J Neurophysiol 115: 1587–1595, 2016.
First published January 20, 2016; doi:10.1152/jn.00801.2015.
Phase-amplitude coupling, an indication of bursting in parkinsonism, is
masked by periodic pulses
Teresa H. Sanders
Biology Department, Emory University, Atlanta, Georgia
Submitted 17 August 2015; accepted in final form 15 January 2016
burst; deep brain stimulation; parkinsonism; phase-amplitude coupling; simulation
SINCE THE EARLY 1900S, rhythmic oscillations have been observed
in EEGs (Berger 1931). The oscillations were lumped into
different frequency bands, and each band was characterized by
the type of behavior that coincided with the brain rhythms in
that band (Pfurtscheller and Aranibar 1977). Eventually looking at the power in each band became common practice for
classifying segments of steady-state brain activity such as
depth of anesthesia, sleep stages, and stress levels (Lewis et al.
2012; Weiss et al. 2011; Wolf et al. 1988).
Measures of power in frequency bands provide some limited
and widely accepted information about brain activity and
Address for reprint requests and other correspondence: T. H. Sanders,
Dept. of Biology, Dieter Jaeger Lab, Emory Univ., Rollins Research
Ctr., Rm. 2164A, 1510 Clifton Rd., Atlanta, GA 30322 (e-mail:
[email protected]).
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health. However, measures that quantify nonstationary oscillations and multiple interacting oscillations (Cannon et al. 2014)
may reveal greater information, although they are not currently
well understood.
Phase-amplitude coupling (PAC) belongs to the class of
cross-spectral measures along with the bispectrum (Gajraj et al.
1998), spectral cross-correlation, and cross-covariance. These
measures enable analysis of interactions between oscillations
in neural recordings. One implementation, referred to here as
the PAC map, is computed with a phase-amplitude histogram,
quantified with a modulation index (MI) (Tort et al. 2010), and
then displayed in a comodulation heat map. This approach is
becoming increasingly popular, perhaps because it is straightforward to calculate and is available in several spectral analysis
packages.
Recently, PAC measures have been shown to correlate with
certain types of brain activities and pathologies (Igarashi et al.
2014; Sanders et al. 2013b; Tort et al. 2009). For example, in
patients with Parkinson’s disease, coupling between beta phase
(13–30 Hz) and higher frequency (50 –200 Hz) amplitude has
been observed in subdural electrocorticography recordings
from the primary motor cortex (M1) (de Hemptinne et al.
2013) and in bipolar deep brain stimulation (DBS) electrode
recordings from the subthalamic nucleus (STN) (Lopez-Azcarate et al. 2010). In further work by de Hemptinne et al. (2015),
STN DBS in 23 patients (stimulation frequencies ranging from
130 to 213 Hz) was reported to reduce PAC in M1. However,
as with other cross-spectral measures, the interpretation of the
neural basis for PAC is often not well understood. The following analyses used PAC mapping as an example method to shed
light on what cross-spectral measures can imply about interacting oscillations, as well as to reveal some of the common
pitfalls in interpreting these results in biological signals. Since
PAC has recently been suggested as a potential feedback signal
for closed-loop brain stimulation (DBS) in Parkinson’s disease
(Gunduz et al. 2015), particular attention was given to the
neuronal firing changes that may lead to elevated PAC in
parkinsonism and the dramatic PAC signal reduction (masking) induced by artifacts from periodic pulses similar to those
used for clinically therapeutic DBS.
The early PAC papers focused on the interactions between
two phase-locked oscillating signals in noise (Canolty et al.
2006; Jensen and Colgin 2007; Tort et al. 2009, 2010). The
assumed underlying composite signal can be thought of as the
modulation of the amplitude of the faster signal by the slower
one, e.g.,
y 共t兲 ⫽ 兵sin关2␲t xslow共t兲兴 ⫹ 1其 · sin关2␲t xfast共t兲兴
⫹ sin关2␲t xslow共t兲兴 ⫹ noise
0022-3077/16 Copyright © 2016 the American Physiological Society
1587
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Sanders TH. Phase-amplitude coupling, an indication of bursting in parkinsonism, is masked by periodic pulses. J Neurophysiol
115: 1587–1595, 2016. First published January 20, 2016;
doi:10.1152/jn.00801.2015.— Interactions between neural oscillations in the brain have been observed in many structures including
the hippocampus, amygdala, motor cortex, and basal ganglia. In
this study, one popular approach for quantifying oscillation interactions was considered: phase-amplitude coupling. The goals of
the study were to use simulations to examine potential causes of
elevated phase-amplitude coupling in parkinsonism, to compare
simulated parkinsonian signals with recorded local field potentials
from animal models of parkinsonism, to investigate possible relationships between increased bursting in parkinsonian single cells
and elevated phase-amplitude coupling, and to uncover potential
noise and artifact effects. First, a cell model that integrates incremental input currents and fires at realistic voltage thresholds was
modified to allow control of stochastic parameters related to firing
and burst rates. Next, the input currents and distribution of integration times were set to reproduce firing patterns consistent with
those from parkinsonian subthalamic nucleus cells. Then, local
field potentials were synthesized from the output of multiple
simulated cells with varying degrees of synchronization and compared with subthalamic nucleus recordings from animal models of
parkinsonism. The results showed that phase-amplitude coupling
can provide important information about underlying neural activity. In particular, signals synthesized from synchronized bursting
neurons showed increased oscillatory interactions similar to those
observed in parkinsonian animals. Additionally, changes in bursting parameters such as the intraburst rate, the mean interburst
period, and the amount of synchronization between neurons influenced the phase-amplitude coupling in predictable ways. Finally,
simulation results revealed that small periodic signals can have a
surprisingly large masking effect on phase-amplitude coupling.
