The oscillating brain: Complex and reliable
Xi-Nian Zuoa, Adriana Di Martinoa, Clare Kellya, Zarrar E. Shehzada, Dylan G. Geea, Donald F. Kleina,b,d,
F. Xavier Castellanosa,b, Bharat B. Biswalb,c,⁎, Michael P. Milhama,⁎
aPhyllis Green and Randolph Cōwen Institute for Pediatric Neuroscience at the New York University Child Study Center, New York, NY, USA
bNathan Kline Institute for Psychiatric Research, Orangeburg, NY, USA
cDepartment of Radiology, University of Medicine and Dentistry of New Jersey, Newark, NJ, USA
dDepartment of Psychiatry, Professor Emeritus, College of Physicians and Surgeons, Columbia University, New York, NY, USA
a b s t r a c t a r t i c l ei n f o
Received 17 July 2009
Revised 18 August 2009
Accepted 17 September 2009
Available online 24 September 2009
The human brain is a complex dynamic system capable of generating a multitude of oscillatory waves in
support of brain function. Using fMRI, we examined the amplitude of spontaneous low-frequency oscillations
(LFO) observed in the human resting brain and the test–retest reliability of relevant amplitude measures. We
confirmed prior reports that gray matter exhibits higher LFO amplitude than white matter. Within gray
matter, the largest amplitudes appeared along mid-brain structures associated with the “default-mode”
network. Additionally, we found that high-amplitude LFO activity in specific brain regions was reliable across
time. Furthermore, parcellation-based results revealed significant and highly reliable ranking orders of LFO
amplitudes among anatomical parcellation units. Detailed examination of individual low frequency bands
showed distinct spatial profiles. Intriguingly, LFO amplitudes in the slow-4 (0.027–0.073 Hz) band, as
defined by Buzsáki et al., were most robust in the basal ganglia, as has been found in spontaneous
electrophysiological recordings in the awake rat. These results suggest that amplitude measures of LFO can
contribute to further between-group characterization of existing and future “resting-state” fMRI datasets.
© 2009 Elsevier Inc. All rights reserved.
The human brain is a complex dynamical system generating a
multitude of oscillatory waves. To characterize the diverse oscillatory
array, Buzsáki and colleagues proposed a hierarchical organization of
10 frequency bands they termed ‘oscillation classes,’ extending from
0.02 to 600 Hz (Buzsáki and Draguhn, 2004; Penttonen, 2003). They
noted that oscillations within specific classes have been linked with a
variety of neural processes, including input selection, plasticity,
binding, and consolidation (Buzsáki and Draguhn, 2004) as well as
cognitive functions including salience detection, emotional regula-
tion, attentionandmemory (Knyazev, 2007). Recently, low-frequency
oscillations (LFO; typically defined as frequencies b0.1 Hz) have
gained increased attention based on observations using fMRI
approaches and direct current coupled electroencephalographic
scalp recordings (Demanuele et al., 2007; Fox and Raichle, 2007).
Using these modalities, researchers have consistently identified
coherent spontaneous low-frequency fluctuations in the 0.01–0.1 Hz
range during both resting and active-task conditions that are thought
to reflect cyclic modulation of gross cortical excitability and long
distance neuronal synchronization (Balduzzi et al., 2008; Buzsáki and
Draguhn, 2004; Vanhatalo et al., 2004).
Despite the increased appreciation of spontaneous LFO in BOLD
fMRI resting state data (Fox and Raichle, 2007), the properties and
regional characteristics of spontaneous LFO rarely have been
examined directly. Instead, most resting state fMRI studies have
focused on mapping the spatial distribution of temporal correlations
among these spontaneous fluctuations. This is commonly referred to
as “resting-state functional connectivity” (RSFC). RSFC approaches
generate highly detailed maps of complex functional systems (Di
Martino et al., 2008b; Fox and Raichle, 2007; Margulies et al., 2007),
which have been shown to be both reliable over time (Deuker et al.,
2009; Shehzad et al., 2009) and reproducible across different data sets
(He et al., 2009). Using these approaches, numerous clinical studies
have already identified a variety of abnormalities in RSFC thought to
reflect pathophysiological processes (Broyd et al., 2009; Greicius,
2008; Seeley et al., 2009). Between-subject differences in RSFC
measures also correlate strongly with individual traits and behavioral
characteristics (Di Martino et al., 2009; Fox et al., 2007; Hampson
et al., 2006; Hesselmann et al., 2008; Kelly et al., 2008). Overall, RSFC
has proven to be a powerful and efficient tool for neuroimaging
studies of brain physiology and pathophysiology.
Although infrequently examined, other aspects of LFO observed
during rest may also prove informative. Of particular interest to the
present work is LFO amplitude information, which is commonly
overlooked as a potential index of spontaneous fluctuations during
NeuroImage 49 (2010) 1432–1445
⁎ Corresponding authors. M.P. Milham is to be contacted at 215 Lexington Avenue
14th Floor, New York, NY 10016, USA. Fax: +1 212 263 4675. B.B. Biswal, Suite 575, 30
Bergen Street, Newark, NJ 07103, USA. Fax: +1 973 972 7363.
E-mail addresses: email@example.com (B.B. Biswal), firstname.lastname@example.org
1053-8119/$ – see front matter © 2009 Elsevier Inc. All rights reserved.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/ynimg
rest. The few fMRI studies that have directly examined variations in
LFO amplitudes have found meaningful differences among brain
regions and among clinical populations. Around 15 years ago, the first
studies reported regional differences in LFO amplitude (Biswal et al.,
1995; Jezzard et al., 1993). Specifically, they observed amplitudes that
were higher in gray matter than in white matter. Kiviniemi et al.
(2003) found distinct LFO patterns across visual, auditory and
sensorimotor regions; LFO in visual regions had the highest magni-
tude. Severalrecentstudies locatedthe highestLFO amplitudeswithin
posterior structures along the brain's midline (Zang et al., 2007; Zou
et al. , 2008, 2009). The feasibility of detecting regional differences in
LFO amplitudes is also supported by a recent computational
simulation, in which the highest oscillatory amplitudes emerged in
cingulate and medial prefrontal cortices (Ghosh et al., 2008).
Beyond within-subject regional differences, recent work suggests
that LFO amplitudes differ in clinical populations compared to healthy
controls. Specifically, children with attention-deficit/hyperactivity
disorder (ADHD) showed increased LFO amplitude in anterior
cingulate and sensorimotor cortices and decreased LFO amplitude in
inferior frontal cortex (Zang et al., 2007). More recently, patients with
mesial temporal lobe epilepsy (Zhang et al., 2008) exhibited marked
to decreases in amplitude within the “default-mode” network (Raichle
et al., 2001), particularly in the posterior cingulate, medial frontal and
anterior cingulate cortices. Although these reports have yet to be
replicated, the detection of between-group differences in LFO ampli-
tude suggests that these measures may reflect stable trait properties.
While these studies imply that LFO amplitudes may represent a
potentially meaningful and stable property of the human brain,
several physiological and neural factors also can impact LFO
amplitudes. Biswal et al. (1997) observed that LFO amplitudes are
sensitive to carbon dioxide (CO2) levels (i.e., room air vs. 5% CO2),
with amplitudes suppressed by hypercapnea. Similarly, Wise et al.
(2004) demonstrated that a component of low frequency BOLD
fluctuations could reflect carbon dioxide-induced changes in cerebral
blood flow. Several studies have demonstrated task-related modula-
tion of LFO amplitude measures. During working memory task
performance, regions of the “default-mode” network (e.g., anterior
and posterior midline areas) exhibited task-related reductions in LFO
amplitude (Fransson, 2006). Duff et al. (2008) also demonstrated
task-related reductions in LFO amplitude measures, affecting both
task-activated regions (e.g., supplementary motor area, motor
cortices) and task-deactivated regions (e.g., posterior cingulate
cortex). Some studies suggest that the specific instructions (e.g., rest
with eyes open vs. rest with eyes closed) impact LFO amplitude in
regions such as visual cortex (McAvoy et al., 2008; Yang et al., 2007).
Similarly, LFO amplitude is sensitive to arousal level. Sleep produces
stage-dependent alterations in amplitude patterns (Fukunaga et al.,
2008; Horovitz et al., 2008; Picchioni et al., 2008). Degree of
anesthesia and sedation also affect LFO amplitude (Kiviniemi et al.,
2000; Kiviniemi et al., 2005). Finally, an increasing number of studies
have drawn attention to the potential artifactual contributions of
cardiac and respiratory-related processes to LFO amplitude measures
(Bianciardi et al., 2009; Birn et al., 2006; Chang et al., 2009; van
Buuren et al., 2009; Yan et al., 2009). In summary, the various
physiological and state factors that can impact regional measures of
LFO amplitude raise concerns regarding test–retest reliability.
