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Systems/Circuits
Cortical Electrocorticogram (ECoG) Is a Local Signal
XAgrita Dubey and XSupratim Ray
Centre for Neuroscience, Indian Institute of Science, Bangalore, India 560012
Electrocorticogram (ECoG), obtained by low-pass filtering the brain signal recorded from a macroelectrode placed on the cortex, is
extensively used to find the seizure focus in drug-resistant epilepsy and is of growing importance in cognitive and brain–machine-
interfacing studies. To accurately estimate the epileptogenic cortex or to make inferences about cognitive processes, it is important to
determine the “spatial spread” of ECoG (i.e., the extent of cortical tissue that contributes to its activity). However, the ECoG spread is
currently unknown; even the spread of local field potential (LFP) obtained from microelectrodes is debated, with estimates ranging from
a few hundred micrometers to several millimeters. Spatial spread can be estimated by measuring the receptive field (RF) and multiplying
by the cortical magnification factor, but this method overestimates the spread because RF size gets inflated due to several factors. This
issue can be partially addressed using a model that compares the RFs of two measures, such as LFP and multi-unit activity (MUA). To use
this approach for ECoG, we designed a customized array containing both microelectrodes and ECoG electrodes to simultaneously map
MUA, LFP, and ECoG RFs from the primary visual cortex of awake monkeys (three female Macaca radiata). The spatial spread of ECoG
was surprisingly local (diameter ⬃3 mm), only 3 times that of the LFP. Similar results were obtained using a model to simulate ECoG as
a sum of LFPs of varying electrode sizes. Our results further validate the use of ECoG in clinical and basic cognitive research.
Key words: electrocorticogram; local field potential; magnification factor; primary visual cortex; receptive field; spatial spread
Introduction
Electrocorticogram (ECoG) refers to the signal obtained from
macroelectrodes (typically 2–3 mm in diameter) placed directly
on the pial surface of cortex of epileptic patients for localization
of the seizure focus (Lesser et al., 2010;Buzsa´ki et al., 2012;Mor-
shed and Khan, 2014;Yang et al., 2014;Im and Seo, 2016), which
is also being increasingly used to study cognition in humans (En-
gel et al., 2005;Mukamel and Fried, 2012;Parvizi and Kastner,
2018).
To accurately estimate the epileptogenic cortex from ECoG
activity or to make inferences about cortical areas involved in
cognition, it is essential to determine the spatial spread of ECoG
(the cortical tissue around the ECoG electrode that contributes to
its activity), but this is currently unknown.
Spatial spread is best studied for multiunit activity (MUA) and
local field potential (LFP) recorded using microelectrodes im-
planted in sensory areas, especially in visual (Xing et al., 2009;
Dubey and Ray, 2016) or auditory (Kajikawa and Schroeder,
2011) cortices that contain topographic maps, by presenting
small visual stimuli or tone pulses. For example, small visual
stimuli activate a small part of the cortex, which can be shifted
relative to the electrode by shifting the stimulus in the visual field.
This allows an estimation of the “visual spread” or receptive field
(RF), which is the visual area (typically measured by fitting a 2D
Gaussian and reporting the SD in degrees) that elicits a response.
Received Nov. 15, 2018; revised March 6, 2019; accepted March 6, 2019.
Author contributions: A.D. and S.R. designed research; A.D. performed research; A.D. and S.R. analyzed data; A.D.
wrote the first draft of the paper; A.D. and S.R. edited the paper; A.D. and S.R. wrote the paper; S.R. contributed
unpublished reagents/analytic tools.
This work was supported by the Wellcome Trust/DBT India Alliance (Intermediate Fellowship 500145/Z/09/Z to
S.R.), a Tata Trusts grant, and the DBT-IISc Partnership Programme. We thank John Maunsell and Gaute T. Einevoll
for insightful comments on an earlier version of this manuscript; John Maunsell for help with experimental design
and data collection from Monkeys 1 and 2; Steven Sleboda and Vivian Imamura for technical support; Ad-Tech
MedicalInstrument Corporation and Blackrock Microsystems for the hybrid electrode grid; and Sebastian Chandu for
assistance in surgeries.
The authors declare no competing financial interests.
Correspondence should be addressed to Supratim Ray at sray@iisc.ac.in.
https://doi.org/10.1523/JNEUROSCI.2917-18.2019
Copyright © 2019 Dubey et al.
This is an open-access article distributed under the terms of the Creative Commons Attribution License
Creative Commons Attribution 4.0 International, which permits unrestricted use, distribution and reproduction in
any medium provided that the original work is properly attributed.
Significance Statement
Brains signals capture different attributes of the neural network depending on the size and location of the recording electrode.
Electrocorticogram (ECoG), obtained by placing macroelectrodes (typically 2–3 mm diameter) on the exposed surface of the
cortex, is widely used by neurosurgeons to identify the source of seizures in drug-resistant epileptic patients. The brain area
responsible for seizures is subsequently surgically removed. Accurate estimation of the epileptogenic cortex and its removal
requires the estimation of spatial spread of ECoG. Here, we estimated the spatial spread of ECoG in five behaving monkeys using
two different approaches. Our results suggest that ECoG is a local signal (diameter of ⬃3 mm), which can provide a useful tool for
clinical, cognitive neuroscience, and brain–machine-interfacing applications.
The Journal of Neuroscience, May 29, 2019 •39(22):4299 – 4311 • 4299
This, when multiplied with the linear cortical magnification fac-
tor (MF, defined as the length of cortex that processes a unit
degree of visual space), yields the cortical spread. Using this ap-
proach, the cortical spread of LFP in the primary visual cortex
(V1) has been reported to be local (SD of ⬍⬃0.5 mm (Xing et al.,
2009;Dubey and Ray, 2016), which has been confirmed by other
methods as well (Katzner et al., 2009). However, using analogous
methods in auditory cortex, the LFP spread has been shown to be
much larger than MUA, extending up to several millimeters
(Kajikawa and Schroeder, 2011).
This approach has been used to estimate the RFs of ECoG in
humans in a clinical setting as well (Yoshor et al., 2007). Unfor-
tunately, this method overestimates the cortical spread because
the RF gets inflated for a variety of reasons such as retinotopic
scatter (Albus, 1975) and eye movements. To overcome this is-
sue, Xing et al. (2009) observed that some of these factors inflate
the RFs of different types of brain signals, such as MUA and LFP,
by the same amount. Therefore, a model that estimates the cor-
tical spread based on the difference of the RFs of MUA and LFP
can partially cancel out common factors. In their model, “spatial
spread” represented a spatial weighting function that primarily
depends on the properties of the recording electrode such as its
size, impedance, and location and potential filtering properties of
the tissue, but not on the spatial extent of cortical activation
(which were captured by other terms that eventually cancelled
out). In their data, this approach reduced estimates of the cortical
spread of LFP by ⬃40%. This model can be applied for estimation
of LFP spread because microelectrodes simultaneously provide
MUA and LFP signals, but it cannot be applied using only ECoG
electrodes, which provide only one signal. Further, a direct com-
parison of the spreads of LFP in monkeys and ECoG in humans is
difficult because of differences in referencing schemes, eye move-
ments, and other experimental details.
To address these issues, we designed a hybrid electrode array
that allowed us to simultaneously record MUA, LFP, and ECoG
and used the model developed by Xing et al. (2009) to estimate
the spatial spread of LFP and ECoG. We also estimated the spread
by simulating the ECoG as the sum of LFPs over a progressively
larger area and comparing the slope of the power spectral density
(PSD) of the simulated and actual ECoG.
Materials and Methods
Animal preparation and recording. Data used in this study were collected
in two separate sets of experiments. The first set was conducted on two
male monkeys (Macaca mulatta; weight 11 and 14 kg) at Harvard Med-
ical School and animal protocols were approved by the Harvard Medical
School Institutional Animal Care and Use Committee. For this set of
experiments, microelectrode and ECoG recordings were performed sep-
arately. The behavioral task and recording set up for microelectrode
recordings are described in detail in our previous study (Dubey and Ray,
2016). We describe them only briefly here. After monkeys learned the
behavioral task, a 10 ⫻10 microelectrode array grid (96 active channels;
Blackrock Microsystems) was implanted in the right V1 (⬃15 mm ante-
rior to the occipital ridge and ⬃15 mm lateral to the midline). The
microelectrodes were 1 mm long and 400
m apart, with an active elec-
trode region made of platinum and a tip diameter of 3–5
m. After the
microelectrode recordings were completed, we performed a second sur-
gery to insert a custom-made 8 ⫻8 array of
ECoG electrodes (diameter
of 40
m spaced 800
m apart) and 2 single contact ECoG electrodes
(one on each side of the
ECoG array) over V1 of the left cerebral hemi-
sphere of the same monkeys. These electrodes were made of platinum
(Ad-Tech Medical Instrument) and were attached to the connector made
by Blackrock Microsystems (used for microelectrode array recordings)
such that the same data acquisition system could be used to record from
all types of electrodes. ECoG electrodes were slid under the dura so that
they were far away from the
ECoG grid. The presence of the large
ECoG grid prevented us from putting more ECoG electrodes in V1.
