Boonstra, T.W.

Houweling, S.

Muskulus, M.

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Does Asynchronous Neuronal Activity Average out on a Macroscopic Scale?

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Does asynchronous neuronal activity average out on a macroscopic scale?

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Editor’sNote: These short, critical reviewsof recent papers in the Journal, written exclusively by graduate students orpostdoctoral
fellows, are intended to summarize the important findings of the paper andprovide additional insight and commentary. Formore
information on the format and purpose of the Journal Club, please see http://www.jneurosci.org/misc/ifa_features.shtml.
Does Asynchronous Neuronal Activity Average out on a
Macroscopic Scale?
TjeerdW. Boonstra,1,2 Sanne Houweling,3 andMichael Muskulus4
1School of Psychiatry, University of New South Wales, Randwick NSW 2031, Australia, 2Black Dog Institute, Randwick NSW 2031, Australia, 3Research
Institute MOVE, VU University Amsterdam, 1081 BT Amsterdam, The Netherlands, and 4Mathematical Institute, Leiden University, 2300 RA Leiden,
The Netherlands
Review of Miller et al.
The integration of related findings from
different levels of observation is a prereq-
uisite for a comprehensive understanding
of brain activity. Although a central ques-
tion in neuroscience, it remains unclear
how the neuronal dynamics observed by
single-cell recordings relates tomodalities
such as functional magnetic resonance
imaging and electroencephalography. It is
generally assumed that the occurrence of
recordable amplitude fluctuations in
macroscopic recordings reflects coherent
activation of a large number of neurons
synchronized at a specific frequency
(Singer, 1993). Electrophysiological re-
cordings, on the other hand, also exhibit a
slowly decreasing power law in the spectral
domain (Novikov et al., 1997) (cf. Fig. 1). It
has been argued that thebraindoesnot gen-
erate this complex 1/f noise directly, but in-
stead generates a large family of narrow
frequency-band oscillations whose spatio-
temporal integration gives rise to the ob-
served power law (Buzsa´ki, 2006).
The recent findings of Miller et al.
(2009) are important in this regard, since
the authors report a broadband power in-
crease during finger movements as ob-
tained by electrocorticography (ECoG). If
the validity of the employed method can
be confirmed, the spatial resolution of the
ECoG electrodes (2–7 mm) would chal-
lenge the above views. That is, such a short
time interval and small volume would
only allow integration over a limited
number of neural ensembles, and if these
ensembles generate narrow frequency-
bandoscillations, thismight not result in a
power-law distribution. The results of
Miller et al. (2009) therefore suggest that
the observed short-term macroscopic re-
sponses partially arise through increased
firing rate, i.e., neuronal rate coding, in-
stead of by the activity of locally synchro-
nized neuronal populations.
To discuss the findings of Miller et al.
(2009) in this light, we shortly describe the
background and the analysis of their ex-
periment. During movements, macro-
scopic recordings show characteristic
power decreases in the alpha (8–12 Hz)
and beta (13–30 Hz) frequency bands
over the sensorimotor cortex
(Pfurtscheller and Lopes da Silva, 1999).
The reduction in power is generally
thought to reflect desynchronization of
neuronal activity and cannot be directly
explained by increased neuronal firing
rate, as evidenced by microscopic record-
ings (Georgopoulos et al., 1982). Using
ECoG, an increase in gamma band (30–
100 Hz) was also reported during motor
responses (Crone et al., 1998). Compared
with the alpha and beta decrease, the in-
crease in gamma power was more local-
ized in time and somatotopically specific.
The neuronalmechanisms responsible for
generating activity in these different fre-
quency bands may be partly independent
and therefore occupy distinct functional
roles.
