Maturation trajectories of cortical resting-state networks depend on the
mediating frequency band
, Javeria A. Hashmi
, Fahimeh Mamashli
, Manfred G. Kitzbichler
, Hari Bharadwaj
, Yousra Bekhti
, Keri-Lee A. Garel
, Susan Whitﬁeld-Gabrieli
, Randy L. Gollub
, Lucia M. Vaina
, Kunjan D. Rana
, Steven M. Stufﬂebeam
Matti S. H€
, Tal Kenet
Department of Neurology, MGH, Harvard Medical School, Boston, USA
Department of Psychiatry MGH, Harvard Medical School, Boston, USA
Department of Radiology, MGH, Harvard Medical School, Boston, USA
Athinoula A. Martinos Center for Biomedical Imaging, MGH/HST, Charlestown, USA
McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, USA
Department of Biomedical Engineering, Boston University, Boston, USA
The functional signiﬁcance of resting state networks and their abnormal manifestations in psychiatric disorders
are ﬁrmly established, as is the importance of the cortical rhythms in mediating these networks. Resting state
networks are known to undergo substantial reorganization from childhood to adulthood, but whether distinct
cortical rhythms, which are generated by separable neural mechanisms and are often manifested abnormally in
psychiatric conditions, mediate maturation differentially, remains unknown. Using magnetoencephalography
(MEG) to map frequency band speciﬁc maturation of resting state networks from age 7 to 29 in 162 participants
(31 independent), we found signiﬁcant changes with age in networks mediated by the beta (13–30 Hz) and
gamma (31–80 Hz) bands. More speciﬁcally, gamma band mediated networks followed an expected asymptotic
trajectory, but beta band mediated networks followed a linear trajectory. Network integration increased with age
in gamma band mediated networks, while local segregation increased with age in beta band mediated networks.
Spatially, the hubs that changed in importance with age in the beta band mediated networks had relatively little
overlap with those that showed the greatest changes in the gamma band mediated networks. These ﬁndings are
relevant for our understanding of the neural mechanisms of cortical maturation, in both typical and atypical
Synchronous neuronal activity in the brain gives rise to rhythms, that
are known to be functionally signiﬁcant. These rhythms are commonly
divided into ﬁve fundamental frequency bands, most commonly classi-
ﬁed as delta (1–2 Hz), theta (3–7 Hz), alpha (8–12 Hz), beta (13–30 Hz),
and gamma (31–80 Hz) (Buzs
aki, 2006). One of the hypothesized roles of
these rhythms is in forming neuronal ensembles, or networks, via local
and longer-range synchronization, across spatially distributed regions
(Fries, 2005, 2015; Siegel et al., 2012; Bastos et al., 2015). Brain net-
works that emerge in the absence of any directive task or stimulus,
referred to as resting state networks (Raichle et al., 2001; Raichle, 2015),
* Corresponding author. Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Massachusetts Institute of
Technology, 149 13th Street, CNY-2275, Boston, MA 02129, USA.
E-mail address: email@example.com (S. Khan).
Now at Department of Anesthesia Pain Management and Perioperative Medicine, Dalhousie University, Halifax, Canada.
Now at Department of Computer Science at Rutgers University, New Jersey, USA.
Now at Department of Psychiatry, University of Cambridge, Cambridge, UK.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/neuroimage
Received 14 June 2017; Accepted 10 February 2018
Available online 17 February 2018
1053-8119/©2018 Published by Elsevier Inc.
NeuroImage 174 (2018) 57–68
have attracted particular interest due to their consistency across and
within individuals. Abnormalities in these networks are also emerging as
a hallmark of psychiatric and developmental disorders (Broyd et al.,
2009; Toussaint et al., 2014; Kitzbichler et al., 2015), further under-
scoring their functional signiﬁcance. While resting state networks have
been studied extensively using fcMRI (functional connectivity MRI), a
technique that relies on the slow hemodynamic signal and thus has a
maximal temporal resolution of about 1 Hz, studies using high temporal
resolution magnetoencephalography (MEG), have conﬁrmed that the
ﬁve fundamental faster rhythms mediate these networks in
non-overlapping patterns (de Pasquale et al., 2010; Hipp et al., 2012).
As part of understanding the function of resting state networks in
general, and their role in cognitive development and neuro-
developmental disorders in particular, it is important to map their
maturational trajectories, from childhood to adulthood. To date, our
knowledge of maturational changes in macro-scale functional networks
in the developing brain is largely based on task-free fcMRI studies.
Several such studies have shown developmental changes in resting state
brain networks, where regions associated with separate networks
become connected while closely linked local subnetworks lose some of
their connections with maturation (Dosenbach et al., 2010; Sato et al.,
2014, 2015). Most of these studies have concluded that network inte-
gration, how well different components of the network are connected,
increases with maturation, while network segregation, the differentia-
tion of the network into modules, or clusters, decreases with maturation.
The spatial distribution of hubs, the most highly connected brain regions,
also changes with maturation. Another feature examined in prior studies
is the small-world property of brain networks. Small world networks
optimize the balance between local and global efﬁciency. fcMRI studies
have not documented a change in the small world property of brain
networks with maturation from childhood, around age 7, to adulthood,
around age 31 (Fair et al., 2009). Network resilience, a measure of the
robustness of the network as hubs are removed, which has been used to
assess robustness in psychiatric disorders (Lo et al., 2015), has been
shown to be age dependent in infants (Gao et al., 2011), but age de-
pendency through maturation has not been studied. It has also been
shown that the association between global graph metrics characterizing
network properties and the ages of the participants follows an asymptotic
growth curve (Dosenbach et al., 2010).
While fMRI studies have greatly increased our understanding of the
development of resting state networks from childhood to adulthood,
the relative temporal coarseness of fcMRI makes it impossible to
differentiate maturational trajectories by frequency bands (Hipp and
Siegel, 2015). Mapping the contributions of distinct frequency bands to
maturational trajectories is critical because these rhythms are associ-
ated with distinct neurophysiological generators (Uhlhaas et al., 2008;
Ronnqvist et al., 2013), have been mapped to a multitude of cognitive
functions (Harris and Gordon, 2015), are known to themselves change
in power and phase synchrony with maturation (Uhlhaas et al., 2009,
To better understand the contribution of individual rhythms to
network maturation, we used MEG, which measures magnetic ﬁelds
associated with neural currents with millisecond time resolution, and has
a spatial resolution on the order of a centimeter (Lin et al., 2006a). We
chose to use graph theory with connectivity measured using envelope
correlations (Hipp et al., 2012) as the core metric, to analyze cortical
resting state (relaxed ﬁxation) MEG signals from 131 individuals (64
females), ages 7 to 29, in each of the ﬁve fundamental frequency bands.
