Functional connectivity density mapping
Dardo Tomasia,1and Nora D. Volkowa,b
aNational Institute on Alcohol Abuse and Alcoholism, Bethesda, MD 20892; andbNational Institute on Drug Abuse, Bethesda, MD 20892
Edited by Robert Desimone, Massachusetts Institute of Technology, Cambridge, MA, and approved April 21, 2010 (received for review February 4, 2010)
Brain networks with energy-efficient hubs might support the high
cognitive performance of humans and a better understanding of
their organization is likely of relevance for studying not only brain
development and plasticity but also neuropsychiatric disorders.
However, the distribution of hubs in the human brain is largely
unknown due to the high computational demands of comprehen-
sive analytical methods. Here we propose a 103times faster
method to map the distribution of the local functional connectivity
density (lFCD) in the human brain. The robustness of this method
was tested in 979 subjects from a large repository of MRI time
series collected in resting conditions. Consistently across research
sites, a region located in the posterior cingulate/ventral precuneus
(BA 23/31) was the area with the highest lFCD, which suggest that
this is the most prominent functional hub in the brain. In addition,
regions located in the inferior parietal cortex (BA 18) and cuneus
(BA 18) had high lFCD. The variability of this pattern across subjects
was <36% and within subjects was 12%. The power scaling of the
lFCD was consistent across research centers, suggesting that that
brain networks have a “scale-free” organization.
resting state functional MRI connectivity|functional connectomes|default
mode networks|scale-free networks|consciousness
of connections (1–7). The energy-efficient regions (densely con-
nected nodes) are thought to serve as the interconnection hubs,
brain has been hindered by the cumbersome computational
requirements of comprehensive analytical methods.
During the last decade, numerous studies have evaluated the
functional connectivity among brain regions by using correlation
analyses of spontaneous fluctuations of brain activity measured
with MRI time series in resting conditions (10). A popular tech-
nique used for the analysis of resting-state time series is based on
regions-of-interest (seed regions). This technique uses correlation
analysis of blood oxygenation level-dependent (BOLD) signals for
the identification of brain regions functionally connected to the
seed regions (reviewed inref. 11).Clusteranalysesarealsoused to
evaluate the degree of functional connectivity among multiple
seed regions (12). These methods are constrained by the fact that
they rely strongly on a priori selection of specific seed regions
rather than allowing for the characteristics of the network to
identify and locate the node regions; these methods are also
assessing the topological organization of the human brain re-
stricted their analysis to ∼102seed regions (5, 13). More recently
researchers have started to use data-driven approaches that are
based on graph theory to assess the functional connectivity of the
human brain using datasets obtained with MRI (14). Moreover,
the overall resting functional connectivity (short- and long-range
interconnections) of the gray matter (4-mm isotropic spatial res-
olution) was shown to correspond well with the structural con-
nections determined with diffusion tensor imaging (DTI) (15) and
to be associated with intellectual performance (16).
Here we propose an alternative voxelwise data-driven method
o support fast communication with minimal energy cost, cor-
tical brain networks may have few nodes with dense local
overcome the limitations of seed-based approaches for the identi-
fication of hubs in the human brain, using resting-state functional
connectivity datasets. This ultrafast technique allows calculation of
individual functional connectivity maps with higher spatial resolu-
tion (≥3 mm isotropic) to take full advantage of the native resolu-
tion of the functional MRI datasets. The method is based on the
up the computation of the number of functional connections (i.e.,
edges in graph theory), we restricted the temporal correlation
analysis to the local functional connectivity cluster.
Thus, we aimed to determine the location of the functional
connectivity hubs in the human brain by using data from the
“1000 Functional Connectomes Project” (17), which is a large
public database of resting-state time series that were collected
independently at 35 sites around the world (http://www.nitrc.org/
projects/fcon_1000/). We further aimed to evaluate the vari-
ability of the local functional connectivity density (lFCD) across
subjects and imaging parameters as well as its reproducibility
within and between subjects. We hypothesized that the lFCD
would have low within-subjects variability and that its spatial
distribution would be rather constant across research sites in the
world. We also hypothesized that the probability distribution of
the lFCD would have a power scaling with the number of func-
tional connections per node, which is the main characteristic of
the “scale-free” networks (6), rather than a Poisson distribution,
the landmark of random and “small-world” networks (2).
