scheffer-Teixeira, Belchior,
Le˜ao, Ribeiro, & Tort, 2013) and asynchronous “broadband” activity at
frequencies above about 100 Hz (Manning, Jacobs, Fried, & Kahana, 2009;
Miller et al., 2009; Ray & Maunsell, 2011A). Jedoch, fewer reports have
studied the PSD slopes at frequencies above about 100 Hz. Milstein and

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Effect of Reference on LFP

905

colleagues (2009) recorded LFP from humans using intracranial electrodes
(40 μm microwires) and reported a slope of about 2 zwischen 1 Hz and
400 Hz, which they related to slow dendro-synaptic decay or up-down
state changes characteristic of slow wave sleep (telegraph noise). Miller and
colleagues (2009) recorded ECoG data from humans and reported a slope of
4 between approximately 80 Hz and 500 Hz. These results are inconsistent
with our ﬁndings (slopes of about 1.4 über 200 Hz). One reason for this
difference could be the difference in species (monkey versus human) oder der
size of electrodes (microelectrode versus ECoG electrodes). Another reason
could be the fast stimulus presentation rates and short analysis periods
used in our study. We used a brief temporal window of up to 500 ms for
computing PSDs, while most of the other reports have used data spanning
seconds to minutes with either no task or passive ﬁxation. Zum Beispiel,
the slope of 2 observed by Milstein and colleagues (2009) was due to the
alternation of up and down states due to slow waves, but that possibility
cannot be tested in our data due to the fast stimulus presentation times
during which the monkeys performing our task had to constantly be in
an attentive state and had short recovery periods between stimuli. Das
could also explain why our different stimulus or behavioral conditions did
not change the PSDs except at alpha and gamma ranges, unlike previous
studies that have shown that slopes generally tend to decrease on stimulus
presentation (Podvalny et al., 2015) or as one goes from a state of rest to
elevated levels of alertness or wakefulness as demanded by the task and
cognitive load (see He, 2014, for a discussion).

A careful characterization of PSD slope is essential because it reveals
properties of the underlying network. Zum Beispiel, a slope of approxi-
mately 2, found in many studies (see above), can arise from Brownian
noise, and several mechanisms have been suggested that could generate
this noise. Some of the mechanisms explored in modeling studies and at-
tributed to the observed PSD slopes are temporal dynamics of the synaptic
processes (fast rise and slow decay exponentially) triggered by Poisson
spiking (Milstein et al., 2009; B´edard et al., 2006A; Freeman & Zhai, 2009),
dendritic ﬁltering properties (Miller et al., 2009; Pettersen & Einevoll, 2008;
Lind´en et al., 2010), ionic diffusion processes across the membrane, Und
ﬁltering properties of extracellular medium (B´edard, Kr ¨oger, & Hand,
2004; B´edard et al., 2006B; B´edard & Hand, 2009; Logothetis et al., 2007).
In this study, since the PSD slopes are observed to depend critically on the
reference scheme and stimulus condition at low frequencies, it is difﬁcult to
infer the noise or ﬁltering properties of the network using LFP data. Wie-
immer, at higher frequencies, the slope was invariant to reference scheme or
whether a stimulus was presented. It was about 1.4 for the two monkeys,
inconsistent with the mechanisms described in the studies mentioned above
that produce an integer value of the PSD slope (um 2 for Milstein et al.,
2009, Und 3 for B´edard et al., 2006A). This is instead indicative of a fractal
(self-organized critical or SOC) behavior (Bak, Tang, & Wiesenfeld, 1987,

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V. Shirhatti, A. Borthakur, and S. Ray

1988; Beggs & Plenz, 2003; Dehghani et al., 2012), although simply show-
ing a power law form in the PSD does not guarantee SOC behavior (für
a detailed review on this topic, see Beggs & Timme, 2012). Endlich, PSD
slopes of signals like ECoG and EEG could potentially be used to infer ab-
normalities in the underlying network activity in pathological conditions
such as schizophrenia and autism spectrum disorders (Voytek & Ritter,
2015).