Miller et al. (2009) argue that this in-
crease is not specifically restricted to the
gamma frequency range, but rather is part
of a broadband increase in power with a
power-law distribution. They arrive at
this conclusion based on principal com-
ponent analysis (PCA) of ECoG record-
ings in 10 epileptic patients. Each had
subdural ECoG grids placed on the sur-
face of the brain overlying the motor cor-
tex. Participants were asked to move
fingers independently during 2 s move-
ment trials. Power spectral density was
calculated for each electrode from 1 s ep-
ochs centered at the time of maximum
flexion during each movement and inter-
mediate rests. The power spectral densi-
ties were mean centered independently
per frequency before applying the loga-
rithmic transform [Miller et al. (2009),
their supplemental Eq. 3] and then sub-
mitted to PCA for unsupervised (blind)
classification of different movement con-
ditions based on covariation of power at
different frequencies. The analysis resem-
bles partial least squares using a mean-
centering approach, but with one crucial
difference: covariances were not com-
puted between spectra of different trials
but on the transposed matrix, to “identify
Received April 29, 2009; revised May 28, 2009; accepted May 29, 2009.
Correspondence should be addressed to Tjeerd W. Boonstra, School of
Psychiatry, University of New South Wales, Black Dog Institute Building,
Hospital Road, Randwick NSW 2031, Australia. E-mail:
t.boonstra@unsw.edu.au.
DOI:10.1523/JNEUROSCI.2020-09.2009
Copyright©2009SocietyforNeuroscience 0270-6474/09/298871-04$15.00/0
The Journal of Neuroscience, July 15, 2009 • 29(28):8871–8874 • 8871
motifs ofmovement-related change in the
PSD [power spectral density].” Thereby,
the principal components correspond to
linear combinations of “spectral densi-
ties” instead of trials and/or conditions.
The main finding was that the first
principal component corresponds to a
broadband increase in power spectral
density, as reflected by nonzero frequency
element magnitudes (eigenvector coeffi-
cients), and the second and third modes
represent beta and alpha modulations
[Miller et al. (2009), their Fig. 1A,C–G].
These results were highly consistent over
subjects and electrodes as evidenced by an
almost identical mode separation [Miller
et al. (2009), their supplemental Fig. S4].
The projection weights in the first mode
weremirrored in the secondmode [Miller
et al. (2009), their Fig. 1B], reflecting a
simultaneous broadband power increase
and a decrease in the lower frequency
range during finger movements. The rel-
ative strength of the first principal mode
revealed separable individual finger so-
matotopy in all subjects and was more fo-
cally distributed than the second and third
modes, as reflected by the distribution of
projection weights over neighboring elec-
trodes [Miller et al. (2009), their Fig. 2,
Fig. 3, and supplemental Fig. S5]. To ad-
dress the relation between the obtained
principal components and the movement
trajectories, separately computed time-
resolved power spectral densities from
wavelet decomposition were projected
onto the first three eigenvectors. The re-
sulting time course of the first principal
component was correlated with finger po-
sition and was specific for individual dig-
its [Miller et al. (2009), their Fig. 2, Fig. 4].
The observed broadband power increase
might therefore be used as a macroscopic
measure to assess the activity of local cor-
tical populations.
These conclusions critically depend on
the specific application of PCA, and there
are severalmethodological considerations
that need to be addressed. First, applying
the logarithmic transform strongly affects
the signal’s distribution, but can be justi-
fied from a statistical perspective to stabi-
lize variance (Bartlett, 1947). The
decomposition of the transformed power
spectral densities is based on what the au-
thors refer to as “covariance matrix.” This
is, however, not a covariance measure but
a mere inner product, since the deviation
from the logarithmic transform of the
mean is used (as opposed to the mean of
the logarithms). In practice this means
that the first mode describes the baseline
(mean) of the (logarithms of) frequency-
wise relative power, a quantity that is dif-
ficult to interpret. A nonzero first mode,
as reported by Miller et al. (2009), might
thus result from the manner in which the
data are normalized. The linear combina-
tion of the “spectral densities” in an eigen-
mode corresponds to a nonlinear
combination of the spectral densities
when transformed back. Explicitly, con-
Figure 1. Spectral analysis of simple models of neuronal activity. A, Typical spike train generated by a single Poisson process. B, The interarrival times of spikes in the Poisson process are
independent of earlier interarrival times, i.e., the Poisson process is memoryless. This implies that spikes are not correlated in time, and the autocorrelation function of the signal is zero for positive
time lags. C, The power spectral density is the Fourier transform of the autocorrelation function and quantifies the amount of variance (“power”) per frequency component. For the Poisson process
the power spectral density is flat. D, Three Poisson processes (#1–3) with distinct intensities (“firing rates”) contribute to the total signal (bottom). Only one process is active at each time, as
determined by a hidden Markov process. The time series to be analyzed is the number of spikes in each fixed, small time interval along the time axis (interval length 2 ms, not shown). E, The
autocorrelation function of the spike count time series falls off slowly for increasing time lags and indicates long-range correlations. F, The estimated power spectral density of the spike count time
series seemingly follows a1/fpower-law, as assessedby fitting a line (dashed, slope1.8) in a double-logarithmic plot. Similar power lawbehavior is often seen in spectral densities from
electrophysiological recordings. Note that both power spectral densities have been smoothed by a moving average filter for easier visualization.