Metaanalysis of FCDM. Fig. 1 shows the average distribution of the
lFCD in the human brain across all 979 subjects included in this
study. A region localized within the posterior cingulate cortex/ven-
the cuneus, inferior parietal cortex, middle occipital, cingulate,
middle temporal, precentral, inferior, and middle frontal gyri and
claustrum, thalamus, putamen, caudate, and cerebellum also in-
cluded lFCD maxima (Table 1). However, these other hubs had
much lower lFCD values. The standard deviation of the hub loca-
tions was 7.3 ± 3.4 mm; thus positions of the three main hubs were
the main hub (posterior cingulate cortex/ventral precuneus) across
research sites was minimal(D= 4.4±2.7 mm from the coordinates
listed in Table 1) and comparable to the average image resolution
parietal) was larger than that for the main hub (P = 0.05, t test)
but still small (D = 6.7 ± 4.1 mm). The spatial variability of the oc-
cipital hub (right cuneus, BA 18; D = 10.7 ± 7.5 mm) was larger
than that for the main and inferior parietal hubs (P < 0.05; t test).
The average strength of the lFCD varied across research
centers (Fig. 2), which is likely due to differences in acquisition
parameters, instruments, demographic variables, and potential
Author contributions: D.T. and N.D.V. designed research; D.T. performed research; D.T.
contributed new reagents/analytic tools; D.T. analyzed data; and D.T. and N.D.V. wrote
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
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differences in resting conditions (e.g., eyes opened/closed, awake/
sleep, etc). For most research sites the average distribution of the
lFCD reached the highest values in a region located in the pos-
terior cingulate cortex (BA 23) and extends to the precuneus (BA
also reached high lFCD values for some of the imaging datasets
(Dallas, New York A, Ontario, Orangeburg, and Oxford). The
variability of the lFCD across research sites increased the stan-
dard deviation of the lFCD, which did not have a normal distri-
bution across subjects (Fig. S1 Left). However, the use of a single
scaling factor for each research site, 1/k0, reflecting the mean
lFCD across subjects and voxels in the brain, k0, allowed us to
normalize the distribution of the lFCD (Fig. S1 Right) and merge
the datasets from different research sites (Fig. S2).
Using principal component analysis (PCA) we determined
that the average intersubjects variability of the lFCD maps across
centers was only 23.5 ± 1.3%. The first principal component (PC
1) of the lFCD accounted for 34.1 ± 1.3% of the variability and
11 ± 8 principal components were needed to account for 75% of
the variance (Fig. 3). Using factor analysis on datasets with
narrow age range (Beijing, Cambridge, Leiden, Oulu, and Saint
Louis) we found that the factors of the mean lFCD were higher
for women than for men (P < 0.01, t test) and that for two of the
datasets (Baltimore and Cleveland) the factors of the mean
lFCD were negatively correlated with age (R < −0.37; P < 0.036;
Pearson’s linear correlation). These gender and aging effects did
not reach statistical significance for the remaining datasets.
We accessed the statistical significance of the rescaled lFCD
patterns using the 22 available datasets listed in Table 2. The
the human brain (radiological convention). These maps reflect the average
number of functional connections per voxel (k) across 979 subjects from 19
research sites around the world. Green labels indicate the axial distance to
the origin of the stereotactic space (Montreal Neurological Institute). The
lFCD reaches maximal value in posterior cingulate/ventral precuneus (red–
orange). FCDM parameters: TSNR= 50 and TC= 0.6.
Spatial distribution of the lFCD superimposed on axial MRI views of
sagital MRI plane for all research sites (green labels) in this study (Table 2).
FCDM parameters: TSNR= 50 and TC= 0.6.
Spatial distribution of the average lFCD superimposed on the middle
| www.pnas.org/cgi/doi/10.1073/pnas.1001414107Tomasi and Volkow
rescaled lFCD was rather constant across these 979 subjects,
regardless of differences in demographic variables between
studies, and was statistically significant in all gray matter regions,
even when correcting for multiple comparisons at the voxel level
with a conservative familywise error (FWE) threshold PFWE<
0.05 (one-sample t test). Across subjects, the lFCDs in the pos-
terior cingulate/ventral precuneus and parietal hubs were 8.5 ±
0.2 (mean ± SE) and 5.9 ± 0.2 times higher than the average
lFCD in the brain, respectively (Table 1 and Fig. S2).
P(k) Distribution. The probability distribution of the lFCD can be
calculated as P(k)= n(k)/n0, where n(k) is the number of voxels
with k functional connections and n0is the total number of voxels
in the brain. Fig. S3 shows P(k) as a function of k for a typical
subject and three different threshold TCcriteria. For voxels with
more than five functional connections, P(k) decreases with k
following a power scaling:
PðkÞ ¼ kγ·
The scaling factor, γ, did not vary significantly across threshold con-
ditions and the power scaling between P(k) and k was robust across
centers (Table 2 and Fig. S4).