The present work provides a comprehensive examination of two
Fast Fourier Transform (FFT)-based indices of LFO amplitude: (1)
amplitude of lowfrequency fluctuations (ALFF) (Zang et al., 2007) and
(2) fractional amplitude of low frequency fluctuations (fALFF) (Zou
et al., 2008). ALFF is defined as the total power within the frequency
range between 0.01 and 0.1 Hz. Although ALFF is effective at detecting
LFO fluctuations, the fluctuations detected can extend over 0.1 Hz,
particularly near major vessels (Zou et al., 2008), which are
characterized by widespread oscillations across both low and high
frequencies. In contrast, fALFF is defined as the total power within the
low-frequency range (0.01–0.1 Hz) divided by the total power in the
entire detectable frequency range, which is determined by sampling
rate and duration. As a normalized index of ALFF, fALFF can provide a
more specific measure of low-frequency oscillatory phenomena.
For both ALFF and fALFF, we (1) characterized their spatial
distributions and (2) investigated their test–retest reliabilities. Prior
work has consistently demonstrated gray vs. white matter distinc-
tions for ALFF and fALFF measures, with low-frequency fluctuations
being more detectable within gray matter (Jezzard et al., 1993; Biswal
et al., 1995; Zang et al., 2007; Zou et al., 2008). However, regional
differences among gray matter regions have not been examined in
detail. Furthermore, ALFF and fALFF have yet to be directly compared.
Second, the increasing application of LFO amplitude measures in
clinical studies requires that the reliability of these measures be
addressed directly. We conducted our analyses using a previously
collected fMRI dataset (Shehzad et al., 2009), comprising 26
participants scanned on three different occasions, which allowed us
to assess both inter-session (5–16 months apart) and intra-session
(b1 h apart) reliability.
Finally, while the RSFC literature has typically focused on all
fluctuations below 0.1 Hz (Cordes et al., 2001), specific frequency
bands within the LFO range may contribute differentially to RSFC
(Salvador et al., 2008). For example, Buzsáki and colleagues noted that
neuronal oscillation classes are arrayed linearly when plotted on the
natural logarithmic scale (Buzsáki and Draguhn, 2004; Penttonen,
2003). They asserted that this regularity and much empirical data at
higher frequencies suggest that independent frequency bands are
generated by distinct oscillators, each with specific properties and
physiological functions. However, with a few exceptions (Cordes
et al., 2001; Salvador et al., 2007, 2008), fMRI studies rarely consider
divisionsof thepower spectrumbeyond the mostbasic division of low
(b0.1 Hz) and high (N0.1 Hz) frequencies. Accordingly, in our
analyses, we incorporate the Buzsáki framework, which allows us to
differentiate four frequency bands instead of two.
Participants and data acquisition
We used a dataset comprising 26 participants (mean age 20.5±
4.8 years, 11 males) who were scanned three times as part of an
earlier study that examined the test–retest reliability of RSFC
(Shehzad et al., 2009). All participants were without a history of
psychiatric or neurological illness as confirmed by psychiatric clinical
assessment. Informed consent was obtained prior to participation.
Data collection was carried out according to protocols approved by
the institutional review boards of New York University (NYU) and the
NYU School of Medicine.
Three resting-state scans were obtained for each participant using
a Siemens Allegra 3.0-Tesla scanner. Each scan consisted of 197
contiguous EPI functional volumes (TR=2000 ms; TE=25 ms; flip
angle=90°, 39 slices, matrix=64×64; FOV=192 mm; acquisition
voxel size=3×3×3 mm). Scans 2 and 3 were conducted in a single-
scan session,45 minapart,andwere5–16 months(mean11±4) after
scan 1. All individuals were asked to relax and remain still with eyes
open during the scan. For spatial normalization and localization, a
high-resolution T1-weighted magnetization prepared gradient echo
sequence was also obtained (MPRAGE, TR=2500 ms; TE=4.35 ms;
TI=900 ms; flip angle=8°; 176 slices; FOV=256 mm).
Preliminary data preprocessing was carried out using both FMRIB
Software Library (FSL: http://www.fmrib.ox.ac.uk/fsl, version 4.1) and
Analysis of Functional NeuroImaging (AFNI: http://afni.nimh.nih.gov/
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
afni, version 2008_07_18_1710). Image preprocessing was mostly
consistent with previous studies on ALFF (Zang et al., 2007; Zou et al.,
2008) and included (1) slice time correction for interleaved acquisi-
tions using Sinc interpolation with a Hanning windowing kernel (FSL
command: slicetimer), (2) 3D motion correction via a robust and
accurate intra-modal volume linear registration (FSL command:
mcflirt), (3) despiking of extreme time series outliers using a
hyperbolic tangent function (AFNI command: 3dDespike), (4) 4D
normalization of the entire data set by a single scaling factor (i.e., all
volumes scaled by the same amount) to ensure a valid high-level
analysis (FSL command: fslmaths), (5) spatial smoothing via a
Gaussian kernel with FWHM=6 mm (FSL command: fslmaths), (6)
removal of linear trends (AFNI command: 3dTcat), and (7) estimation
of a nonlinear transformation from individual functional space into
MNI152 space (FSL commands: flirt and fnirt). Of note, the 4D data
normalization in step 4 differs from the so-called “global signal
normalization” frequently used in the RSFC literature, which forces
each 3D volume to have a same mean value (Fox et al., 2009; Murphy
et al., 2009). No temporal filtering was implemented during
preprocessing. This assures that the entire frequency band below
the Nyquist frequency (0.25 Hz) can be examined in subsequent
analyses of LFO amplitude.
Computing ALFF and fALFF
For each scan and each participant, we performed ALFF and
fractional ALFF (fALFF) analyses to identify those voxels with
significantly detectable LFO amplitude (ALFF) or proportion of LFO
amplitude (fALFF). For a timeseries x(t), ALFF is calculated as the sum
of amplitudes within a specific low frequency range (in equation (1):
0.01–0.1 Hz). Fractional ALFF is the ALFF of given frequency band
expressed as a fraction of the sum of amplitudes across the entire
frequency range detectable in a given signal. The two measures reflect
different aspects of LFO amplitude: ALFF indexes the strength or
intensity of LFO, while fALFF represents the relative contribution of
specific LFO to the wholedetectable frequency range. In fact, as shown
in equation (2), fALFF can be regarded as a normalized ALFF, using the
total energy over the detectable frequency range. In practice, the total
energy of entire signals may be different across brain regions (e.g.,
voxels), which can lead fALFF to differ from ALFF in some regions
more than others. The ALFF measure is analogous to Resting-State
is a time-domain LFO amplitude measure calculated as the standard
deviation of low-pass filtered (b0.1 Hz) “resting state” timeseries.
However, computing measures of LFO amplitude in the frequency
domain has the advantage of offering the ability to simultaneously
examine specific bands within the LFO frequency range.
x t ð Þ =
ðÞ + bksin 2πfkt
kf ð Þ + b2
kf ð Þ
ð Þ + b2
ð Þ + b2
to subsequent analyses, subject-level voxel-wise ALFF maps were
standardized into subject-level Z-score maps (i.e., by subtracting the
mean voxel-wise ALFF obtained for the entire brain, and then dividing
by the standard deviation). The same Z-transform was applied to
subject-level fALFF maps. The standardized ALFF and fALFF can
improve the subsequent statistical analyses on group-level LFO amp-
litude measures and their test–retest reliability (see Supplementary
Text “The Usage of Standardized LFO Amplitude Measures”). Fig. 1
provides a schematic of the computation procedure. We consider the
mean LFO amplitude (ALFF and fALFF) for the entire brain to be the
baseline of LFO amplitude (ALFF and fALFF).
The nonlinear transformation from preprocessing step 7 was used
for two spatial normalization procedures. First, to perform group
statistical analyses, we converted all individual Z-score maps to
MNI152 standard space with 2×2×2 mm spatial resolution. Second,
in order to provide an anatomical template for visualizing the group
statistical maps, individual anatomical images were transformed to
1×1×1 mm MNI-152 space and then were averaged across
Fig. 1. Computational diagram for individual amplitude of low frequency fluctuations (ALFF) and fractional ALFF (fALFF) maps. This sketch summarizes the main steps taken to
conduct power spectral density (PSD) analyses of the resting state fMRI signal and to compute the amplitude measures of low frequency oscillations implemented here: the
amplitude of low frequency fluctuations (ALFF), and the fractional ALFF (fALFF). All calculations are done in a participant's native space. The red line is at 0.1 Hz. For group-level
statistical analysis, these ALFF and fALFF maps are converted into Z-score maps by subtracting mean and dividing standard deviation within a whole brain mask for the participant.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
Group voxel-wise analyses
Group-levelanalyses were carried out using a mixed-effects model
(as implemented in the FSL program FLAME). First, a fixed-effects
analysis was carried out for each participant, which combined all
three scans for each participant. We then performed a standard
mixed-effect analysis on these fixed-effects results. Cluster-based
statistical corrections for multiple comparisons were performed using
Gaussian random field theory (ZN2.3; pb0.05, corrected). This group-
level analysis produced thresholded Z-statistic maps showing brain
regions with significantly detectable ALFF or fALFF (i.e., differing
significantly from the global brain baseline of ALFF or fALFF). The
group-level ALFF map shows those brain areas that exhibited LFO
amplitudes that were significantly higher than the baseline, across
subjects. The group-level fALFF map shows those regions whose
contribution to the low frequency amplitudes was significantly higher
than the baseline.