8872 • J. Neurosci., July 15, 2009 • 29(28):8871–8874 Boonstra et al. • Journal Club
sidering just two spectral densities P1( f)
and P2( f), the combination log(P1( f)/
( f))  log(P2( f)/( f)) results in
(P1( f)/( f))
(P2( f)/( f))
when expo-
nentiated. It is therefore not clear how the
proposed “principal spectral compo-
nents” relate to the original spectral den-
sities. Put differently, since the back
transformation is multiplicative, even
small projection weights ( and ) can
have a large influence on the composite,
projected spectral density. In combina-
tion with the omitted eigenvalues, the in-
terpretation of the reported principal
components is difficult, that is, it remains
unclear whether the first mode is neces-
sarily caused by a broadband increase in
power during finger movements.
Another issue is that the authors seem
to regard all samples as independent, al-
though theremight well be low-frequency
fluctuations. In fact, this would be a con-
sequence of the assumed power law be-
cause the autocorrelation function of such
a signal would exhibit long-range correla-
tions. As the timing of beta amplitude is
related to the movement frequency, high-
pass filtering (as the authors did) will not
exclude all movement-frequency related
effects. The analysis of Miller et al. (2009)
is insensitive to changes related to the
movement trajectory because their
method does not capture changes in
power relative to the onset of movement,
but rather uses an average of the total
power during a single time window
around each event. To overcome this lim-
itation, the authors used the above men-
tioned wavelet approach, but only after
the identification of spectral modes.
Other analyses might be better suited
to identify motifs of movement-related
power changes. For instance, PCA in the
frequency domain is well known for its
capacity to separate conditions based on
the principal components’ contribution
to the spectral content. This is related to
conventional PCA in the time domain in
that the frequency domain PCA can be
obtained by decomposing the covariance
matrix of the time series and their Hilbert
transforms (Brillinger, 1981). Thereby,
the cross-spectral densities of a multivar-
iate signal, which in the case ofMiller et al.
(2009) are the cross-spectra between all
combinations of epochs, are decomposed
by PCA for each frequency separately.
When transformed back into the time do-
main, this results in a set of time series,
called principal component series, whose
spectral densities are uncorrelated. In
contrast, when using PCA on power spec-
tral densities to blindly identify principal
components separating frequencies be-
tween conditions, the resulting decomposi-
tion cannot immediately be interpreted as
an actual spectrum. It would indeed be in-
teresting to submit the data of Miller et al.
(2009) to comparable analyses whose out-
comemeasures are readily interpretable.
Regardless of alternative methods,
genuine “power-law” increases are diffi-
cult to prove. Even when assuming that
the true spectral densities exhibit power-
law behavior, it is not enough to simply fit
a regression line to the logarithm of the
spectrum (Miller et al., 2007). At the very
least, one should search for self-similar
behavior in the time domain by calculat-
ing the Hurst exponent (see Table 1). The
authors mention that such a power spec-
tral distribution could be obtained from
an average of a large number of Poisson-
distributed neuronal activities without a
Table 1. Glossary of technical terms
Term Description
1/f noise A signal with a frequency content such that its power spectral density S(f) is proportional to a small power of the reciprocal of the frequency,
i.e., S(f) 1/f, where the exponent satisfies 0 3. Such signals are characteristic of complex processes without a preferred timescale,
e.g., long-range-dependent signals.
