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Propagating patterns of activity across motor cortex facilitate movement
initiation
Karthikeyan Balasubramanian1, Vasileios Papadourakis1, Wei Liang2, Kazutaka Takahashi1,
Matt Best2, Aaron J. Suminski3,4, Nicholas G. Hatsopoulos12*
1. Department of Organismal Biology and Anatomy, University of Chicago, Chicago, IL 60637
2. Committee on Computational Neuroscience, University of Chicago, Chicago, IL 60637
3. Department of Neurological Surgery, University of Wisconsin Madison, Madison WI 53792
4. Department of Biomedical Engineering, University of Wisconsin Madison, Madison, WI, 53706
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Abstract
Voluntary movement initiation involves the modulation of neurons in the primary motor cortex
(M1) around movement onset. Yet, similar modulations of M1 activity occur during movement
planning when no movement occurs. Here, we show that a sequential spatio-temporal pattern of
excitability based on beta oscillation amplitude attenuation propagates across M1 prior to the
initiation of reaching movements in one of two oppositely oriented directions along the rostro-
caudal axis. Using spatiotemporal patterns of intracortical microstimulation, we find that reaction
time increases significantly when stimulation is delivered against but not with the natural
propagation orientation suggesting that movement initiation requires a precise recruitment pattern
in M1. Functional connections among M1 units emerge at movement onset that are oriented along
the same rostro-caudal axis but not during movement planning. Finally, we show that beta
amplitude profiles can more accurately decode muscle activity when these patterns conform to the
natural propagating patterns. These findings provide the first causal evidence that large-scale,
spatially organized propagating patterns of cortical excitability and activity are behaviorally
relevant and may be a necessary component of movement initiation.
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Introduction
The initiation of voluntary skeletal movements is often associated with large-scale
modulations of neurons in the primary motor cortex (M1)1,2. It remains a mystery, however, why
similar modulations in M1 neurons during movement preparation, visual observation of action,
and motor imagery occur in the absence of movement 3–7. One possibility is that modulation is
weaker during these conditions and fails to exceed non-linear, thresholds in downstream spinal
circuitry, thus resulting in no movement5,8,9. Yet, preparatory activity as measured during an
instructed-delay paradigm often equals or exceeds movement-related activity particularly in
premotor cortex which is known to provide substantial projections to the spinal cord10,11. Another
possibility is that there is an active inhibitory gating mechanism preventing movement initiation
that is released when movement needs to begin12 as has been shown during REM sleep13,14. There
is, however, no evidence that such a gate exists in the context of voluntary skeletomotor behaviors.
A third possibility argues that the motor cortex resides in a very high dimensional state space that
allows patterns of ensemble activity related to preparation to evolve in dimensions that do not
generate movement (i.e. the “output null space”) in contrast to movement-relevant activity patterns
that reside in an “output potent space”15. Aligned with this idea, we argue that a specific spatio-
temporal pattern of M1 excitability and unit modulation is required for voluntary movement
initiation.
Oscillations in the beta frequency range (i.e. 15-35 Hz) as measured by the local field
potential (LFP) are prevalent in various motor structures including the cerebellum, basal ganglia,
and cortical areas such as M116–18. Immediately prior to movement onset, the amplitude of these
beta oscillations attenuates (i.e. desynchronize) in M1 when single units begin modulating19,20
(Figure 1a). The degree of beta oscillation attenuation is correlated with the magnitude of motor-
evoked potentials as measured with transcranial magnetic stimulation21. Furthermore, the timing
of beta attenuation with respect to the go signal varies with reaction time but is fixed with respect
to movement onset indicating that beta attenuation is a neural correlate of movement initiation
(Figure 1b; Supplementary Figure 1; see 22,23).
We have previously documented that trial-averaged, beta attenuation timing (BAT) does
not occur synchronously across the upper limb area of M1 but rather forms a propagating sequence
of cortical excitability24. Here, we extract single-trial beta amplitude attenuation profiles and find
that attenuation propagates along one of two oppositely oriented directions along the rostro-caudal
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axis. By applying propagating patterns of subthreshold intracortical microstimulation (ICMS)
prior to movement onset, we significantly delayed reaction time when ICMS patterns were
incongruent with the natural propagating patterns. Using a network analysis on spiking activities
of simultaneously recorded units, we observe that functional connections emerge immediately
prior to movement onset that are oriented along the same rostro-caudal axis. Finally, by decoding
muscle EMG activity from patterns of beta amplitude profiles and then applying spatial
perturbations, we provide evidence that these natural propagating sequential patterns lead to
normal recruitment of muscle activity.
Results
Single-trial propagating patterns of cortical excitability
Three rhesus macaque monkeys (Mk, Ls, and Bx) were trained on a simple reaction time
task to perform planar reaching movements by moving a cursor to visual targets using a two-link
robotic exoskeleton (BKIN Technologies, ON, Canada) while single units and LFPs were
simultaneously recorded from multi-electrode arrays implanted in the upper limb area of M1
(Supplementary Figure 2a). Monkeys Mk and Ls made movements to one direction (270o and 45o,
respectively), and Bx was trained to make movements in two opposing directions (45o and 225o).
LFP signals were band-pass filtered centered at the frequency of peak power in the beta frequency
range (15-35 Hz: 31±3 Hz for monkeys Mk and Bx, and 21±3 Hz for monkey Ls; see Methods)
from which beta amplitude profiles were computed using the Hilbert transform. Traditionally, beta
amplitude dynamics are determined by trial-averaging beta profiles in order to reduce noise25–27.
However, trial-averaging conceals possible interesting beta dynamics that vary from trial to trial28.
To extract single-trial beta profiles, we used an auto-encoder that was trained to generate de-noised
versions of the input beta signals (Supplementary Figure 2b). These single-trial, de-noised profiles
exhibited characteristic attenuation (i.e. desynchronization) prior to movement initiation, a
mesoscopic signature of cortical excitability21. More importantly, these beta dynamics revealed
spatial gradients that evolved in time indicative of spatio-temporal patterns that propagated in one
of two oppositely oriented directions along a rostro-caudal axis in MI (Figure 1c).