However, data from the
ECoG array were very noisy and the RFs could
not be accurately measured, so these data were not used for further
analysis. The ECoG electrodes were discs with an exposed diameter of 2.3
mm, a standard design used in human subdural recordings for monitor-
ing epilepsy. One ECoG electrode in Monkey 2 did not show any stimulus
evoked response and was therefore excluded from analysis, yielding three
ECoG electrodes from these two monkeys.
In the second set of experiments, we simultaneously recorded spikes,
LFP, and ECoG signals from three awake adult female monkeys (Macaca
radiata; weight 3.3, 4, and 4.3 kg) at the Indian Institute of Science,
Bangalore. The Institutional Animal Ethics Committee of the Indian
Institute of Science and the Committee for the Purpose of Control and
Supervision of Experiments on Animals approved the guidelines. After
monkeys learned the fixation task, a custom-made hybrid electrode array
(Fig. 1) was implanted in the left (Monkeys 3 and 4) or right (Monkey 5)
hemisphere. This hybrid array had 9 (3 ⫻3) ECoG electrodes (Ad-Tech
Medical Instrument) and 81 (9 ⫻9) microelectrodes (Blackrock Micro-
systems), both attached to same connector made by Blackrock Microsys-
tems. As in the previous case, the ECoG contacts were platinum discs of
2.3 mm diameter with a center-to-center inter electrode distance of 10
mm and the microelectrodes were 1 mm long, separated by 400
with a
tip diameter of 3–5
m. The silastic between four ECoG electrodes was
removed so that the microelectrode array could be inserted in the gap
(Fig. 1). Under general anesthesia, a large craniotomy (⬃2.8 ⫻2.2 mm)
and a smaller duratomy were performed. Next, the ECoG sheet was
inserted through the durotomy and slid on the cortex such that the gap in
the silastic was aligned with the duratomy. Finally, the microelectrode
array was inserted (Fig. 1). Microelectrode array was placed 10–15 mm
from the occipital ridge and 10 –15 mm lateral from the midline with the
entire length inserted into cortex. Six ECoG electrodes in Monkeys 3 and
5 were posterior to the lunate sulcus (electrodes 1, 2, 4, 5, 7, and 8 in Fig.
1) and were considered for analysis. For Monkey 4, the ECoG grid did not
slide easily on the cortex, so one column (electrodes 1–3) had to be
removed. Therefore, only four electrodes were in V1 for this monkey.
Two reference wires, common for both microelectrode and ECoG grid,
were either inserted near the edge of the craniotomy or secured to the
metal strap that was used to secure the bone on the craniotomy.
The mean impedance of microelectrodes was ⬃0.9 M⍀(range: 0.2–
1.8 M⍀) at 1 kHz for Monkeys 1 and 2 and ⬃0.6 M⍀(range: 0.1–1.8) for
Monkeys 3–5. ECoG electrodes had an impedance of ⬃50 k⍀for Mon-
keys 1 and 2 and between 8 and 12 k⍀for Monkeys 3–5. It is unclear why
the impedances varied so much, but despite the difference in impedance,
the results were very similar across the two sets of recordings.
All signals were recorded using the Blackrock Microsystems data ac-
quisition system (Cerebus neural signal processor). LFP and MUA were
recorded from the microelectrode array. LFP and ECoG were obtained
by band-pass filtering the raw data between 0.3 Hz (Butterworth filter,
first order, analog) and 500 Hz (Butterworth filter, fourth order, digital),
sampled at 2 kHz, and digitized at 16-bit resolution. MUA was derived by
filtering the raw signal between 250 Hz (Butterworth filter, fourth order,
digital) and 7500 Hz (Butterworth filter, third order, analog), followed by
an amplitude threshold (set at ⬃6.25 (Monkey 1), ⬃4.25 (Monkey 2)
and ⬃5 (Monkey 3, 4 and 5) SDs of the signal).
Behavioral task and RF mapping. Monkeys 1 and 2 were trained to do
an orientation change detection task, in which they held their gaze within
1° of a small central dot (0.05°-0.10° diameter) 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 flashed for 200
ms with an interstimulus period of 300 ms. The monkeys were cued to
attend to a low-contrast (⬃2.6% for Monkey 1 and ⬃5.4% for Monkey
2) Gabor stimulus outside of the RF and to respond to a change in the
orientation of the Gabor stimulus by 90° in one of the presentations by
making a saccade within 500 ms of orientation change. The second stim-
ulus was a small static Gabor [SD of 0.05° and 0.1° for the two monkeys;
spatial frequency of 5 cycles per degree (CPD), 100% contrast, 4 orien-
tations: 0°, 45°, 90° and 135°, chosen psuedorandomly] that was flashed
over a large rectangular grid covering the RFs of the microelectrodes
4300 •J. Neurosci., May 29, 2019 •39(22):4299 – 4311 Dubey and Ray •ECoG Is a Local Signal
(interstimulus distance of 0.25° and 0.3° for the two monkeys). In sepa-
rate experiments, the RFs of each of the three ECoG electrodes were
mapped by flashing the stimulus in a pseudorandom order at locations
surrounding the center of the RFs (SD of 0.1° for both monkeys, other
parameters were the same as microelectrode recordings). At each loca-
tion, stimuli were presented on average 16.9 times (range 11–21) for
Monkey 1 and 13.3 times (range 8 –17) for Monkey 2 (pooled across
orientations) for the microelectrode recordings. For ECoG experiments,
stimuli were presented 17.8 times (range 14 –21) and 19.7 times (15–27)
for the two electrodes in Monkey 1 and 21.5 (range 15–26) times for
Monkey 2.
Monkeys 3, 4, and 5 performed a fixation task while they were in a
monkey chair with their head fixed by the head post. The monkeys were
required to hold their gaze within 2° of a small central dot (0.10° diame-
ter) located at the center of a monitor (BenQ XL2411, LCD, 1280 ⫻720
pixels, 100 Hz refresh rate, gamma corrected) and were rewarded with
juice at the end of the trial upon successful fixation. The stimulus was a
grating with radius of 0.3°, spatial frequency of 4 CPD (Monkeys 3 and 4)
or 1 or 2 CPD (Monkey 5; for this monkey lower spatial frequencies
produced a stronger response), full contrast, and one of four different
orientations (0°, 45°, 90°, and 135°). The stimulus was flashed for 200 ms
(interstimulus period was set to 0) at various locations in the visual space
spanning the RF centers of microelectrode array and ECoG electrodes.
For Monkey 3, the RF estimates of ECoG 7 and 8 (Fig. 1) were mapped in
separate experiments because these electrodes had large eccentricities
(see Fig. 3B). On average, at each location, stimuli were presented 19
times (range 11–26) for Monkey 3, 17.7 times (range 12–22) for Monkey
4, and 15 times (range 9 –19) for Monkey 5 (pooled across orientations).
For the two separate ECoG experiments, the average number of stimuli at
each stimulus location were 20 (range 12–28) and 19.3 (range 11–26). All
data were analyzed using custom codes written in MATLAB (The Math-
Works, RRID:SCR_001622).
RF estimation. To estimate the RF sizes, we first averaged the MUA,
LFP, and ECoG responses across stimulus repeats (for details, see Mate-
rials and Methods and Fig. 2 in Dubey and Ray, 2016). Next, the mini-
mum (Min) values of the mean LFP signal were calculated for stimulus
(40 to 100 ms) and baseline (0 to 40 ms) epochs. We found that the
trough for ECoG electrodes was at longer latencies and therefore used the
stimulus epoch between 40 and 150 ms. The baseline epoch was taken
after stimulus onset to avoid any stimulus offset transients in Monkeys
3–5 because the interstimulus period was zero. We used Min values (as
used in Xing et al., 2009) as opposed to root-mean-square (RMS) values
because we observed nonspecific, small positive fluctuations at many
stimulus positions. For example, small positive fluctuations at ⬃100 ms
after the stimulus onset in the evoked response can be seen in Figure 2A,
the top right corner of Figure 3A, and in Figure 3Ain Dubey and Ray
(2016), which shows data from Monkeys 1 and 2. The reasons for these
fluctuations are unclear, but we suspect that these are due to volume
conduction because they were not observed in the corresponding current
source density plots (Fig. 3Bin Dubey and Ray, 2016). Because these
positive peaks at positions far from the RFs were not accompanied by
pronounced negative peaks, taking the Min essentially removed the pos-
itive peaks and yielded RFs with centers that were well aligned with the
MUA.