Test–Retest Reliability. The within-subjects reproducibility of
FCDM was evaluated using the New York test–retest reliability
(NYU_TRT) dataset (18). For all sessions, lFCD was high bi-
laterally in posterior cingulate/ventral precuneus, inferior pari-
etal and occipital cortices, cingulate gyrus, anterior insula,
caudate, thalamus, and cerebellar vermis (Fig. S5). The lFCD in
the rostral anterior cingulate cortex, pons, and cerebellum were
higher for session 1 than for session 2 whereas only the lFCD in
the rostral anterior cingulate cortex was higher for session 1 than
for session 3. There were no statistically significant lFCD dif-
ferences between sessions 2 and 3. Using PCA we found that the
global variability of the lFCD data across subjects was <26%.
Consistently for all three sessions, PC 1 was similar to the map of
the average lFCD (especially for session 1) and accounted for
20% of variance of the data (Fig. 3 and Fig. S6). Differently, the
spatial distribution of the second component (PC 2) was variable
across sessions (Fig. S6) and accounted for 10% of the variance
of the data. Using region-of-interest (ROI) analyses we verified
that the lFCD data had 36 ± 8% between-subjects variability and
12 ± 6% within-subjects variability on average across the 19
ROIs listed in Table 1.
lFCD Versus Global (g)FCD. Only two datasets (Ontario and Balti-
more, 34 subjects) were used to contrast lFCD against gFCD due
to the CPU time demands of the gFCD calculation. Whereas the
ultrafast lFCD calculation required only 4 min/subject using
a standard Windows XP platform (3.0-GHz dual core Intel pro-
cessor), the computer-demanding gFCD calculation required
5,406 min/subject using the same platform. Thus, the (local cluster
restricted) lFCD calculation was 1,351 times faster than the (un-
restricted) gFCD calculation. The rescaled gFCD, K/K0, had
similar spatial distribution to the lFCD, k/k0, but did not show the
posterior cingulate/ventral precuneus hub, a brain region where
connectivity density normalized across research sites (k/k0)
Location, average strength (mean), and SD of the local maxima of the functional
Brain region BA or nucleusx, mmy, mmz, mm Mean (k/k0)SD (k/k0)
The sample consisted of 979 healthy subjects from all research sites in Table 2. The (x, y, z) coordinates are in
the Montreal Neurological Institute (MNI) stereotaxic space.
across all research sites showing the brain regions with high lFCD variance
(red–yellow: 10–30%, radiological convention). Scatter plot shows lFCD
variance as a function of the principal components for each of the sessions of
the New York test–retest dataset.
Average spatial distribution of the first principal component (PC 1)
Tomasi and VolkowPNAS
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therescaledlFCD wassignificantly higher than therescaledgFCD
(PFWE-corr< 0.001, paired t test; Fig. 4 and Fig. S7A). In other
regions, however, there were not significant differences between
lFCD and gFCD (PFWE-corr> 0.2, paired t test). The probability
distribution was similar for both approaches but its scaling factor
was higher (less negative) for gFCD than for lFCD (Fig. S7B).
Here we propose a data-driven method to map the lFCD from
resting-state MRI time series. FCDM achieves ultrafast compu-
tation by restricting the calculation to the local functional con-
the lFCD in the whole brain from single-subject data, which
is >1,000 times faster than what can be achieved using traditional
global approaches. The methodology further includes the neces-
sary preprocessing steps to minimize motion and physiologic ar-
parametric mapping (SPM) t tests were used to quantify the ro-
bustness of FCDM using resting-state functional MRI datasets
from the image repository “1000 Functional Connectomes.” The
subjects variability of the lFCD was 12%.