For each trial, we quantified the propagation direction of beta attenuation time prior to
movement initiation by first determining when each electrode’s normalized beta profile dropped
below a threshold. We then used linear regression to predict beta attenuation times (BATs) from
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the spatial locations of each electrode (see Equation 1), where the electrode location on the array
(x and y coordinates) was the independent variable and the corresponding BAT was the dependent
variable. The regression coefficients could then be used to compute the orientation from early to
late BATs (see Equation 2) which we refer to as the beta attenuation orientation (BAO) for that
trial. Trials that satisfied the criterion of R2 ≥ 0.2 (p ≤ 0.05, F-Statistic; number of trials = 278/366
(76%) for Mk; 1626/1723 (94%) for Ls; 1369/1868 (73%) for Bx making 45 degree arm
movements; 1417/1909 (74%) for Bx making 225 degree arm movements where 0, 90, 180 and
270 degree movements correspond to directions to the right, away from the body, left, and into the
body, respectively) for the regression fit were retained for further analyses. As suggested by Figure
1c, single trial BAOs were directed in one of two oppositely oriented directions (Figure 1d). For
all three monkeys, the distributions of single-trial BAOs (pooled over 4 sessions for monkey Mk,
9 sessions for Ls, 11 sessions for Bx making 45 degree movement and 11 sessions for Bx making
225 degree movement) were bimodally distributed along a roughly rostro-caudal axis
(rostromedial-caudolateral axis for Mk and Bx and rostrolateral-caudomedial axis for Ls) albeit
the two modes were not always equal in size (Figure 1e). The BAO distributions were well fit by
a mixture of von Mises functions model with means of 137° and -20° for Mk; 33° and -126° for
Ls; 143° and -33° for Bx for 45 degree arm movements, and 137° and -32° for 225 degree arm
movements. The BAO distributions for the two movement directions in Bx were not statistically
different (p=0.1, Kuiper’s two sample test). Multi-unit activity was not statistically different for
trials in either of the modes and the few trials that fell outside of the two modes (one-way ANOVA
for 3 groups, p-values ranging from 0.21 to 0.99 for different datasets; Supplementary Figure 3).
However, trials in which the BAO propagated in the rostro-to-caudal direction had significantly
shorter reaction times as compared to trials with caudal-to-rostral propagation in two of the
monkeys (mean reaction time of 387 and 405 milliseconds, respectively, for Monkey Bx making
45 degree movements, p = 0.0049, two-sample t-test (not significant for 225 degree movements,
p=0.4); 119 and 143 milliseconds for Monkey Ls, p = 0.0002, two-sample t-test).
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Figure 1. Single trial beta attenuation and their orientations. a. Beta frequency oscillations (gray) and
amplitude envelope (red) on one trial from one electrode. MO-movement onset. b. Normalized beta
envelopes averaged over different trial groups (trials sorted by reaction time, 50 trials per group) aligned
on the GO cue (top left) or on movement onset (bottom left) from one session in Ls. (Right) Channel-
averaged beta attenuation time regressed on mean reaction times (big colored dots) in each trial group with
respect to the GO cue (black line, r2= 0.996, p=0.00018) or movement onset (red line, r2= 0.126, p=0.558).
Black dots represent single channel values (offset by 10ms and jittered for clarity). c. Beta envelopes across
channels from Monkey Ls for two trials (left) along with their corresponding spatial patterning (right) at
different times (corresponding to vertical colored lines on left panel). Orientations of regression fits to the
spatial patterning are denoted with arrows. d. Beta envelopes of two trials (left; inset shows spatial positions
of three electrodes with early (blue), intermediate (green), and late (red) attenuation times) and their
corresponding spatial maps of beta attenuation times (right) are shown for monkey Bx. Regression fits to
the pattern show the beta attenuation orientation (BAO) directed rostrally or caudally (red arrows). e. Polar
histograms show the distributions of BAOs across multiple single trials and recording sessions for three
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monkeys. A mixture of two von Mises functions was fit to the BAO distributions (red curves) to estimate
the two direction modes of the BAO (blue arrows). Insets represent the initial hold (filled red) and target
positions (filled gray) of the hand.
Propagating sequences and somatotopy
We examined the spatial relationship between the propagating sequences and the
somatotopic organization of M1 using suprathreshold electrical stimulation. We documented
muscle twitches through visual observation and muscle palpation in our three animals by
stimulating each electrode (Supplementary Figure 4). Given the nature of the behavioral task (i.e.
a reaching task involving primarily proximal muscles), we confined our analysis of propagating
sequences on arrays placed primarily in proximal zone even though we had an additional array (in
Ls and Bx) placed in the distal zone. Despite the crude somatotopy as others have documented29–
32, we found that the axis of propagation was nearly orthogonal to the medio-lateral gradient from
proximal to distal representations.
Causal evidence linking propagating patterns to movement initiation
To provide more direct causal evidence that propagating patterns facilitate movement
initiation, we conducted experiments designed to perturb movement initiation in which
subthreshold, patterned electrical stimulation across a set of electrodes was delivered during the
reaction time period (Figure 2a). We hypothesized that patterned electrical stimulation that
propagated against (INCONGRUENT) the natural propagating pattern of beta attenuation would
delay movement initiation as compared to patterned stimulation that propagated with
(CONGRUENT) the natural propagating pattern (see Methods). Given that the BAO varies from
trial to trial (i.e. along the rostro-caudal or caudo-rostral directions), we could not assume a
particular BAO on any given stimulation trial. Moreover, stimulation artifacts made it difficult to
measure the BAO on stimulation trials. This was not an issue for monkey Ls as the bimodal
distribution of BAOs was highly asymmetric on non-stimulation trials (i.e. nearly unimodal).