Continuous-time Markov chain A stochastic process X(t) in continuous time for which the conditional probability distribution at time t depends only on a finite number n of
values X(s1), X(s2), . . ., X(sn) from its past, s1 s2 . . . sn t. Such a process is also called a process with finite memory. The special case
where n 0 is a memoryless process.
Eigenvalue Principal component analysis decomposes the covariance matrix of a multivariate data set into an ordered set of eigenvectors along which the
data varies the most. The corresponding eigenvalues represent the variance of the data explained by each eigenvector.
Eigenvector coefficients The components of a principal mode (or eigenmode), i.e., of an eigenvector of the covariance matrix in principal component analysis.
Hilbert transform A tool from signal processing that shifts the phase factors of a bandpass-filtered signal. Adding the Hilbert transform as imaginary part to the
original signal results in an analytic signal, from which the instantaneous phase and the envelope of the signal can be calculated.
Hurst exponent The Hurst exponent H (where 1/2 H 1) quantifies the self-similarity of a signal. A stochastic process X(t) is called self-similar if X(at) has the
same probability distribution as aHX(t) for each a 0. Long-range-dependent signals (e.g., arising from a process with a 1/f power spectral
density) exhibit values of H close to 1.
Long-range dependence A stochastic process is long-range dependent if its autocorrelation function R() falls off slower than exponentially for large values of the lag .
Such processes have infinite memory and typically give rise to power spectral densities with a 1/f distribution.
Power spectral density The power spectral density S(f) is the Fourier transform of the autocorrelation function of a stochastic process X(t). It is closely related to the
Fourier transform of the signal (which does not exist if X(t) is long-range dependent) and quantifies the frequency content of X(t), i.e., S(f) is the
contribution to the variance (or power) of X(t) at the frequency f.
Projection weight The scalar product of the original signal with an eigenvector of the covariance matrix in principal component analysis, i.e., the coefficient the
eigenvector has when the signal is written as a linear combination of all eigenvectors. This quantifies the amount the eigenvector in question
contributes to the signal.
Wavelet decomposition A time–frequency representation of a signal X(t) that quantifies its local frequency content, similar to windowed Fourier analysis. The signal X(t)
is convolved with a family of short test signals that are rescaled and translated copies of a single mother signal (wavelet).
Boonstra et al. • Journal Club J. Neurosci., July 15, 2009 • 29(28):8871–8874 • 8873
preferred timescale, i.e., such that their
sum does not display frequency-specific
oscillations. We should remark here that
even simpler models could explain such
an observation.One example is aMarkov-
modulated Poisson process, in which dis-
tinct Poisson distributions are switched
on or off by a continuous-time Markov
chain in a purely random manner. For fi-
nite time series, such a nonstationarymix-
ture of stochastic processes exhibits
power-law behavior and seems to be long-
range dependent (Robert and Le Boudec,
1996) (cf. Fig. 1 for an example). This does
offer an alternative explanation for the
observed phenomenon that appears more
physiologically feasible: instead of a large
number of asynchronous neurons, a few
synchronized neural clusters may gener-
ate the signal in question.
To summarize, if the movement-
related power increases are broadband in
nature, as Miller et al. (2009) suggest, this
seemingly implies that ECoG can pick up
theeffectof asynchronousneuronal activity.
This contradicts common ideas about the
nature of electrophysiological signals (e.g.,
Buzsa´ki, 2006). Given the small time win-
dow (1 s) and the small spatial scale (1
cm) it is questionable that such averages
yield a broadband spectrum. We offer a
morerealistic alternative in the formofnon-
stationary behavior from a few synchro-
nized clusters. Although the possibility of
measuring asynchronous activity cannot be
excluded and remains intriguing,we believe
thatmore substantial evidence is neededbe-
fore that conclusion can be reached.
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Does asynchronous neuronal activity average out on a macroscopic scale?

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