We focused on ﬁve well-studied graph theory metrics because the
approach is well-suited for studying global network properties also in the
functional domain (Bullmore and Sporns, 2009, 2012; Rubinov and
Sporns, 2010; Misic et al., 2016; Bassett and Sporns, 2017). The results
were then validated using similar data from 31 individuals (16 females,
ages 21–28) from an independent early adulthood resting state data set
(Niso et al., 2015). The full distribution of participants is shown in Fig. S1
in SM. Lastly, to determine the relevance of these graph metrics to the
maturation of resting state networks within each frequency band, we
used machine learning to quantify the extent to which the MEG derived
graph metrics can be used to predict age, similarly to a prior resting state
networks study that used fMRI data (Dosenbach et al., 2010). We then
assessed whether the data from the independent dataset ﬁt on the same
Materials and methods
The analysis stream we followed is illustrated in Fig. 1.
The resting state paradigm consisted of a red ﬁxation cross at the
center of the screen, presented for 5 min continuously, while participants
were seated and instructed to ﬁxate on the cross. The ﬁxation stimulus
was generated and presented using the psychophysics toolbox (Brainard
and Vision, 1997;Pelli, 1997), and projected through an opening in the
wall onto a back-projection screen placed 100 cm in front of the partic-
ipant, inside a magnetically shielded room.
Fig. 1. Schematic illustration of pipeline.
From top left in a clockwise direction:
Resting state data are acquired using MEG,
and then mapped to the cortical surface. The
surface is then divided into regions (parcel-
lated), and envelopes are calculated for each
frequency band, in each region. The con-
nectivity between the regions is then
computed from the envelopes, and, ﬁnally,
connectivity metrics are derived.
S. Khan et al. NeuroImage 174 (2018) 57–68
Massachusetts general hospital (MGH) based participants
Our primary data were collected from 145 healthy subjects, ages
7–29, at MGH. Due to excessive motion, data from 14 subjects were
discarded. Because datasets from different MGH based studies were
combined here, no uniform behavioral measures were available across all
participants. IQ measured with the Kaufman Brief Intelligence Test –II
(Kaufman and Kaufman, 2004) was available for 68 of the participants.
Within this subgroup, no signiﬁcant change in IQ with age was observed
(Fig. S2), as expected, given that IQ is normalized by age. All the studies
that were pooled for this analysis screened for typical development and
health, but the approach varied. The full age and gender distribution of
the participants is shown in Figs. S1–A.
OMEGA project participants (McGill university)
To test our results on an independent dataset, resting-state MEG scans
from 31 additional young adult participants (ages 21–28) were obtained
from the OMEGA project (Niso et al., 2015), and chosen by order with
gender matching to the MGH cohort in that same age range, subject to
age restrictions. Note that the OMEGA project spans ages 21–75. While
we would have liked to test our results on data from younger subjects, no
pediatric MEG resting state data are currently openly available, so this
was not possible. The age and gender distributions of the participants are
shown in Figs. S1–B.
MRI/MEG data acquisition
MRI data acquisition and processing
T1-weighted, high resolution MPRAGE (Magnetization Prepared
Rapid Gradient Echo) structural images were acquired on either a 1.5 T
or a 3.0-T Siemens Trio whole-body MRI (magnetic resonance) scanner
(Siemens Medical Systems) using either 12 channels or 32 channel head
coil at MGH and MIT.
The structural data was preprocessed using FreeSurfer (Dale et al.,
1999; Fischl et al., 1999). After correcting for topological defects, cortical
surfaces were triangulated with dense meshes with ~130,000 vertices in
each hemisphere. To expose the sulci in the visualization of cortical data,
we used the inﬂated surfaces computed by FreeSurfer. For the 31 OMEGA
dataset participants, templates were constructed from age and gender
matched subjects from our data. The same processing steps are followed
on this template MRIs.
MEG data acquisition and processing
MEG data were acquired inside a magnetically shielded room (Khan
and Cohen, 2013) using a whole-head Elekta Neuromag VectorView
system composed of 306 sensors arranged in 102 triplets of two
orthogonal planar gradiometers and one magnetometer. The signals were
ﬁltered between 0.1 Hz and 200 Hz and sampled at 600 Hz. To allow
co-registration of the MEG and MRI data, the locations of three ﬁduciary
points (nasion and auricular points) that deﬁne a head-based coordinate
system, a set of points from the head surface, and the locations of the four
HPI coils were determined using a Fastrak digitizer (Polhemus Inc.,
Colchester, VT) integrated with the VectorView system. ECG as well as
Horizontal (HEOG) and Vertical electro-oculogram (VEOG) signals were
recorded. The position and orientation of the head with respect to the
MEG sensor array were recorded continuously throughout the session
with the help of four head position indicator (HPI) coils (Cheour et al.,
2004). At this stage, we monitored the continuous head position, blinks,
and eye movements in real time, and the session was restarted if exces-
sive noise due to the subject's eyes or head movement is recorded. In
particular, the subjects and head coils position were carefully visually
monitored continusouly, and the session was also restarted if any
slouching in the seated position was observed. Pillows, cushions, and
blankets were ﬁtted to each individual to address slouching, and read-
justed as needed if any slouching was observed. In addition to the human
resting state data, 5 min of data from the room void of a subject were
recorded before each session for noise estimation purposes.
The acquisition parameters are published elsewhere for the 31-sub-
jects from the OMEGA dataset (Niso et al., 2015). The OMEGA CTF ﬁles
were converted into a. ﬁfﬁle using mne_ctf2ﬁf function from MNE
(Gramfort et al., 2014). After this conversion, the subsequent processing
was the same as for the Vector View data.
Noise suppression and motion correction
The data were spatially ﬁltered using the signal space separation
(SSS) method (Taulu et al., 2004; Taulu and Simola, 2006) with Elekta
Neuromag Maxﬁlter software to suppress noise generated by sources
outside the brain. Since shielded room at MGH is three layers and we
have exclusion criteria for subject having dental artifact, only SSS is
applied and it temporal extension tSSS was not used. This procedure also
corrects for head motion using the continuous head position data
described in the previous section.
Since SSS is only available for Electa MEG systems, it was not applied
for OMEGA subjects, where data were collected with a CTF MEG system.
The heartbeats were identiﬁed using in-house MATLAB code modiﬁed
from QRS detector in BioSig (Vidaurre et al., 2011). Subsequently, a
signal-space projection (SSP) operator was created separately for mag-
netometers and gradiometers using the Singular Value Decomposition
(SVD) of the concatenated data segments containing the QRS complexes
as well as separately identiﬁed eye blinks (Nolte and H€
Data were also low-pass ﬁltered at 144 Hz to eliminate the HPI coil
Cortical space analysis
Mapping MEG data onto cortical space
The dense triangulation of the folded cortical surface provided by
FreeSurfer was decimated to a grid of 10,242 dipoles per hemisphere,
corresponding to a spacing of approximately 3mm between adjacent
source locations. To compute the forward solution, a boundary-element
model with a single compartment bounded by the inner surface of the
skull was assumed (H€
ainen and Sarvas, 1989). The watershed algo-
rithm in FreeSurfer was used to generate the inner skull surface tri-
angulations from the MRI scans of each participant. The current
distribution was estimated using the regularized minimum-norm estimate
(MNE) by ﬁxing the source orientation to be perpendicular to the cortex.