Spatial Distribution of lFCD. The main finding of this study is that
in resting conditions the spatial distribution of the lFCD is highly
localized in posterior cingulate/ventral precuneus and middle
cingulum as well as occipital (cuneus and calcarine cortex) and
inferior parietal regions. Thus, as suggested by previous studies
(8), these regions are likely the functional hubs of the brain. The
posterior and middle cingulum and the ventral precuneus are
interconnected core regions of the default mode network (19)
that also connect to motor regions and include dorsal and ventral
visual stream inputs (20). These regions are more active at rest
than during cognitive performance and show negative BOLD
responses during cognitive functional MRI tasks (21). The pre-
cuneus is a brain region whose activity is associated with the
overall state of consciousness (22) and positron emission to-
mography (PET) studies consistently show it has the highest
metabolism in brain (along with cingulate and visual cortical
areas) (23, 24), suggesting that it is an important hub for intrinsic
activity in the human brain. Because glucose metabolism sup-
ports the energy requirements of neuronal activity (25, 26), and it
is assumed that the capacity of the human brain depends on
energy-efficient cortical networks (1–5), our findings suggest that
higher glucose metabolism in ventral precuneus, cingulate, and
visual regions serves to support a higher communication rate in
these regions. In the posterior cingulate/ventral precuneus the
gFCD was lower than the lFCD, suggesting that the functional
connectivity of this region is well localized rather than globally
distributed as for the remaining brain regions. The neuronal
density might explain the high lFCD in the visual regions (cal-
functional MRI datasets from the image repository for the 1000 Functional Connectomes Project
and the corresponding variability, principal component PC 1, and average scaling factor γ, of P(k)
Dataset Subjects Age, yearstp
Available demographic data and imaging parameters for the selected resting-state
TR, s Variability, %PC 1, %γ
New York A
New York B
8 M/15 F
20 M/0 F
76 M/122 F
13 M/13 F
75 M/123 F
18 M/20 F
11 M/20 F
12 M/12 F
23 M/8 F
16 M/21 F
9 M/10 F
40 M/19 F
8 M/12 F
10 M/17 F
15 M/5 F
37 M/66 F
12 M/10 F
11 M/8 F
14 M/17 F
−6.5 ± 0.2
−5.2 ± 0.1
−5.4 ± 0.1
−5.4 ± 0.1
−5.0 ± 0.1
−5.8 ± 0.2
−5.1 ± 0.1
−4.9 ± 0.1
−4.8 ± 0.1
−4.7 ± 0.1
−5.3 ± 0.1
−4.0 ± 0.1
−5.2 ± 0.1
−5.6 ± 0.6
−5.0 ± 0.1
−5.4 ± 0.1
−4.6 ± 0.1
−5.3 ± 0.1
−4.9 ± 0.1
−4.8 ± 0.1
−4.4 ± 0.1
−5.1 ± 0.1
For some of the research sites the factors of the principal component were significantly correlated (P < 0.05)
with age (*) or gender (**). tp, number of time points in the image time series. M, males; F, females.
(blue–red: K/K0= 0–10) and a statistical map (orange–yellow: PFWE-corr< 0.05;
paired t test) of the significant differences between lFCD and gFCD across 34
healthy subjects from two research sites (Ontario and Baltimore), superimposed
on the middle sagittal MRI view of the human brain. TSNR= 50 and TC= 0.6.
| www.pnas.org/cgi/doi/10.1073/pnas.1001414107Tomasi and Volkow
carine cortex and cuneus). These regions are essential for visual
processing (27) and have up to 2.5 times higher neuronal density
than all other cortical regions (28).
FCDM Variability. This study quantified the variability of resting-
state functional connectivity datasets. Across subjects, the vari-
ability of FCDM was <36%. Within subjects the variability of
FCDM was 12%. Numerous principal components (11 ± 8) were
needed to account for 75% of the variability of FCDM although
PC 1 alone accounted for 34% of the variability. Because PC 1
maps into the nodes with the highest connectivity, this result sug-
gests that the highly connected regions account for a significant
portion of the intersubject variability. Multiple factors might in-
the subjects (alertness, fatigue, excitement), and/or genetics. In-
deed our findings on gender effects on the mean lFCD and the
negative correlation of the mean lFCD with age for two of the
variability of lFCD. Similarly lFCD in rostral cingulate gyrus (part
of PC 1) differed between the test–retest sessions, which suggests
that the state of the subjects also influences FCDM variability.
Within subjects, the variability of FCDM (estimated from the
New York dataset, which evaluated subjects in three different
sessions) corresponded to 12 ± 6%. Overall, taking into account
that the reliability of BOLD functional MRI studies typically
ranges between 20 and 80% (29–31), the test–retest variability of
the lFCD in resting conditions seems to be comparable or lower
than that of standard functional imaging techniques.
Study Limitations. FCDM and seed–voxel correlation analysis of
functional connectivity are complementary. FCDM gives a vox-
elwise measure of the amount of functional connections but does
not provide the directionality of the functional connectivity,
which can be assessed with seed–voxel correlation analyses.