We subtracted the Min values obtained during the baseline period
from the stimulus period and fitted the following 2D Gaussian function:
f共x,y兲⫽Cⴱexp
冉
⫺
冉
xg
2
2
x
2⫹yg
2
2
y
2
冊冊
(1)
Where Cis the scaling factor,
x
and
y
denote the SD of the Gaussian
along major and minor axis. The terms x
g
and y
g
are defined as follows:
xg⫽共x⫺xo兲cos(
)⫺(y⫺yo)sin(
)
yg⫽共x⫺xo兲sin(
)⫹(y⫺yo)cos(
)
Where
is the angle of rotation with respect to the coordinate system and
x
0
and y
0
denote the center of the 2D Gaussian. We defined the RF center
as (x
0
,y
0
) and size as follows:
冑
冉
x
2⫹
y
2
2
冊
For MUA responses, instead of Min values, we used the difference be-
tween the mean firing rates between stimulus and baseline epochs.
Electrode selection. We have explained the selection process for LFP
and MUA electrodes in detail for Monkeys 1 and 2 in a previous report
(Dubey and Ray, 2016); here, we briefly describe it for Monkeys 3, 4, and
5. First, we selected electrodes with an absolute Min value (across all
stimulus positions) that exceeded a particular threshold (130, 60, and 65
V for Monkeys 3, 4, and 5, respectively). Next, for each electrode, we
rejected recording sessions for which the estimated RF size was too small
(⬍0.1°), too large (⬎0.5°), or had an RF center that was beyond the area
of stimulus presentation. We only used electrodes for which at least 50%
of the sessions were selected. Overall, we rejected ⬃2.8%, 5.6%, and 37%
recording sessions, which yielded 77, 18, and 26 LFP electrodes for Mon-
keys 3, 4, and 5, respectively. The RF centers of the remaining sessions
were very stable across sessions (SD of ⬍0.1° for Monkeys 4 and 5 and
0.13° for Monkey 5). Finally, for each electrode, we averaged the wave-
forms across selected sessions at each position and calculated the RF for
this pooled data to get a single estimate of RF size and center per elec-
trode. MUA data were less stable across days, so for a particular electrode,
we only used sessions for which at least 10 spikes/s were recorded when
the probe was at the center of the RF. This yielded 44, 13, and 9 electrodes
for the three monkeys.
In all cases, the RF centers of the MUA and LFP matched closely and
followed the known retinotopy in V1. For example, Figure 3Bshows the
RF centers for 77 LFP color coded based on their position on the grid. The
left edge of the microelectrode grid (blue to red) was most medial (almost
parallel to midline), whereas the bottom edge (blue to green) was most
anterior (Fig. 1). This corresponds to the retinotopic organization of V1
(see Fig. 3B): moving along yellow to green or red to blue (i.e., lateral
direction) yielded more foveal receptive fields. Similarly, moving from
green to blue or yellow to red decreased the elevation. Similar results can
be observed in Figure 1 Din Dubey and Ray (2016) for Monkeys 1 and 2.
Not all of the ECoG electrodes in a 3 ⫻3 grid were in V1; we visually
examined the electrode positions during the surgery and from the pic-
tures taken and selected electrodes that were posterior to the lunate sul-
cus (see Fig. 1). The subset of ECoG electrodes with an absolute Min
value that was ⬎100
V were used for further analysis, yielding 5, 4, and
4 ECoG electrodes for Monkeys 3, 4, and 5, respectively. For all three
measures, the final RF centers and sizes computed from the pooled data
were very similar to the average of the RF centers and sizes computed for
individual sessions.
Conversion from visual to cortical spread. The cortical spread of LFP and
ECoG was computed using two approaches. First, simply as the product
of the experimentally estimated RF size (
v
) and MF (calculated as shown
in Fig. 4Afor LFPs and estimated from previous reports for ECoGs as
shown in Fig. 4B) as follows:
c⫽MF ⴱ
v(2)
Second, we estimated the cortical spread of LFP and ECoG using a model
proposed by Xing et al. (2009) that accounts for several factors that inflate
the visual spread. In their model, the visual spread of LFP is obtained by
convolving the spatial weighting function of the LFP (multiplied by the
MF) with the visual spread of single-unit activity (SUA). However, be-
cause of the scatter present in retinotopic map on the cortex, the visual
spread of SUA also gets convolved by a scattering function. All of the
spreads are assumed to be Gaussian, such that the convolution yields
another Gaussian with a spread that is the sum of the spreads of the
individual Gaussians. Therefore, for LFP recorded at eccentricity “x”, the
visual spread is denoted as follows (equation 5 from Xing et al., 2009):
MFx
2
v
2LFPx⫽
c
2LFPx ⫹MFx
2
v
2vx⫹MFx
2
v
2SUAx(3)
Here,
vLFP
is the visual spread of LFP that we can measure experimen-
tally,
cLFP
is the cortical spread of LFP that we are interested in,
vSUA
is
the visual spread of SUA, and
vv
represents the visual variation or RF
scatter (unknown). Compared with the “no model” condition (for which
Dubey and Ray •ECoG Is a Local Signal J. Neurosci., May 29, 2019 •39(22):4299 – 4311 • 4301
MFx
2
v
2LFPx⫽
c
2LFPx), the visual spread therefore gets inflated because of
the last two terms, which are difficult to compute experimentally. Note
that the last two terms (MF2䡠
vv
2⫹MF2䡠
vSUA
2) have been described
as the cortical point image (CPI) in previous studies (Albus, 1975;Dow et
al., 1981), which is the cortical representation of a geometric point on the
sensory epithelium (Palmer et al., 2012).
To determine the cortical spread, Xing et al. (2009) argued that the
visual spread of MUA
vMUA
at the distance “x” from the fovea would be
inflated in a similar fashion as follows:
MFx
2
v
2MUAx⫽
c
2MUAx⫹MFx
2
v
2vx⫹MFx
2
v
2SUAx(4)
Because MUA and LFP are recorded from the same electrode and their
RFs have the same eccentricity (“x”; see Fig. 4 Ain Dubey and Ray, 2016),
the difference in
vLFP
2and
vMUA
2(Eqs. 3 and 4) cancels the unknown
terms and yields the cortical/spatial spread of LFP in terms of MF, visual
spreads of LFP and MUA, and the cortical spread of MUA as follows:
cLFPx⫽
冑
MFx
2
v
2LFPx⫺MFx
2
v
2MUAx⫹
c
2MUAx(5)
Because we recorded from awake animals whereas Xing et al. (2009) used
anesthetized monkeys, our visual spreads are further inflated due to eye
jitter. Similarly, whereas Xing et al. (2009) used sparse noise, we used
small Gabor/grating, so the size of the stimulus could also inflate the
visual spread. Accommodating the variables for eye jitter and stimulus
size, the visual spread of LFP (
vLFP
) estimated experimentally at a dis-
tance “x” from the fovea can be defined as follows:
MFx
2
v
2LFPx⫽
c
2LFPx⫹MFx
2
v
2vx⫹MFx
2
v
2SUAx
⫹F共Eye Jitter ⫹Stimulus Size兲(6)
Where Fis a function that depends on the eye jitter and stimulus size.
However, because these additional terms are independent of the type of
measure, they get canceled out in a similar fashion as before.
In our analysis, the cortical spread of MUA (
cMUA
) was set at 60
m,
which was the value used by Xing et al. (2009) based on previous studies
(Gray et al., 1995;Buzsa´ ki, 2004). We used the MF for LFP in Equation 5
to compute the cortical spread; results were similar if MFs obtained from
MUA were used instead (data not shown).
Model extension. We now extend this model to ECoG. Assuming that
the visual spread of ECoG can be obtained by applying a different weight-
ing function on the visual spread of SUA, this model can be modified to
define the spread of ECoG at a distance “x” from fovea as follows:
MFx
2
v
2ECoGx⫽
c
2ECoGx⫹MFx
2
v
2vx⫹MFx
2
v
2SUAx⫹F共Eye Jitter
⫹Stimulus Size兲(7)
Note that, unlike the previous case with LFP and MUA, the spatial spread
of LFP is not available at “x” but a different location (say “y”). We first
rearrange the terms to have the visual and cortical spreads on one side
and the inflation terms on the other as follows:
MFx
2
v
2ECoGx⫺
c
2ECoGx⫽MFx
2
v
2vx⫹MFx
2
v
2SUAx
⫹F共Eye Jitter ⫹Stimulus Size兲(8)
For the LFP obtained at eccentricity “y,” we get:
共MFy
2
v
2LFPy⫺
c
2LFPy兲⫽MFy
2
v
2vy⫹MFy
2
v
2SUAy
⫹F共Eye Jitter ⫹Stimulus Size兲(9)
To proceed further, we make an assumption that CPIs (MF2䡠
vv
2⫹
MF2䡠
vSUA
2) are comparable for eccentricities “x” and “y.” The magni-
tude of error because of this assumption is unlikely to be large because the
MF tends to decrease, whereas
vv
and
vSUA
tend to increase with ec-
centricity (Albus, 1975;Dow et al., 1981) such that the CPI is almost
constant. For example, Albus (1975) showed that the RF scatter increased
from ⬃1° to 3– 4° as the eccentricity increased from 1° to ⬃10° (see Fig.