Therefore, we could assume a single BAO direction across stimulation trials (2086 trials recorded
over 13 sessions). For monkey Bx where the BAO distribution was nearly symmetric, we devised
a method for selecting a subset of stimulation trials that we could assume had a highly unimodal
BAO distribution based on no stimulation (NOSTIM) trials (see Methods). Only this subset of
trials was analyzed for Bx (657/1772 or 37% of stimulation trials for 45 degree movement and
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724/1686 or 43% of stimulation trials for 225 degree movement). Likewise, for monkey Mk, a
similar procedure was applied to select a subset of trials (84/187 or 45% of stimulation trials) from
one of the datasets that showed a bimodal distribution. The second data set from Mk exhibited a
highly unimodal distribution on NOSTIM trials. It should be emphasized that the assumption of
unimodality is conservative and likely leads to weaker differential effects on reaction time given
that some stimulation trials may have had BAOs directed in the opposite direction.
Reaction time distributions for the INCONGRUENT condition were significantly delayed
as compared to those in the CONGRUENT condition for all three monkeys (Figure 2b; p=0.03 for
Mk; p = 0.019 for Ls; p = 0.009 for Bx for 45 degree reaches and p = 0.001 for Bx for 225 degree
reaches, two-sample KS test comparing INCONGRUENT and CONGRUENT conditions). No
significant difference in RT distributions was observed between CONGRUENT and NO STIM
conditions (p=0.49 for Mk; p = 0.64 for Ls; p = 0.17 for Bx for 45 degree reaches and p = 0.08 for
Bx for 225 degree reaches, two-sample KS test). Mean reaction times were significantly longer for
INCONGRUENT trials as compared to CONGRUENT and NOSTIM trials for all three monkeys
(Figure 2c, p < 0.05, F-statistic ANOVA; post-hoc Bonferroni correction). Mean (standard error)
reaction times for Mk were 366 (6.5), 390 (7.2) and 357 (6.0) milliseconds for CONGRUENT,
INCONGRUENT, and NOSTIM, respectively. Likewise, for Ls, the corresponding mean reaction
times were 160 (2.12), 169 (2.18), and 161 (2.15) milliseconds. Monkey Ls tended to anticipate
the presentation of the GO cue leading to very short reaction times. For Bx (45 degree reaches)
mean reaction times were 375 (2.2), 386 (2.2), 372 (2.9) milliseconds and for Bx (225 degree
reaches) they were 363 (2.5), 377 (2.5), 360 (2.75) milliseconds. By comparing session mean
reaction times over all 27 stimulation sessions and over all three monkeys, INCONGRUENT
session reaction times were significantly longer than those in CONGRUENT sessions (p = 2.4e-
5, paired, two-tailed t-test, Figure 2d).
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Figure 2. Effect of spatio-temporal stimulation on reaction time. a. The stimulus was a biphasic pulse
with sub-threshold currents (top), delivered concurrently over sets of electrodes with propagation latency
(Δt) of 10 milliseconds (4 milliseconds for Monkey Mk). Stimulation patterns were delivered to a group
of electrodes propagating from rostral to causal sites or vice versa (Pattern A, middle) or diagonally (Pattern
B, bottom). The stimulus patterns were delivered either along the BAO direction (CONGRUENT) or
against the BAO direction (INCONGRUENT). b. The distributions of reaction times for the two stimulation
conditions along with those trials that received no stimulation (NO STIMULATION) are shown for all
three monkeys. c. Mean (standard error) relative reaction time in the three conditions. Relative reaction
time was computed by subtracting the mean reaction time in the NO STIMULATION condition for each
recording session. d. Scatter plot comparing the mean reaction times between the two stimulation conditions
from 27 individual experimental sessions over all three monkeys. The diagonal dotted line represents the
identity line.
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Functional connectivity emerges along the rostro-caudal axis at movement initiation
If beta attenuation as measured by the LFP is truly a reflection of local network excitability
and ultimately activation, we would expect a similar spatio-temporal pattern to emerge among unit
activity at movement initiation. To characterize spatio-temporal patterning in neuronal spiking, we
estimated functional connectivity among unit activity at different epochs during the reaching
behavior in monkeys Bx and Ls (Figure 3a). Monkey Mk was excluded from this analysis due to
an inadequate number of channels with spiking activity. We used a Granger-type statistical model
applied to point processes33,34 to predict multi-unit activity (MUA) from one electrode based on
the past MUAs of other electrodes (i.e. source) to infer the directed network connectivity among
all simultaneously recorded electrodes (See Methods). The angle of each significant, directed
connection between two electrodes was determined based on the spatial locations of the two
electrodes. Each significant connection was then binned to create polar histograms (accounting for
both excitatory and inhibitory connections as determined by the sign of the sum of history
coefficients associated with the source electrode) representing different directions across the motor
cortical sheet. During the movement preparation epoch (an epoch that spanned the GO cue so
spiking reflected in part generic preparation without movement direction information), polar
distributions of functional connectivity were estimated and were fitted by a mixture of two von
Mises functions with means of -92° and 100° in Bx for 45 degree reaches (Figure 3b, top) and -
72° and 95° for 225 degree reaches (Figure 3b, middle), and -67o and 128o in Ls for 45 degree
reaches (Figure 3b, bottom). For the movement initiation epoch, the von Mises means shifted
orientation to -38° and 119° in Bx for 45 degree reaches (Figure 3c, top) and -50° and 125° for
225 degree reaches (Figure 3c, middle), and -123o and 600 in Ls for 45 degree reaches (Figure 3c,
bottom). A bimodal distribution (p = 0.01 for Ls, p = 0.004 for Bx 45 degree reaches and p = 3.9e-
5 for Bx 225 degree reaches; Rayleigh test for uniform circular distribution modified to test for
bimodality) of connectivity emerged along a rostro-caudal axis during movement initiation that
was similar to the BAO distribution (p = 0.1 in Bx for 45 degree reaches and p = 0.05 for 225
degree reaches, and p = 0.055 for Ls; Kuiper’s two sample test). Moreover, the functional
connectivity distributions for the two movement directions in Bx were not statistically different
(p=0.9, Kuiper’s two sample test). In contrast, functional connectivity during movement
preparation showed a distribution that was significantly different from the BAO distribution (p =
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0.02 in Bx for 45 degree reaches and p = 0.001 for the 225 degree reaches, and p = 0.0001 in Ls;
Kuiper’s two sample test).