Although the PSD slopes did not change with increasing stimulus con-
trast, the power increased over a broad frequency range leading to an
upward shift of the PSD, similar to previous studies that have related this
“broadband shift” to an increase in ﬁring rates of neurons near the micro-
electrode (Manning et al., 2009; Ray, Crone, Niebur, Franaszczuk, & Hsiao,
2008; Ray & Maunsell, 2011A). To accurately estimate this broadband power
increase, we need to discount the changes in power in narrow-band oscilla-
tions such as delta, theta, alpha, beta, and gamma, which was achieved by
Manning and colleagues (2009) by using a robust regression ﬁt instead of a
least squares ﬁt. In their case, data were recorded from many different brain
areas where different oscillations were prevalent, which necessitated their
Ansatz. In unserem Fall, this was not required because data were recorded
from primary visual cortex, where only an alpha peak was observed in the
PSD. Calculation of slopes between 0 Hz to 150 Hz after ignoring the power
in classical frequency bands (similar to the approach used by Manning and
colleagues) yielded similar results (data not shown).

4.3 Signiﬁcance of Absolute Phases. In most reports, the absolute sig-
nal phase or phase difference between two electrodes is computed using any
one referencing scheme and the change in phase across stimulus or behav-
ioral conditions is studied. Had the change in phase with stimulus/behavior
been the only important factor, the shift in phase by 180 degrees due to av-
erage referencing would not have mattered because the change would have
remained the same. Jedoch, there are many cases in which the absolute
phase or phase difference between electrodes is mapped to physiological
properties. Zum Beispiel, the communication through coherence (CTC) hy-
pothesis (Fries, 2005) proposes that if two neuronal assemblies oscillate with
a phase difference equal to the conduction delay (of spikes) between them,
spikes produced at the most excitable phase of the ﬁrst assembly reach
precisely when the second assembly is most excitable, so that the second
assembly can ﬁre as well. If the phase difference is not at the optimum
value, the second assembly does not produce a spike, thereby allowing
ﬂexible long-range communication between neuronal assemblies depend-
ing on the magnitude and consistency of the phase differences (Fries, 2005;
Schoffelen, Oostenveld, & Fries, 2005; Womelsdorf et al., 2007; Gregoriou,
Gotts, Zhou, & Desimone, 2009; Bosman et al., 2012; Roberts et al., 2013; Jia,
Tanabe, & Kohn, 2013). Here the phase difference is mapped to the efﬁcacy

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Effect of Reference on LFP

907

of communication channels: zero degrees implies efﬁcient communication,
while 180 degrees implies poor communication, and the results get com-
pletely ﬂipped if average referencing is used instead of single-wire refer-
enz. Phase differences are also sometimes used to determine the direction
of information transmission between two brain areas (van Kerkoerle et al.,
2014; see their Figure 7C), which would get reversed if average reference is
gebraucht (these authors used single-wire or bipolar reference).

Ähnlich, some hypotheses make speciﬁc predictions about the absolute
phase of an oscillation with spiking activity or perceptual or attentional
state. Zum Beispiel, in theta/gamma phase coding hypothesis (Buzsaki &
Chrobak, 1995; Fries, Nikoli´c, & Singer, 2007), the phase of the signal is
mapped to the level of inhibition in the network (which is maximum at the
peak of the oscillation and minimum at the trough), such that the position
of the spike with respect to the oscillation can be used to code the strength of
the stimulus. Average referencing ﬂips the phase by 180 degrees whenever
the signal amplitude is less than the reference signal, which happens for
a large proportion of trials at low frequencies (see Figure 7E). For such
Versuche, if the spike actually occurs at the trough of the signal, after average
referencing, it would appear at the peak instead, completely changing the
results. Ähnlich, several studies have reported that perceptual threshold
or attentional state depends on the phase of theta or alpha oscillations
(Ai & Ro, 2014; Busch, Dubois, & Van Rullen, 2009; Busch & VanRullen,
2010; Jensen, Gips, Bergmann, & Bonnefond, 2014; Mathewson, Gratton,
Fabiani, Beck, & Ro, 2009). Wieder, using the average referencing scheme
would change the phase of a subset of trials by 180 degrees, leading to
an incorrect interpretation. This would happen even if the same reference
scheme were used for all the behavioral conditions, because the hypothesis
posits a speciﬁc relationship between behavior and the absolute phase of
the signal.

In den vergangenen Jahren, there has been an increase in LFP recordings with several
microelectrodes, a critical step toward understanding the network proper-
ties at a ﬁner scale and studying connectivity, communication, and informa-
tion transfer in small networks. Our results highlight the changes in power
and phase relationship due to different reference schemes, which must be
properly accounted for before using this information to gain insights into
the network.

Danksagungen

We thank John Maunsell for his help in experimental design and data
collection and Steven Sleboda and Vivian Imamura for technical sup-
port. This work was supported by the Wellcome Trust/DBT India Alliance
(Intermediate Fellowship to S.R.) and the DBT-IISc Partnership Programme.
We declare no competing ﬁnancial interests.

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