9Bin Albus, 1975). However, the magnification factor over this range of
eccentricities decreased from ⬃2.5 to ⬃0.5 mm/° (see Fig. 9Ain Albus,
1975). Therefore, the product was about the same. Similarly, using
voltage-sensitive dyes, Palmer et al. (2012) have shown that CPI does not
vary appreciably with eccentricity in V1.
Under these assumptions, the right side of the two equations are equal
and therefore can be subtracted and rearranged to yield the following:
cECoGx⫽
冑
MFx
2
v
2ECoGx⫺MFy
2
v
2LFPy2⫹
c
2LFPy(10)
In Monkey 4, only a few MUAs were available and their RFs were com-
parable to the LFPs such that the model could not be used for this mon-
key. To compute the ECoG spread for this monkey, we used average
estimate of
cLFP
from the other four monkeys. Note that whereas this
model reduced the LFP spread by ⬃32%, for ECoG, the reduction was
only ⬃9%. Therefore, none of the results shown here critically depended
on the model.
Factors affecting the spatial spread. Although the Xing et al. (2009)
model accounts for differences in the CPIs (which may depend on lateral/
feedforward connectivity profile), there are other properties that criti-
cally determine the cortical spread. This is easiest to understand by
comparing the spreads of LFP and MUA because the difference is mainly
based on the frequency content of the signal recorded from the same
microelectrode. In this case, conductance or filtering properties of the
tissue become crucial (Be´ dard et al., 2004,2006,2010;Logothetis et al.,
2007;Linde´ n et al., 2011). For example, if the tissue is capacitive (for
arguments and debates on this topic, see Be´ dard et al., 2004,2006,2010;
Linde´ n et al., 2011), then lower frequencies can travel farther than higher
frequencies, such that the spatial spread of MUA is lower than LFP and
this should be captured in the weighting functions (i.e.,
cLFP
should be
larger than
cMUA
). Note that the proposed model places MUA and LFP
on an “equal footing” because it does not imply that the spatial spread of
LFP is necessarily larger than MUA (e.g., if the cortical medium were then
the inductive,
cMUA
would be larger than
cLFP
and we would subtract
Eq. 3 from Eq. 4 instead of the other way around). The tissue does not
even necessarily have to capacitive: even in a purely resistive medium, the
shrinkage in the dipole length with increasing frequencies causes an ef-
fective “low-pass filtering” of the signal (Pettersen and Einevoll, 2008),
which would reduce the spatial spread of MUA compared with LFP.
Consistent with this, we have previously shown that the spatial spreads of
different frequencies of the LFP are different, with a higher spread in the
high-gamma band (see (Dubey and Ray, 2016)), and the spread of higher
LFP frequencies (⬎250 Hz) approaches the spread of the MUA. There-
fore, factors that could govern conductance and filtering characteristics
of the cortical tissue, which could include the morphology of the cortical
neurons, their density, cell type, level of myelination, the presence of glial
cells, etc. (Be´ dard et al., 2004,2006), could change the spatial spread of
the LFP.
Another important property that could play a role in determining the
spatial spread is noise. To observe a measurable signal on the electrode
upon the activation of a small part of the cortex, this signal must be above
the noise floor. However, the noise recorded from an electrode may be
frequency dependent and therefore different for MUA and LFP. For
example, several studies have suggested that the slope of the PSD could be
⬃2 because of shot noise, the origin of which might be due to an expo-
nential relaxation process of synaptic currents that are driven by random
spiking or due to up-down states that have properties of a telegraphic
process (Miller et al., 2009;Milstein et al., 2009;Baranauskas et al., 2012).
Systematic differences in noise characteristics between MUA and LFP
will also not cancel out in this model and therefore will contribute to the
spatial spread of LFP (larger noise will reduce the spatial spread).
While extending this model to ECoG by comparing its RF size with
LFP, an important factor that is not accounted in the model is that LFP
and ECoG may be reflecting fundamentally different aspects of the neu-
ronal activity. Specifically, it has been suggested that, as the size of the
neural population increases, the contribution of synchronous activity
increases. Specifically, power in the signal due to asynchronous activity
scales as N, but scales as N
2
for synchronous activity, where Nis the size
of the recorded population (Nunez and Srinivasan, 2006;Ray et al.,
2008). When a small stimulus is presented, the spatial profiles of asyn-
chronous and synchronous activity may be different. For example, it is
4302 •J. Neurosci., May 29, 2019 •39(22):4299 – 4311 Dubey and Ray •ECoG Is a Local Signal
possible that the initial stimulus-locked response is restricted to a local
population of neurons and therefore has a narrow spatial spread. How-
ever, this activated cortical area may activate nearby neurons over a
broader time scale, leading to an increase in asynchronous firing that is
more spread out in the cortex. Therefore, LFP and ECoG could be dif-
ferentially sensitive to the synchronous sources/sinks and this could also
be reflected in their spatial spreads.
PSD slope analysis. For slope analysis, segments of 500 ms length dur-
ing stimulus-free (spontaneous) period were used, as reported elsewhere
for Monkeys 1 and 2 (Shirhatti et al., 2016). Monkeys 3 and 4 performed
the fixation task while a full screen grating was presented for 800 ms with
an interstimulus period of 700 ms. The grating was static with one of the
five spatial frequencies, 0.5, 1, 2, 4, and 8 cpd, and eight orientations
evenly spaced between 0° and 157.5° chosen randomly (a period between
500 and 0 ms before the stimulus onset was used). We observed high-
frequency noise in case of Monkey 5 and therefore did not use this dataset
for PSD analysis. PSDs were computed using the multitaper method with
three tapers, implemented in Chronux 2.0 (Bokil et al., 2010). We calcu-
lated the slopes for frequency ranges 20 –100 Hz and 200 – 400 Hz by
fitting the function log10共P兲⫽mⴱlog10共f兲⫹cwhere Pis the PSD, fis
the frequency, cis the constant or noise floor, and mis the slope (Miller
et al., 2009;Shirhatti et al., 2016). The frequency range of 20 –100 Hz was
chosen to avoid the alpha band (see Fig. 5A). The PSDs were normalized
to have the value of 0 at 20 Hz (this normalization only affects the vertical
offset (c), not the slope (m).
The slope of the PSDs have been interpreted to reflect important char-
acteristics of the brain such as state, filtering properties, noise, etc. (Be´-
dard and Destexhe, 2009;Miller et al., 2009;Milstein et al., 2009).
However, the error-free estimation of PSD slope requires correction of
the low-pass filter as well as the noise floor of the amplifier (Miller et al.,
2009). We have previously used a similar procedure and shown that the
transfer function of the amplifier is almost close to 1 (and consequently
the correction factor is negligible) up to ⬃400 Hz and therefore not
critical for PSD slopes up to 400 Hz (Shirhatti et al., 2016; the transfer
function is shown in supplementary Figure 1 in that paper). In that
dataset, the noise floor was also negligible (i.e., the PSD did not flatten up
to 500 Hz). To make sure that our results shown in Figure 5 were not
affected by noise, we experimentally determined the noise floor by recording
signals (using the same amplifier and same filter settings) from six passive
disc electrodes (Grass Technologies) that were kept in a saline solution and
contacted each other. Because the inputs were shorted, the output signal
mainly reflected amplifier noise. A comparison of PSDs of this noise signal
and PSDs of the LFP and ECoG signals revealed that instrument noise was at
least an order of magnitude smaller (and ⬎30 times in the frequency ranges
of interest), so none of our results in Figure 5 could be affected by the noise or
filtering characteristics of the amplifier.
ECoG data modeling. ECoG and LFP signals capture the activity of the
underlying neuronal population depending on their size and location.