The regularized (regularization ¼0.1) noise covariance matrix that was
used to calculate the inverse operator was estimated from data acquired in
the absence of a subject before each session. This approach has been
validated using intracranial measurements (Dale et al., 2000). To reduce
the bias of the MNEs toward superﬁcial currents, we incorporated depth
weighting by adjusting the source covariance matrix, which has been
shown to increase spatial speciﬁcity (Lin et al., 2006b). All forward and
inverse calculations were done using MNE-C (Gramfort et al., 2014).
Correlation between age, and the norms of the columns of the gain matrix
We also examined the correlation between age, and the norms of the
columns of the gain matrix, separately for magnetometers and gradi-
ometers. The magnetometers showed no signiﬁcant correlation with age.
The gradiometers showed a small correlation in the frontal pole, in a
region that was not identiﬁed as a signiﬁcant hub in our results (see
Fig. S3). This is most likely due to the different in head size between the
youngest participants and the oldest ones. To minimize the effect of these
differences, we use both magnetometer and gradiometer data in our
source estimation procedure.
Cortical parcellation (labels)
FreeSurfer was used to automatically divide the cortex into 72 regions
(Fischl et al., 2004). After discarding “medial wall”and “corpus callosum”,
these regions were further divided in to a total of N¼448 cortical “labels
S. Khan et al. NeuroImage 174 (2018) 57–68
(Fig. S4)”, so that each label covers a similar area again using FreeSurfer.
We employed this high-resolution parcellation scheme because cortical
surface is very convoluted and averaging across a large label, which crosses
multiple sulci and gyri, can result in signal cancellation across the parcel.
Lastly, a high-resolution parcellation also reduces the dependence of the
results on the speciﬁc selection of the parcels.
We also checked that ﬁeld spread (spatial signal leakage) between
labels is not impacted by age by examining the correlation between age
and the mean cross-talk across labels (Hauk et al., 2011). The results
showed no correlation (Fig. S5).
Averaging the time series across a label
Owing to the ambiguity of individual vertex (dipole) orientations,
these time series were not averaged directly but ﬁrst aligned with the
dominant component of the multivariate set of time series before
calculating the label mean. In order to align sign of the time series across
vertices, we used SVD of the data XT¼UΣWT. The sign of the dot
product between the ﬁrst left singular vector Uand all other time-series
in a label was computed. If this sign was negative, we inverted the time-
series before averaging.
To verify that the label time series are meaningful, we computed the
Power Spectral Density (PSD, see Spectral Density, below) for occipital,
frontal, parietal, and temporal cortical regions within each age group, see
Time series analysis
Filtering and hilbert transform
The time series were band-pass ﬁltered and down sampled for faster
processing, while making sure that the sampling frequency was main-
tained at fs>3fhi (obeying the Nyquist theorem and avoiding aliasing
artifacts). The chosen frequency bands were delta (1–4 Hz), theta
(4–8 Hz), alpha (8–12 Hz), beta (13–30 Hz), and gamma (31–80 Hz). The
line frequency at 60 Hz was removed with a notch ﬁlter of bandwidth
1 Hz. Hilbert transform was then performed on this band pass data.
For each individual frequency band the analytic signal b
calculated by combining the original time series with its Hilbert trans-
form into a complex time series:
The resulting time series b
XðtÞcan be seen as a rotating vector in the
complex plane whose length corresponds to the envelope of the original
time series xðtÞand whose phase grows according to the dominant fre-
quency. Fig. 1, step 4 shows an example of a modulated envelope on the
top of the band pass data (carrier). An example of envelope PSD for the
gamma frequency band is shown in Fig. S7.
At this stage further artifact cleaning was performed as follows: signal
spikes where the amplitude is higher than 5
over the course were
identiﬁed and dropped over a width of 5 periods.
To remove the effect of microsaccades, HEOG and VEOG channels
were ﬁltered at a pass-band of 31–80 Hz. The envelope was then calcu-
lated for the ﬁltered signals and averaged to get REOG. Peaks exceeding
three standard deviations above the mean calculated over the whole-time
course, were identiﬁed and the corresponding periods were discarded
from subsequent analysis.
Head movement recordings from the HPI coils were used to drop
these 1 s blocks where the average head movement exceeded 1.7 mm/s
(empirical threshold). The amount of data lost through cleaning was well
below 10% and did not differed signiﬁcantly with age.
We used a method based upon envelope correlations to reliably es-
timate synchronicity between different cortical labels (Colclough et al.,
2016). In contrast to phase-based connectivity metrics envelope corre-
lations measure how the amplitude of an envelope within a frequency
band is synchronously modulated over time across distinct cortical re-
gions, as illustrated in the fourth panel of Fig. 1. Previous studies
(humans and primates) have demonstrated the validity and functional
signiﬁcance of these synchronous envelope amplitude modulations
(Brookes et al., 2011, 2016; Vidal et al., 2012; Wang et al., 2012; Col-
clough et al., 2016) for both oscillatory and broadband signals.
To address the ﬁeld-spread problem associated with MEG data
(Sekihara et al., 2011), we used the previously described orthogonal
(Hipp et al., 2012) variation of envelope correlation metric. This method
requires any two putatively dependent signals to have non-zero lag and is
thus insensitive to the zero-lag correlations stemming from ﬁeld-spread.
Mathematically, the connectivity between two complex signals b
Yis calculated by “orthogonalizing”one signal with respect to the other
Y?Xðt;fÞ, and subsequently taking the Pearson correlation be-
tween their envelopes. This is done in both directions and the two results
are averaged to give the ﬁnal connectivity measureC?ðb
Due to the slow time course of these envelopes and to ensure enough
independent samples are available in the correlation window (Hipp et al.,
2012), we calculated the orthogonal connectivity using an overlapping
sliding window of 30 s with a stride of 1=8 of the window size. Fig. S7
demonstrate this method on gamma envelopes.
Lastly, note that this method does not address the problem of spurious
correlations appearing due to source spread (Sekihara et al., 2011),
which is difﬁcult to address. Therefore, spurious correlations coupled
with the use of high resolution cortical parcellation can skew the topo-
logical metrics used in this study. Please see (Palva et al., 2017) for a
comprehensive and detailed discussion of these confounds.