As suggested in the original fALFF paper (Zou et al., 2008), because
fALFF provides a ratio of power at low frequencies to the power of
lower and higher frequencies within the range sampled by a given
fMRI BOLD signal, fALFF may provide a more reasonable measure of
LFO that controls for contributions from several nuisance sources.
Such nuisance signals are likely to have a different spatial distribution
to that of neurophysiologically meaningful LFO. We therefore tested
for differencesbetweenALFFandfALFF by performing a paired-test on
the individual fixed-effects maps. Multiple comparisons correction
based on Gaussian random field theory (ZN2.3; pb0.05, cluster-level
corrected) was applied. This group-level analysis generated Z-statistic
maps of regions in which ALFF differed significantly from fALFF. We
used a peak detection algorithm as implemented in the AFNI
command (3dmaxima) to identify peaks for the group-level Z-statistic
maps using a minimum threshold of Z ≥ 2.3 and minimum distance
between peaks of 20, 2-mm isomorphic voxels.
In order to demonstrate previously reported distinctions between
gray and white matter with respect to LFO amplitudes, voxels were
labeled as gray, white and neither, based upon corresponding 152-
brain average tissue prior maps (MNI152 space) provided by FSL
(tissue belong probability threshold=50%).
Test–retest reliability analyses
To investigate the test–retest reliability of ALFF and fALFF, we
calculated intraclass correlation (ICC), a common index of test–retest
reliability (Shrout and Fleiss, 1979). For each brain unit (e.g., voxel),
the ALFF (or fALFF) was first merged into two 26×2 ALFF (or fALFF)
matrices. Here the two 26×2 matrices can represent ALFF (or fALFF)
across scans 2 and 3 (intra-session, short-term reliability) or between
scan 1 and the average of scans 2 and 3 (inter-session, long-term
reliability). Scans 2 and 3 were averaged to improve the estimation of
long-term reliability. Using a one-way ANOVA on each of the two
matrices, with random subject effects, we split the total sum of the
squares into between-subject (MSb) and within-subject (MSw, i.e.,
residual error) sum of squares. ICC values were subsequently
calculated according to the following equation where k is the number
of repeated observations per subject (Shrout and Fleiss, 1979):
MSb+ k − 1
As per equation (3), for a measure to be reliable (exhibiting high
ICC) there should be low within-subject variance relative to between-
subject variance. Thus, ICC ranges from 0 (no reliability) to 1 (perfect
reliability) and can be understood as a measure of discrimination
between participants (Bland and Altman, 1996). We used the same
methods of peak detection applied to the group-level Z-statistic maps
to detect ICC peaks (thresholded at ICC≥0.5).
Parcellation-basedmasks were generatedfrom the 50% probability
thresholded Harvard-Oxford Structural Atlas, a probabilistic atlas that
defines regions based on standard anatomical boundaries (Kennedy
et al., 1998; Makris et al., 1999). Masks overlapping the midline were
divided at X=0, creating a total of 110 regional masks (55 in each
hemisphere). ALFF and fALFF measures were calculated for each
parcellation region from the mean Z-score in the region. For each
participant, ALFF and fALFF measures were obtained for each scan
separately and then averaged. The Friedman test was used to examine
the presence of a significant ordering of anatomical regions with
respect to each of the amplitude measures (ALFF and fALFF).
Decomposing LFO in different frequency bands
We subdivided the low frequency range into four bands as
previously defined (Buzsáki and Draguhn, 2004; Penttonen, 2003):
slow-5 (0.01–0.027 Hz), slow-4 (0.027–0.073 Hz), slow-3 (0.073–
0.198 Hz) and slow-2 (0.198–0.25 Hz). We computed group level
ALFFand fALFF spatialmapsand ICCfor all four bands (slow-5,slow-4,
slow-3 and slow-2) in the same manner as for the primary broadband
analysis. To further examine region-based differences in LFO
amplitude between these slow bands, for each of four slow bands,
we computed the percentage of voxels exhibiting significantly
detectable ALFF (or fALFF) for each of the 110 Harvard–Oxford
Of note, the frequencies subtended by the slow-5 and slow-4
bands are those typically utilized for RSFC analyses (0.01–0.1 Hz). To
test for the presence of regional differences in significantly detectable
LFO amplitude at the two bands, we carried out paired tests using a
mixed-effect group analysis between the slow-5 and slow-4 bands for
each of the measures (ALFF and fALFF).
We divided our examination of LFO into three domains of
investigation. First, based on resting state fMRI timeseries' power
spectral density, we systematically characterized the spatial distribu-
tions of both LFO amplitude measures (ALFF and fALFF) (Zou et al.,
2008) within the traditional low frequency range (0.01–0.1 Hz).
Second, we evaluated short-term or intra-session (b1 h) test–retest
reliability and long-term or inter-session (N5 months) test–retest
reliability for each of the two amplitude measures. Finally, we
provided a more comprehensive examination of the power spectrum
of the spontaneous BOLD fluctuations by subdividing it into four
different slow frequency ranges based on prior work (slow-5: 0.01–
0.027 Hz, slow-4: 0.027–0.073 Hz, slow-3: 0.073–0.198 Hz, slow-2:
0.198–0.25 Hz) (Buzsáki and Draguhn, 2004; Di Martino et al., 2008a;
Penttonen, 2003). For each of these subdivisions, we repeated our
primary analyses and compared the spatial distribution and test–
retest reliability of the signals observed.
Amplitude measures of oscillatory fMRI waves
Jezzard et al., 1993; Yan et al., 2009), LFO amplitudes were consistently
greater in gray matter than in white matter. Specifically, across
participants, paired t-tests (one for each scan) showed that mean
ALFF observed for voxels located within gray matter was consistently
greater than mean ALFF for voxels within white matter (scan 1:
Figure S1). Similarly, mean fALFF for voxels within gray matter was
consistently greater across participants than measures obtained within
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
white matter (scan 1: pb1×10−12; scan 2: pb1×10−11; scan 3:
pb1×10−11; see Fig. 2C and Figure S1). Together, these findings
matter than white matter.
ALFF and fALFF exhibit highly similar distributions among gray
matter regions, particularly within the cortex (see Fig. 2A and B).
Areas of maximal significance for both ALFF and fALFF measures
included visual cortex, posterior cingulate cortex/precuneus, thala-
mus, medial prefrontal cortex, anterior cingulate cortex, temporal
gyrus and lateral frontal cortex (see Table S1 for complete listing of
peak activations). As indicated by Kendall's coefficient of concordance
(Legendre, 2005), the group statistical maps for the two measures
(ALFF and fALFF) are highly similar, but not entirely concordant
Accordingly, in order to identify areas of difference between the
two measures, we compared Z-scores for ALFF and fALFF at each voxel
using paired t-tests across participants. Consistent with a prior report
by Zou et al. (2008), ALFF was markedly greater than fALFF near large
blood vessels, and in areas adjacent to CSF (particularly in the
brainstem), which are susceptible to the effects of pulsatile motion
(Fig. 3A ZN2.3, pb0.05, cluster-level corrected). These differences
between ALFF and fALFF suggest that in perivascular and periven-
tricular areas, LFO are more likely to reflect vascular pulsatility (e.g.,
aliasing of cardiac signal, Meyer waves) rather than neuronal
fluctuations (Dagli et al., 1999; Julien, 2006).
In further characterizing voxels exhibiting significantly greater
ALFF than fALFF, we noted that 76.5% were located within gray matter,
3.4% in white matter and 20.1% in neither compartment (i.e., blood
vessels and CSF). The gray matter voxels exhibiting significantly
greater ALFF than fALFF accounted for 15.3% of total brain gray matter.
Of note, among voxels exhibiting greater ALFF compared to fALFF,
those within gray matter still exhibited higher fALFF levels than the
voxels not located in gray matter (Fig. 3C). Thus, despite increased
noise in perivascular and periventricular regions, gray matter is
characterized by greater LFO amplitude, relative to white matter.
Beyond gross distinctions in LFO amplitude measures among gray
and white matter, we also tested for amplitude differences among
anatomical regions. We did so by rank-ordering brain regions based
upon ALFF and fALFF. Specifically, we divided the brain into 110
anatomical units (55 in each hemisphere) based on the Harvard-
Oxford Atlas (50% threshold criteria were employed, see Table 1 for a
list of all parcellation units and their abbreviations) (Kennedy et al.,
1998; Makris et al., 1999). For each participant, ALFF and fALFF
measures were calculated for each regionby averaging ALFF and fALFF
Z-scores within the region. Since each participant had three scans,
ALFF and fALFF measures were obtained for each scan separately, and
then averaged across scans. For both ALFF and fALFF, we tested for the
presence of a significant ordering of anatomical regions with respect
to the corresponding amplitude measure (the Friedman test denotes
whether the within-subject rankings of a measure differ systemati-
cally between subjects). Significant orderings were observed for both
measures (ALFF in left hemisphere: χ54
ALFF in right hemisphere: χ54
cortices (precuneus, posterior cingulate) being among the highest
ranked for both measures (see Fig. 4 and Figure S2). Of note, some
regions differed markedly in their relative rankings for ALFF and
fALFF. Consistent with our voxel-based analyses, portions of the
temporal lobe and subcortical regions (e.g., pallidum and brainstem,
2= 122.33, p=3.25×10−7; fALFF in left
2=104. 82, p=4.18×10−5; fALFF in right hemi-
2=110.47, p=9.29×10−6) with visual and posteromedial
Fig. 2. Amplitude of spontaneous low frequency oscillations in the resting brain. (A) Group-level Z-statistic maps showing significantly detectable amplitude of low frequency
fluctuations (ALFF) across the whole brain. A one-sample statistical test was carried out combining a fixed-effects model (within participant) with a mixed-effects model (across
participants: see Methods for details). Cluster-level multiple comparisons correction was performed using Gaussian random field theory (ZN2.3; pb0.05, corrected). (B) Group-level
Z-statistic maps showing significantly detectable fractional ALFF (fALFF) across the whole brain. The statistical test is the same as in (A). (C) Mean voxel-wise ALFF and mean voxel-
wise fALFF were greater for gray matter (GM) than white matter (WM) across participants. LH=left hemisphere; RH=right hemisphere.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
see Table 1) most likely to be affected by vascular and pulsatile effects
exhibited marked differences between their ALFF and fALFF rankings
(i.e., ALFF NN fALFF).