The microelectrodes sample the activity from the layer 2/3, whereas
ECoG electrode is placed on the surface of the cortex. We estimated the
slope of ECoG signal from the LFP activity in a simple model-based
approach proposed by Ray et al. (2008). We briefly explain the model
here for simulating ECoG from LFPs (see the Materials and Methods
section of Ray et al., 2008 for details). This model is based on the obser-
vation that, once an electrode is sufficiently far away from a neuron, the
waveform recorded at that location and another location farther away are
usually scaled versions of each other (the scaling factor depends on the
distance) because both can be expressed in terms of the transmembrane
currents flowing through the neuron (Gold et al., 2006). Specifically,
suppose a microelectrode records LFP
(t) near a neuron and the ECoG
electrode records the potential
(t) due to the activity of the k
th
neuron
(as shown in supplementary Fig. 1 in Ray et al., 2008). The two potentials
can be related using the following equation:
共t兲⫽C
共t兲
Rn(11)
where Ris the distance between the ECoG electrode and the neuron. The
constant Cincorporates several factors such as the distance between the
soma and the microelectrode, the conductivity of the medium, the size of
the soma, and the orientation of the current sources, and the exponent n
accounts for the distribution of transmembrane currents across the
membrane. Because in our case the LFPs were all recorded from the same
layer (layer 2/3 or 4) that was far away from the surface of the cortex, the
relative difference in Ris likely to be negligible across neurons and there-
fore the denominator can be dropped. Under the assumption of linear
superposition, the neuronal activity recorded by an ECoG electrode due
to a population of Nneurons is therefore given by the following:
共t兲⫽
冘
k⫽1
NCk
k共t兲(12)
Where
(t) is the mean LFP signal recorded from a microelectrode (in
our setup, a 500 ms period of spontaneous activity before stimulus
onset).
In our model, we averaged the LFP activity of nearby electrodes that
constituted either a square grid (1 ⫻1, 2 ⫻2,3⫻3, and so on) or
rectangular grids in which one side was greater than the other by one (i.e.,
2⫻3, 3 ⫻4, 4 ⫻5). For smaller grid sizes, we considered all combina-
tions for which the grid had no missing electrodes. For higher grid sizes
(3 ⫻3 onwards), the number of combinations was lower, so to increase
the number of different combinations, we also allowed up to 1 missing
electrode (for example, if a 3 ⫻3 grid had one missing electrode, it was
still averaged, and the resultant slope was put against 8 instead of 9). For
Monkey 3, for which all but 4 microelectrodes could be used for analysis
(77 out of 81), the grid combinations (number of electrodes) were 1 ⫻1
(1), 1 ⫻2 (2), 2 ⫻2 (4), 2 ⫻3 (6), 3 ⫻3 (9), 3 ⫻4 (12), 4 ⫻4 (16), 4 ⫻
5 (20), 5 ⫻5 (25), 5 ⫻6 (30), 6 ⫻6 (36), 6 ⫻7 (42), 7 ⫻7 (49), and 7 ⫻
8 (56). Only a few electrodes were selected for RF analysis for Monkeys 1
and 4 (27 and 18, respectively), so this analysis could be performed only
for grid combinations up to 3 ⫻4 for both the monkeys. For Monkey 2,
the highest grid size was 6 ⫻6.
The coefficient Cin Equation 12 was varied randomly between 0 and 1
(uniformly distributed) to incorporate the diversity in cell size/type/con-
ductivity/orientation, etc. We estimated the ECoG potential
(t) 1000
times for each grid combination to get the standard deviation. For the
“without model” condition, Cwas set to 1 (see Fig. 5B). Other ranges
were also tried (e.g., Cuniformly distributed between 0.4 and 0.6) and
yielded similar results. Further, results without the model (for which the
random factor was set to 1) produced similar results (compare circles vs
squares in Fig. 5B).
Cortical spread in spectral domain. The cortical spreads as a function of
frequency were estimated by first decomposing the signal in time–fre-
quency domain by using the matching pursuit (MP) (Mallat and Zhang,
1993) algorithm and then fitting a 2D Gaussian to the difference in the
root of the average energy values for stimulus (40 –150 ms) and baseline
(0 –40 ms) time epochs for each frequency. This time range was used for
both LFP and ECoG for better comparison. The MP algorithm is ex-
plained in detail in our previous study (Dubey and Ray, 2016). Briefly,
MP is an iterative algorithm that decomposes the signal into a linear
combination of waveforms selected from an overcomplete dictionary. As
in our previous study (Dubey and Ray, 2016), we used a dictionary of
Gaussian-modulated sinusoidal functions (Gabor functions). MP was
performed on signals of length 2048 points (⫺549.5 to 474 ms at 0.5 ms
resolution, where 0 denotes the time of stimulus onset), yielding a
2048 ⫻2048 array of time–frequency energy values (with a time resolu-
tion of 0.5 ms and frequency resolution of 2000/2048 ⫽⬃1 Hz). This was
downsampled by a factor of 8 in the time domain and a factor of 2 in the
frequency domain, yielding a time resolution of 4 ms and a frequency
resolution of ⬃2 Hz. The cortical spreads were estimated for each fre-
quency by applying the model proposed by Xing et al. (2009) as explained
in the “Conversion from visual to cortical spread” section. As described
in that section, the model could not be applied to Monkey 4 because the
MUA RFs were comparable to the LFPs. Further, this analysis could not
be performed on Monkey 5 because of high-frequency noise (this mon-
key was excluded from the PSD slope analysis for the same reason).
Therefore, the LFP spreads as a function of frequency (see Fig. 6B) were
estimated only for Monkeys 1–3 (total 175 electrodes). Importantly, the
model could be used for Monkey 4 for estimation of the ECoG spread (by
Dubey and Ray •ECoG Is a Local Signal J. Neurosci., May 29, 2019 •39(22):4299 – 4311 • 4303
using the average LFP spread, same as Fig. 4E), yielding 12 ECoG elec-
trodes from four monkeys (see Fig. 6D).
Statistical analysis. The LFP and ECoG slopes in the 20–100 Hz and
200 – 400 Hz frequency ranges were compared using a two-sample ttest.
The null hypothesis assumed mean from the same distribution and un-
equal variances.
The SEs of mean or medians were computed using bootstrapping.
Given a sample of nelements, a new sample was first created (termed
“resample” or bootstrap sample) by randomly taking nelements with
replacement from the original dataset. The mean or median was com-
puted for this bootstrap sample. This process was iterated 1000 times,
yielding 1000 means or medians. The SD of this population of means or
medians was reported as SE.
Results
Data were collected in two separate set of experiments. The first
dataset involved ECoG recordings from three electrodes in two
monkeys (Monkeys 1 and 2) in which microelectrode data had
been collected previously (Dubey and Ray, 2016). For the second
set, we performed simultaneous recordings of MUA, LFP, and
ECoG in three trained, behaving monkeys using a custom-made
hybrid electrode array (Monkeys 3–5; Fig. 1). This hybrid grid
consisted of 9 (3 ⫻3) ECoG electrodes and 81 (9 ⫻9) microelec-
trodes, both attached to the same connector and referenced to the
same wire. The ECoG electrodes were circular platinum record-
ing surfaces 2.3 mm in diameter, the standard size used in clinical
applications, with a center-to-center distance of 10 mm. During
surgery, the ECoG grid was first placed on the pia and then the
microelectrode array was inserted in a previously made gap be-
tween four ECoG electrodes (Fig. 1). Only ECoG electrodes that
were posterior to lunate sulcus lying over V1 were used for fur-
ther analysis. In total, we recorded from 16 ECoG and 219 LFP
electrodes in five monkeys.
Visual evoked responses of ECoG
We estimated the RFs by presenting a small Gabor/grating stim-
ulus in random order at locations spanning the RFs of microelec-
trode and ECoG electrodes (see Materials and Methods for
details). Figure 2Ashows the evoked responses of three neighbor-
ing ECoG electrodes: 1 (red), 4 (green), and 5 (blue) from Mon-
key 3 (electrode positions are shown in Fig. 1), averaged across
trials and recording sessions for 475 (19 ⫻25) stimulus positions.
Interestingly, the RFs of ECoGs were highly localized in the visual
field: stimulus positions that elicited strong evoked responses in
one ECoG electrode produced almost no response in a neighbor-
ing electrode that was separated by only 10 mm. The responses
were very robust across trials and sessions (Fig. 2B–D, SEs com-
puted after bootstrapping are shown in light shades). Therefore,
we averaged the data across recording sessions for which robust
activity was observed and estimated the RF parameters by fitting
a 2D Gaussian to the pooled data (see Materials and Methods for
details).
Comparison of ECoG, LFP, and MUA visual spreads
Next, we compared the evoked responses of one ECoG electrode
(Fig. 3A, blue trace, ECoG 5 shown in Fig. 1 and Fig. 2) and one
microelectrode (LFP in red and MUA in green) in Monkey 3. The
ellipses are the estimated RFs, which were taken as 1 SD of the
fitted Gaussians (see Materials and Methods). Surprisingly, al-
though the ECoG electrode had an exposed diameter of 2.3 mm
whereas the microelectrode had a tip diameter of only a few mi-
crometers, the RF size of ECoG was only ⬃1.7 times the LFP (SD
of the fitted Gaussians were 0.52°, 0.32°, and 0.26° for ECoG, LFP,
and MUA, respectively). Similar results were obtained for full
dataset of 5 ECoG, 77 LFP, and 44 MUA electrodes for Monkey 3,
although the RF sizes of ECoGs varied depending on the eccen-
tricity (Fig. 3B; see Materials and Methods for electrode selection
procedure). The medians ⫾1 SE (computed by bootstrapping) of
the RF sizes of ECoG, LFP, and MUA were 0.72° ⫾0.120°, 0.37°
⫾0.003°, and 0.28° ⫾0.006°, respectively, for this monkey (Fig.
