Available via license: CC BY-NC-ND 4.0
Content may be subject to copyright.
NeuroImage 224 (2021) 117429
Contents lists available at ScienceDirect
NeuroImage
journal homepage: www.elsevier.com/locate/neuroimage
Signal diusion along connectome gradients and inter-hub routing
dierentially contribute to dynamic human brain function
Bo-yong Park
a , ∗
, Reinder Vos de Wael
a
, Casey Paquola
a
, Sara Larivière
a
, Oualid Benkarim
a
,
Jessica Royer
a
, Shahin Tavakol
a
, Raul R. Cruces
a
, Qiongling Li
a
, Soe L. Valk
b , c
,
Daniel S. Margulies
d
, Bratislav Mi š i ća
, Danilo Bzdok
a , e
, Jonathan Smallwood
f
,
Boris C. Bernhardt
a , ∗
a
Multimodal Imaging and Connectome Analysis Lab, McConnell Brain Imaging Centre, Montreal Neurological Institute and Hospital, McGill University, Montreal,
Quebec, Canada
b
Institute of Neuroscience and Medicine (INM-7: Brain & Behaviour), Research Centre Jülich, Jülich, Germany
c
Institute of Systems Neuroscience, Medical Faculty, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
d
Frontlab, Institut du Cerveau et de la Moelle épinière, UPMC UMRS 1127, Inserm U 1127, CNRS UMR 7225, Paris, France
e
Mila - Quebec Artificial Intelligence Institute, Montreal, Quebec, Canada
f
Department of Psychology, York Neuroimaging Centre, University of York, New York, United Kingdom
Keywords:
structural connectome
gradients
functional dynamics
Hidden Markov Model
multimodal imaging
diusion MRI
Human cognition is dynamic, alternating over time between externally-focused states and more abstract, often
self-generated, patterns of thought. Although cognitive neuroscience has documented how networks anchor par-
ticular modes of brain function, mechanisms that describe transitions between distinct functional states remain
poorly understood. Here, we examined how time-varying changes in brain function emerge within the constraints
imposed by macroscale structural network organization. Studying a large cohort of healthy adults (n = 326), we
capitalized on manifold learning techniques that identify low dimensional representations of structural connec-
tome organization and we decomposed neurophysiological activity into distinct functional states and their tran-
sition patterns using Hidden Markov Models. Structural connectome organization predicted dynamic transitions
anchored in sensorimotor systems and those between sensorimotor and transmodal states. Connectome topology
analyses revealed that transitions involving sensorimotor states traversed short and intermediary distances and
adhered strongly to communication mechanisms of network diusion. Conversely, transitions between trans-
modal states involved spatially distributed hubs and increasingly engaged long-range routing. These ndings
establish that the structure of the cortex is optimized to allow neural states the freedom to vary between distinct
modes of processing, and so provides a key insight into the neural mechanisms that give rise to the exibility of
human cognition.
1. Introduction
A core assumption of neuroscience is that brain structure governs
ongoing function ( Batista-García-Ramó and Fernández-Verdecia, 2018 ;
Baum et al., 2020 ; Becker et al., 2018 ; Ciric et al., 2017 ;
Hermundstad et al., 2013 ; Honey et al., 2009 ; Mi ŝ ic et al., 2016 ;
Park and Friston, 2013 ; Rubinov et al., 2009 ; Snyder and Bauer, 2019 ;
Suárez et al., 2020 ; Vázquez-Rodríguez et al., 2019 ; Wang et al., 2019 ,
2015 ). However, at the heart of this question is a puzzle: Brain struc-
ture remains relatively constant across time, yet the neural hardware
ultimately supports the exible manner that an organism alters its reper-
toire of responses in line with changing external and internal demands.
∗ Corresponding authors.
E-mail addresses: bo.y.park@mcgill.ca (B.-y. Park), boris.bernhardt@mcgill.ca (B.C. Bernhardt).