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PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
interpretation of the signal interactions behind the PAC can be
problematic. One such instance is the observed correlation
between elevated PAC in local field potential (LFP) (and EEG)
signals and parkinsonism (Connolly et al. 2015; de Hemptinne
et al. 2013; Lopez-Azcarate et al. 2010; Sanders et al. 2013b).
MATERIALS AND METHODS
Since parkinsonism is associated with episodes of bursting in basal
ganglia neurons (Bergman et al. 1994; Miller and DeLong 1987;
Sanders et al. 2013a), and the bursting is hypothesized to be synchronized across multiple neurons (Gatev et al. 2006; Hammond et al.
2007), a simple bursting simulation with selectable synchronization
was tested to see whether the synthetic bursting could be made to
produce PAC patterns similar to those generated by LFPs recorded
from parkinsonian mammals. The simulation generated normally
distributed bursting patterns for individual neurons. The neuron firing
x10-5 Volts
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Fig. 1. Classical phase-amplitude coupling (PAC) with xslow at 10 Hz and xfast at 80 Hz. Top and middle: sample local field potential (LFP). Bottom: power spectral
density (left) and PAC map (right).
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(see Fig. 1 for xslow at 10 Hz and xfast at 80 Hz). The PAC map
then shows a hot spot at the intersection of the “amplitude
frequency” (fast signal) and “phase frequency” (slow signal).
For this synthetic example, the two frequency components can
easily be observed in the power spectral density of the composite signal. However, the relationship between the power and
the PAC is not always this straightforward in actual neural
recordings, leaving room for ambiguity in the interpretation of
signal dynamics.
The PAC example above, with two phase-locked sinusoids,
elevated power at the frequencies of the two sinusoids, and
visible modulation of the amplitude of the faster sinusoid by
the phase of the slower one, is considered the “classical” form
of PAC. However, significant PAC may occur without significant peaks in the power spectral density or clear periodic
modulations in the envelope of the signal. In these instances,
PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
␶m
dV
dt
⫽ EL ⫺ V ⫺ rmgsra共V ⫺ EK兲 ⫹ RmIin
␶sra
dgsra
dt
⫽ ⫺gsra
I共 t兲 ⫽ Cm
dV共t兲
dt
The equation parameters were leakage potential (EL) ⫽ ⫺65 mV;
membrane time constant (␶m) ⫽ 10 ms; membrane resistance (Rm) ⫽
10 M⍀; potassium reversal potential (Ek) ⫽ ⫺70 mV; spike-rate
adaptation time constant (␶sra) ⫽ 100 ms; spike-rate adaptation conductance (rm⌬gsra) ⫽ 0.06; neuron threshold voltage (VT) ⫽ ⫺54 mV;
post-action potential reset voltage (Vreset) ⫽ ⫺80 mV; and capacitance (Cm) ⫽ ␶m/Rm.
To produce periodic bursting, for each neuron a fixed Iin (from 3 to
14 pA) was applied at 1-ms intervals throughout the burst duration at
the beginning of each burst cycle.
When membrane voltage V exceeded VT, the neuron produced a
spike, rmgsra was incremented by rm⌬gsra, and the potential was reset
to Vreset.
Synchronization calculation. The synchronization parameter used
to quantify the degree of cell firing alignment was calculated as
follows. Currents were calculated for each neuron in the population
using the specified input current and burst parameters. For this study,
all neurons in a particular population had the same mean interburst
rate, mean burst duration, and input current. Desynchronization was
modeled by delaying subpopulations of the neurons by user-selected
mean offsets (“synchronization offset”; must be ⬍ interburst rate). In
this study, subpopulations within a population were delayed by
multiples of a single synchronization offset. For example, if three
subpopulations were to be modeled with a synchronization offset of 5
ms, the currents from the first subpopulation of neurons start with
mean time t ⫽ ⫺10 ms, the currents from the second at mean time
t ⫽ ⫺5 ms, and the currents from the third at mean time t ⫽ 0 ms. This
allowed calculation of a “synchronization factor” for each subpopusynchronization offset
lation, defined as 1 ⫺
. The composite synchrointerburst rate
nization was then defined as the product of the subpopulation synchronization factors. See Table 1 for example synchronization factor
calculations for a set of five neuron subpopulations. Note that, while
the synchronization factor was useful for selecting modeling parameters in this study and generally correlated with increasing PAC (see
Fig. 2K), the measure is not a precise calculation of synchronization.
For large numbers of neurons with complex dynamics, coherence
Table 1. Synchronization factors for five subpopulations of
neurons
Interburst Period, ms
Synchronization Offset
40
60
80
100
0
3
5
7
9
Composite (1 of each offset)
1
0.426541
0.205078
0.098536
0.013853
0.185
1
0.5814
0.3819444
0.2347704
0.1309
0.3705
1
0.671629
0.499878
0.360879
0.250622
0.49268
1
0.730169
0.5814
0.454926
0.348625
0.599247
between neurons or other measures should be used to evaluate the
degree of synchronization.
Forming the LFP. The single-cell currents were summed to form
the LFP with the point current source model (Bedard et al. 2004; Koch
and Segev 1998).
V共 r兲 ⫽
1
Ij
4␲␴ 兺
j ⱍ r ⫺ r jⱍ
where ␴ is the electrical conductivity of the extracellular medium, r is
the location of the measured LFP, and rj is the location of the jth
single cell. For this study, the electrical conductivity was assumed to
be a constant, non-frequency-dependent 0.35 S/m and each neuron
was assumed to be located 500 ␮m from the recording electrode. The
output of the model was low-pass filtered (⬍500 Hz), sampled at
1,000 Hz, and then input to the cross-frequency-coupling analysis
software where the PAC was calculated as described in the next
section.