3C) and 0.66° ⫾0.07°, 0.28° ⫾0.02°, and 0.24° ⫾0.02° for the full
dataset of 16 ECoG, 219 LFP, and 151 MUA electrodes in five
monkeys, respectively. These monkey ECoG RF sizes were com-
parable to those in humans (Yoshor et al., 2007).
Conversion of visual (in degrees) to cortical (in
millimeters) spread
To obtain the cortical spread, we first estimated the MF (in mil-
limeters/degree) for the LFP electrodes by plotting the cortical
distance between electrode pairs against the distance between
their RF centers (Fig. 4A). These experimentally determined
MF
LFP
values were in good agreement with previous studies
(Daniel and Whitteridge, 1961;Guld and Bertulis, 1976;Dow et
al., 1981;Xing et al., 2009), which had estimated the MFs over a
broad range of eccentricities (Fig. 4B, which is adapted from Fig.
6inDow et al., 1981). Although, in our experimental setup, we
could not measure the MF at the eccentricity of the ECoG, we
extrapolated the MF
ECoG
based on previous measurements (Fig.
4B). Figure 4Cshows the cortical spread of LFP (pink) and ECoG
(blue) for Monkey 3 estimated using the model (for details, see
Materials and Methods and Xing et al., 2009; light shades) and
without the model (simply the product of MF and RF size; dark
shades). The median ⫾1 SE estimates of the cortical spread with
Figure 1. Image of the hybrid grid during surgery. Four corners of the microelectrode array
are color coded to provide a reference to the RF centers plotted in Figure 3B. ECoG electrodes
posterior to the lunate sulcus are in V1. Only ECoG electrodes 5 and 6 are visible; the remaining
electrodes are under the skull and their approximate positions are indicated. ECoG electrodes
were 4 mm in diameter with an exposed recording area of 2.3 mm.
4304 •J. Neurosci., May 29, 2019 •39(22):4299 – 4311 Dubey and Ray •ECoG Is a Local Signal
and without the model were 0.51 ⫾0.011 and 0.79 ⫾0.007 mm
for LFP and 1.59 ⫾0.311 and 1.70 ⫾0.287 mm for ECoG (Fig.
4D). For the full dataset (Fig. 4E), these values were 0.51 ⫾0.006
and 0.75 ⫾0.011 mm for LFP and 1.57 ⫾0.244 and 1.73 ⫾0.229
mm for ECoG (Fig. 4F). Although we observed some variability
across monkeys, the ratio between LFP and ECoG spreads typi-
cally remained similar across monkeys. Further, although the RF
sizes were variable, the LFP spreads were comparable across
monkeys (gray symbols in Fig. 4E). Note that we have used the SD
of the fitted Gaussian as a measure of spatial spread to be consis-
tent with the study of Xing et al. (2009). The diameter of the
spread could be approximated as 2 SDs or ⬃3 mm for the ECoG.
Therefore, an ECoG electrode measures the activity of a brain
area only slightly larger than its own diameter.
PSD and slope analysis
Next, we estimated the spatial spread using a different approach
based on the observation that the slope of the PSDs, which could
reflect important characteristics of the network such as noise
(Freeman et al., 2000;Be´dard and Destexhe, 2009;Miller et al.,
2009;Milstein et al., 2009) and filtering characteristics (Be´dard et
al., 2006;Linde´n et al., 2010;Łe˛ski et al., 2013;Dubey and Ray,
2016), was much steeper for ECoG than LFP between 20 and 100
Hz (Fig. 5A). This can be explained based on the LFP–LFP coher-
ence profile, which is typically high at low frequencies and de-
creases to very low values beyond ⬃200 Hz (Srinath and Ray,
2014;Shirhatti et al., 2016). Further, the phase difference across
microelectrode pairs is on average zero (Shirhatti et al., 2016).
This means that the low-frequency components of the LFP are
more phase aligned than high-frequency components. Therefore,
if LFPs from nearby electrodes are averaged, then there is greater
reduction in amplitude at high frequencies (because the phases
are random and cancel each other out) than low frequencies,
which increases the overall slope. Indeed, in a simple model based
on linear superposition (see Materials and Methods) in which we
simulated the ECoG signal by averaging LFP signals over a pro-
gressively larger set of microelectrodes, we found that the slopes
of the simulated ECoG increased (1 ⫻1to7⫻7; Fig. 5A; see
Materials and Methods for details). For this monkey, averaging
⬃50 to ⬃110 microelectrodes yielded slopes comparable to the
actual ECoG slopes (Fig. 5B). Similar results were observed over
the population (Fig. 5C): the mean slopes and SEs of ECoG and
LFP were significantly different between 20 and 100 Hz (ECoG:
2.89 ⫾0.06, n⫽12; LFP: 1.87 ⫾0.033, n⫽193; p⫽4.22 ⫻
10
⫺11
, two-sample ttest) and averaging 49 ⫾14.5 microelec-
trodes yielded a slope comparable to the ECoG (Fig. 5D). Al-
though this approach makes a series of simple assumptions
(discussed in Materials and Methods) and the simulated and real
ECoG PSDs do not match over the entire frequency range (Fig.
5A), the final estimate of the ECoG spread obtained only from
spontaneous data is similar to the first method (⬃50 microelec-
trodes correspond to a 7 ⫻7 grid that corresponds to summation
⬎7⫻400
m⫽2.8 mm; this measure of spread should be
approximately twice the previous measure that was based on the
SD of a fitted Gaussian). Also note that this model predicts that
the ECoG and LFP slopes should not be different at high frequen-
cies (200 – 400 Hz) because the phases are completely random
over this range and therefore the reduction in amplitude should
be the same throughout. Indeed, the slopes between 200 and 400
Hz were comparable (ECoG: 1.69 ⫾0.08, n⫽12; LFP: 1.54 ⫾
0.02, n⫽193; p⫽0.098, two-sample ttest).
Figure 2. Mean evoked ECoG responses. A, Simultaneously recorded mean evoked responses for three ECoG electrodes: 1 (red), 4 (green), and 5 (blue) from Monkey 3 (electrode positions shown
inFig. 1) averaged across trials and sixrecording sessions ateach of the 475(19 ⫻25 rectangular grid)stimulus positions. B–D,Mean evoked responses ofthe three ECoGs shownin Afor thestimulus
position that generated the maximum response. SEs (after bootstrapping) computed after pooling trials across all the recording sessions are shown in lighter shades.
Dubey and Ray •ECoG Is a Local Signal J. Neurosci., May 29, 2019 •39(22):4299 – 4311 • 4305
Cortical spread as a function
of frequency
We further studied the cortical spread of
LFP and ECoG as a function of frequency
(as done previously for LFPs; Dubey and
Ray, 2016) for Monkeys 1– 4 (as for the
PSD slope analysis, Monkey 5 was ex-
cluded because of high-frequency noise).
Figure 6Ashows the median cortical
spread of LFP across 77 electrodes for
Monkey 3. Similar to our previous find-
ings (Dubey and Ray, 2016), LFP spread
showed a band-pass effect in this monkey
also, with high-gamma (60 –150 Hz)
range spreading more than lower- and
higher-frequency ranges. Also note that
the spatial spread increased at very low
frequencies, as was observed in our previ-
ous study as well (Dubey and Ray, 2016).
This was due to nonspecific, small positive
fluctuations observed for many micro-
electrodes and ECoG electrodes ⬃100 ms
after the stimulus onset in the evoked re-
sponse (see top right corner of Fig. 3Aand
in Fig. 3Ain Dubey and Ray, 2016), which,
in the frequency domain, had energy at
low frequencies (for the RF analysis
shown before, this issue was largely ad-
dressed by using the absolute Min value
for RF estimation instead of RMS values;
see Materials and Methods for details).
Figure 6Bshows the population corti-
cal spread across 175 electrodes from
three monkeys (data from Monkey 4 was
excluded because the model to convert vi-
sual to cortical spread could not be ap-
plied; see Materials and Methods for
details). For Monkey 4 also, the visual
spread was larger in the high-gamma
range than higher frequencies (⬎250 Hz),
although the spread remained large at
lower frequencies (gamma range and be-
low), likely because the nonspecific fluc-
tuations described above were sharper in
this monkey. Unlike LFP, ECoG showed
no frequency-specific increase in cortical
spread in the high-gamma range (Fig. 6C,
median cortical spread across 5 ECoG
electrodes in Monkey 3), but instead at
frequencies up to ⬃100 Hz before flatten-
ing out. Similar results were seen for a population dataset of 12
ECoG electrodes across four monkeys (Fig. 6D). Interestingly, for
higher frequencies (⬎100 Hz), the median cortical spread was
⬃1.2 mm, comparable to the radius of the exposed surface of the
ECoG electrode. This suggests that, at high frequencies, the ECoG
electrode measures the activity of brain area that is about the size
of its diameter.