Test–retest reliability of amplitude measures on oscillatory fMRI waves
In order to assess the test–retest reliability of LFO amplitude
measures, we calculated the voxel-wise intra- and inter-session ICC
for both ALFF and fALFF (Fig. 5A). Voxels within gray matter generally
exhibited moderate to high test–retest reliability, while those within
white matter were characterized by low test–retest reliability (see
Fig. 5B). For both ALFF and fALFF, areas of maximal ICC (intra- and
inter-session) were located within anterior cingulate cortex, posterior
cingulate cortex, medial prefrontal cortex, thalamus, inferior parietal
lobule, superior temporal gyrus, inferior frontal gyrus, middle frontal
gyrus and superior frontal gyrus (see Table S2 for a detailed maximal
While both measures (ALFF and fALFF) exhibited moderate to high
test–retest reliability within gray matter regions, reliability for ALFF
tended to be higher than for fALFF. At least in part, this difference can
be explained by the fact that fALFF is a proportional measure (Arndt
et al., 1991). This finding suggests that ALFF is more reliable than
fALFF in gray matter regions, and thus potentially more sensitive for
discerning differences between individuals and groups.
Finally, we examined whether or not regional differences in LFO
amplitude measures (ALFF and fALFF) are consistent across intra- and
inter-session scans. In order to accomplish this, we examined the
Pearson correlation of LFO amplitude rank orderings for all parcella-
tion units between the intra- and inter-session scans. Within and
between sessions, we found highly consistent rank orderings of ALFF
and fALFF for the 110 brain regions examined both at the group level
(Fig. 6A) and at the individual level (Fig. 6B). Supplementary results
provide further verification of the consistency of these regional
findings, as they were reliable across two different scanner sites with
distinct sets of participants (see Supplementary Text “Verification of
Ranking Orders of Parcellation-Based LFO Amplitudes”). Further,
supplementary analyses suggest that vascular effects alone do not
appear to produce these regional differences, highlighting potential
neural contributions (see Figure S3).
Oscillatory fMRI waves in different frequency bands
Penttonen and Buzsáki observed that neuronal oscillations are
distributed linearly on the natural logarithmic scale (Buzsáki and
Draguhn, 2004; Penttonen, 2003). We applied Buzsáki's nomencla-
ture by implementing an approach previously used to subdivide the
frequency spectrum (Di Martino et al., 2008a). Accordingly, we
reanalyzed our data using the following divisions: slow-5 (0.01–
0.027 Hz), slow-4 (0.027–0.073 Hz), slow-3 (0.073–0.198 Hz) and
slow-2 (0.198–0.25 Hz; note: the upper bound was constrainedby the
repetition time of the BOLD acquisition). Voxel-wise ALFF and fALFF
maps for each of the four low-frequency bands are presented in Figure
S4. For both ALFF and fALFF measures, significant slow-4 and slow-5
oscillations were primarily detected within gray matter. In contrast,
slow-3 and slow-2 oscillations were primarily restricted to white
matter (Fig. 7 and S4). This distinction of slows 2/3 vs. slows 4/5 is
especially noteworthy given prior demonstrations that respiratory
and aliased cardiac signals fall in the range of slows 2–3 (Cordes et al.,
2001), while the oscillatory signals upon which resting state
functional connectivity is based are primarily located within slows
4–5 (De Luca et al., 2006; Salvador et al., 2008). In order to summarize
differences in the distribution of fALFF among each of the four
frequency bands as well as the classic (b0.1 Hz) low frequency band,
voxels within each of the 110 anatomical parcellation units previously
described (Figure S5). This analysis was limited to fALFF since ALFF is
more likely to include artifacts that disproportionately impact
subcortical and periventricular regions.
Focusing on slows 4 and 5, which were both broadly distributed
through gray matter, voxel-wise paired comparisons of slow-4 and
Fig. 3. Brain areas with higher amplitude of low frequency fluctuations (ALFF) than fractional ALFF (fALFF). (A) Group-level Z-statistic maps showing regions with significantly
higher standardized ALFF than fALFF. Using standardized ALFF and fALFF (i.e., Z-scores), a paired two-sample statistical test was carried out (see Methods). Cluster-level multiple
comparisons correction was performed using Gaussian random field theory (ZN2.3; pb0.05, corrected). (B) The scatter plot shows averaged ALFF and fALFF Z-score for all voxels
within a mask selected to comprise the regions exhibiting higher ALFF than fALFF Z-scores in (A). (C) The scatter plot shows the mean ALFF and fALFF Z-score within gray matter
(GM), white matter (WM) and other (CSF, vasculature) constrained with the mask depicted in (B). The generation of these three ROIs within the mask depicted in B (GM, WM and
other) is detailed in the Methods section. LH=left hemisphere; RH=right hemisphere.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
Fig. 4. Parcellation-based amplitude of low frequency fluctuations (ALFF) and fractional ALFF (fALFF) and their ranking orders. The figure depicts Tukey box-and-whiskers plots
showing the distribution of (A) right hemispheric ALFF Z-scores and ranked ALFF Z-scores and of (B) right hemispheric fALFF Z-scores and ranked fALFF Z-scores for all 55
parcellation regions across participants (circle with center black point=median; blue box=interquartile range; blue whiskers=1.5 times the interquartile range; red
crosses=individual values lying outside 1.5 times the interquartile range). All abbreviations for parcellation region names are listed in Table 1.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
slow-5 revealed some noteworthy differences. Compared to slow-5,
slow-4 fALFF was higher throughout the basal ganglia, thalamus and
several sensorimotor regions and was lower within ventromedial
regions (Fig. 8).
Finally, we examined the test–retest reliability of slow-5 and slow-
4. Specifically, we calculated the voxel-wise intra- and inter-session
ICC for both ALFF and fALFF in these two slow bands. Figure S6
presents the sphere maps of test–retest reliability showing voxels
with significantly detectable LFO amplitudes and high test–retest
reliability (i.e., ICC ≥ 0.5). On visual inspection, slow-4 demonstrates
greater and more widely distributed intra-session ICC values than
slow-5. Moreover, to provide a more comprehensive examination of
the spatial distribution of ICC values for both slow bands, we used
distinct ICC thresholds for slow-5 and slow-4 and then computed the
percentage of reliable voxels within gray matter. The results indicate
that for both ALFF and fALFF, slow-4 has higher test–retest reliability
and more widespread spatial distribution of reliable voxels than slow-
5 (see Figure S7).
We considered the possibility that our differential findings for the
four slow bands may have reflected differences in the number of
samples in the power spectrum for each of the frequency bands,
rather than their specific spectral properties. Accordingly, we
reanalyzed our data using the same number of samples in each
band (centered around each band's middle frequency). A highly
consistent pattern of findings was obtained, mitigating concern about
this possible confound.
Several observations emerged from this examination of sponta-
neous LFO in the human brain at rest. Beyond confirming prior
demonstrations of higher LFO amplitude within gray matter (Biswal
et al., 1995; Cordes et al., 2001), we found that ALFF measures in the
brain are more susceptible to gross pulsatile effects, and that these are
attenuated in fALFF. Despite these differences in sensitivity to
artifacts, both ALFF and fALFF exhibit regional differences within the
brain, with the largest amplitudes found along the midline and in
visual cortices. We also found that both ALFF and fALFF exhibit
moderate to high intra- and inter-session test–retest reliability
throughout the brain, though primarily in gray matter. Furthermore,
we found that rankings of regional differences in LFO amplitude
measures are strikingly consistent, showing little variability within or
across sessions. Supplementary analyses conducted on an indepen-
dent dataset suggest that these regional differences generalize to
other scanners and are not simply attributable to vascular effects.