Calculation of phase-amplitude coupling and power measures. All
signals were band-pass filtered between 3 Hz and 500 Hz and then
downsampled to 1,000 Hz. Power spectral densities (psd) were calculated with the standard MATLAB Welch spectrogram. A 60-Hz
FIRLS filter (MATLAB filtfilt) with a bandwidth of 4 was applied to
the parkinsonian animal data to remove residual line noise before psd
and PAC calculations.
PAC was calculated with EEGfilt subroutines with a Morlet wavelet and the MI measure proposed by Tort et al. (2010). Briefly, the
LFPs were filtered into 2-Hz bands from which the amplitude and
phase were extracted. The coupling between bands was then quantified by calculating the average of the amplitudes in each band from 50
to 300 Hz that co-occurred with the phase in each band from 3 to 50
Hz. The MI measure was used to assign a single value to the degree
of coupling by comparing the phase-amplitude quantification curve to
a uniform distribution (the expected distribution is uniform if no
coupling is present).
Addition of symmetrical periodic artifact. Four symmetrical periodic artifacts with 1-ms pulse widths were tested to evaluate the
effects of periodic signals on the PAC map. In the first two experiments, a 20-␮A, 143-Hz symmetrical pulsed current and a 20-␮A,
125-Hz symmetrical pulsed current were added to simulated bursting
currents. In the third experiment, a 250-Hz pulsed signal was added to
an LFP recorded from a parkinsonian primate. The magnitude of the
pulsed signal was set equal to 1 standard deviation of the magnitude
distribution from the primate LFP (z score ⫽ 1). In the fourth
experiment, a 100-Hz pulsed signal was added to an LFP recorded
from a mouse with parkinsonism. The pulsed signal magnitude was
set to one-fourth of the standard deviation of the mouse LFP magnitude distribution. To examine the feasibility of recovering the masked
PAC by filtering out the stimulus frequency, notch filters were applied
at the stimulus frequency (100 Hz) and its next higher harmonic (200
Hz) for the fourth example. The procedures used to record the
experimental data are described below.
Experimental procedures. All experimental procedures were conducted in accordance with the Guide for the Care and Use of
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for each burst cycle was calculated as shown below. A user-specified
fixed incremental input current was injected into the model at 1-ms
intervals for a burst duration (width) drawn from a normal distribution. The current injections were repeated after a burst cycle time
period (referred to as the interburst period; also drawn from a normal
distribution). The burst cycles were repeated until the desired epoch
length was reached (⬎10 s). The means for the burst duration and
interburst period were specified by the user.
The individual neuron bursting patterns were combined with a
user-specified degree of synchronization to produce a composite
signal (see below for synchronization calculation). The composite
signals were low-pass filtered and sampled with the same filter (⬍500
Hz) and sampling rate (1,000 Hz) used for the analysis of the primate
and rodent recordings.
Simulated neuron firing calculation. The following neural firing
equations with spike-rate adaptation (sra) from Dayan and Abbott’s
theoretical neuroscience text were used to calculate each neuron’s
membrane potential, current, and spike firing (Dayan and Abbott
2001):
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PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
medial forebrain bundle 5 wk prior to recording are shown for
comparison purposes. Both mouse recordings were made while the
mice were awake but stationary during freely moving recording
sessions.
Parkinsonism was confirmed behaviorally in both the 6-OHDAinjected mouse and the MPTP-treated monkeys. The degree of parkinsonism in the mouse was assessed by calculating the distance
traveled and net number of rotations (in the direction ipsilateral to the
lesioned side) during biweekly video recording sessions. Monkey
motor signs such as bradykinesia, tremor, and freezing were assessed
biweekly and assigned component and overall motor scores reflecting
the degree of observed parkinsonism as described in detail in Devergnas et al. (2014).
Limitations of the methods. As with any synthetic or simulated
data, differences may exist between experimental recordings and the
data output by the model. In particular, the use of fixed regular current
application times and Gaussian burst parameters will not produce all
possible (and likely) bursting patterns. Gamma or other distributions
may provide more realistic results depending on the type and state of
neurons to be simulated. The use of a single incremental input current
rather than separate Na⫹, K⫹, Ca2⫹, and other currents limits the
shaping of the burst and may result in nonphysiological bursting.
RESULTS
The results show that synchronized single-cell bursting can
cause PAC and that certain characteristics of the resulting PAC
can be calculated from the burst parameters. To evaluate the
effects of varying burst and synchronization parameters, fixed
incremental input currents from 3 to 14 pA and mean burst
periods from 40 to 120 ms were tested. Standard deviations of
5–10 ms for each burst period and for each burst width were
also examined. Composite signals from five neuron populations with synchronization factors from 0.1 to 1.0 were simulated.
As expected, larger input currents increased the intraburst
rate (Fig. 2, A–D and I). The on/off burst periods generated a
slow oscillation at a frequency equal to the inverse of the burst
period. Thus the mean phase frequency for the resulting slow
oscillation (and the region of elevated PAC) was determined by
the simulated interburst rate. Increasing the burst period from
40 ms to 100 ms resulted in mean phase frequencies from 25
Hz down to 10 Hz (1/burst period) and shifted the PAC region
to the left (Fig. 2, E–H and J) accordingly. Increased synchronization of the simulated neurons resulted in increased PAC
magnitude (Fig. 2K).
Matching experimental data from parkinsonian animals.
The 10-pA input current for the simulated example in Fig. 3
resulted in a mean intraburst rate of 124 Hz, a rate that agrees
with previous results showing an increased intraburst firing rate
(⬎100 Hz) in STN cells in parkinsonian primates (Sanders et
al. 2013a).