Figure 3. Functional connections among neurons emerge along the BAO axis during movement onset.
a. Multi-unit activity (MUA) from a population of M1 neurons was used to estimate functional connectivity
during movement preparation and movement onset epochs. MUA for each electrode was normalized to its
peak activity and sorted by time of peak activity. b. Polar histograms of the orientation of functional
connections during the movement preparation epoch (top, Bx for 45 degree movements; middle, Bx for 225
degree movements; bottom, Ls for 45 degree movements). The von Mises fits (red curves and dashed blue
arrows) show functional connectivity distributions that were different from the BAO distributions. c. During
the movement onset epoch, the neuronal functional connection distributions were oriented similar to the
BAO distributions.
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In order to more effectively isolate the neural dynamics of movement planning from
movement execution, we also examined functional connectivity during an instructed delay task for
monkey Bx where the target stimulus was presented for a random duration ranging from 500 to
1200 milliseconds before a go cue to initiate the movement. Only trials with instructed delay
durations longer than 1000 ms were used for the functional connectivity analysis. It is known that
single units in primary motor cortex modulate during the instructed delay period where there is no
movement35,36. We assessed the orientation of directed functional connections during the early
(Supplementary Figure 5, left) and late planning (Supplementary Figure 5, right) epochs during
the instructed delay period. Mixture models fit to these epochs showed von Mises means that were
oriented nearly orthogonal to the BAO axis.
Propagating patterns along the rostro-caudal axis more reliably predict muscle activity
We hypothesized that downstream areas such as the spinal cord (and motor neuron pools)
may be sensitive to the spatio-temporal recruitment order of cortical neurons. Beta oscillation
dynamics are likely not involved in the detailed components of movement execution25. However,
evidence has shown that cortical oscillations and muscle EMGs are related and exhibit significant
coherence in the beta frequency range under certain behavioral conditions37. More importantly,
this coherence can modulate continuously and is related to motor parameters38. One way to test
the idea that propagating beta attenuation may facilitate muscle recruitment is to decode muscle
activity from beta amplitude profiles in cortex and then apply different spatial perturbations to the
beta profiles. Using cortical LFP and EMG data from Bx and Ls, we trained a feed-forward neural
network (Figure 4a, see Methods) using the Levenberg-Marquardt algorithm39,40 to reconstruct a
subset of 5 EMG signals (muscles recruited during the task condition; reaching movements to the
target at 45o) from a set of cortical beta profiles (Figure 4b and Supplementary Figure 6a).
Reconstruction performance on test data not used to train the network was assessed by the fraction
of variance accounted for (FVaF in percentage) and ranged from 18% to 55% on all five muscles
with an average of 40.5% for Bx and ranged from 15% to 51% on all muscles with an average of
36.5% for Ls. Our goal here was not to develop an accurate decoding algorithm for brain-machine
interface applications, but rather to adequately reconstruct muscle activity with a model that could
then be used to apply desired spatial perturbations. We applied two kinds of spatial perturbations
(random swaps) to the model’s input: a swap 1) parallel to or 2) orthogonal to the BAO axis (See
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Methods; Figure 4c). A total of 5000 swaps were performed for each perturbation type from which
a distribution of FVaFs were generated and compared to each other as well as to the unperturbed
FVaF (Figure 4d and Supplementary Figure 6b). Only the parallel perturbation would disrupt the
natural sequencing of beta attenuation propagation, and, therefore, we predicted that such
perturbations would more effectively disrupt EMG output from the neural network model. Mean
FVaFs were, in fact, significantly lower for the parallel perturbations as compared to orthogonal
perturbations (p = 6.6e-200 for Bx and p = 3.6e-84 for Ls, two sample t-test).
Figure 4. EMG prediction is more sensitive to perturbations parallel to the BAO axis. a. A feed-
forward back propagation neural network architecture that maps instantaneous beta amplitudes to
electromyographic (EMG) from 5 muscles that were active during the particular movement condition. b.
Trial-averaged predicted EMG values (red) are overlaid on the actual trial-averaged EMG signals (blue)
for Bx. c. Perturbation of the spatiotemporal pattern was performed along the BAO axis (parallel swap) or
orthogonal to it (orthogonal swap), and FVaF of the model’s performance was computed. d. Distributions
of FVaFs over 5000 swaps are shown for the parallel swap condition (yellow; mean FVaF of 12%) and
the orthogonal swap condition (blue; mean FVaF of 6.5%) along with the FVaF of the original
unperturbed model (red line; mean FVaF of 40.5%). Inset represent the initial hold (filled red) and target
positions (filled gray) of the hand.
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Discussion
This work provides important evidence demonstrating that a specific, propagating rostro-
caudal pattern of M1 excitability and unit modulation is required for voluntary movement
initiation. First, using subthreshold patterned electrical stimulation, we showed that patterned
stimulation that propagates against (INCONGRUENT) the natural propagating direction leads to
longer reaction times whereas stimulation propagating with (CONGRUENT) the natural pattern
did not affect reaction times. While any form of electrical stimulation will perturb the natural
cortical dynamics associated with movement initiation, we suggest that the patterned stimulation
propagating against the natural sequence provides a more potent perturbation. Subthreshold ICMS
at single sites has been previously shown to lead to increased reaction time in dorsal premotor
cortex followed by normal motor execution41. Interestingly, similar effects on reaction time were
absent for similar single site, subthreshold ICMS in M1. We argue that single site stimulation may
not be the ideal paradigm for perturbing the cortical dynamics in M1 associated with movement
initiation. Second, functional network connectivity among an ensemble of spiking neurons
emerges at movement initiation that is spatially anisotropic and oriented along a similar rostro-
caudal axis. This was not observed during movement preparation or planning even though it is
known that M1 neurons modulate during these periods (See Figure 3 and Supplementary Figure
5). Spatial structure in functional connectivity was often weak during movement preparation and
planning, and, if anything, its spatial anisotropy was oriented orthogonal to the rostro-caudal axis.