Therefore, FCDM could be used to identify hub locations that
could then be used to select seed regions for subsequent func-
tional connectivity analyses.
The ultrafast FCDM calculation is restricted to the local
functional connectivity cluster. Thus, the FCDM results do not
account for long-range functional connections. However, this
should not be interpreted as a strong limitation because previous
studies have shown the free-scale topology of the brain, sug-
gesting that its networks are highly clustered (14), and the re-
striction of the calculation enhances the regional specificity of
the results. Indeed, we show that the lFCD calculation produces
similar results and has higher sensitivity for local hub detection
than the computer-demanding gFCD calculation.
The functional connectivity datasets may contain physiological
noise (heart rate) (10). Taking into account that band-pass fil-
tering removes the magnetic field drift (32), the main source of
low-frequency fluctuations (33), we estimate that heart rate
could explain up to 10% of the variability of the functional
connectivity patterns across subjects.
Conclusion. Here we showed that as hypothesized, the probability
distribution of lFCD had a power scaling with k and that this
scaling was robust across different threshold conditions, subjects,
and research sites. These findings suggest that functional brain
networks have a scale-free organization that shows a high degree
of consistency across and within individuals.
Subjects. To evaluate the test–retest reliability as well as the within- and
between-subjects variability of FCDM we used data from 979 healthy subjects
(see demographic information in Table 2) from the image repository for the
1000 Functional Connectomes Project, which includes resting-state functional
MRI datasets independently collected at 35 sites and can be assessed at http://
www.nitrc.org/projects/fcon_1000/. Specifically, the dataset analyzed in this
study includes data from 19 of these sites (Table 2). Datasets from the
available (pending verification of IRB status) or did not meet the imaging
acquisitioncriteria (3s ≥ repetition time,full braincoverage,time points>100,
spatial resolution better than 4 mm) and were not included in this study.
FCDM. Standard functional MRI and FCDM share similar data processing steps
(Fig. S8). For multisubject studies, FCDM required two consecutive pre-
processing steps: imaging realignment was required to minimize spurious
motion-related effects (34), and spatial normalization was required to ac-
count for differences in brain size, shape, and orientation across subjects
(35). We used the statistical parametric mapping package SPM2 (Wellcome
Trust Centre for Neuroimaging, London, UK) for these purposes. Specifically,
the images were motion corrected with a 12-parameter affine trans-
formation and spatially normalized to the standard brain using a 12-pa-
rameter affine transformation with medium regularization, 16-nonlinear
iterations, voxel size of 3 × 3 × 3 mm3, and the SPM2 EPI.mnc template.
Because of magnetic susceptibility differences at air/tissue interfaces in the
head, the MRI signal is sensitive to head motion (36). Therefore, the MRI
signal can be correlated with motion, even after image realignment. Be-
cause the spontaneous signal fluctuations in the MRI signal are very small
(<0.5%), it is essential to minimize motion-related fluctuations in the MRI
signal, a step that we refer to as motion filtering. Specifically, motion fil-
tering involved multilinear regression of the time-varying MRI signals, yn= f
(tn), using the six realignment parameters (xn: three translations and
yn¼ axnþ y0
where the fitting parameters ai(1 < i < 6) are the amplitudes of the signal
drift as a function of each motion component, and y0
imaging time series. The removal of motion-correlated fluctuations from the
imaging time series,
nis the motion-filtered
occurred for all volume elements (voxels) of the image and partially removed
physiologic noise of cardiac and respiratory origin. A similar approach
(physiologic noise filtering) could be used to further remove physiologic
noise, which is one of the most important confounds of functional connec-
tivity datasets (37), if respiratory and/or pulse rate data (ϕn) are collected
simultaneously with the resting-state imaging time series ðy00
We were not able to perform physiologic noise filtering because physiologic
data were not available in this study. As in standard analyses of functional
connectivity datasets, 0.01- tο 0.10-Hz band-pass temporal filtering was used
to remove magnetic field drifts of the scanner (32) and physiologic noise of
high-frequency components (38).