In both humans and non-human primates, links between brain structure
and specic cognitive functions have been well established in a station-
ary manner ( Han et al., 2009 ; Mi ŝ ic et al., 2016 ; Wang et al., 2019 ). Al-
though these studies highlight links between specic neural patterns and
particular aspects of cognition ( Honey et al., 2009 ; Mi ŝ ic et al., 2016 ;
Wang et al., 2015 ), such analyses are not well suited to understanding
how the brain exibly changes between dierent modes of operation
( Allen et al., 2012 ; Bertolero et al., 2015 ; Friston et al., 2003 ; Kucyi et al.,
2018 ; Taghia et al., 2018 ). At the same time, contemporary neuroscience
has begun to recognize that global features of the connectome are also
important in how structure gives rise to function. Such views suggest
that systematic transitions across the cortex from sensorimotor regions
https://doi.org/10.1016/j.neuroimage.2020.117429
Received 14 April 2020; Received in revised form 13 September 2020; Accepted 30 September 2020
Available online 7 October 2020
1053-8119/© 2020 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license
( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
to transmodal association areas may support increasingly abstract ele-
ments of cognition ( Margulies et al., 2016 ; Mesulam, 1998 ). Moreover,
although these transmodal regions are spatially distributed, they are
also strongly interconnected, showing a rich-club architecture that im-
plies a role in the control of more integrated cognitive states ( Avena-
Koenigsberger et al., 2019 , 2018 ; Gria and van den Heuvel, 2018 ;
Mi ŝ ic et al., 2016 ; van den Heuvel et al., 2012 ). In this study, we explore
the hypothesis that specic features of cortical structural connectome or-
ganization support the transitions that brain makes between naturally
occurring neural states.
Recent advances in techniques for measuring brain organization and
function in vivo , such as diusion magnetic resonance imaging (dMRI)
and functional MRI (fMRI), have put systems neuroscience in an un-
precedented position to understand features of brain organization that
support exible transitions between dierent modes of neural opera-
tion ( Allen et al., 2012 ; Bertolero et al., 2015 ; Damaraju et al., 2014 ;
Friston et al., 2003 ; Kucyi et al., 2018 ; Lee et al., 2019 ; Park et al., 2019 ,
2018b; Razi et al., 2017 ; Taghia et al., 2018 ; Vidaurre et al., 2017 ). Our
current study combines state-of-the-art manifold learning techniques to
identify compact spatial representations of cortical structural connec-
tome organization, and we applied dynamic fMRI ananlysis to estimate
transient functional brain states ( Margulies et al., 2016 ; Vidaurre et al.,
2017 ). In the structural domain, we build on work capturing topological
organization of the cortex in a low dimensional manifold space, which
has recently provided novel insights into human cognition at macroscale
( Huntenburg et al., 2018 ; Margulies et al., 2016 ). Such techniques have
been widely adopted in resting-state fMRI (rs-fMRI) studies of specic
regions and the whole brain ( Hong et al., 2019 ; Larivière et al., 2019a ;
Margulies et al., 2016 ; Vos de Wael et al., 2018 ). However, manifold
learning applications to dMRI tractography data have so far focused on
specic areas ( Bajada et al., 2017 ; Cerliani et al., 2012 ), rather than
addressing whole-brain connectivity. In the functional domain, we use
dynamic functional connectivity analysis to capture transient features
of brain function. Dynamic functional connectivity analysis has recently
provided novel insights into large-scale brain organization ( Allen et al.,
2012 ; Ashourvan et al., 2017 ; Chai et al., 2017 ; Damaraju et al., 2014 ;
Khambhati et al., 2018 ; Razi et al., 2017 ), inter-individual dierences
in cognitive functions ( Bassett et al., 2011 ; Bertolero et al., 2015 ;
Braun et al., 2015 ; Chai et al., 2016 ; Kucyi et al., 2018 ; Park et al., 2019 ;
Taghia et al., 2018 ; Vidaurre et al., 2017 ), and network perturbations
in prevalent brain disorders ( Damaraju et al., 2014 ; Khambhati et al.,
2015 ; Lee et al., 2019 ; Park et al., 2018a , 2018b). One method that can
resolve functional dynamics is the Hidden Markov Model (HMM), a gen-
erative probabilistic framework that identies time-varying brain states
and associated connectivity proles ( Vidaurre et al., 2017 ). Recent stud-
ies have capitalized on HMMs to estimate the hierarchical organization
of the dynamic state space in rs-fMRI data and assessed associations to
cognitive phenotypes ( Vidaurre et al., 2017 ) and task-related brain ac-
tivations ( Vidaurre et al., 2016 ). Here, HMMs were used to characterize
brain states that occur at rest and to assess the correspondence between
these patterns and those derived purely from structural connectomics.
In particular, we examined how these changes map onto both low di-
mensional cortical representations of macroscale features of the cortex.
We did not make a-priori predictions how structurally-dened low di-
mensional manifolds may relate to measures of functional dynamics, as
whole-brain gradients derived from dMRI tractography data have not
been systematically studied in humans nor integrated with HMM data.