Anatomical and physiological studies have suggested a spatial anisotropy of horizontal
connectivity in M1 that might support these spatially organized propagating sequences. Retrograde
axon degeneration following punctate lesions in M1 has indicated longer range horizontal
connectivity along the rostro-caudal axis as compared to the medial-lateral axis42. Moreover, an
ICMS study has provided evidence for dominant functional connectivity along the rostro-caudal
axis43.
The bimodal distribution of propagation that we observed here is similar in orientation to
the bimodal distribution of beta waves (as measured by the phase gradient of the beta oscillations)
along the rostro-caudal axis we and others have previously documented to occur during movement
preparation33,44–47. This may suggest a mechanism by which on-going beta waves propagating
along the rostro-caudal axis during movement preparation lead to a sequential pattern of neural
activation prior to movement initiation. Beta waves alternately propagate either in the rostral-to-
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caudal direction or vice versa in a seemingly random fashion during movement preparation. It is
also known that excitability is enhanced at particular phases of the beta oscillation25 (Murthy and
Fetz 1996b). Therefore, as a particular beta wave travels across the cortical sheet in one direction,
a wave front of excitability moves across the motor cortex in the same direction. Assuming input
originating from outside of motor cortex signaling movement initiation interacts with this beta
wave, the combination will more likely lead to firing at that position in motor cortex. The traveling
wave front may, therefore, lead to a sequential pattern of activation.
An open question is how these propagation patterns are mechanistically related to
appropriate muscle activations for movement initiation. One possibility is that rostro-caudal
propagation enhances M1 output through recurrent connectivity due to stronger rostro-caudal
horizontal connectivity. However, M1 firing rates for trials when propagating excitability occurred
along the rostro-caudal axis were not statistically different from those few trials when propagation
occurred outside the rostro-caudal axis. Another possibility is that downstream areas such as the
spinal cord are sensitive to the recruitment order of cortical sites. Our muscle decoding results
indirectly supports this second alternative. Perturbing the spatial order of beta amplitude inputs
along the rostro-caudal axis more effectively disrupts the natural propagating patterns and leads to
significantly weaker EMG predictions as compared to orthogonal perturbations which preserve the
overall propagation pattern.
The sensitivity of downstream receiving populations to these cortical propagating
sequences could be due to the specific characteristics of these patterns. For example, the
propagation axis can be thought of as a composition of two phenomena: simultaneous activation
of populations orthogonal to the propagating axis (i.e. along the medio-lateral axis) and sequential
activation of populations along the propagating axis. Either or both of these phenomena could be
responsible for downstream activations that lead to movement initiation. One possibility is that
synchronous activation along the medio-lateral axis and rostro-caudal cortical sequencing lead to
non-linear amplification of muscle activity which support movement initiation and generation.
Further experiments will be needed to shed light on the exact nature of the downstream sensitivity
to these natural spatiotemporal patterns.
Our results suggest that these propagating sequences serve a generic role in initiating
movements and do not depend on the nature of the movement or the temporal sequencing of limb
segments. Although we have not examined this question in great depth, our findings from monkey
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Bx demonstate that the bimodal distributions of BAOs and functional connectivity are not
statistically different between movements toward and away from the animal. Moreover, the spatial
structure of these propagating patterns are nearly orthogonal to the medio-lateral gradient from
proximal to distal representations. This suggests that these propagating sequences are likely not
the result of proximal-to-distal sequencing that is observed in certain motor behaviors48,49.
These results have broad significance because they suggest that large-scale, spatially
structured propagating patterns of activity may be a common strategy used in various cortical areas
to perform behaviorally relevant computations. Spatio-temporal patterns such as traveling planar,
radial, circular, and spiral waves have been documented across different cortical areas including
somatosensory50,51, visual52–57, auditory58,59 cortices, and hippocampus. Various functional roles
for these spatio-temporal patterns have been put forth but it remains a possibility that they are
epiphenomena of the recurrently connected cortex60. Multi-site, spatio-temporal stimulation using
electrical or optogenetic stimulation may be an important approach to provide more direct support
for a role of these patterns in cortical processing.
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Acknowledgements: We would like to thank Carrie Anne Balcer for assistance in animal care
and training as well as Callum Ross, Juan Alvaro Gallego, and Raeed Chowdhury for assistance
in chronic EMG implants. This work was supported by the National Institute of Neurological
Disorders and Stroke at the National Institutes of Health (Grant R01 NS045853 to N.G.H.). This
work used the Beagle supercomputer resources provided by the Computation Institute and the
Biological Sciences Division of the University of Chicago and Argonne National Laboratory, and
the Midway cluster at the Research Computing Center of the University of Chicago.
Author Contributions: K.B., V.P. and W.L. contributed to multiple aspects of the work
including surgical procedures, experimental design, data analysis, and manuscript
writing/editing as well as data collection for monkeys Ls and Bx. K.B. and N.G.H. were
responsible for the single-trial BAO estimation techniques. K.B., K.T. and N.G.H. contributed
to the development of the functional connectivity analyses. K.T., M.B. and A.J.S. helped
conceive of the patterned stimulation paradigm and contributed to surgical procedures,
manuscript editing, and data collection for monkey Mk. N.G.H. supervised the study and
contributed to surgical procedures, experimental design, data analysis, and manuscript writing.
Author information: N.G.H. serves as a consultant for BlackRock Microsystems, Inc., the
company that sells the multi-electrode arrays and acquisition system used in this study
Correspondence and requests for materials should be addressed to N.G.H.
(nicho@uchicago.edu).