The recorded parkinsonian animal LFPs and the simulated
bursting LFPs were unremarkable, with the main distinguishing feature being irregular high gamma (150 –300 Hz) power
(Fig. 3). The composite simulated signal from five populations
of bursting neurons with a sample rate of 1,000 Hz, a burst
period of 60 ms, an incremental input current of 10 pA, and an
across-population synchronization factor of 0.23 produced
LFPs with characteristics similar to the LFPs recorded from the
monkeys with moderate parkinsonism. The PAC patterns from
the simulated LFPs, while not identical to the patterns from the
recorded primate data (Fig. 3), clearly showed burst-driven
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Laboratory Animals (8th ed.), the PHS Policy on Humane Care and
Use of Laboratory Animals, and the American Physiological Society’s
“Guiding Principles for the Care and Use of Vertebrate Animals in
Research and Training” (updated 2014) and approved by the Emory
Animal Care and Use Committee. Every effort was made to minimize
the number of animals used and their discomfort.
The experimental data shown here were obtained from completed
studies with the permission of the researchers who collected the data
(see ACKNOWLEDGMENTS). No additional experiments were conducted
to obtain the data shown. Detailed surgical and experimental procedures for the primates are available in previous publications (Devergnas et al. 2014; Sanders et al. 2013b).
Animals. The rhesus monkeys (Macaca mulatta, 4 –5 kg) that were
used for these studies were housed under conditions of environmentally controlled protected contact housing, with free access to standard
primate chow, water, and supplemental fruit and vegetables. Before
the recording sessions, the animals were adapted to the laboratory
environment and trained to sit in a primate chair and permit handling
by the experimenter.
Male C57BL/6J mice (Jackson Labs) were housed with free access
to chow and water in environmentally controlled conditions with a
reversed 12:12-h light-dark cycle (lights on at 7 PM). Mice were
handled daily for 1 wk before surgery and habituated to the arena used
for freely moving recording in the study. Video was recorded for the
purpose of baseline movement assessment.
Surgical procedures. Monkeys underwent aseptic surgery under
isoflurane anesthesia (1–3%) during which they were implanted with
EEG recording electrodes above M1 and two stainless steel recording
chambers above the STN as described in detail in Devergnas et al.
(2014).
Mice were anesthetized with isoflurane (3% for initial sedation,
then 1.5–2.0% delivered via nose cone throughout surgery), administered subcutaneous buprenorphine (0.1 mg/kg), and placed in a
stereotaxic frame. Ophthalmic ointment was applied to prevent corneal dehydration, and a heating pad was used to maintain body
temperature at 37°C. Anesthesia levels were adjusted as needed to
ensure ongoing deep anesthesia (assessed by visual monitoring and
toe pinches). An incision was made to allow 0.9-mm-diameter
craniotomies above the medial forebrain bundle, M1, and STN. One
microliter of 6-hydroxydopamine (6-OHDA) was injected in the
medial forebrain bundle (⫺1.2 AP, ⫺1.2 ML, ⫺4.75 DV) with the
procedure described in Cenci and Lundblad (2007). Four 50-␮m
tungsten microwires were inserted; one pair was inserted in M1 (2.0
AP, ⫺1.56 ML, ⫺1.0 DV) and one pair in STN (⫺1.76 AP, ⫺1.56
ML, ⫺4.2 DV). An additional wire was attached to a skull screw
above the cerebellum to serve as an instrument ground. All wires were
then attached to a Neuralynx EIB-16 with gold pins and affixed to the
skull with dental cement. Immediately after surgery, Bacitracin ointment with pramoxine was applied to the region around the incision to
prevent infection and alleviate pain. Mice were weighed twice daily
and assessed for overall health and comfort for 1 wk after surgery.
Subcutaneous buprenorphine injections (0.1 mg/kg) were administered (up to twice daily) if the animal showed discomfort.
Recordings. The primate data were recorded acutely with tungsten
microelectrodes (0.5–1.0 M⍀ at 1 kHz) inserted through the chambers
into the STN of head-fixed monkeys during awake periods. The
monkeys were made progressively parkinsonian with weekly 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) injections (0.2– 0.6
mg/kg im) as described in Sanders et al. (2013b) and Devergnas et al.
(2014). Data were collected from each monkey before MPTP treatment, thus allowing each monkey to serve as its own control. Awake
periods were assessed by visual analysis of videos and EEG
recordings.
Mouse recordings were made with two 1-M⍀ tungsten electrodes
chronically implanted in the left STN and two 0.5- to 1.0-M⍀
electrodes in left M1 (20 kHz sample rate). Examples from one
control mouse and one mouse injected with 6-OHDA in the left
PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
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Fig. 2. Simulated bursting and resulting PAC. A–D: effect of varying incremental input current. E–H: effect of varying interburst period. I–K: summary of effects
of varying incremental input current, mean interburst period, and synchronization factor. A: spiking pattern for a single burst cycle with incremental input current
of 5 pA (interburst period of 76 ms and SD of 10 ms). B: PAC map for single neuron with parameters specified in A. C: spiking pattern for a single burst cycle
with incremental input current of 6 pA. D: PAC map for single neuron with parameters specified in C. E: 10-s output from a single cell with interburst period
of 40 ms. F: PAC map for cell specified in E. G: 10-s output from a single cell with mean interburst period of 80 ms. H: PAC map for cell specified in G. I:
mean firing rate as a function of incremental input current for a cell with mean interburst period of 60 ms. J: mean phase frequency at region of highest (peak)
PAC. K: mean PAC magnitude as a function of synchronization factor for 100 cells phasically firing (bursting) with periods synchronized about 5 evenly spaced
offsets (offset interval in ms shown in parentheses), all with mean interburst period of 60 ms and incremental input current of 10 pA. Red dashed lines indicate
the simulation parameters that produced the best match to the parkinsonian primate LFPs and PAC map. Note: all standard deviations are 5 ms unless otherwise
specified.