Finally, our analyses of four previously characterized subdivisions of
the power spectrum suggest that (1) gray matter related oscillations
primarily occur in the slow-4 and slow-5 range (0.01–0.073 Hz), (2)
slow-4 fluctuations are more robust in basal ganglia than slow-5,
while slow-5 is more dominant within ventromedial prefrontal
cortices than slow-4, and (3) although robust for both, test–retest
reliability was greater and more widely distributed for slow-4 than for
In considering the areas exhibiting maximal LFO amplitudes, we
note that many are components of what has come to be known as the
“default-mode” network. Characterized by greater metabolic and
neural activity during rest than active task performance, activity
within this medial wall-based network has been proposed to reflect a
physiological baseline for the brain (Gusnard and Raichle, 2001;
Raichle, 2009; Raichle et al., 2001; Raichle and Mintun, 2006). Our
finding of greater reliability in these medial wall structures is
consistent with the conclusion that these regions represent the
functional core underlying resting brain dynamics, a notion recently
supported by a computational model of the resting brain and network
analyses combining functional and structural measures (Ghosh et al.,
2008; Hagmann et al., 2008; Honey et al., 2009). These same regions
Fig. 5. Test–retest reliability maps on standardized amplitude of low frequency fluctuations (ALFF) and fractional ALFF (fALFF). (A) This figure depicts the voxel-wise ICC maps
showing the intra- and inter-session (left and right column, respectively) test–retest reliability for each of the two LFO amplitude measures examined in this study: ALFF and fALFF
(top and bottom row, respectively). Only the regions with high reliability (ICCN0.5) are shown. As evident by inspection of these ICC maps ALFF has greater reliability than fALFF. (B)
The graphs indicate the percentage of gray matter (GM) and white matter (WM) voxels above each ICC threshold ranging from 0 to 0.85 for ALFF and fALFF (top and bottom graph,
respectively). LH=left hemisphere; RH=right hemisphere.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
show marked reductions in LFO amplitudes during task performance,
suggesting a discernible redistribution of resources associated with
attentional and cognitive demands (Duff et al., 2008; Fransson, 2006).
Ongoing work will examine the impact of attentional states and
cognitive demands on LFO.
Origins and potential significance of spontaneous low-frequency
Despite the increasing popularity of studies of spontaneous
fluctuations in the BOLD signal, the origins and functional significance
of LFO remain unclear (Bianciardi et al., 2009; Buckner and Vincent,
2007). The spectral coincidence between BOLD signal LFO and
fluctuations of systemic vascular phenomena (Shmueli et al., 2007),
such as Mayer waves (Julien, 2006), has led to the suggestion that
BOLD LFO reflect cardiovascular or respiratory fluctuations (Birn et al.,
2006; Birn et al., 2008; Chang et al., 2009; Shmueli et al., 2007; van
Buuren et al., 2009). However, a recent application of near-infrared
optical topography approaches capable of distinguishing cerebral
pulsations from cardiovascular phenomena suggests that cerebral LFO
are at least partially independent of cardiovascular fluctuations
(Yamazaki et al., 2007). Some authors have suggested that sponta-
neous low-frequency fluctuations in the BOLD signal may be the
byproduct of low-pass filtering via neurovascular coupling, rather
than reflecting low-frequency fluctuations present in neural activity.
However, a recent study of visual stimulation found that such filtering
is insufficient to explain BOLD LFO phenomena (Anderson, 2008).
In considering the major candidates capable of producing low-
frequency phenomena, increasing evidence is mounting for neural
activity as the primary contributor (Balduzzi et al., 2008). First, the
dominance of LFO in gray matter compared to white matter, together
with studies of fMRI dynamics showing greater persistence or long-
memory in gray matter regions (Suckling et al., 2008; Wink et al.,
2008), suggest a possible link to neuronal processes. Our findings of
greater test–retest reliability for LFO amplitudes in gray matter
provide further support for such a link. Moreover, our supplementary
analyses, showing preservation of regional rank ordering of ALFF and
fALFF measures during breath-holding, a condition that markedly
disrupts vascular dynamics, further support the contributions of
Potentially the most intriguing are recent studies directly linking
BOLD oscillations to those observed in EEG. For example, by recording
full-bands and resting-state BOLD signals simultaneously, He et al.
(2008) directly related BOLD LFO to infra-slow fluctuations (b0.1 Hz)
observed in neuronal activity. Although long considered as noise in
the EEG literature, meaningful infra-slow fluctuations are increasingly
being appreciated in EEG studies of humans (Monto et al., 2008), as
well as monkeys (Leopold et al., 2003) and rats (Chen et al., 2009).
Similarly, recent work has demonstrated low-frequency amplitude
modulation of various higher frequency signals (i.e., delta, alpha, beta,
gamma) (Lu et al., 2007; Mantini et al., 2007).
In considering the potential significance of low-frequency neural
fluctuations, several authors have drawn attention to variations in
cortical excitability and in cognitive performance (Fox et al., 2007;
Monto et al., 2008). Fox et al. (2007) found a significant relationship
between resting state brain activity and the spontaneous trial-to-trial
variabilityof buttonpressforcein somatomotorcortex.Morerecently,
the phase of EEG LFO has been linked to the slow fluctuations in
human psychophysical performance during a somatosensory detec-
tion task (Monto et al., 2008). In a behavioral study, the response time
Fig. 6. Reliable rank ordering for anatomical parcellation. Given that each participant had three scans, standardized amplitude of low frequency fluctuations (ALFF) and fractional
ALFF (fALFF) measures (i.e., Z-scores) were obtained for each parcellation region separately for each scan. The parcellation regions were then ranked based upon their standardized
ALFF and fALFF. For each scan, the mean rank for a parcellation region was obtained by averaging all individual ranks for the region. (A) The reliability of mean ranks. (B) The
reliability of subject-level ranks. Overall these panels illustrate the consistency of ALFF- and fALFF-based rank orderings for the parcellation regions over the short- and long-term
(intra-session and inter-session, respectively).
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
fluctuations of children with ADHD exhibited significantly greater
power within the slow-4 range (Di Martino et al., 2008a). We note
that we found slow-4 LFO to be particularly prominent in the basal
ganglia — a key putative site of dysfunction in ADHD (Bush et al.,
2005; Castellanos and Tannock, 2002). Intriguingly, similar oscilla-
tions (∼0.028 Hz) evident in basal ganglia neuronal recordings from
awake, locally anesthetized rats, are selectively modulated by low
doses of dopaminergic drugs such as those used to treat ADHD
(Ruskin et al., 1999a,b, 2001). Thus, our findings add to the increasing
body of evidence that slow-4 neuronal fluctuations characterize basal
ganglia spontaneous intrinsic activity (Hutchison et al., 2004).
Test–retest reliability of LFO amplitude measures
While prior work has suggested that LFO amplitudes may be
affected by a variety of factors (Biswal et al., 1997; Fransson, 2006;
Kiviniemi et al., 2000, 2005; McAvoy et al., 2008; Suckling et al., 2008;
Yang et al., 2007), our findings suggest that inter-individual differ-
ences in LFO amplitudes are relatively stable. Both ALFF and fALFF
measures derived from gray matter were markedly more reliable than
those derived from white matter. That gray matter exhibits higher-
amplitude LFO and higher test–retest reliability, relative to white
matter, is consistent with the idea that BOLD LFO reflects meaningful
neuronal activity, which is absent from white matter. Second, the
parcellation-based reliability analyses demonstrated a highly consis-
tent and reliable rank ordering of LFO amplitudesacross the brain. The
robustness of these findings, both across subjects and scanners,
indicate a potential area of interest for future studies of the functional
architecture in brain, as well as the possible impact of developmental
and pathological processes (Greicius et al., 2009; Honey et al., 2009;
van den Heuvel et al., 2009).
Fig. 7. Tissue distribution of amplitude of low frequency fluctuations (ALFF) and fractional ALFF (fALFF) for different frequency bands. For each amplitude measures (i.e., ALFF and
fALFF), the percentage of voxels within a tissue-type: gray matter (GM), white matter (WM), and others and the percentage of voxel with the significant amplitude measure were
calculated for four frequency bands defined as follows: Slow-5 (0.01–0.027 Hz), Slow-4 (0.027–0.073 Hz), Slow-3 (0.073–0.198 Hz), Slow-2 (0.198–0.25 Hz).
Fig. 8. Spatial regions with higher fractional amplitude of low frequency fluctuations
(fALFF): Slow-4 versus Slow-5. Color maps depict voxels exhibiting significant
differences in fALFF obtained for the slow-4 and slow-5 bands, as detected by paired
two-sample statistical test carried out using a mixed-effect. Cluster-level multiple
comparisons correction was performed using Gaussian random field theory (ZN2.3;
pb0.05, corrected). As illustrated, compared to Slow-5, Slow-4 fALFF measures were
significantly greater in the basal ganglia and significantly lower in the medial prefrontal
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
In recent years, a burgeoning literature has emerged examining
the resting brain in clinical populations (Broyd et al., 2009; Greicius,
2008). With a few exceptions, amplitude measures have received
relatively little attention. Instead, most studies have examined the
impact of psychiatric and neurological illness on the spatial
distribution of correlated low-frequency fluctuations, commonly
referred to as functional connectivity. The present work suggests
that analyses of LFO amplitudes may represent an additional
potentially reliable and robust marker of inter-individual and group
differences, with the advantage of being easily amenable to full-brain
exploration. Fortunately, no new data collection is required to explore
Despite the various forms of support for ALFF and fALFF measures
provided by the present work, some noteworthy cautions emerge.