Two parameters were used to calculate the lFCD: The correlation
threshold, TC, was used to determine significant correlations between voxels
and the MRI signal-to-noise ratio threshold, TSNR, was used to evaluate which
voxels of the image will be subject to correlation analyses. Taking into ac-
count that TC< 0.4 leads to increased false positive rate and increased CPU
time to compute the maps and that TC> 0.7 lead to lFCD maps with lower
sensitivity due to reduced dynamic range, we fixed TC= 0.6 for all calcu-
lations of FCDM. Similarly we fixed TSNR= 50 for all calculations of FCDM to
minimize the false positive rate of lFCD maps especially near air/tissue
interfaces, which are known to produce MRI signal loss artifacts (near the
sinus cavity and temporal bone). The number of functional connections
between a given voxel and other voxels was computed through correlation
using these threshold parameters. Specifically, we used Pearson’s linear
correlations to evaluate the strength of the functional connectivity between
voxels. Functional connections with correlation coefficient R > TC were
considered significant. The number of significant functional connections per
voxel in the local cluster, k, was computed using a three-dimensional
searching algorithm developed in IDL (ITT Visual Information Solutions) that
detects the boundaries of the voxel’s cluster using TCand TSNR. Thus, k is
determined when the boundary of the voxel’s functional cluster is com-
pletely detected. Then, the calculations involving cluster detection and
computation of significant functional connections are repeated for the next
imaging voxel. Thus, an lFCD map reflecting k was computed and saved in
Analyze format in hard drive for each subject. As in standard functional MRI
studies, spatial smoothing (8 mm) was necessary to minimize the differences
in the functional anatomy of the brain across subjects (35).
Global FCD. To evaluate the differential effect of long-range connectivity
on FCD and on CPU time we computed the gFCD for two of the datasets
(Baltimore and Ontario). The voxelwise and computer-demanding gFCD
calculation had the same spatial resolution, as well as preprocessing (re-
alignment, spatial normalization, and motion and temporal filtering) and
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postprocessing (spatial smoothing) steps as for lFCD, but it determines the Download full-text
number of significant connections (R > TC) without local cluster restrictions.
Principal Component Analyses. PCA was used to analyze the variability of
FCDMacrosssubjects.lFCD mapswithzero empirical meanwere calculated by
subtracting the average lFCD value across subjects from the lFCD data. Then,
we computed the principal components of FCDM datasets using the co-
variance of the data in IDL.
Statistical Analyses. GroupanalysesofFCDMwereperformedwithttestsusing
the general lineal model in SPM2. Clusters with pcorr< 0.05, corrected for
multiple comparisons using a familywise error (FWE) threshold, were consid-
ered significant in group analysis of FCDM. The Montreal Neurological In-
stitute (MNI) coordinates of the lFCD-cluster maxima were transformed to the
Talairach space using a best-fit transform (icbm_spm2tal; http://brainmap.org/
brain regions were labeled according to the Talairach daemon (http://www.
talairach.org/) and a query range of 5 mm to account for the spatial un-
included in the MRIcro software (http://www.cabiatl.com/mricro/).
Variability of the Hub Coordinates. A map of average lFCD across subjects was
computed and thecoordinates of thelFCD maximawere determined for each
research site using an automatic feature from accelerated segment test
(FAST) algorithm that was developed in IDL. The Euclidian distance,
across research sites, ðx0;y0;z0Þ, in Table 1 to the hub position for the i-
research site, ðxi;yi;ziÞ, was computed for the three main cortical hubs
[posterior cingulate/precuneus (BA 23/31), left inferior parietal (BA 40), and
right cuneus (BA 18)] and all research sites.
Di¼ðxi−x0Þ2þ ðyi−y0Þ2þ ðzi−z0Þ2
, from the average hub position
ROI Analyses. Isotropic cubic masks containing 27 imaging voxels (0.73 mL)
were defined at the centers of relevant functional connectivity hubs (Table 1)
to extract the average strength of the lFCD signal from individual lFCD maps.
The average and standard deviation values of the lFCD within these ROIs
were computed for each subject using a custom program written in IDL.
lFCD Retest Reliability. The three sessions of the New York test–retest
(NYU_TRT) dataset were used to evaluate the reliability of FCDM. Specifi-
cally, the ROI-averaged lFCD coefficients kmijcorresponding to the 1 ≤ m ≤
M = 19 ROIs in Table 1, 1 ≤ i ≤ I = 25 subjects, and 1 ≤ j ≤ J = 3 sessions, were
used to compute the within,
subjects variance for each ROI from which the relative lFCD variability
within subjects ¼ 100×∑M
between subjects ¼ 100×∑M
were estimated. Note that km
sessions, subjects, and both sessions and subjects for each ROI, respectively.
i:; and km
::are the averages of kmacross
ACKNOWLEDGMENTS. This work was accomplished with support from
National Institutes of Alcohol Abuse and Alcoholism Grant 2RO1AA09481.
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| www.pnas.org/cgi/doi/10.1073/pnas.1001414107Tomasi and Volkow