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24
Methods
Electrophysiology
Three Rhesus (Macaca Mulatta) monkeys (Mk, Ls and Bx) were implanted with Utah
multi-electrode arrays (1.0 mm electrode length for Mk and Ls; 1.5 mm for Bx and 400 µm pitch
from Blackrock Microsystems, Inc. Salt Lake City, UT) in the upper limb region of primary motor
cortex (M1), on the contralateral side of the active limb used in the task. Monkeys Ls and Bx
received two arrays with 64 recording electrodes per array (8 × 8 grid), positioned on the precentral
gyrus along the medio-lateral axis and monkey Mk was implanted with one array of 100 electrodes
(10 × 10 grid) (see Supplementary Figure 2a). Surface electrical stimulation during surgical
implantation was performed to guide the placement of each electrode array in the arm/hand area
of primary motor cortex. Monkeys Ls and Bx were implanted with bi-polar electromyographic
(EMG) electrodes in 13 individual muscles (Anterior Deltoid, Posterior Deltoid, Pectoralis Major,
Biceps Lateral, Biceps Medial, Triceps Long head, Triceps Lateral, Brachioradialis, Flexor Carpi
Ulnaris, Flexor Digitorum Superficialis, Extensor Carpi Radialis, Extensor Digitorum Communis,
Extensor Carpi Ulnaris). The surgical and behavioral procedures involved in this study were
approved by the University of Chicago Institutional Animal Care and Use Committee and conform
to the principles outlined in the Guide for the Care and Use of Laboratory Animals.
Neural data recorded as analog signals were amplified with a gain of 5000, bandpass
filtered between 0.3Hz and 7.5 kHz, and digitized at 30 kHz. For monkey Mk, the local field
potentials were sampled at 2 kHz from the digitized data after low-pass filtering the signals with a
4th order Butterworth filter and a cut-off frequency of 500 Hz. For Ls and Bx, the neural data were
zero-phase low-pass filtered with a 10th order Butterworth filter and a cut-off frequency of 500 Hz,
and down-sampled to 2 kHz. Multi-unit activity (MUA) was extracted as threshold crossings from
the raw data after high-pass filtering with a cut-off frequency of 250 Hz. The threshold limit was
set to be -5.5 times of the signal RMS value. For EMG recordings, signal from the thirteen muscles
were amplified individually and bandpass filtered between 0.3 and 1 kHz prior to digitization and
sampled at 10 kHz.
Behavioral Task
The animals were operantly trained to perform a center-out planar reaching task using a
two-link exoskeletal robot (BKIN Technologies). The tool-tip of the robot determined the position
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25
of a cursor on a screen, and the monkeys were able to freely move the robot in the horizontal plane
using their upper limb. Monkey Mk used a horizontal screen with his arm and robot underneath
the screen, while monkeys Ls and Bx had a vertical screen facing them such that the horizontal
movements forward and back corresponded to upward and downward cursor movements. The
animals had to hold the cursor on a center target for a fixed duration (600 ms for Mk, 900 ms for
Ls, and 1000 ms for Bx) to trigger a peripheral target appearance (GO cue). The animal had to
move the cursor to reach the peripheral target to get a juice reward. Monkey Mk was presented
with targets at 270o on a circle of radius 6 cm (where 0o corresponded to rightward movements
and 180o corresponded to leftward movements), and for monkey Ls the peripheral target was at
450. Monkey Bx was trained with two targets, one at 45o and another at 225o.
Beta Band and Single-trial Beta Attenuation Orientation
The frequency associated with the peak power in the beta frequency range (15-35 Hz) was
estimated from the channel-averaged power spectral density of the neural signals from each array
over a large number of trials. For monkey Ls, the beta peak occurred at 21 Hz (approximated to
the nearest integer value), and for monkeys Bx and Mk the peak occurred at 31 Hz. For the latter
two monkeys, a second smaller peak also occurred at 21 Hz but was not used for further analysis.
The signal was then band-pass filtered with a bandwidth of 6 Hz centered on the peak beta, i.e.,
21±3 Hz for monkey Ls and 31±3 Hz for monkeys Bx and Mk. The beta envelopes of the signal
were computed using the magnitude of the Hilbert transformation applied to the band-pass filtered
signal (see Figure 1a).
Single-trial beta envelopes were extracted using an auto-encoder neural network where the
inputs are the same as the targets. Segments of the signal (-500 ms to 600 ms with respect to the
GO cue) from all the recorded channels were extracted for each trial and decimated to 100 Hz. A
vector of length nChannels × mSamples was created for each trial and fed through the auto-encoder
(see Supplementary Figure 2b). The hidden layer was set to be half the size of the input layer so
as to form a bottleneck architecture, and the data were projected to the output layer. With training,
the auto-encoder was able to reconstruct the signal that preserved both spatial patterns and
significant temporal variance of the signal. The output beta envelopes from the auto-encoder were
then low-pass filtered with a 10th order filter and cut-off frequency of 5 Hz. The filtered signals
were normalized to have an amplitude range of [0, 1].
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The normalized single-trial beta envelope attenuates and crosses an amplitude threshold
value at a particular time (referred to as beta attenuation time or BAT) which varies depending on
the channel (see Figure 1d). These BATs, when arranged spatially on their corresponding electrode
locations on the array, exhibit a propagating pattern with a particular orientation. The orientation
of the beta attenuation (BAO) was estimated using a linear regression fit to the BATs as follows,
(1)
where, and are the coefficients of the rows and columns of the array, and denotes the
constant offset time. The direction of BAO was then estimated as,
(2)
The F-statistic of the model was used to ascertain statistical significance of the fit. For each trial,
a BAO and its associated coefficient of determination (R2) were calculated. On any given trial, the
amplitude threshold for determining the BATs was determined by varying the amplitude from 0.5
to 0.15 in steps of 0.05 and finding the threshold with the largest associated R2.
Patterned Electrical Stimulation
A spatio-temporal pattern of intracortical microstimulation (ICMS) was delivered to a fixed
set of electrodes on the single array in Mk and the medial arrays for Ls and Bx with a fixed onset
latency after the GO cue (150 ms for Mk, 50 ms for Ls and 200 ms for Bx). The patterned ICMS
propagated either rostro-caudally or caudo-rostrally which was either congruent or incongruent to
the BAO for a given trial (see Figure 2a). As a control, there were also trials without stimulation.