PAC with similar magnitude centered at the same amplitude
and phase frequencies. The LFPs and PAC maps from the
parkinsonian mice, with their slower phase frequency and
visible oscillatory characteristics (possibly indicating more
synchronization), were simulated with burst firing having a
period of 120 ms, an incremental input current of 8 pA, and a
synchronization factor of 0.3.
Effect of adding symmetrical periodic signals. As described
in MATERIALS AND METHODS, four examples were explored to
evaluate the effect of adding small symmetrical pulsed signals
to LFPs. The first example added a 20-␮A, 143-Hz symmetrical pulsed current to currents from five bursting cells, each
with a 14-pA incremental input current and an interburst period
of 80 ms, with a synchronization factor of 0.2. The second
example added a 20-␮A, 125-Hz symmetrical pulsed current to
currents from five bursting cells, each with a 14-pA incremental input current and an interburst period of 80 ms, with a
synchronization factor of 0.36. The 20-␮A current was simulated as a point source located 127 mm from the electrode,
while the bursting cells were point sources located 500 ␮m
from the electrode. The currents were summed with the conductivity value and the equations specified in MATERIALS AND
METHODS. This small symmetrical pulsed current masked the
previously visible PAC at the primary frequencies and their
harmonics (Fig. 4).
In the third example, a 250-Hz symmetrical pulsed signal
was added to a 10-s-epoch LFP collected from the STN of a
parkinsonian primate. For this experimental data case, since the
input currents were unknown, the magnitude of the pulsed
signal was set equal to 1 standard deviation of the primate LFP
distribution (z score of 1). The small 250-Hz pulsed signal
masked the previously visible PAC in a large band about 250
Hz in the parkinsonian primate LFP.
The fourth example shows the effect of adding a 100-Hz
pulsed signal to a 10-s-epoch LFP collected from the STN of
a 6-OHDA mouse (Fig. 5). The small 100-Hz signal masked
the previously visible PAC at 100 Hz and also at the 200 Hz
harmonic frequency. These examples show that the addition of
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Volts
0
-0.02
0.02
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80
Time (milliseconds)
E
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200
Mean Peak PAC (x10-2)
10
Amplitude Frequency (Hz)
-0.08
0
D
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Amplitude Frequency (Hz)
Volts
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C
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Amplitude Frequency (Hz)
0.02
250
Volts
0.04
Volts
B
Amplitude Frequency (Hz)
A
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2
50
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1.5
0
µV
150
1
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-50
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µV
0
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x 10-3
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2
0
-2
500
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50
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Frequency
600
Number of ISIs
zscore of voltage
6
400
60
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7
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300
Frequency
Time (ms)
Phase Frequency (Hz)
300
600
50
500
500
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100
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0
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Interspike Interval (ms)
80
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100
1
10
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0
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Phase Frequency (Hz)
1600
2400
3200
0
4000
0
Time (milliseconds)
x 10-3
8
300
800
20
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Interspike Interval (ms)
4
700
6
5
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150
3
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600
Number of ISIs
250
zscore of voltage
7
2
0
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10
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Phase Frequency (Hz)
400
300
200
100
1
0
500
-4
0
800
1600
2400
3200
4000
Time (milliseconds)
0
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Interspike Interval (ms)
Fig. 3. PAC maps, voltage traces, power spectral densities (psds), and interspike interval (ISI) histograms from normal and parkinsonian sources. Top row: PAC
map, LFP, and psd from the subthalamic nucleus (STN) of a normal mouse. Second row: PAC map, LFP, and psd from the STN on the lesioned side of a unilateral
6-hydroxydopamine (6-OHDA) mouse [lesion histologically confirmed and behavior measured at net 10 ipsilateral rotations/min; note the irregular broadband
gamma frequencies (150 –300 Hz) in the psd]. Third row: PAC map from LFP recorded from a monkey with mild parkinsonism, corresponding LFP voltage trace,
and ISI histogram (inset shows histogram for a normal monkey). Bottom row: elevated PAC in simulated synchronized bursting, simulated LFP, and ISI
histogram for LFP data (bimodal histogram with large peak for ISIs ⬍ 20 ms indicates bursting). Simulation parameters: 60-ms burst period, 10-pA incremental
input current, 100 neurons with 5 primary offsets, synchronization factor of 0.23.
a symmetrical periodic signal can reduce the total PAC at and
near the stimulus frequency and also at its harmonic frequencies, obscuring PAC that would otherwise be present.
Application of notch filters at the stimulus frequency (100 Hz)
and its next higher harmonic (200 Hz) for the fourth example
allowed partial recovery of the PAC signal. However, the result-
ing PAC pattern changed and was no longer clearly recognizable
as true PAC because of distortion across the phase axis (Fig. 5).