Discussion
Here, we compared the spatial spreads of two distinct brain sig-
nals: LFP (typically recorded using microelectrodes inserted in
the brain) and ECoG (or intracranial field potentials, typically
recorded using large macroelectrodes placed on the surface of
brain). Using a unique hybrid electrode array containing both
microelectrode and macroelectrode arrays to simultaneously re-
cord MUA, LFP, and ECoG RFs at several cortical sites from
awake, behaving monkeys, we here show that the spatial spread of
ECoG is surprisingly local (SD of ⬃1.5 mm or 2 SDs of ⬃3 mm),
not much larger than the diameter of the ECoG electrode (2.3
mm) and only ⬃3 times the spread of the LFP, even though the
size of the ECoG electrode is several hundred times larger than
the microelectrode. Furthermore, we confirmed this result using
an independent approach in which we compared the change in
the slope of the PSD of ECoG and a simulated ECoG signal ob-
tained by averaging LFPs over progressively larger square or rect-
angular grids. Similar to the first approach, the estimated ECoG
0 0.2
-1
0
1
Time (s)
Response
1
5
4
7
8
02468
-8
-6
-4
-2
0
2
Azimuth (deg)
Elevation (deg)
Azimuth (deg)
0
0.2
0.4
0.6
0.8
1
Visual spread (deg)
MUA
LFP
ECoG
A
CB
03.3
Elevation (deg)
-0.6
-3.9
Figure 3. Comparison of ECoG, LFP, and MUA visual spreads recorded from Monkey 3. A, Mean evoked ECoG of one electrode
(blue) along with LFP (red) and MUA (green) responses from one microelectrode averaged across trials and recording sessions at
each of the 144 positions (12 ⫻12 square grid, a subset of the 19 ⫻25 rectangular grid that was used for mapping). Estimated RF
sizes (
of the best fitted 2D Gaussian) are plotted in solid traces. B, Estimated RF centers of the LFP electrodes color coded based
on their position on the microarray grid (Fig. 1). The RF size and center of the example LFP electrode plotted in Ais shown in black.
Estimated RF centers and sizes of ECoG electrodes are plotted in blue. C, Median RF size of MUA (n⫽44), LFP (n⫽77), and ECoG
(n⫽5) for Monkey 3. Error bars indicate SEM computed using bootstrapping.
4306 •J. Neurosci., May 29, 2019 •39(22):4299 – 4311 Dubey and Ray •ECoG Is a Local Signal
LFP
with Model
LFP
without Model
ECoG
with Model
ECoG
without Model
Cortical spread (mm)
M3
0
0.5
1
1.5
2
2.5
Cortical spread (mm)
0
1
2
3
4
5
00.511.5 2.5
2
Visual distance (deg)
Cortical distance (mm)
Magnification factor : 2.18 mm/deg
Dow et al., 1981
Guld & Bertulis., 1976
Hubel & Wisel., 1974
Daniel & Whitteridge, 1961
Talbot & Marshall, 1941
Weymouth et al., 1928
Wertheim, 1984
10 100 1000
10
100
1000
Eccentricity (min)
Inverse magnification factor (min/mm)
BA
DC
EF
1.5
0.5
0
1
2
2.5
Cortical spread (mm)
0.5
1.5
0
1
2
2.5
Cortical spread (mm)
0
1
2
3
4
12 4 68
Eccentricity (deg)
M1
M2
M3
M4
M5
1
4
5
7
8
357
Figure 4. Conversion of visual (in degrees) to cortical (in millimeters) spread. A, Estimation of MF for LFP for Monkey 3. Visual distance between the RF centers for each electrode pair is plotted
on the x-axis and the corresponding cortical distance is plotted on the y-axis. B, MF of ECoG obtained from previous studies. The area shown in black is adapted from Figure 6 of Dow et al. (1981). The
magenta plus indicates the experimentally calculated MF of Monkey 3 ( y-axis) at the average eccentricity of the RF centers in this monkey (x-axis), which falls on the black curve. Blue plus markers
on the x-axis are the experimentally determined RF eccentricities of the five ECoG electrodes and the corresponding markers on the y-axis are the estimated MFs for these ECoG electrodes. C, Cortical
spreadestimated with (light shades) and without (darkshades) model for Monkey3 (blue: ECoG; pink:LFP). The median valuesfor the LFPare plotted in gray(with model) and black(without model).
D, Median and SE (after bootstrapping) estimates of the cortical spread for Monkey 3. E,F, Same as Cand Dfor the full dataset. For Monkey 4, the model could not be applied for the estimation of
the LFP spread and therefore is not shown in E(see Materials and Methods for details).
Dubey and Ray •ECoG Is a Local Signal J. Neurosci., May 29, 2019 •39(22):4299 – 4311 • 4307
spread corresponded to summation over a square of side ⬃2.8
mm, suggesting local origins of ECoG. Although the use of mul-
tiple recording modalities allowed us to use a model that ac-
counted for some factors that inflate the estimates of spatial
spread, the results were similar even without the model.
Comparison with previous studies
Our estimates of LFP spread using the model proposed by Xing et
al. (2009) were similar to previous studies reporting the LFP spread
in V1 to be a few hundred micrometers (Katzner et al., 2009;Xing et
al., 2009). However, recording from auditory cortex, Kajikawa and
Schroeder (2011)reported the LFP spread to be several millimeters.
The differences in their results and other studies could potentially be
due to differences in recording areas (for further discussion on LFP
spread estimates, see Dubey and Ray, 2016).
Unlike LFP, there are only a few reports on the spatial spread
of ECoG (Yoshor et al., 2007;Winawer et al., 2013;Winawer and
Parvizi, 2016). For example, Yoshor et al. (2007) performed their
experiments in humans using the same type of ECoG electrodes
(diameter of ⬃2.3 mm) and estimated the RFs of ECoG placed in
different visual areas. However, their RF estimates (in degrees)
were not converted to the spatial spread (in millimeters). In two
previous studies, Winawer and colleagues correlated ECoG re-
sponses with blood oxygen level-dependent (BOLD) responses
(Winawer et al., 2013) and electrical stimulation (Winawer and
Parvizi, 2016). They measured the stimulus-locked and broad-
band components of the ECoG responses (obtained after com-
puting the Fourier transform of the recorded response) to a
moving flickering bar and estimated the visual spreads of ECoG
using a pRF model (Kay et al., 2013). To estimate the spatial
spread, they multiplied the visual spreads with the magnification
factor, similar to our “no model” approach. The ECoG spread
estimated for broadband responses was comparable to our ECoG
spread estimates. However, spatial spread estimated this way es-
10 100 400
-4
-3
-2
-1
0
1
Frequency (Hz)
Normalized PSD
Slope
Number of electrodes
125 50 75 100 125 150
1.5
2
3
2.5
3.5 with model
without model
1x1
2x2
3x3
4x4
5x5
6x6
7x7
ECoG
AB
10 100 400
-4
-3
-2
-1
0
1
Frequency (Hz)
Normalized PSD
Number of electrodes
0
100
150
50
CD
1x1
ECoG
Figure 5. PSD and slope analysis. A, Mean PSD across 77 LFP (pink; indicated as 1 ⫻1) and 5 ECoG (blue) electrodes and mean PSDs of signals obtained by first averaging the LFPs over
progressively larger subgrids (pink to yellow). Slopes calculated for the 20 –100 Hz and 200 –400 Hz frequency ranges are plotted in dotted black (see Materials and Methods for details). The PSDs
are normalized to have a value of 0 at 20 Hz for comparison of slopes. B, Average slopes and SDs (for 20 –100 Hz frequency range) of the electrode grid combinations estimated with model (as
described in Materials and Methods; circles) and without model (squares) are plotted on the y-axis (pink to yellow) for Monkey 3. The number of electrodes in each grid combination is plotted on the
x-axis. Apart from squares as shown in A, we also considered rectangles of microelectrode populations (such as 2 ⫻3, 3 ⫻4, 4 ⫻6, etc.). The curve fitted on these slopes is shown in black. Blue
horizontal lines are the experimentally determined slopes of the five ECoG electrodes for this monkey. The intersection of the fitted curve and ECoG slope yielded the number of LFP electrodes that
needed to be averaged to produce the same slope as ECoG. C, Mean PSD of the LFP (pink) and ECoG (blue) averaged across four monkeys (Monkeys 1– 4; data from Monkey 5 were not used because
of the presence of noise at high frequencies). The SE is shown in lighter shade. Slopes are plotted in dotted black as before. D, Number of LFP electrodes that need to be averaged to match the slope
of each of the 11 ECoG electrodes from four monkeys between 20 and 100 Hz (for Monkey 3, slope of one ECoG electrode was too steep and did not intersect the fitted black curve; see B). The symbols
on the x-axis indicate the monkey (same as used in Fig. 4E). Red trace shows the median.