These three conditions (congruent, incongruent, and no stimulation) were randomly interleaved
across trials for monkeys Ls and Bx. For monkey Mk, each of the three conditions was presented
in multiple 25-trial blocks where each block was randomly given. The patterned ICMS consisted
of trains of biphasic (200 µs negative and positive pulses with an interphase latency of 55 µs)
pulses with constant subthreshold amplitude (5 µA for Ls and 12 µA for Bx). The subthreshold
current for Mk during the experiments was set to be 2 µA lesser than the current levels that resulted
in evoked responses during the two stimulation conditions, tested immediately prior to the
experimental session. For one data set, the current per electrode was set as 13 µA for the congruent
stimulation and 14 µA for the incongruent condition while in the other stimulation data set, the
currents were 12 µA and 14 µA for the congruent and incongruent conditions, respectively. For
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27
monkeys Ls and Bx, a set of 8 or 16 electrodes were stimulated simultaneously at any given time
(see Pattern A in Figure 2a). Pulse trains on a successive column were initiated at a latency of 10
milliseconds relative to the previous column. For Mk, 3 or 6 electrodes were stimulated at any
instance, with inter-stimulation latency of 4 milliseconds (see Pattern B in Figure 2a).
Determining BAO for Trials with Stimulation
For trials that received patterned stimulation, recovering the complete beta envelopes was
not possible due to large saturating electrical artifacts during stimulation. For monkey Ls the
bimodal BAO distribution was highly asymmetric on non-stimulation trials (i.e. nearly unimodal).
Also, for one data session examined in Mk, the BAO distribution was highly unimodal. Therefore,
we could assume a single BAO direction across stimulation trials. To determine the BAOs for the
stimulation trials in monkey Bx and for the second session in Mk, an alternative approach was
taken by examining the dynamics of the beta envelopes in trials when no stimulation occurred.
Typically, the channel-averaged beta envelope exhibits a local peak in amplitude at different times
prior to attenuation depending on the trial. The approach was to find a time window around the
GO cue where the local beta peaks occurred on a subset of no stimulation trials such that their
BAO distribution was highly unimodal. This time window (set to 300 ms in duration; 150 ms for
monkey Mk) was found by sliding the window in 100 ms steps starting at -300 ms with respect to
the GO cue, selecting no stimulation trials whose local beta peak occurred in that window, and
computing the BAO distribution (Supplementary Figure 7). The window whose selected trials
were highly unimodal (where at least two thirds of the trials in the window were oriented along
one BAO mode) in their BAO was chosen and then used to select stimulation trials whose local
beta peak occurred in the same window. The assumption was that these stimulation trials exhibited
a similar unimodal BAO distribution and, therefore, all these stimulation trials had BAOs pointing
roughly in the same direction. To detect local beta peaks in stimulation trials, partial beta envelopes
(-500 ms to 200 ms with respect to the GO cue; -500 to 25 ms for monkey Mk) that were not
corrupted by electrical artifacts were extracted using the auto-encoder. Whenever multiple time
windows exhibited unimodal BAOs in the no stimulation trials, the window that was closer to or
overlapping the GO cue was chosen. To compute reaction time means and distributions for all
three conditions, we excluded trials whose movement onset times occurred before the onset of the
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stimulation as well as trials with very long reaction times (>500 ms for Mk and Bx and >300 ms
for Ls).
Computing Reaction Times of Single Trials
Tangential velocity trajectories estimated from the Cartesian position of the reaching
kinematics data sampled at 2 kHz were used for reaction time computation. From the normalized
trajectories of each trial, movement onset times were computed when the velocity crossed 10% of
the peak velocity. When there were smaller velocity peaks that exceeded the 10% threshold prior
to final velocity peak associated with the actual movement to the target, movement onset was
computed using the final threshold crossing.
Firing rates
Multi-unit firing rates were calculated for each trial in 150 ms temporal windows, shifted
over time with steps of 10 ms. Rates were then averaged over trials to obtain the mean firing rate
of each channel’s multi-unit. For the heatmaps of Figure 3, mean firing rates were normalized by
dividing by the multi unit’s maximum rate. A different normalization procedure was used to
compare the firing rates of each mode. First the average baseline activity over all trials (500ms
prior to the go cue) was subtracted from each trial’s firing rate. Then, trials were separated into
three groups according to BAO mode (rostro-to-caudal BAO, caudo-to-rostral BAO, out of modes)
and the average firing rate of each group was calculated. If the multi-unit displayed suppressed
modulation, its rates were converted to the additive inverse. Finally, the three average rates were
divided by the global maximum, in order to retain possible mode differences. Population response
for the three modes was then estimated by averaging over multi-units. To compare the population
responses between modes, we used the normalized unit responses at two different epochs: reaction
(from go cue to movement onset) and movement (from movement onset to movement end). A one-
way AVOVA was done separately at each epoch [factor: BAO mode (three levels), sample size:
number of multi units] to determine differences between the population firing rate across BAO
modes.
Directed Functional Connectivity
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A granger-type causality estimation technique generalized for point-processes was used to
infer directed connectivity among simultaneously recorded neurons. For each candidate multi-unit,
the instantaneous spiking was modeled as its conditional intensity function (CIF), λ(t|H(t)), where
H(t), is the spiking history of all the multi-units in the ensemble up to time t. Using a generalized
linear model, the log CIF of each multi-unit was modeled in terms of the spiking of its covariate
(i.e. source) multi-units, initially with a history of 60 milliseconds binned at 3 millisecond
resolution for each source multi-unit. The final model was then found by optimizing the length of
the history term using the AIC (Akaike information criterion). To determine the influence of a
source multi-unit on a candidate multi-unit, the log-likelihood ratio between models (i) including
and (ii) excluding the source multi-unit was computed, and when the model performance decreased
significantly (p ≤ 0.05, χ2-test, false detection rate corrected for multiple comparison) with the
source multi-unit excluded, a directed connectivity from the source multi-unit to the candidate
neuron was inferred.