DISCUSSION
The simulation results in this report are the first to show that
synchronized single-cell bursting can cause PAC and that
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Amplitude Frequency (Hz)
x 10-3
Amplitude Frequency (Hz)
800
Time (ms)
Phase Frequency (Hz)
Amplitude Frequency (Hz)
600
60
Counts
Amplitude Frequency (Hz)
x 10-3
250
Power Spectrum Magnitude (dB)
PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
Power Spectrum Magnitude (dB)
1592
PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
1593
12
10
200
8
150
6
4
100
2
30
40
50
0
-0.5
-1
0
20
Phase Frequency (Hz)
Amplitude Frequency (Hz)
200
0.02
150
0.015
0.01
100
0.005
50
20
30
40
50
0
-2
400
800
1200
1600 2000
Time (milliseconds)
Amplitude Frequency (Hz)
zscore of voltage
2
6
150
4
100
2
10
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20
0.5
0
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20
40
x 10-4
9
8
250
7
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1
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Phase Frequency (Hz)
50
60
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0.025
200
0.02
0.015
150
0.01
100
0.005
50
10
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20
Time (milliseconds)
300
40
250
1
-1
0
30
Phase Frequency (Hz)
125 Hz
Phase Frequency (Hz)
4
80
8
200
30
40
50
Phase Frequency (Hz)
x 10-4
300
4
8
7
250
6
200
5
4
150
3
2
100
1
10
20
30
40
50
Phase Frequency (Hz)
2
0
-2
-4
0
400
800
1200
1600 2000
Time (milliseconds)
Fig. 4. Masking effect of symmetrical periodic artifacts. Top: simulated effect of adding a 143-Hz pulsed-current stimulus from a 20-␮A source located 127 mm
away from the electrode. Left: PAC map from LFP simulated with 100 neurons bursting with periods synchronized relative to 5 primary offsets, 14-pA
incremental input current, interburst period of 80 ms, and a synchronization factor of 0.2. Center: 143-Hz pulsed signal with 1-ms pulse width. Right: PAC map
for summed currents from bursting signal and pulsed stimulus. Note how a wide section of the PAC is masked at the primary frequency (143 Hz) as well as at
the harmonics above and below (286 Hz and 71.5 Hz). Middle: simulated effect of 125-Hz pulsed-current stimulus. Left: PAC map from simulated LFP with
14-pA incremental input current, interburst period of 80 ms, and a synchronization factor of 0.36. Center: 125-Hz pulsed signal with 1-ms pulse width. Right:
PAC map for summed currents from LFP and pulsed stimulus. Bottom: parkinsonian primate data recorded from STN. Left to right: LFP, corresponding PAC
map, masking effect in PAC map due to addition of a 250-Hz pulsed signal with magnitude equal to 1 standard deviation of the LFP, and LFP with pulsed signal
added.
measurable characteristics of the resulting PAC are directly
related to the burst parameters. This suggests that population
bursting characteristics may be estimated from PAC, an important finding since PAC is calculated from LFPs, which are
generally more straightforward to record than single-cell firing
patterns.
These results are also the first to show that the presence of
a periodic stimulus occurring at common therapeutic stimulation frequencies and voltages/currents may reduce the
apparent PAC without inducing any physiological changes.
This is a significant finding since PAC has become an
important clinical measure for Parkinson’s disease and has
been proposed as a feedback signal for closed-loop DBS
(Gunduz et al. 2015). If the DBS stimulus artifact causes the
PAC signature to be reduced without any therapeutic effect,
it may not be a useful measure for patients undergoing DBS
treatments, much less an appropriate closed-loop feedback
signal.
However, apart from its use during stimulation, PAC may be
a particularly effective analysis tool for understanding neural
signals because of the nature and structure of neural activity.
The oscillatory tendency of neural firing, the modulation of
interconnected cells by their afferents, and the tendency for
bursting to be associated with peaks or troughs of oscillating
potentials in the brain are all factors that result in field potentials composed of superimposed and interacting oscillations.
The results in this study specifically show that PAC, in
addition to indicating potential modulation of one sinusoid by
another, can provide a measure of the amount and characteristics of bursting in a signal. For example, in the simulated
bursting signal, increased PAC magnitude corresponded to increased synchronization as shown in Fig. 2K. Additionally, the
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0.025
Normalized Signal Magnitude
0.03
10
60
10
Time (milliseconds)
250
-4
0
40
12
250
Amplitude Frequency (Hz)
20
0.5
Amplitude Frequency (Hz)
10
143 Hz
1
300
zscore of voltage
14
250
Amplitude Frequency (Hz)
x 10-3
16
Normalized Signal Magnitude
Amplitude Frequency (Hz)
x 10-3
300
PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
1
250
0.8
200
0.6
150
0.4
100
0.2
10
20
30
40
50
300
9
7
6
200
5
4
150
3
2
100
1
10
Phase Frequency (Hz)
20
30
40
50
300
0.9
0.7
0.5
0.2
0
mV
0.1
mV
0.1
0
-0.1
Time (ms)
800
1000
-0.2
20
30
40
50
0
Phase Frequency (Hz)
0.1
600
0.1
10
0.2
400
0.3
100
0.2
200
0.4
150
0.2
-0.2
0
0.6
200
Phase Frequency (Hz)
-0.1
0.8
250
0
-0.1
0
200
400
600
800
1000
-0.2
Time (ms)
0
200
400
600
800
1000
Time (ms)
Fig. 5. Masking effect of periodic pulsed signal added to mouse LFP and attempted recovery of PAC using filters at the artifact and harmonic frequencies. Top,
left to right: PAC from parkinsonian mouse data recorded from STN, masking effect due to addition of a 100-Hz pulsed signal with magnitude 1/4␴ of the LFP.
Note that notch filtering at 100 Hz and 200 Hz allowed partial retrieval of the PAC but altered its pattern (the PAC phase frequency is no longer distinct from
0° phase). Bottom: LFPs corresponding to PAC maps at top. Left to right: original STN LFP from parkinsonian mouse, LFP with simulated stimulus added, and
LFP after notch filtering. Note that the PAC maps vary significantly despite minimal changes in the LFP.
mean PAC phase frequency for the simulated bursting was the
inverse of the mean interburst period. These results suggest that
PAC maps may be useful for detection and characterization of
bursting synchrony in measured LFPs with unknown underlying
signal dynamics. In future work, it will be of interest to see
whether different types of physiological bursting such as Ttype calcium channel bursts, hippocampal bursts, and pathological bursting in neurological diseases can be characterized
and detected with PAC measures.
Of course, if single-unit spiking data from individual neurons are available, the type of bursting present in the neurons
can be determined directly. However, in chronic electrode
implants, single units can be difficult to record from reliably, so
an additional measure of bursting from LFP signals would
likely be beneficial. Additionally, since single-unit spike data
may be recorded from only a few local units, these burst
measures may not reflect the nature of the population bursting
as well as bursting measures such as PAC that are calculated
from LFPs.