Most notably, ALFF measures are more susceptible to possible
artifactual findings in the vicinity of blood vessels and the cerebral
ventricles, presumably reflecting pulsatile effects. The greater specific-
ity of fALFF for gray matter appears to favor its use over that of ALFF.
However, there is a cost, since ALFF has somewhat higher test–retest
reliability in gray matter regions — not surprising given that fALFF is a
ratio measure and thus intrinsically less reliable (Arndt et al., 1991). In
the end, it is probably most advisable to report findings with both
measures, takinginto account their respective limitations, until a larger
literature with these measures emerges to further guide selection.
Mean ALFF and fALFF Z-scores and ranking across scans and participants for parcellation regions.
Parcellation regionsALFF: RH ALFF: LHfALFF: RH fALFF: LH
Full name Abbreviation
Cingulate gyrus, anterior division
Cingulate gyrus, posterior division
Supplementary motox cortex
Frontal medial cortex
Superior frontal gyrus
Lateral occipital cortex, superior division
Supramarginal gyrus, posterior division
Superior temporal gyrus, anterior division
Superior parietal lobule
Middle temporal gyrus, temporooccipital part
Supramarginal gyrus, anterior division
Inferior frontal gyrus, pars opercularis
Inferior temporal gyrus, temporooccipital part
Middle frontal gyrus
Middle temporal gyrus, posterior division
Occipital fusiform gyrus
Parahippocampal gyrus, anterior division
Lateral occiptal cortex, inferior division
Inferior frontal gyrus, pars triangularis
Parahippocampal gyrus, posterior division
Temporal occipital fusiform cortex
Superior temporal gyrus, posterior division
Frontal orbital cortex
Inferior temporal gyrus, anterior division
Frontal Opercular cortex
Central opercular cortex
Middle temporal gyrus, anterior division
Temporal fusiform cortex, anterior division
Temporal fusiform cortex, posterior division
Inferior temporal gyrus, posterior division
Parietal operculum cortex
LH=left hemisphere; RH=right hemisphere; Z=Z-score; R=ranking.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
Limitations and future directions
The present work has several potential limitations worth
considering. Most notable is the lack of simultaneous measurement
of cardiac and respiratory processes during the resting scan, as
multiple studies using 3.0 and 7.0 T magnet strengths have drawn
attention to the potential of physiological processes to contribute
artifactual signals in the low-frequency range (Bianciardi et al., 2009;
Birn et al., 2006; Chang et al., 2009; van Buuren et al., 2009; Yan et al.,
2009). However, several points mitigate this concern. First, the
impact of cardiac and respiratory-related processes on LFO phenom-
ena within gray matter appears to be relatively small. Correction
methods such as RETROICOR typically adjust the measures of LFO
amplitudes by less than 5% in gray matter (Petridou et al., 2009).
Second, our work demonstrated robust test–retest reliability
throughout the entire brain, not simply regions that were previously
reported to be influenced by respiratory or cardiac signals (Birn et al.,
2006). Finally, our supplementary analyses show that the regional
differences we demonstrated in ALFF were not markedly affected by
breath-holding — a process that robustly manipulates the vascular
contributions to the BOLD signal. In order to minimize artifactual
contributions of respiratory and cardiac signals to LFO amplitude
measures, our findings suggested that fALFF is generally more
effective, particularly in perivascular, periventricular and periaque-
ductal regions (see Fig. 3).
Also worth noting is the choice to use the periodogram for power
spectral density (PSD) to calculate LFO amplitudes and their
reliability, consistent with prior work (Zang et al., 2007; Zou et al.,
2008). Despite its ease of use and computation, the periodogram
method is subject to sampling error or variability (Warner, 1998),
which may negatively affect the estimation of test–retest reliability.
Furthermore, it is insensitive to non-stationary characteristics of LFO
appreciated by previous work (Bullmore et al., 2004; Maxim et al.,
2005; Wink et al., 2008). In the future, it may be helpful to employ
more robust methods of power spectra estimation (e.g., the Welch
method, multi-tapers method or wavelet-based methods) (van Vugt
et al., 2007). Another important factor for estimating the PSD is the
repetition time (TR) used during fMRI scanning. In order to attain
whole brain coverage, we used a TR=2 s for our resting state fMRI
scans. A faster TR can reduce frequency leakage and improve PSD
resolution (Uitert, 1978), though at the cost of whole brain coverage
and/or spatial resolution. Of note, previous studies comparing PSD
results with slower (2 s) and faster TR's (e.g., 0.25–0.4 s) noted highly
similar patterns of results in the low-frequency range, arguing in favor
of slower repetition rates to increase spatial resolution and/or
coverage (Biswal et al., 1995; De Luca et al., 2006; Yang et al., 2007).
The current work represents the systematic and quantitative
evaluation of the amplitude, spatial distribution and test–retest
reliability of spontaneous LFO within the broad low-frequency
range, and within four narrowly defined slow frequency bands. We
observed differential spatial distribution of these LFO amplitudes
within the resting brain, such that higher amplitude LFO were
observed in gray matter, relative to white matter, and were
particularly prominent along the midline of the brain. Detailed
examination of individual low frequency bands showed distinct
spatial profiles. In particular, LFO amplitudes in the slow-4 (0.027–
0.073 Hz) band were most robust in the basal ganglia, as previously
suggested by spontaneous electrophysiological recordings in the
awake rat (Ruskin et al., 2001). Furthermore, we found that reliability
ranged from minimal to robust. Our results provide a foundation for
continued examination of LFO amplitude in typical and atypical
populations. Our findings also shed further light on the potential
neurophysiological significance of LFO.
This work was partially supported by grants from NIMH
(R01MH081218) and the Stavros S. Niarchos Foundation to F.X.C.
and from the Leon Levy Foundation to M.P.M. and by gifts from Linda
and Richard Schaps and Jill and Bob Smith to F.X.C. We wish to
acknowledge the invaluable contributions of Dr. Yufeng Zang from
Beijing Normal University and the two anonymous reviewers.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.neuroimage.2009.09.037.
Anderson, J.S., 2008. Origin of synchronized low-frequency blood oxygen level-
dependent fluctuations in the primary visual cortex. Am. J. Neuroradiol. 29,
Arndt, S., Cohen, G., Alliger, R.J., Swayze II, V.W., Andreasen, N.C., 1991. Problems with
ratio and proportion measures of imaged cerebral structures. Psychiatry Res. 40,
Balduzzi, D., Riedner, B.A., Tononi, G., 2008. A BOLD window into brain waves. Proc.
Natl. Acad. Sci. U. S. A. 105, 15641–15642.
Bianciardi, M., Fukunaga, M., van Gelderen, P., Horovitz, S.G., de Zwart, J.A., Shmueli, K.,
in the human brain at rest: a 7 T study. Magn. Reson. Imaging 27, 1019–1029.
Birn, R.M., Diamond, J.B., Smith, M.A., Bandettini, P.A., 2006. Separating respiratory-
variation-related fluctuations from neuronal-activity-related fluctuations in fMRI.
Neuroimage 31, 1536–1548.
Birn, R.M., Murphy, K., Bandettini, P.A., 2008. The effect of respiration variations on
independent component analysis results of resting state functional connectivity.
Hum. Brain Mapp. 29, 740–750.
Biswal, B., Yetkin, F.Z., Haughton, V.M., Hyde, J.S., 1995. Functional connectivity in the
motor cortex of resting human brain using echo-planar MRI. Magn. Reson. Med. 34,
Biswal, B., Hudetz, A.G., Yetkin, F.Z., Haughton, V.M., Hyde, J.S., 1997. Hypercapnia
reversibly suppresses low-frequency fluctuations in the human motor cortex
during rest using echo-planar MRI. J. Cereb. Blood Flow Metab. 17, 301–308.
Bland, J.M., Altman, D.G., 1996. Measurement error and correlation coefficients. BMJ
Broyd, S.J., Demanuele, C., Debener, S., Helps, S.K., James, C.J., Sonuga-Barke, E.J., 2009.
Default-mode brain dysfunction in mental disorders: a systematic review.
Neurosci. Biobehav. Rev. 33, 279–296.
Buckner, R.L., Vincent, J.L., 2007. Unrest at rest: default activity and spontaneous
network correlations. Neuroimage 37, 1091–1096 discussion 1097-1099..
Bullmore, E., Fadili, J., Maxim, V., Sendur, L., Whitcher, B., Suckling, J., Brammer, M.,
Breakspear, M., 2004. Wavelets and functional magnetic resonance imaging of the
human brain. Neuroimage 23 (Suppl. 1), S234–249.
Bush, G., Valera, E.M., Seidman, L.J., 2005. Functional neuroimaging of attention-deficit/
hyperactivity disorder: a review and suggested future directions. Biol. Psychiatry
Buzsáki, G., Draguhn, A., 2004. Neuronal oscillations in cortical networks. Science 304,
Castellanos, F.X., Tannock, R., 2002. Neuroscience of attention-deficit/hyperactivity
disorder: the search for endophenotypes. Nat. Rev. Neurosci. 3, 617–628.