The connectivity and adjacency matrices
As a starting point for calculating the graph theoretic metrics we used
the connectivity matrix, which contained the orthogonal correlations
between all NNnode pairs and at each time window. A separate
matrix was computed for each frequency band. The ﬁnal result of the
processing pipeline is a connectivity array of dimension NNNTime
NBands for each subject. In order to increase signal to noise, we collapsed
the connectivity array along the temporal dimension by taking the me-
dian of each pairwise orthogonal correlation across time windows.
Thresholding and binarizing the connectivity matrix results in the
We used a threshold proportional scheme to retain a given proportion
of the strongest connectivity matrix entries inA. Speciﬁcally, adjacency
matrixA, were constructed using a ﬁxed cost threshold, ensuring that the
density or number of connections of the network is equated across all
individuals and age groups. Cost is a measure of the percentage of con-
nections for each label in relation to all connections of the network. Since
the total number of connections is the same for all participants, and is
determined by the number of nodes being considered, the use of a ﬁxed
cost, i.e. ﬁxed percentage threshold, allows for exactly equal numbers of
connections across participants. This is important to ensure graph metrics
can be compared across all individuals and age groups. As there is no
rationale for using a cost threshold, therefore we compared graph
network properties for a wide range of cost, we used thresholding range
from 5% to 30% at increments of 5%. For the graph metrics to be reliable,
it should be consistent over range of thresholds. Please see Table S1 for
example of consistency of our results. We also checked that important
S. Khan et al. NeuroImage 174 (2018) 57–68
hubs for all frequency bands are in line with previous published studies
(Brookes et al., 2011; Hipp et al., 2012; Colclough et al., 2016) as shown
in Fig. S8.
The adjacency matrix Adeﬁnes a graph Gin the form of pairs of
nodes that are connected by an edge. Thus, Ais deﬁned such that its
binary elements Aij are either 1 or 0 depending whether the edge eij
between nodes viand vjexists or not:
In addition, we also computed a weighted adjacency matrix which
preserves the correlation values above the same thresholds. A more
comprehensive description can be found elsewhere (Watts and Strogatz,
1998). For Fig. 3B, D and 4B,D, the original adjacency matrices were
averaged within age-groups and then thresholded for visualization
The average shortest path length between all pairs of nodes was
where the topological distance dij between nodes viand vjis deﬁned as
the minimum number of edges one has to traverse in order to get from
one node to the other
dij ¼min njAn½i;j 6¼ 0g
where Andenotes the nth power of the adjacency matrix Aand iand jare
row and column indices of the resulting matrix.
The degree of a node viin a Graph Gis deﬁned as
where eij is the ith row and jth column edge of adjacency matrix A.
The degree maps, averaged across all participants in the adult group
(ages 22–29), for all bands, are shown in Fig. S8.
We also computed weighted degree (unthresholded mean connec-
tivity with respect to age, also known as mean node strength) for alpha
and beta (Fig. S9), and, as expected, the results are in line with prior
ﬁndings showing increase in overall connectivity with age (Sch€
afer et al.,
Fig. 2. Network efﬁciency increases locally in beta
band networks and globally in gamma band net-
works. A. LOESS plot (solid white line) for the rela-
tionship between age and local network efﬁciency of
beta band mediated networks. The individual data
points are represented using a normalized density col-
ormap, where each data point corresponds to one
realization of the bootstrap procedure. B. Same, for
gamma band mediated networks, and global efﬁciency.
Fig. 3. Spatial distribution and connec-
tivity patterns of growing and shrinking
betwnness centrality of hubs.A. Hub re-
gions with growing (red) and shrinking
(blue) betweenness centrality scores, in beta
band mediated networks. B. Visual repre-
sentation of the connections from 4 hubs
with shrinking betweenness centrality
scores (blue) and 1 hub with growing
betweenness centrality scores (red), aver-
aged for children (7–13), adolescents
(14–21) and young adults (22–29), dis-
played at 0.25 thesholding in beta band
mediated networks. C. Same as A, for the
gamma band mediated networks. D. Same
as B, for 3 growing and 1 shrinking hubs, for
the gamma band mediated networks. No-
tation: IPS: right intraparietal sulcus, PFC:
right dorsolateral prefrontal cortex, IFG:
right inferior frontal gyrus, OFC: right
orbitofrontal cortex, STG: superior temporal
gyrus, FEF: right frontal eye ﬁeld, IPS: right
intraparietal sulcus, SMA: supplementary
motor areas, Occ: Occipital cortex.
S. Khan et al. NeuroImage 174 (2018) 57–68
The local clustering coefﬁcient in the neighborhood of vertex viis
deﬁned as the ratio of actual and maximally possible edges in the graph
Gi, which is equivalent to the graph density of Gi:
Global and local efﬁciencies
Global efﬁciency measures the efﬁciency of information transfer
through the entire network, and is assessed by mean path length. While
the concept of path length is intuitive in anatomical networks, it is also
relevant for functional networks, since a particular functional connection
may travel different anatomical paths, and while the correspondence
between the two is generally high, it is not necessarily identical (Bull-
more and Sporns, 2009; Misic et al., 2016; Bassett and Sporns, 2017).
Local efﬁciency is related to the clustering of a network, i.e. the extent to
which nearest neighbors are interconnected. Thus, it assesses the efﬁ-
ciency of connectivity over adjacent brain regions.
The average global efﬁciency of information transfer in graph G
having nnodes can be calculated from the inverse of the edge distances
Eglob ¼EðGÞ¼ 1
The quantity above is a measure of the global efﬁciency of informa-
tion transfer for the whole graph G. There is also a local efﬁciency for
each vertex vimeasuring how efﬁciently its neighbors can communicate
when vertex viis removed. If the subgraph of all neighbors of viis denoted
by Gi, then its local efﬁciency EðGiÞis approximately equivalent to the
clustering coefﬁcient Ci(Achard and Bullmore, 2007).
We also computed weighted analogues of local and global efﬁciencies
which used C?-weighted edge distances di;j. This weighted analogue
shows the same trend as a function of age as the unweighted one, please
see Fig. 2 and Fig. S10.
Small world property is a measure of optimization of the balance
between short and long-range connections (Bassett and Bullmore, 2006).
When graph Gthat provides optimal balance between local and global
information transfer, it is called a small-world graph. The
small-worldness of a network is often characterized by two key metrics:
the clustering coefﬁcient Cand the characteristic path length L:To
evaluate the small-world topology of brain networks, these topological
parameters must be benchmarked against corresponding mean values of
a null random graph. A network Gis a small-world network if it has a
similar path length but greater clustering of nodes than an equivalent
enyi (E–R) random graph Grand:
where Crand and Lrand are the mean clustering coefﬁcient and the char-
acteristic path length of the equivalent Grand graph.
Betweenness centrality pertains to individual nodes in the network,
rather than the network as a whole, and assesses how many of the
shortest paths between all other node pairs in the network pass through
that node. Nodes with high betweenness centrality (hubs) are therefore
more important for overall network efﬁciency.