The dramatic masking effects that may occur because of the
addition of symmetrical periodic signals must be considered
when interpreting electrophysiological effects of neuromodulation, such as DBS, since the presence of a small periodic
stimulus artifact may reduce the apparent PAC without inducing any physiological changes. The shorter pulse width of
typical DBS (⬍100 ␮s) may lessen the effect shown in the
simulation (1-ms pulse width). However, it is feasible that the
typical 4-V DBS signal could induce a 20-␮A current, even
with a very small pulse width. For this reason, PAC measures
may not be practical for closed-loop neuromodulation unless
complete isolation from the stimulus artifact can be ensured.
Note that, since stimulus or other symmetrical periodic artifacts may be difficult to observe in PAC maps, inspection of
the psd to assist in identifying potential problematic frequency
artifacts and harmonics is recommended.
This study does not address other issues that may alter
cross-spectral measures, such as the variability of spectral
results between users caused by the wide variety of filtering
and smoothing processes that may be applied to the raw signal.
Clearly, these factors can have a large effect on the resulting
power and PAC measures and can induce artifacts and falsely
elevate or mask aspects of a signal. Because of the potential for
false and variable results in PAC analysis, caution should be
exercised in interpreting results and signal processing experts
should be involved in the analysis and review of results. Also,
continued conversations regarding best methods and data sharing will be important to ensure that PAC results in the literature
are sound and can be replicated.
The simulation in this study provides evidence that observed
PAC may be related to synchronized bursting in LFPs. The
simulation does not give insight into the physiological factors
that might be behind the synchronized bursting. However, the
PAC measures related to the interburst and intraburst rates and
the degree of synchronization in the bursting may provide a
useful starting point for further exploration with more detailed
models (e.g., Rubin and Terman 2004) that consider a full
range of ionic currents, along with afferent and efferent projections, receptor densities, and other cellular and molecular
properties.
Conclusions. The simulation and experimental results in this
report are the first to show that 1) synchronized single-cell bursting can cause physiologically realistic PAC and 2) the presence of
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mV
8
250
0
0
x 10-3
1
x 10-4
Amplitude Frequency (Hz)
Amplitude Frequency (Hz)
x 10-3
300
Amplitude Frequency (Hz)
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PAC, A BURST MEASURE, IS MASKED BY PERIODIC PULSES
a periodic stimulus occurring at common therapeutic stimulation
settings may reduce apparent PAC without inducing any therapeutic benefits. Specifically, PAC patterns similar to those measured in recorded data from parkinsonian primates and mice were
successfully simulated by summing currents from synchronized
bursting neurons. Changes in the simulated intraburst and interburst rates and in the degree of synchronization were shown to
predictably impact the PAC map, suggesting that, in some cases,
underlying spiking activity may be characterized from LFP PAC
maps. Finally, the results suggest that caution is advised when
interpreting PAC maps for neuromodulation applications such as
closed-loop DBS since a small symmetrical periodic pulse can
create a wide null in the PAC heat map, potentially masking
evidence of oscillatory interactions and thus giving the false
impression that a physiological change has occurred.
The author thanks Nancy Kopell very much for listening to the initial ideas
for the paper and giving recommended directions. The parkinsonian monkey
data excerpts were collected by Annaelle Devergnas and used with permission.
Mouse experiments and data collection were performed by the author in Dieter
Jaeger’s lab.
GRANTS
This study was supported by National Institute of Neurological Disorders
and Stroke Grant T32 NS-007480.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
AUTHOR CONTRIBUTIONS
Author contributions: T.H.S. conception and design of research; T.H.S.
performed experiments; T.H.S. analyzed data; T.H.S. interpreted results of
experiments; T.H.S. prepared figures; T.H.S. drafted manuscript; T.H.S. edited
and revised manuscript; T.H.S. approved final version of manuscript.
REFERENCES
Bedard C, Kroger H, Destexhe A. Modeling extracellular field potentials and
the frequency-filtering properties of extracellular space. Biophys J 86:
1829 –1842, 2004.
Berger H. Über das Elektrenkephalogramm des Menschen. Eur Arch Psychiatry Clin Neurosci 94: 16 – 60, 1931.
Bergman H, Wichmann T, Karmon B, DeLong MR. The primate subthalamic nucleus. II. Neuronal activity in the MPTP model of parkinsonism. J
Neurophysiol 72: 507–520, 1994.
Cannon J, McCarthy MM, Lee S, Lee J, Börgers C, Whittington MA,
Kopell N. Neurosystems: brain rhythms, and cognitive processing. Eur J
Neurosci 39: 705–719, 2014.
Canolty RT, Edwards E, Dalal SS, Soltani M, Nagarajan SS, Kirsch HE,
Berger MS, Barbaro NM, Knight RT. High gamma power is phase-locked
to theta oscillations in human neocortex. Science 313: 1626 –1628, 2006.
Cenci MA, Lundblad M. Ratings of L-DOPA-induced dyskinesia in the
unilateral 6-OHDA lesion model of Parkinson’s disease in rats and mice.
Curr Protoc Neurosci 2007: 9 –25, 2007.
Connolly AT, Jensen AL, Baker KB, Vitek JL, Johnson MD. Classification
of pallidal oscillations with increasing parkinsonian severity. J Neurophysiol
114: 209 –218, 2015.
Dayan P, Abbott LF. Theoretical Neuroscience: Computation and Mathematical Modeling of Neural Systems. Cambridge, MA: MIT Press, 2001.
de Hemptinne C, Ryapolova-Webb ES, Air EL, Garcia PA, Miller KJ,
Ojemann JG, Ostrem JL, Galifianakis NB, Starr PA. Exaggerated
phase-amplitude coupling in the primary motor cortex in Parkinson disease.