Decoding Muscle Activity from Beta Envelopes
A feed-forward neural network was developed to map instantaneous beta amplitudes from
multiple channels to the EMG activity of a group of muscles. Normalized beta envelopes from 60
channels (100 samples/second) were projected first through the auto-encoder and then fed into the
feed-forward neural network to decode 5 muscles based on their relevance to the task and the
quality of the signal (Anterior Deltoid, Pectoralis Major, Biceps Lateral, Triceps Long head, Flexor
Digitorum Superficialis). The inputs were vectors of 60 × 1 elements, and the outputs were vectors
of 5 × 1 elements. The neural network architecture (see Figure 4a) used 120 hidden neurons with
logarithmic sigmoid activation function. The output layer that predicts the EMG activities used a
linear transfer function. Of the available trials, 80% were used for training and 20 % for testing.
The prediction accuracy was computed for each individual muscle as the fraction of variance
accounted for (FVaF) between the actual EMG and the EMG predicted from the neural network
as,
(3)
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The input to the network was perturbed by swapping the spatial locations of the channels in two
different ways. For each swap, beta profiles on eight electrodes were randomly selected on the 64
electrode array and then randomly swapped spatial locations with other beta profiles with the
constraint that swapping occurred either parallel to or orthogonal to the BAO axis. A total of 5000
swaps were performed for each of the directions (parallel or orthogonal) and the FVaF for each
swap was estimated.
Somatotopic Maps
In order to determine the somatotopy of M1, supra-threshold electrical stimuli (a train of 25
biphasic pulses with 200 µS pulse width per phase and 55 µS interphase interval and 330 Hz;
current levels varied from 10 µA to 70 µA per electrode) were delivered to each single electrode
one at a time and the corresponding evoked responses documented. Two observers noted the
responses while a third individual delivered the stimuli using a Blackrock Microstimulator R96
system (Blackrock Microsystems, Inc. Salt Lake City, UT). Certain muscles were also palpated to
identify any evoked responses. We used a 7-point scale (color-coded in Supplementary Figure 4)
to label each site from (fingers, red), to wrist (yellow), to elbow (baby blue), to shoulder (blue)
joint and/or muscle twitches.
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Supplementary Figure 1. Beta attenuation times are correlated with reaction times and time-
locked to movement initiation. Normalized beta envelopes averaged over different trial groups
from one session in monkey Bx. Trials were sorted based on reaction time and grouped in bins of
55 trials. Color represents reaction time average of each group from shortest (blue) to longest
(yellow) trials. Average beta power for each group is plotted aligned on reaction time (top left) or
on movement onset (top right). (bottom) Channel-averaged beta attenuation time regressed on
mean reaction time in each trial group with respect to the GO cue (black line, r2 = 0.998, p = 8e-
9) or movement onset (red line r2 = 0.009, p = 0.853). Each big colored dot represents channel-
averaged values and each black dot represents single channel values. Color represents reaction
time average of each group from fastest (blue) to slowest (yellow) trials.
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Supplementary Figure 2. Multi-electrode array implantation and autoencoder architecture.
a. Multi-electrode arrays were implanted in the primary motor cortex (M1) of three macaques (Mk,
Ls and Bx). The arrays marked with red border were used for analyses and patterned stimulation
experiments. b. Single trial beta envelopes were auto-encoded to de-noise the neural signals. Beta
envelopes from N-channels sampled at 100 Hz (M-samples) were projected using the auto-
encoder. The hidden layer consisted of (NM)/2 neurons, resembling a bottleneck architecture.
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Supplementary Figure 3. Population firing rate profiles in and outside BAO modes.
Population peri-movement time histograms based on 32 to 60 multi-unit sites for trials in the
caudal-to-rostral BAO mode (red line), rostral-to-caudal BAO mode (blue line), and trials outside
of the two modes (green line) for representative datasets. Trials were aligned on movement onset
(black vertical line) and each multi-unit site’s firing rate profile was normalized before averaging
(see Methods). Dotted vertical lines represent the median go cue and movement end. Shaded areas
represent standard error of the mean.
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Supplementary Figure 4. Relationship between propagating sequence directions and
somatotopy. The somatotopic maps across the arrays implanted in the three monkeys show the
proximal-to-distal somatotopy oriented along the medio-lateral axes. The somatotopic maps for Ls
and Bx are based on two 8x8 arrays implanted medio-laterally in M1. The BAO axes (blue arrows),
computed for the medial arrays in Ls and Bx, and the one array in Mk, propagate nearly orthogonal
to the proximal-to-distal gradient.
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Supplementary Figure 5. Distribution of Functional Connections during Movement
Planning in an Instructed Delay Task. Directional distributions of functional connections
estimated using multi-unit activity is shown for early (100 to 350 ms after the instruction cue onset)
and late (600 to 850 ms after the instruction cue onset) phases of the instructed delay period. The
top panels are for monkey Bx reaching to the target at 45 degrees, and the bottom panels
corresponds to reaches at 225 degrees. The distributions were fit with a mixture of two von Mises
functions (red curves).
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Supplementary Figure 6. Effects of spatial perturbations on EMG predictions in monkey Ls.
a. Trial-average predicted EMG (red) and actual EMG (blue) and profiles using a neural network
trained with beta envelopes from Monkey Ls. b. Distributions of FVaFs over 5000 swaps are
shown for the parallel swap condition (yellow; mean FVaF of 5%) and the orthogonal swap
condition (blue; mean FVaF of 10%) along with the FVaF of the original unperturbed model (red
line; mean FVaF of 36.5% (varying from 15 % to 51% across muscles). Inset represent the initial
hold (filled red) and target positions (filled gray) of the hand.
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Supplementary Figure 7. Identification of unimodal BAO window for trial selection. The
panels in the two rows (corresponding to two sessions) show the BAO distribution for trials with
no stimulation whose channel-averaged beta envelopes had their peaks in the time window [-
300ms, 0ms] (left), [-200ms 100ms] (middle), or [-100ms 200ms] (right) with respect to the GO
cue. The window with highly unimodal von Mises fit was selected as the preferred window (top
left and bottom right panels highlighted by blue squares), and those trials in the stimulation
condition whose peaks fell within this window were assumed to be unimodal in their BAO
distribution.
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