The betweenness centrality of node iis deﬁned as:
is the total number of shortest paths (paths with the shortest
path length) from node mto node n, and
(i) is the number of shortest
paths from node mto node nthat pass through node i. Betweenness
centrality of a node thus reﬂects the control and inﬂuence of that node on
other nodes. Nodes with high betweenness centrality have a high impact
on information transferal and collaboration between disparate sub-
Resilience measures the robustness of the network if the most heavily
connected nodes (hubs) are removed. This measure is inversely related to
small world property (Peng et al., 2016). We chose this measure because
it has been studied, mostly using fMRI, in the context of psychiatric
disorders, where multiple hubs might be functioning abnormally (Achard
et al., 2006; Lo et al., 2015). It has also been shown that greater resilience
in a functionally derived task-driven network is associated with greater
inhibitory control cognitively (Spielberg et al., 2015), a function that is
often impaired in neurodevelopmental and psychiatric disorders.
Importantly, the measure incorporates network topology in conjunction
with the spatial distribution of hubs, because it takes the degree, i.e. the
number of connections, of individual nodes into account.
Resilience quantiﬁes the Graph G’s robustness to targeted or random
attacks. Targeted attacks remove nodes in the descending order of de-
gree. At each attack, global efﬁciency is computed. Robustness is deﬁned
as the ratio of the original efﬁciency with efﬁciency calculated after
attack. This process is repeated until all nodes are removed. Graph where
the connectivity probability follows a power law distribution (i.e. scale
free networks) are very robust in the face of random failures. This
property of networks mathematically described by a power law function
pðkÞ∝kywhere pðkÞis the probability of a node having k links is and y is
the exponent. When plotted in a log-log plot, this relationship follows a
straight line with slope -y, i.e. resilience is the slope of the degree
The Power Spectral Density (PSD) (0.1–80 Hz, logarithmically
distributed) in Fig. S6 was computed on single trial data from each label
using the multitaper method (MTM) based on discrete prolate spheroidal
sequences (Slepian sequences) taper (Thomson, 1982) with 1.5 Hz
smoothing as implemented in MNE-Python. PSD (0.033–1 Hz, logarith-
mically distributed) in Fig. S7 of gamma envelope was also computed
using multitaper method with spectral smoothing of 0.02 Hz.
To evaluate the relationship between a network quantity and age, we
used Spearman correlation (degree of freedom ¼129). The p-values were
computed after correcting for multiple comparisons across the correction
space of frequency bands, thresholds, and graph metrics by controlling
for family-wise error rate using maximum statistics through permutation
testing (Groppe et al., 2011).
The corrected p-values are shown in Table S1. Speciﬁcally, the
correction for multiple comparisons was done by constructing an
empirical null distribution. For this purpose, np¼1000,000 realizations
were computed by ﬁrst randomizing age and then correlating it with all
graph metrics at all thresholds and frequency bands, and ﬁnally taking
maximum correlation value across this permuted correction space. This
null distribution is shown in Fig. S11. The corrected p-values (pc) were
S. Khan et al. NeuroImage 174 (2018) 57–68
where nis the number values in the empirical null distribution greater or
lower than the observed positive or negative correlation value, respec-
tively. The factor of two stems from the fact that the test is two-tailed.
Correlations resulting in signiﬁcant p-values were then again tested
using Robust Correlation (Pernet et al., 2013), which strictly checks for
false positive correlations using bootstrap resampling.
Effect size for correlation was computed using cohen's d:
where ris the correlation coefﬁcient.
For the purposes of visualizing the signiﬁcance of age effects and
assessing uncertainties in the graph metrics with respect to age, we used
nested bootstrapping with 1024 realizations.
The nested bootstrap procedure approximates the joint distribution of
age xwith the age-dependent network metric f(y
), where f(y
) is the
average network metric over many subjects of age x(see notes below).
We observed npairs ðxi;yiÞ, where xiis the age and yithe corresponding
imaging data for the ith subject. Ideally, we would like to observe (x
denotes the (conceptual) average of subjects chosen at random
from a population, where each subject is of age x. Let f(y) denote the
function which maps imaging data to a scalar metric describing some
aspect of a network. Since y
contains noise, to visualize and estimate
uncertainties in graph metrics we can approximate (x
where the * denotes a bootstrap sample. We can then evaluate f(y
instead of f(y
). Each realization of bootstraping yielded one average
network metric and one value for the mean age of the group. Each data
point on the normalized density colormap corresponds to one realization
of the bootstrap (Figs. 2 and 4A and B and Fig. 5 inserts). Lastly, the
correlation values were computed using the original data only, not on the
bootsrapped data described here.
We used the non-parametric LOESS regression to ﬁt a curve to the
data (Cleveland and Loader, 1996). To protect against overﬁtting in
estimating bandwidth, we used 10-fold cross validation. We generated
our predictive model using the data in the training set, and then
measured the accuracy of the model using the data in the test set. We
tested a range of bandwidths from .01 to .99 with .01 step. The band-
width resulting in least sum of squares error was then selected (Webel,
Machine learning (multivariate regression using random forest)
All the graph metrics calculated for each band were combined under a
single non-parametric multivariate regression model using Random-
Forest (Breiman, 2001; Liaw and Wiener, 2002).
a) Maturity Index (prediction of age using random forest regression
model) for beta band (MI-beta) was computed using the beta band
network graph metrics: local efﬁciency, small world property, and
b) Maturity Index for gamma band (MI-gamma) was computed using the
gamma band network graph metrics: global efﬁciency, small world
property and resilience.
c) Maturity Index for both beta and gamma band (MI-combined) was
computed using all of the above features.
Lastly, we ﬁt a parametric curve to each of the maturity index,
parametric model for curve ﬁtting was selected using Akaike information
criterion (AIC). Below we provide details for each step of this procedure.
Random forest regression analysis
Random forest (RF), a method for non-parametric regression which is
robust in avoiding overﬁtting (Breiman, 2001), was implemented in R
using the randomForest package (Liaw and Wiener, 2002). As a further
step to avoid overﬁtting, each RF regressor model was trained on the
Fig. 4. Small world property is age and frequency band dependent.A. LOESS plot (solid white line) for the relationship between age and small world property for
beta band mediated networks. The individual data points are represented using a normalized density colormap, where each data point corresponds to one realization
of the bootstrap procedure (same colorbar as in Fig. 2A). B. A visual representation of connections and hubs in the three age groups, averaged for children (7–13),
adolescents (14–21) and young adults (22–29), in the beta band mediated networks, displayed at 0.25 thesholding. Degree represents the size of the hub. C. Same as A,
but for the gamma band mediated networks. D. Same as B, but for the gamma band mediated networks.