Proc Natl Acad Sci USA 110: 4780 – 4785, 2013.
de Hemptinne C, Swann NC, Ostrem JL, Ryapolova-Webb ES, San
Luciano M, Galifianakis NB, Starr PA. Therapeutic deep brain stimula-
tion reduces cortical phase-amplitude coupling in Parkinson’s disease. Nat
Neurosci 18: 779 –786, 2015.
Devergnas A, Pittard D, Bliwise D, Wichmann T. Relationship between
oscillatory activity in the cortico-basal ganglia network and parkinsonism in
MPTP-treated monkeys. Neurobiol Dis 68: 156 –166, 2014.
Gajraj RJ, Doi M, Mantzaridis H, Kenny GN. Analysis of the EEG
bispectrum, auditory evoked potentials and the EEG power spectrum during
repeated transitions from consciousness to unconsciousness. Br J Anaesth
80: 46 –52, 1998.
Gatev P, Darbin O, Wichmann T. Oscillations in the basal ganglia under
normal conditions and in movement disorders. Mov Disord 21: 1566 –1577,
2006.
Gunduz A, Morita H, Rossi PJ, Allen WL, Alterman RL, Bronte-Stewart
H, Butson CR, Charles D, Deckers S, de Hemptinne C, DeLong M,
Dougherty D, Ellrich J, Foote KD, Giordano J, Goodman W, Greenberg
BD, Greene D, Gross R, Judy JW, Karst E, Kent A, Kopell B, Lang A,
Lozano A, Lungu C, Lyons KE, Machado A, Martens H, McIntyre C,
Min HK, Neimat J, Ostrem J, Pannu S, Ponce F, Pouratian N, Reymers
D, Schrock L, Sheth S, Shih L, Stanslaski S, Steinke GK, Stypulkowski
P, Tröster AI, Verhagen L, Walker H, Okun MS. Proceedings of the
Second Annual Deep Brain Stimulation Think Tank: What’s in the Pipeline.
Int J Neurosci 125: 475– 485, 2015.
Hammond C, Bergman H, Brown P. Pathological synchronization in Parkinson’s disease: networks, models and treatments. Trends Neurosci 30:
357–364, 2007.
Igarashi KM, Lu L, Colgin LL, Moser MB, Moser EI. Coordination of
entorhinal-hippocampal ensemble activity during associative learning. Nature 510: 143–147, 2014.
Jensen O, Colgin L. Cross-frequency coupling between neuronal oscillations.
Trends Cogn Sci 11: 267–269, 2007.
Koch C, Segev I (Editors). Methods in Neuronal Modeling (2nd ed.).
Cambridge, MA: MIT Press, 1998.
Lewis LD, Weiner VS, Mukamel EA, Donoghue JA, Eskandar EN,
Madsen JR, Anderson WS, Hochberg LR, Cash SS, Brown EN, Purdon
PL. Rapid fragmentation of neuronal networks at the onset of propofolinduced unconsciousness. Proc Natl Acad Sci USA 109: E3377–E3386,
2012.
Lopez-Azcarate J, Tainta M, Rodriguez-Oroz MC, Valencia M, Gonzalez
R, Guridi J, Iriarte J, Obeso JA, Artieda J, Alegre M. Coupling between
beta and high-frequency activity in the human subthalamic nucleus may be
a pathophysiological mechanism in Parkinson’s disease. J Neurosci 30:
6667– 6677, 2010.
Miller WC, DeLong MR. Altered tonic activity of neurons in the globus
pallidus and subthalamic nucleus in the primate MPTP model of parkinsonism. In: The Basal Ganglia II, edited by Carpenter MB, Jayaraman A. New
York: Plenum, 1987, p. 415– 427.
Pfurtscheller G, Aranibar A. Event-related cortical desynchronization detected by power measurements of scalp EEG. Electroencephalogr Clin
Neurophysiol 42: 817– 826, 1977.
Rubin JE, Terman D. High frequency stimulation of the subthalamic nucleus
eliminates pathological thalamic rhythmicity in a computational model. J
Comput Neurosci 16: 211–235, 2004.
Sanders TH, Clements MA, Wichmann T. Parkinsonism-related features of
neuronal discharge in primates. J Neurophysiol 110: 720 –731, 2013a.
Sanders TH, Devergnas A, Wichmann T, Clements M. Canonical correlation to estimate the degree of parkinsonism from local field potential and
electroencephalographic signals. Int IEEE/EMBS Conf Neural Eng 2013:
6695896, 2013b.
Tort AB, Komorowski R, Eichenbaum H, Kopell N. Measuring phaseamplitude coupling between neuronal oscillations of different frequencies. J
Neurophysiol 104: 1195–1210, 2010.
Tort AB, Komorowski R, Manns JR, Kopell NJ, Eichenbaum H. Thetagamma coupling increases during the learning of item-context associations.
Proc Natl Acad Sci USA 106: 20942–20947, 2009.
van der Meij R, Kahana M, Maris E. Phase-amplitude coupling in human
electrocorticography is spatially distributed and phase diverse. J Neurosci
32: 111–123, 2012.
Weiss B, Clemens Z, Bódizs R, Halász P. Comparison of fractal and power
spectral EEG features: effects of topography and sleep stages. Brain Res
Bull 84: 359 –375, 2011.
Wolf ME, Alavi A, Mosnaim AD. Posttraumatic stress disorder in Vietnam
veterans clinical and EEG findings; possible therapeutic effects of carbamazepine. Biol Psychiatry 23: 642– 644, 1988.
J Neurophysiol • doi:10.1152/jn.00801.2015 • www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.2 on June 18, 2017
ACKNOWLEDGMENTS
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