Chang, C., Cunningham, J.P., Glover, G.H., 2009. Influence of heart rate on the BOLD
signal: the cardiac response function. Neuroimage 44, 857–869.
Chen, G., Popa, L.S., Wang, X., Gao, W., Barnes, J., Hendrix, C.M., Hess, E.J., Ebner, T.J.,
2009. Low-frequency oscillations in the cerebellar cortex of the tottering mouse.
J. Neurophysiol. 101, 234–245.
Cordes, D., Haughton, V.M., Arfanakis, K., Carew, J.D., Turski, P.A., Moritz, C.H., Quigley,
M.A., Meyerand, M.E., 2001. Frequencies contributing to functional connectivity in
the cerebral cortex in “resting-state” data. AJNR Am. J. Neuroradiol. 22, 1326–1333.
Dagli, M.S., Ingeholm, J.E., Haxby, J.V., 1999. Localization of cardiac-induced signal
change in fMRI. Neuroimage 9, 407–415.
De Luca, M., Beckmann, C.F., De Stefano, N., Matthews, P.M., Smith, S.M., 2006. fMRI
resting state networks define distinct modes of long-distance interactions in the
human brain. Neuroimage 29, 1359–1367.
Demanuele, C., James, C.J., Sonuga-Barke, E.J., 2007. Distinguishing low frequency
oscillations within the 1/f spectral behaviour of electromagnetic brain signals.
Behav. Brain Funct. 3, 62.
Deuker, L., Bullmore, E.T., Smith, M., Christensen, S., Nathan, P.J., Rockstroh, B., Bassett,
D.S., 2009. Reproducibility of graph metrics of human brain functional networks.
Neuroimage 47, 1460–1468.
Di Martino, A., Ghaffari, M., Curchack, J., Reiss, P., Hyde, C., Vannucci, M., Petkova, E.,
Klein, D.F., Castellanos, F.X., 2008a. Decomposing intra-subject variability in
children with attention-deficit/hyperactivity disorder. Biol. Psychiatry 64,
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
Di Martino, A., Scheres, A., Margulies, D.S., Kelly, A.M., Uddin, L.Q., Shehzad, Z.,Biswal, B.,
Walters, J.R., Castellanos, F.X., Milham, M.P., 2008b. Functional connectivity of
human striatum: a resting state FMRI study. Cereb. Cortex 18, 2735–2747.
Di Martino, A., Shehzad, Z., Kelly, A.M.C., Roy Krain, A., Gee, D., Uddin, L., Gotimer, K.,
Klein, D.F., Castellanos, F.X., Milham, M.P., 2009. Relationship between cingulo-
insular functional connectivity and autistic traits in neurotypical adults. Am. J. of.
Psychiatry 166, 891–899.
Duff, E.P., Johnston, L.A., Xiong, J., Fox, P.T., Mareels, I., Egan, G.F., 2008. The power of
spectral density analysis for mapping endogenous BOLD signal fluctuations. Hum.
Brain Mapp. 29, 778–790.
Fox, M.D., Raichle, M.E., 2007. Spontaneous fluctuations in brain activity observed with
functional magnetic resonance imaging. Nat. Rev. Neurosci. 8, 700–711.
systems account for intertrial variability in human behavior. Neuron 56, 171–184.
Fox, M.D., Zhang, D., Snyder, A.Z., Raichle, M.E., 2009. The global signal and observed
anticorrelated resting state brain networks. J. Neurophysiol. 101, 3270–3283.
Fransson, P., 2006. How default is the default mode of brain function? Further evidence
from intrinsic BOLD signal fluctuations. Neuropsychologia 44, 2836–2845.
Fukunaga, M., Horovitz, S.G., de Zwart, J.A., van Gelderen, P., Balkin, T.J., Braun, A.R.,
Duyn, J.H., 2008. Metabolic origin of BOLD signal fluctuations in the absence of
stimuli. J. Cereb. Blood Flow Metab. 28, 1377–1387.
Ghosh, A., Rho, Y., McIntosh, A.R., Kotter, R., Jirsa, V.K., 2008. Noise during rest
enables the exploration of the brain's dynamic repertoire. PLoS Comput. Biol. 4,
Greicius, M., 2008. Resting-state functional connectivity in neuropsychiatric disorders.
Curr. Opin. Neurol. 21, 424–430.
Greicius, M.D., Supekar, K., Menon, V., Dougherty, R.F., 2009. Resting-state functional
connectivity reflects structural connectivity in the default mode network. Cereb.
Cortex 19, 72–78.
Gusnard, D.A., Raichle, M.E., 2001. Searching for a baseline: functional imaging and the
resting human brain. Nat. Rev. Neurosci. 2, 685–694.
Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C.J., Wedeen, V.J., Sporns, O.,
2008. Mapping the structural core of human cerebral cortex. PLoS Biol. e159, 6.
Hampson, M., Driesen, N.R., Skudlarski, P., Gore, J.C., Constable, R.T., 2006. Brain
He, B.J., Snyder, A.Z., Zempel, J.M., Smyth, M.D., Raichle, M.E., 2008. Electrophysiological
correlates of the brain's intrinsic large-scale functional architecture. Proc. Natl.
Acad. Sci. U. S. A. 105, 16039–16044.
He, Y., Wang, J., Wang, L., Chen, Z.J., Yan, C., Yang, H., Tang, H., Zhu, C., Gong, Q., Zang, Y.,
Evans, A.C., 2009. Uncovering intrinsic modular organization of spontaneous brain
activity in humans. PLoS ONE 4, e5226.
Hesselmann, G., Kell, C.A., Eger, E., Kleinschmidt, A., 2008. Spontaneous local variations
in ongoing neural activity bias perceptual decisions. Proc. Natl. Acad. Sci. U. S. A.
Honey, C.J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., Hagmann, P.,
2009. Predicting human resting-state functional connectivity from structural
connectivity. Proc. Natl. Acad. Sci. U. S. A. 106, 2035–2040.
Horovitz, S.G., Fukunaga, M., de Zwart, J.A., van Gelderen, P., Fulton, S.C., Balkin, T.J.,
Duyn, J.H., 2008. Low frequency BOLD fluctuations during resting wakefulness and
light sleep: a simultaneous EEG-fMRI study. Hum. Brain Mapp. 29, 671–682.
Brown,P.,2004. Neuronaloscillations inthebasalgangliaandmovementdisorders:
evidence from whole animal and human recordings. J. Neurosci. 24, 9240–9243.
Jezzard, P., LeBihan, D., Cuenod, C., Pannier, L., Prinster, A., Turner, R., 1993. An
investigation of the contribution of physiological noise in human functional MRI
studies at 1.5 Tesla and 4 Tesla. Proceedings of the 12th Annual Meeting of SMRM,
New York, p. 1392.
Julien, C., 2006. The enigma of Mayer waves: Facts and models. Cardiovasc. Res. 70,
Kannurpatti, S.S., Biswal, B.B., 2008. Detection and scaling of task-induced fMRI-BOLD
response using resting state fluctuations. Neuroimage 40, 1567–1574.
Kelly, A.M., Uddin, L.Q., Biswal, B.B., Castellanos, F.X., Milham, M.P., 2008. Competition
between functional brain networks mediates behavioral variability. Neuroimage
Kennedy, D.N., Lange, N., Makris, N., Bates, J., Meyer, J., Caviness Jr, V.S., 1998. Gyri of the
human neocortex: an MRI-based analysis of volume and variance. Cereb. Cortex 8,
Kiviniemi, V., Jauhiainen, J., Tervonen, O., Paakko, E., Oikarinen, J., Vainionpaa, V.,
Rantala, H., Biswal, B., 2000. Slow vasomotor fluctuation in fMRI of anesthetized
child brain. Magn. Reson. Med. 44, 373–378.
Kiviniemi, V., Kantola, J.H., Jauhiainen, J., Hyvarinen, A., Tervonen, O., 2003.
Independent component analysis of nondeterministic fMRI signal sources.
Neuroimage 19, 253–260.
Kiviniemi, V.J., Haanpaa, H., Kantola, J.H., Jauhiainen, J., Vainionpaa, V., Alahuhta, S.,
Tervonen, O., 2005. Midazolam sedation increases fluctuation and synchrony of the
resting brain BOLD signal. Magn. Reson. Imaging 23, 531–537.
Knyazev, G.G., 2007. Motivation, emotion, and their inhibitory control mirrored in brain
oscillations. Neurosci. Biobehav. Rev. 31, 377–395.
Legendre, P., 2005. Species associations: The Kendall coefficient of concordance
revisited. J. Agric. Biol. Environ. Stat. 10, 226–245.
Leopold, D.A., Murayama, Y., Logothetis, N.K., 2003. Very slow activity fluctuations in
monkey visual cortex: implications for functional brain imaging. Cereb. Cortex 13,
Lu, H., Zuo, Y., Gu, H., Waltz, J.A., Zhan, W., Scholl, C.A., Rea, W., Yang, Y., Stein, E.A., 2007.
Synchronized delta oscillations correlate with the resting-state functional MRI
signal. Proc. Natl. Acad. Sci. U. S. A. 104, 18265–18269.