S. Khan et al. NeuroImage 174 (2018) 57–68
stratiﬁed 70% of the data (training set) and then tested in remaining
stratiﬁed 30% test-set. The possibility of bias introduced by the random
choice of the test set was avoided by repeating the sampling 1000 times.
The ﬁnal model represents the aggregate of the 1000 sampling events.
Random forest parameter optimization
The optimal number of variables randomly sampled as candidates at
each split was selected as p/3 where p is the number of features in the
model (Breiman, 2001). A total of 1000 decision trees were grown to
ensure out-of-bag (OOB) error converges (Breiman, 2001).
Features (MI-beta, MI-gamma, MI-combined)
MI-beta (Fig. 6A) was derived using machine learning with three
features computed in the beta band networks: local efﬁciency, small
world property, and resilience as manifested by the slope of the degree
distribution. MI-gamma (Fig. 6B) was derived using machine learning
with three features computed in the gamma band networks: global efﬁ-
ciency, small world property and resilience as manifested by the slope of
the degree distribution. MI-combined (Fig. 6C), as its name implies, was
computed using machine learning with all six of the above features. The
predicted ages for all subjects from the random forest regression model
were converted to the maturation indices deﬁned above, using a pub-
lished scaling scheme (Dosenbach et al., 2010), by setting the mean
predicted brain age to 1, for typically developed young adults. Feature
(variable) importance was also computed using random forest regression
model by estimating Percent Increase Mean Square Error (%IncMSE). %
IncMSE was obtained by permuting the values of each features of the test
set and comparing the prediction with the unpermuted test set prediction
of the feature (normalized by the standard error)., where %IncMSE is the
average increase in squared residuals of the test set when the feature is
permuted. A higher %IncMSE value represents a higher variable impor-
tance (Fig. 6D).
The models (Linear, exponential, quadratic, Von Bertalanffy) for best
ﬁtted curve (Matlab's Curve Fitting Toolbox) were compared using
Akaike information criterion (AIC). Given a set of models for the data,
AIC is a measure that assesses the quality of each model, relative to the
remaining models in the set. The chosen model minimizes the Kullback-
Leibler distance between the model and the ground truth. The model
with the lowest AIC is considered the best model among all models
speciﬁed for the data at hand. The absolute AIC values are not particu-
larly meaningful since they are speciﬁc to the data set being modeled.
The relative AIC value (ΔAIC
- min [AIC
]) is used to rank models
(Akaike, 1974). The model with the minimum AIC was selected as the
best model. To quantify goodness of ﬁt, we also computed R-squared (R2;
Fig. 5. Resilience in Gamma and beta mediated
networks follows opposite developmental trajec-
tories.A: Main plot - Solid line mean resilience,
combined for all ages, plotted as the decrease in
global efﬁciency as a function of percent nodes
removed in beta band mediated networks, from
largest to smallest. Dashed lines mark conﬁdence in-
terval at two standard deviations. For each point on
the average curve, we computed whether there was a
signiﬁcant age effect. When age was a factor in
resilience, that line between the upper and lower
conﬁdence interval for that point on the curve was
assigned a color. The color marks the correlation co-
efﬁcient of the effect of age, thresholded at p <0.05
corrected (i.e. at signiﬁcance). The colorbar at the
bottom left shows the colormap of strength of the
correlation coefﬁcient. A-Inset: LOESS plot of one
instance of the effect of age, at 54% of nodes
removed, where signiﬁcance of age effect was maximal. The individual data points are represented using a normalized density colormap, where each data point
corresponds to one realization of the bootstrap procedure (same colorbar as in Fig. 2A). While the exact numbers differed for different percent nodes removed, the
pattern was always identical, showing a negative correlation with age for the gamma band mediated networks. B: Main plot - Same as A, but for gamma band mediated
networks. The white patch between 60% and 80% nodes removed indicates there was no impact of age in that range. B-Inset: Same as A-Inset, for the beta band, at
19% of nodes removed, where signiﬁcance of age effect was maximal. Again, whenever there was a signiﬁcant age effect, marked by colors on the main curve, the
pattern was identical, showing a positive correlation with age for the beta band mediated networks.
Fig. 6. Classiﬁcation by maturation curve. Green circles represent results for individual study participants (“MGH”) Orange circles represent values for participants
from the independent OMEGA database (OMEGA), that were not used during the learning phase in the machine learning analysis. A. MI-beta (R2 ¼0.39 MGH,
R2 ¼0.34 OMEGA) plotted relative to age. B. MI-gamma (R2 ¼0.48 MGH, R2 ¼0.33 OMEGA) plotted relative to age. C. The combined MI for beta and gamma
(R2 ¼0.52 MGH, R2 ¼0.41 OMEGA) plotted relative to age. D. The relative contribution (variable importance computed using random forest regression) of each of
the parameters to the model. Notation: GE: global efﬁciency; LE: local efﬁciency; RI: Resilience index (see SM). SW: Small world property. Orange circles in panels A–C
mark the participants from the OMEGA data set.
S. Khan et al. NeuroImage 174 (2018) 57–68
coefﬁcient of determination) for best ﬁtted regression models.
Independent data set veriﬁcation
To verify whether the regression models obtained here were consis-
tent with data collected independently, in a different site, using a
different MEG machine (CTF 275), MEG resting state scans from 31
participants from OMEGA project (Niso G et al., 2015) were also exam-
ined. Random forest regression models learned using our primary, MGH
based, dataset, were then applied to the previously unseen OMEGA
project data, with no additional training. The predicted maturity indices
of the OMEGA sourced subject are shown as orange dots in Fig. 6.To
quantify goodness of ﬁt on this independent dataset, we also computed
R2 between the values from the OMEGA dataset and predictions from
models learned from the MGH dataset.
Prediction interval calculation
The prediction interval for the best ﬁtted curve in Fig. 6 was obtained
using Scheffe's method (Maxwell and Delaney, 1990).
In this method, the prediction interval sð
;gÞis deﬁned as:
where g is the model order (2), n is the number of subjects (131),
signiﬁcance level chosen as 0:05=nc(nc¼3;total number of curves),
;g;n2Þis the F-distribution.
Custom code was written in MATLAB to build circle plots for graph-
ically representing connectivity in the three age groups. To represent
nodes on the brain, custom code in PySurfer was written using Python.