4308 •J. Neurosci., May 29, 2019 •39(22):4299 – 4311 Dubey and Ray •ECoG Is a Local Signal
sentially yields the CPI and depends on the properties of the
stimulus and other factors, as discussed below.
Spatial spread and its interpretation
The term “spatial spread” has been interpreted differently in dif-
ferent experimental and modeling studies. We interpret it based
on the model proposed by Xing et al. (2009) where the “spatial
spread” of a particular measure (such as LFP or MUA) is a spatial
weighting function that primarily depends on the properties of
the electrode (impedance, size, layout, etc.). If an arbitrarily small
part of the cortex can be activated, then this spatial spread func-
tion determines the cortical area over which this activation can be
observed using the electrode. Specifically, if a point on the visual
field stimulated a single neuron in cortex, such that both
vSUA
and
vv
are 0, then the cortical spread would be equal to the
product of visual spread and MF (Eqs. 3 and 4, Materials and
Methods). However, in general, it is not possible to activate an
arbitrarily small part of the cortex because neighboring cortical
regions may be receiving correlated inputs and therefore may also
get activated or because the activated part of the cortex may be
densely connected to its neighboring regions and may activate
those parts (these are captured in the CPI). In the definition used
here, the spatial spread function (
cLFP
) (Eq. 5, Materials and
Methods) is independent of the CPI and in fact could be arbi-
trarily small (in fact,
cMUA
is taken to be only 60
m in this
model). The model captures variations in CPI using
vSUA
and
vv
(which is the variance in the RF centers estimated at a partic-
ular location and therefore could be different for different parts
of the cortex (Albus, 1975;Dow et al., 1981). However, these two
terms get canceled out when comparing across measures (MUA
and LFP). Note that this is different from the definition of cortical
spread used by Linde´n et al. (2011), who measured the LFP
spread based only on the LFP activity recorded from the micro-
electrode, so the spread depended on the level of correlations in
the inputs.
Our estimates of ECoG spread decreased with eccentricity
(Fig. 4C,E). It is unclear why this is the case, especially because
this dependence persisted even after the model was applied (dark
vs light shades of blue). As described earlier, it could be because of
differences in filtering characteristics of the foveal versus parafo-
veal tissue due to differences in cell density, morphology, etc.,
which can produce different filtering characteristics (Be´dard et
al., 2004,2006). Our inability to actually measure the MF at the
eccentricities at each of the ECoG positions could also have po-
tentially biased the results, especially for the most foveal elec-
trodes, where the MF increased quickly. In particular, the MF
may be anisotropic (i.e., MF may depend on the actual azimuth
and elevations and could be different for upper and lower quad-
N=77
N=5 N=12
N=175
500400
300200
1000 500400
300200
1000
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0
0.2
0.4
0.6
0.8
1.0
Frequency (Hz)
Cortical spread (mm)
Monkey 3 Population
LFPECoG
BA
DC
Figure 6. Cortical spread as a function of frequency. A, Median LFP cortical spread for Monkey 3. The RF sizes (in degrees) were first estimated at each frequency and then the model was applied
to obtain the cortical spread (in millimeters). B, Median LFP cortical spread across three monkeys (Monkeys 1–3; for Monkey 4,the model could not be applied; data from Monkey 5 were excluded
because of the presence of noise at high frequencies). C,D, Median ECoG cortical spread for Monkey 3 and population data across four monkeys (Monkeys 1– 4). The SEs (after bootstrapping) are
shown in lighter shades.
Dubey and Ray •ECoG Is a Local Signal J. Neurosci., May 29, 2019 •39(22):4299 – 4311 • 4309
rants even for the same eccentricity), as reported in previous
studies (Van Essen et al., 1984;Palmer et al., 2012), but not con-
sidered in the study of Dow et al. (1981) from which we extrap-
olated the MFs for ECoG positions. Another source of error could
be due to residual eye movements, which could also be eccentric-
ity dependent. Specifically, to map RFs of foveal electrodes, the
visual stimuli need to be close to the fixation point and may
induce large eye jitters than eccentric electrodes. Unlike the spa-
tial spread estimation of LFP, applying the model does not com-
pletely eliminate this error. This is because, to estimate the spatial
spread of ECoG, we subtract the estimated RF parameters from
two signals (ECoG and LFP) obtained from two different elec-
trodes compared with LFP spread, for which both the LFP and
MUA were obtained from the same electrode at the same eccen-
tricity (Eqs. 3 and 4, Materials and Methods). Therefore, if the
residual eye movement error is more for the RF estimates of
foveal ECoG electrodes, then subtracting it from the RF estimates
of an eccentric LFP electrode will not completely eliminate the
eye-movement-related error. A more elaborate recording setup
using multiple small microelectrodes or micro-ECoG arrays that
can be placed near each ECoG electrode (such that the MF can be
experimentally determined at each ECoG position) will be
needed to better study the relationship between ECoG spatial
spread and eccentricity.
Although, while using the model, there was a ⬃32% reduction
in LFP spread, the final effect of the model was modest in case of
the ECoG (⬃9%). This is because the difference in visual spreads
of ECoG and LFP was huge compared with factors that cause the
inflation and thus got overshadowed (especially because taking
the square further reduced the contribution of the smaller term
(Eq. 10, Materials and Methods)). Therefore, although further
refinements in the model can improve the estimate of the spatial
spread, computing the spread without using the model also gave
reasonably accurate results. Therefore, none of our results criti-
cally depended on the validity of the model.
Interestingly, we observed that the final ECoG spread was
approximately equal to the spread of the LFP (⬃0.5 mm) and the
radius of the ECoG electrode (⬃1.15 mm), suggesting that the
ECoG spread should increase linearly with increasing electrode
size, with an offset equal to the spread of an infinitesimally small
conductor. This is also consistent with RF estimation as a func-
tion of frequency (Fig. 6C,D) for which, at higher frequencies, the
total spread was approximately equal to the radius of the elec-
trode and spread of the MUA (assumed to be only ⬃60
minthe
model). More experiments with ECoG electrodes of varying sizes
are needed to verify this experimentally.
ECoG spread as a function of frequency
In our previous study (Dubey and Ray, 2016), we have shown
that, in V1, high-gamma (⬃60 –150 Hz) frequencies of LFP
spread significantly greater than the lower frequencies. Further,
we found that this was accompanied by an increase in phase
coherency across neighboring sites in the same frequency range
and could possibly give rise to the band-pass LFP spread (see
“Factors affecting the spatial spread” section in Materials and
Methods for details). However, unlike LFP, ECoG spread did not
show any frequency-specific preferential increase in the spatial
spread in the high-gamma range, but instead showed a shallow
peak at lower frequencies (beta and gamma ranges). This is a
deviation from the earlier observation that ECoG spread could be
approximated as the LFP spread plus the size of the ECoG elec-
trode. One reason could be that the increase in phase coherency
observed for LFP was very localized (mainly observed between
electrode pairs separated by 1.2 mm or less; see Fig. 7 in Dubey
and Ray, 2016) and thus was not relevant in case of ECoG signals
that involved spatial summation over ⬃3 mm. Unfortunately, we
did not have enough ECoG electrodes (nor were they as closely
spaced as the microelectrodes) to perform an analogous coher-
ence analysis for ECoG (as done for LFPs in Dubey and Ray,
2016), which could have shed some light on the increase in RF
size at beta/gamma frequencies for the ECoG.
Recent studies have shown that different brain signals (e.g.,
LFP, ECoG, EEG, and fMRI) are modulated by different types of
underlying processes (Whittingstall and Logothetis, 2009;Musall
et al., 2014;Hermes et al., 2017 and references therein). For ex-
ample, Hermes et al. (2017) showed that neuronal synchrony
strongly influences gamma oscillations, but not the BOLD signal.
It should be noted that we did not observe stimulus-induced
gamma oscillations in either LFP or ECoG signals because the
stimulus size was very small. Gamma power has been shown to be
critically dependent on the stimulus size (Gieselmann and Thiele,
2008;Ray and Maunsell, 2011;Jia et al., 2013).
To conclude, we found that the ECoG spreads were local and
not much larger than the size of the macroelectrode. Although we
recorded only from V1, it is possible that these results will extend
to other brain areas because the model used here accounted for
differences in cortical activation. Our results present the first
steps toward carefully describing the spatial spread of ECoG and
further validate the use of ECoG for clinical purposes in cognitive
neuroscience and BMI applications.
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