Makris, N., Meyer, J.W., Bates, J.F., Yeterian, E.H., Kennedy, D.N., Caviness, V.S., 1999. MRI-
and applications with systematics of cerebral connectivity. Neuroimage 9, 18–45.
Mantini, D., Perrucci, M.G., Del Gratta, C., Romani, G.L., Corbetta, M., 2007. Electro-
physiological signatures of resting state networks in the human brain. Proc. Natl.
Acad. Sci. U. S. A. 104, 13170–13175.
Margulies, D.S., Kelly, A.M., Uddin, L.Q., Biswal, B.B., Castellanos, F.X., Milham, M.P.,
2007. Mapping the functional connectivity of anterior cingulate cortex. Neuro-
image 37, 579–588.
Gaussian noise, functional MRI and Alzheimer's disease. Neuroimage 25, 141–158.
McAvoy, M., Larson-Prior, L., Nolan, T.S., Vaishnavi, S.N., Raichle, M.E., d'Avossa, G.,
2008. Resting states affect spontaneous BOLD oscillations in sensory and paralimbic
cortex. J. Neurophysiol. 100, 922–931.
Monto, S., Palva, S., Voipio, J., Palva, J.M., 2008. Very slow EEG fluctuations predict the
dynamics of stimulus detection and oscillation amplitudes in humans. J. Neurosci.
Murphy, K., Birn, R.M., Handwerker, D.A., Jones, T.B., Bandettini, P.A., 2009. The impact
of global signal regression on resting state correlations: are anti-correlated
networks introduced? Neuroimage 44, 893–905.
Penttonen, M., 2003. Natural logarithmic relationship between brain oscillators.
Thalamus and Related Systems 2, 145–152.
Petridou, N., Schäfer, A., Gowland, P., Bowtell, R., 2009. Phase vs. magnitude information
in functional magnetic resonance imaging time series: toward understanding the
noise. Magn. Reson. Imaging. 27, 1046–1057.
Picchioni, D., Fukunaga, M., Carr, W.S., Braun, A.R., Balkin, T.J., Duyn, J.H., Horovitz, S.G.,
Raichle, M.E., Mintun, M.A., 2006. Brain work and brain imaging. Annu. Rev. Neurosci.
Raichle, M.E., MacLeod, A.M., Snyder, A.Z., Powers, W.J., Gusnard, D.A., Shulman, G.L.,
2001. A default mode of brain function. Proc. Natl. Acad. Sci. U. S. A. 98, 676–682.
Ruskin, D.N., Bergstrom, D.A., Kaneoke, Y., Patel, B.N., Twery, M.J., Walters, J.R., 1999a.
Multisecond oscillations in firing rate in the basal ganglia: robust modulation by
dopamine receptor activation and anesthesia. J. Neurophysiol. 81, 2046–2055.
Ruskin, D.N., Bergstrom, D.A., Mastropietro, C.W., Twery, M.J., Walters, J.R., 1999b.
Dopamine agonist-mediated rotation in rats with unilateral nigrostriatal lesions is
not dependent on net inhibitions of rate in basal ganglia output nuclei.
Neuroscience 91, 935–946.
Ruskin, D.N., Bergstrom, D.A., Shenker, A., Freeman, L.E., Baek, D., Walters, J.R., 2001.
Drugs used in the treatment of attention-deficit/hyperactivity disorder affect
postsynaptic firing rate and oscillation without preferentialdopamine autoreceptor
action. Biol. Psychiatry 49, 340–350.
Salvador, R., Achard, S., Bullmore, E., 2007. Frequency-Dependent Functional Connec-
tivity Analysis of fMRI Data in Fourier and Wavelet Domains. Handbook of Brain
Connectivity. Springer, Berlin / Heidelberg, pp. 379–401.
Salvador, R., Martinez, A., Pomarol-Clotet, E., Gomar, J., Vila, F., Sarro, S., Capdevila, A.,
Bullmore, E., 2008. A simple view of the brain through a frequency-specific
functional connectivity measure. Neuroimage 39, 279–289.
Seeley, W.W., Crawford, R.K., Zhou, J., Miller, B.L., Greicius, M.D., 2009. Neurodegen-
erative diseases target large-scale human brain networks. Neuron 62, 42–52.
Shehzad, Z., Kelly, A.M., Reiss, P.T., Gee, D.G., Gotimer, K., Uddin, L.Q., Lee, S.H.,
Margulies, D.S., Roy, A.K., Biswal, B.B., Petkova, E., Castellanos, F.X., Milham, M.P.,
2009. The Resting Brain: Unconstrained yet Reliable. Cereb. Cortex 19, 2209–2229.
Shmueli, K., van Gelderen, P., de Zwart, J.A., Horovitz, S.G., Fukunaga, M., Jansma, J.M.,
Duyn, J.H., 2007. Low-frequency fluctuations in the cardiac rate as a source of
variance in the resting-state fMRI BOLD signal. Neuroimage 38, 306–320.
Shrout, P.E., Fleiss, J.L., 1979. Intraclass correlations: uses in assessing rater reliability.
Psychol. Bull. 86, 420–428.
Suckling, J., Wink, A.M., Bernard, F.A., Barnes, A., Bullmore, E., 2008. Endogenous
multifractal brain dynamics are modulated by age, cholinergic blockade and
cognitive performance. J. Neurosci. Methods 174, 292–300.
Uitert, G.C.V., 1978. Reduction of leakage and increase of resolution in power spectral
density and coherence functions. Nucl. Instrum. Methods 157, 583–589.
van Buuren, M., Gladwin, T.E., Zandbelt, B.B., van den Heuvel, M., Ramsey, N.F., Kahn,
R.S., Vink, M., 2009. Cardiorespiratory effects on default-mode network activity as
measured with fMRI. Hum. Brain. Mapp. 30, 3031–3042.
resting-state networks reflectthe underlying structural connectivity architecture of
the human brain. Hum. Brain. Mapp. 30, 3127–3141.
van Vugt, M.K., Sederberg, P.B., Kahana, M.J., 2007. Comparison of spectral analysis
methods for characterizing brain oscillations. J. Neurosci. Methods 162, 49–63.
Vanhatalo, S., Palva, J.M., Holmes, M.D., Miller, J.W., Voipio, J., Kaila, K., 2004. Infraslow
oscillations modulate excitability and interictal epileptic activity in the human
cortex during sleep. Proc. Natl. Acad. Sci. U. S. A. 101, 5053–5057.
Warner, R.M., 1998. Spectral Analysis of Time-Series Data. The Guilford Press, New York.
Wink, A.M., Bullmore, E., Barnes, A., Bernard, F., Suckling, J., 2008. Monofractal and
multifractal dynamics of low frequency endogenous brain oscillations in functional
MRI. Hum. Brain Mapp. 29, 791–801.
Yamazaki, K., Uchida, M., Obata, A., Katura, T., Sato, H., Tanaka, N., Maki, A., 2007.
Comparison between Spontaneous Low-Frequency Oscillations in Regional
Cerebral Blood Volume, and Cerebral and Plethysmographic Pulsations. NOISE
AND FLUCTUATIONS: 19th International Conference on Noise and Fluctuations;
ICNF 2007. AIP Conference Proceedings, pp. 687–690.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445
Yan, L., Zhuo, Y., Ye, Y., Xie, S.X., An, J., Aguirre, G.K., Wang, J., 2009. Physiological origin Download full-text
of low-frequency drift in blood oxygen level dependent (BOLD) functional
magnetic resonance imaging (fMRI). Magn. Reson. Med. 61, 819–827.
Yang, H., Long, X.Y., Yang, Y., Yan, H., Zhu, C.Z., Zhou, X.P., Zang, Y.F., Gong, Q.Y., 2007.
Amplitude of low frequency fluctuation within visual areas revealed by resting-
state functional MRI. Neuroimage 36, 144–152.
Zang, Y.F., He, Y., Zhu, C.Z., Cao, Q.J., Sui, M.Q., Liang, M., Tian, L.X., Jiang, T.Z., Wang, Y.F.,
2007. Altered baseline brain activity in children with ADHD revealed by resting-
state functional MRI. Brain Dev. 29, 83–91.
Zhang, Z.Q., Lu, G.M., Zhong, Y., Tan, Q.F., Zhu, J.G., Jiang, L., Chen, Z.L., Wang, Z.Q., Shi, J.
X., Zang, Y.F., Liu, Y.J., 2008. [Application of amplitude of low-frequency fluctuation
to the temporal lobe epilepsy with bilateral hippocampal sclerosis: an fMRI study].
Zhonghua Yi Xue Za Zhi 88, 1594–1598.
Zou, Q.H., Zhu, C.Z., Yang, Y., Zuo, X.N., Long, X.Y., Cao, Q.J., Wang, Y.F., Zang, Y.F., 2008.
An improved approach to detection of amplitude of low-frequency fluctuation
(ALFF) for resting-state fMRI: fractional ALFF. J. Neurosci. Methods 172, 137–141.
Zou, Q., Wu, C.W., Stein, E.A., Zang, Y., Yang, Y., 2009. Static and dynamic characteristics
of cerebral blood flow during the resting state. Neuroimage 48, 515–524.
X.-N. Zuo et al. / NeuroImage 49 (2010) 1432–1445