The increases and decreases in connections and topography were rep-
resented by using connectivity patterns shown as graphs, with the tool
Gephi. This method uses a spring embedding data-driven technique to
align regions in two dimensional space based on strength of connections
(Fair et al., 2008). For Fig. 3B, D, 4B and 4D, original adjacency matrices
were averaged within age-groups and then thresholded for
Age-dependent trajectories of network integration by frequency band
The local and global efﬁciency graph theory metrics were used to
evaluate the age-dependent trajectory of local and global network inte-
gration, respectively. These metrics were evaluated in each of the ﬁve
frequency bands. Signiﬁcant age-dependent changes in local, but not
global, efﬁciency emerged only in the beta band (Fig. 2A). In parallel,
signiﬁcant age-dependent changes in global, but not local, efﬁciency
emerged only in the gamma band (Fig. 2B). These changes were signif-
icant across multiple thresholds (Table S1-A,B). No other signiﬁcant age
dependent changes emerged in any of the other frequency bands
(Fig. S12). We also tested the weighted network analogues for the same
metrics, and the results followed a similar trend (Fig. S10). Therefore, the
remaining computations were carried out in unweighted networks.
Age-dependent trajectories of cortical hubs by frequency band
To assess age dependent changes in spatial distribution of hubs, we
measured correlation between age and the betweenness centrality of
nodes. In networks mediated by the beta band, loss of betweenness
centrality score with age was seen mostly in frontal and temporal hubs,
while gain of betweenness centrality score with age was seen mostly in
parietal hubs (Fig. 3A,B). In networks mediated by the gamma bands, loss
of betweenness centrality score with age was seen mostly in occipital
hubs, while gain of betweenness centrality score with age was seen
mostly in frontal and parietal hubs (Fig. 3C,D).
Age-dependent trajectories of small world property by frequency band
Given the differentiation in age-dependent trajectories between the
beta and gamma bands, we next examined the small world property of
the networks mediated by each of these frequency bands. While network
coefﬁcients in both the beta and gamma bands met small world criteria,
we found a signiﬁcant increase with age in small world property with
maturation in the beta band (Fig. 4A,B), alongside a signiﬁcant decrease
with age in small world property in the gamma band (Fig. 4C,D). These
changes in beta and gamma bands were also consistent across multiple
thresholds (Tables S1–Cfor threshold speciﬁc p-values).
Age-dependent trajectories of network resilience by frequency band
We next evaluated how network resilience, a graph theoretical metric
which measures the vulnerability of the network to attacks (by removal)
on the most connected hubs, changed with age in beta and gamma band
mediated networks. To assess resilience, we quantiﬁed the reduction in
global efﬁciency as hubs were removed in order of connectedness, from
largest to smallest. We found signiﬁcant age dependent differences in
network resilience in both the beta band (Fig. 5A) and the gamma band
(Fig. 5B) mediated networks. While the signiﬁcance of the age effect
differed by percentage of nodes removed, whenever there was a signiﬁ-
cant age effect, the trend was similar; resilience weakened with age in the
beta band mediated networks, but strengthened with age in the gamma
band mediated networks, as shown in the insets of Fig. 5. We repeated the
same analysis with local efﬁciency as the parameter, as well as with
attacking the connections rather than the hubs. The results followed the
same trajectory in all cases, with resilience weakening with age in the
beta band, and increasing with age in the gamma band.
Age prediction by frequency band speciﬁc properties
We next tested whether the graph metrics assessed here could be used
to predict individual brain maturity. Given the different trajectory
observed in the beta and gamma band mediated networks, we began by
assessing age-based prediction using random forest regression within
each set of networks separately. For the beta band, we deﬁned a beta
Maturity Index, MI-beta, using local efﬁciency, small world property, and
resilience parameters from the beta mediated networks. When MI-beta
was plotted relative to age, we found that age prediction follows a
linear trajectory (Fig. 6A). For the gamma band, likewise, we deﬁned a
gamma maturity index, MI-gamma, using global efﬁciency, small world
property, and resilience parameters from the gamma mediated networks.
When MI-gamma was plotted relative to age, we found that prediction
followed a non-linear quadratic asymptotic growth curve trajectory
(Fig. 6B). Combining the two sets of measures resulted in a non-linear
Von Bertalanffy growth curve that yielded signiﬁcantly increased pre-
diction accuracy (Fig. 6C). The relative information (explained variance)
of each of the parameters is shown in Fig. 6D. MI-beta and MI-gamma
together accounted for 52% of the variance observed in the data. To
further test the reliability of the model, which was trained solely on MGH
data set, it was applied blindly to 31 participants from an independent
dataset (OMEGA), with no additional training. The data were plotted
alongside the MGH data, and indeed follow the same trajectories
We found that from age 7 to 29, resting state networks mediated by
the beta and gamma frequency bands underwent marked topological
reorganization, while resting state networks mediated by the slower
alpha, theta and delta frequency bands showed no signiﬁcant age
dependent changes in network topology, for the examined graph-
S. Khan et al. NeuroImage 174 (2018) 57–68
theoretical metrics. Importantly, the patterns of age-dependent changes
for the beta and gamma mediated networks differed substantially. Beta
band mediated networks became more locally efﬁcient, i.e. tending to-
wards clustering and more connections with adjacent regions with age,
while gamma band mediated networks became more globally efﬁcient,
i.e. tending towards shorter overall path lengths and thus faster
communication across larger cortical distances, with age. Additionally,
the contribution and importance of many hubs to the overall network
efﬁciency, measured using betweenness centrality, grew or shrunk with
age, but a different set of hubs showed this pattern for beta and gamma
mediated networks, with relatively little overlap. Since small world
property and resilience are inversely proportional to one another and
both depend on the relative magnitude of local and global efﬁciencies,
these measures presented opposite age-dependent trajectories for the
beta and gamma mediated networks. Speciﬁcally, small world property,
i.e. overall network optimization in balancing short and long connec-
tions, increased with age, while resilience, i.e. robustness of the network,
decreased with age in the beta band. The pattern was exactly opposite in
the gamma band mediated networks. Remarkably, the two sets of net-
works followed different growth trajectories, with the beta band medi-
ated networks best described with a linear, rather than an asymptotic,
growth curve, and the gamma band mediated networks best described by
a more expected asymptotic growth curve (Dosenbach et al., 2010).
These results extend prior fMRI based ﬁndings in several ways, most
notably by determining that only two out of the ﬁve fundamental fre-
quency bands, beta and gamma, mediated the resting state networks that
showed age-related changes, and that each followed a distinct trajectory,
and in the case of the beta band, that trajectory was unexpectedly linear.
