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Maturation trajectories of cortical resting-state networks depend on the

mediating frequency band

Sheraz Khan

a

,

c

,

d

,

e

,

4

,

*

, Javeria A. Hashmi

a

,

d

,

1

,

4

, Fahimeh Mamashli

a

,

d

,

Konstantinos Michmizos

a

,

d

,

2

, Manfred G. Kitzbichler

a

,

d

,

3

, Hari Bharadwaj

a

,

d

, Yousra Bekhti

a

,

d

,

Santosh Ganesan

a

,

d

, Keri-Lee A. Garel

a

,

d

, Susan Whitﬁeld-Gabrieli

e

, Randy L. Gollub

b

,

d

,

Jian Kong

b

,

d

, Lucia M. Vaina

a

,

f

, Kunjan D. Rana

f

, Steven M. Stufﬂebeam

c

,

d

,

Matti S. H€

am€

al€

ainen

c

,

d

, Tal Kenet

a

,

d

a

Department of Neurology, MGH, Harvard Medical School, Boston, USA

b

Department of Psychiatry MGH, Harvard Medical School, Boston, USA

c

Department of Radiology, MGH, Harvard Medical School, Boston, USA

d

Athinoula A. Martinos Center for Biomedical Imaging, MGH/HST, Charlestown, USA

e

McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, USA

f

Department of Biomedical Engineering, Boston University, Boston, USA

ARTICLE INFO

Keywords:

Development

Brain connectivity

Rhythms

Graph theory

Magnetoencephalography

ABSTRACT

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

development.

Introduction

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: sheraz@nmr.mgh.harvard.edu (S. Khan).

1

Now at Department of Anesthesia Pain Management and Perioperative Medicine, Dalhousie University, Halifax, Canada.

2

Now at Department of Computer Science at Rutgers University, New Jersey, USA.

3

Now at Department of Psychiatry, University of Cambridge, Cambridge, UK.

4

Equal contribution.

Contents lists available at ScienceDirect

NeuroImage

journal homepage: www.elsevier.com/locate/neuroimage

https://doi.org/10.1016/j.neuroimage.2018.02.018

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,

2010).

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

curves.

Materials and methods

The analysis stream we followed is illustrated in Fig. 1.

Experimental paradigm

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

58

Participants

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€

am€

al€

ainen, 2001).

Data were also low-pass ﬁltered at 144 Hz to eliminate the HPI coil

excitation signals.

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€

am€

al€

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

59

(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

Fig. S6.

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.

Hilbert transform

For each individual frequency band the analytic signal b

XðtÞwas

calculated by combining the original time series with its Hilbert trans-

form into a complex time series:

b

XðtÞ¼xðtÞþjH½xðtÞg (1)

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

σ

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.

Orthogonal correlations

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

Xand

b

Yis calculated by “orthogonalizing”one signal with respect to the other

b

Yðt;fÞ→b

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

X;b

Y;t;fÞ.

b

Y?Xðt;fÞ¼ℑb

Yðt;fÞb

Xyðt;fÞ

b

Xðt;fÞb

e?Xðt;fÞ(2)

C?b

X;b

Y;t;f¼Corrb

X;b

Y?XþCorrb

Y;b

X?Y

2(3)

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

adjacency matrixA.

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

60

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:

Aij ¼1if9eij

0if

∄

eij

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

purposes.

Path length

The average shortest path length between all pairs of nodes was

calculated as:

L¼1

nðn1ÞX

i6¼j;vi;vj2G

dij (4)

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.

Degree

The degree of a node viin a Graph Gis deﬁned as

Di¼X

n

j¼1;j6¼i

eij (5)

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.,

2014).

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

61

Clustering coefﬁcient

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:

Ci¼2ejk

kiðki1Þ:vj;vk2Gi(6)

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

di;j

Eglob ¼EðGÞ¼ 1

nðn1ÞX

i6¼j;vi;vj2G

1

dij

(7)

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).

Eloc ¼1

nX

vi2G

EðGiÞ(8)

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

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

Erd€

os-R

enyi (E–R) random graph Grand:

SW ¼C=Crand

L=Lrand 1(9)

where Crand and Lrand are the mean clustering coefﬁcient and the char-

acteristic path length of the equivalent Grand graph.

Betweenness centrality

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:

bi¼X

m6¼i6¼n2G

σ

mnðiÞ

σ

mn

(10)

where

σ

mn

is the total number of shortest paths (paths with the shortest

path length) from node mto node n, and

σ

mn

(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-

networks.

Resilience

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

distribution.

Spectral analysis

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.

Correlation

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

62

calculated as:

pc¼2ðnþ1Þ

npþ1(11)

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:

d¼

2r

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1r2

p(12)

where ris the correlation coefﬁcient.

Bootstraping

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

x

), where f(y

x

) 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

i

,y

x

),

where y

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

i

contains noise, to visualize and estimate

uncertainties in graph metrics we can approximate (x

i

,y

x

)by(x

*

,y

*

),

where the * denotes a bootstrap sample. We can then evaluate f(y

x*

)

instead of f(y

i

). 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.

LOWESS regression

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,

2006).

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).

More speciﬁcally:

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

resilience.

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

63

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).

Curve ﬁtting

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

i

¼AIC

i

- min [AIC

p

]) 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

64

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

α

;gÞis deﬁned as:

sð

α

;gÞ¼ ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

gFð1

α

;g;n2Þ

p(13)

where g is the model order (2), n is the number of subjects (131),

α

is the

signiﬁcance level chosen as 0:05=nc(nc¼3;total number of curves),

and Fð1

α

;g;n2Þis the F-distribution.

Graphical representation

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

visualizations.

Results

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

(Fig. 6A–C).

Discussion

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

65

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-

rietal regions.

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;

Wang, 2010).

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

vulnerable.

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

66

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

disorders.

Acknowledgments

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

1042134, MSH).

Appendix A. Supplementary data

Supplementary data related to this article can be found at https://doi.

org/10.1016/j.neuroimage.2018.02.018.

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