Furthermore, contrary to prior suggestions from fMRI based studies (Fair
et al., 2009; Hwang et al., 2013), we found that the small world property,
which assesses the overall balance of the network in optimizing local
versus distant connections, did not remain constant through this age
range, and similarly, network resilience at a given age depended on the
underlying frequency. Lastly, as reported with fMRI (Fransson et al.,
2011; Menon, 2013), gamma band mediated networks showed devel-
opment of hubs in heteromodal regions such as posterior parietal, pos-
terior cingulate and the anterior insula. But unlike observations in fMRI
studies, beta band mediated networks showed a loss of hubs in
heteromodal-frontal regions, alongside growth in hubs in posterior pa-
The observation that only the resting state networks that were
mediated by the gamma and beta frequency bands showed signiﬁcant
topological reorganization with age may be driven by the fact that these
two bands are strongly associated with cognitive control (Buschman and
Miller, 2014; Roux and Uhlhaas, 2014), which matures over adolescence
(Luna et al., 2015). It is likely also related to the fact that both of these
high frequency rhythms are heavily dependent on GABAergic systems
(Uhlhaas et al., 2008; Sohal et al., 2009), which themselves undergo
extensive changes during development, well into adolescence. The
pattern of reduced frontal hubs observed in the beta band is in line with
observations showing reduced frontal task related activation with
maturation, for instance for inhibitory control, potentially due to
increased efﬁciency of top-down communication, putatively mediated by
the beta band (Ordaz et al., 2013). In particular, the linear growth tra-
jectory of the beta band mediated networks could be the result of the
continuing maturation and development of top-down projections, which
may be more likely to be mediated via the beta band (Buschman and
Miller, 2007; Wang, 2010). Indeed, many processes that are heavily
mediated via top-down connections, such as attention and verbal func-
tioning, peak past the age range examined here (Peters et al., 2014). In
contrast, the gamma band mediated networks followed the more ex-
pected asymptotic trajectory, which may reﬂect the completion of
maturation of bottom-up projections, which have been associated with
greater probability with the gamma band (Buschman and Miller, 2007;
The results using the resilience metric, i. e the measure of the
robustness of networks, are particularly intriguing in the context of
psychiatric disorders (Lo et al., 2015). In our prior studies, we have found
that resting state networks in ASD, ages 8–18, showed increased efﬁ-
ciency in the gamma band, but decreased efﬁciency in the beta band
(Kitzbichler et al., 2015). In parallel, studies have shown reduced efﬁ-
ciency in the alpha band in bipolar disorder and schizophrenia (Hinkley
et al., 2011; Kim et al., 2013, 2014), and abnormal resting state network
connectivity in the gamma band (Andreou et al., 2015). The observation
of resilience, a measure that depends on network efﬁciency, increased
with age in the beta band but decreased with age in the gamma band,
diverges from our original hypothesis of minimal resilience during
adolescence. However, it is possible that greater vulnerability during
adolescence arises from the fact that resilience is not optimized in this
age range in either network, and thus both are relatively more
The study does have several limitations the merit noting. One limi-
tation is that we chose to focus on eyes open with relaxed ﬁxation as our
resting state paradigm, rather than eyes closed, thus minimizing alpha
power. This was done to best align with parallel prior fMRI studies (Fair
et al., 2007, 2009; Dosenbach et al., 2010; Grayson et al., 2014), and to
follow the guidelines of the Human Connectome Project. Eyes-open
resting state networks derived using MEG also have greater test-retest
reliability than eyes-closed derived networks (Jin et al., 2011). While
some MEG/EEG studies do ﬁnd differences between the two conditions
(Jin et al., 2011; Tan et al., 2013; Tagliazucchi and Laufs, 2014; Miraglia
et al., 2016; Yu et al., 2016), overall, the differences between the eyes
closed and eyes open conditions in all of these studies were small.
Another limitation of the proposed study is that we only had IQ measures
available for a subset of the sample (N ¼68), and no other behavioral
measures uniformly across the sample. While we were able to show that
there is no relationship to IQ in the subset of the sample for which IQ was
available (Fig. S2), the absence of behavioral assessments means we were
not able to link the measures to any speciﬁc cognitive measures. A minor
limitation is a different in head size across development. Given that brain
size reaches 95% of its maximum size by age 6 (Giedd et al., 1999;
Lenroot and Giedd, 2006), and our minimum age is 7, the impact of
changing brain size is likely slight (see also Fig. S3 and methods 2.5.2),
but cannot be completely dismissed. Another important limitation is that
this study focuses solely on topological network properties. Develop-
mental studies of coherence for instance, clearly show increased coher-
ence in the beta band as well in the alpha band (Sch€
afer et al., 2014).
Indeed, when we look at changes with age of “degree”, which measures
the mean functional connectivity of each node, we ﬁnd age dependent
changes in the alpha band as well (Fig. S9), reproducing these prior re-
sults. Further studies will need to be carried out to elucidate the contri-
butions and relevance of topological versus more direct non-topological
properties such as coherence, to cognitive development. Lastly, the in-
dependent data set only spans ages 21–28, and not the full age range
studied here. As of now, unfortunately, there are no pediatric shared data
sets of resting state MEG data. Therefore, our independent data set was
by necessity limited in age range.
In summary, we show that developmental reﬁnement of resting state
networks as assessed by graph metrics is dependent on the mediating
frequency band, and age dependent changes in global network properties
occur only in the beta and gamma bands between the ages of 7 and 29.
Speciﬁcally, we show that gamma band mediated networks become more
globally efﬁcient with maturation, while beta band mediated networks
become more locally efﬁcient with maturation. Accordingly, the small
world property, which measures how optimally balanced local and global
efﬁciencies are, increased with age in beta band mediated networks, and
decreased with age in gamma mediated networks. To reconcile our re-
sults with prior fMRI ﬁndings on the development of topological network
properties, we need to consider the fact that since fMRI signal cannot be
used to distinguish signals from different frequency bands (Hipp and
Siegel, 2015), prior fMRI-based studies observed results from all fre-
quency bands combined. In such a scenario, it might indeed appear that
S. Khan et al. NeuroImage 174 (2018) 57–68
the small world property remains unchanged with age, as would resil-
ience, if the signals from the beta and gamma band were weighed
roughly equally in the fMRI signal. Similarly, because the combination of
a linear and a non-linear function results in a non-linear function, as
shown in Fig. 6C, the linear maturation trajectory observed here in beta
mediated networks would likely be missed by fMRI. This observed dif-
ferentiation between beta and gamma band mediated networks could
hint at underlying neural mechanisms in case of abnormal maturation.
For instance, disorders that are more impacted in the gamma band might
be more related to dysfunction in PV þinterneurons (Takada et al.,
2014). In contrast, disturbances in maturation in the beta band might be
more attributable to inhibitory-inhibitory connections (Jensen et al.,
2005). In combination, our ﬁndings signiﬁcantly advance our under-
standing of the complex dynamics behind oscillatory interactions that
subserve the maturation of resting state cortical networks in health, and
their disruptions in developmental and psychiatric or neurological
This work was supported by grants from the Nancy Lurie Marks
Family Foundation (TK, SK, MGK), Autism Speaks (TK), The Simons
Foundation (SFARI 239395, TK), The National Institute of Child Health
and Development (R01HD073254, TK), National Institute for Biomedical
Imaging and Bioengineering (P41EB015896, 5R01EB009048, MSH), and
the Cognitive Rhythms Collaborative: A Discovery Network (NFS
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