To however further contextualize the structure-function relationships
identied in our study, we examined topological properties of structural
network organization and assessed how these may implement dierent
communication mechanisms ( Avena-Koenigsberger et al., 2019 , 2018 ;
de Reus and van den Heuvel, 2013 ; Goñi et al., 2014 ; Gria and van den
Heuvel, 2018 ; Liang et al., 2018 ; Shu et al., 2018 ; van den Heuvel et al.,
2012 ; Zhao et al., 2017 ). These include the rich-club taxonomy, which
classies cortical organizations in terms of degree distributions into a
densely interconnected rich-club core and a more locally connected pe-
riphery ( Gria and van den Heuvel, 2018 ; van den Heuvel et al., 2012 ),
as well as network communication measures that can contrast more pas-
sive network diusion mechanisms against routing strategies that pref-
erentially follow shortest paths ( Avena-Koenigsberger et al., 2019 , 2018 ;
Goñi et al., 2014 ).
Our study provided a low dimensional description of structural con-
nectome architecture and explored its association to transient functional
states in the resting brain. We capitalized on high-denition dMRI and
rs-fMRI data provided by the Human Connectome Project (HCP) repos-
itory ( Van Essen et al., 2013 ) and also assessed an independent locally
acquired datasets with similar imaging parameters. Foreshadowing our
results, we found evidence that cortical structural connectivity is opti-
mized to allow for exibility between states anchored in unimodal re-
gions (that are well described by local properties of these regions cap-
tured by a low dimensional representations of cortical structure) and
states anchored by transmodal regions (which engage in ecient long-
range communication between states).
2. Methods
2.1. Participants
We assessed the minimally processed S900 release of the HCP
( Van Essen et al., 2013 ). Participants who did not complete full imaging
data and who had family relationships were excluded, resulting in a total
of 326 participants (mean ± SD age = 28.56 ± 3.73 years; 55% female).
Participants were randomly divided into a Discovery and Replication co-
hort. The Discovery dataset (n = 163; age = 28.86 ± 3.78 years; 60%
female) was used for constructing a framework of structure-functional
dynamic coupling and the Replication dataset (n = 163; age = 28.26 ±
3.67 years; 51% female) was used for testing reproducibility. All MRI
data used in this study were publicly available and anonymized. Par-
ticipant recruitment procedures and informed consent forms, including
consent to share de-identied data, were previously approved by the
Washington University Institutional Review Board as part of the HCP.
We replicated our ndings in an independent dataset from our local
site (MICA-MTL, n = 47; age = 30.43 ± 6.83 years; 35% female). This
dataset was approved by the Institutional Review Board of Montreal
Neurological Institute and Hospital and written and informed consent
was obtained from all participants.
2.2. MRI acquisition
2.2.1. HCP
HCP participants were scanned using a Siemens Skyra 3T at Wash-
ington University. The T1-weighted images were acquired using a
magnetization-prepared rapid gradient echo (MPRAGE) sequence (rep-
etition time (TR) = 2,400 ms; echo time (TE) = 2.14 ms; eld of
view (FOV) = 224 ×224 mm
2
; voxel size = 0.7 mm
3
; and number
of slices = 256). The T2-weighted structural data were obtained with
the T2-SPACE sequence, with an identical geometry as the T1-weighted
data but dierent TR (3,200 ms) and TE (565 ms). The dMRI data
were acquired with the spin-echo echo-planar imaging (EPI) sequence
(TR = 5,520 ms; TE = 89.5 ms; FOV = 210 ×180 mm
2
; voxel size = 1.25
mm
3
; b-value = three dierent shells i.e., 1,000, 2,000, and 3,000
s/mm
2
; number of diusion directions = 270; and number of b0 im-
ages = 18). The rs-fMRI data were collected using a gradient-echo EPI
sequence (TR = 720 ms; TE = 33.1 ms; FOV = 208 ×180 mm
2
; voxel
size = 2 mm
3
; number of slices = 72; and number of volumes = 1,200).
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
During the rs-fMRI scan, participants were instructed to keep their eyes
open looking at a xation cross. Two sessions of rs-fMRI data were ac-
quired; each of them contained data of left-to-right and right-to-left
phase-encoded directions, providing up to four time series per partic-
ipant.
2.2.2. MICA-MTL
The MICA-MTL imaging data were scanned using a Siemens Prisma
3T scanner at the Montreal Neurological Institute and Hospital. Image
acquisition parameters were similar to the HCP dataset (T1-weighted:
TR = 2,300 ms; TE = 3.14 ms; FOV = 256 ×180 mm
2
; voxel size = 0.8
mm
3
; and number of slices = 320; dMRI: TR = 3,500 ms; TE = 64.4
ms; FOV = 224 ×224 mm
2
; voxel size = 1.6 mm
3
; b-value = three
dierent shells (200, 700, and 2,000 s/mm
2
); number of diusion di-
rections = 140; and number of b0 images = 3; rs-fMRI: TR = 600 ms;
TE = 30 ms; FOV = 240 ×240 mm
2
; voxel size = 3 mm
3
; number of
slices = 48; and number of volumes = 800).
2.3. Data preprocessing
2.3.1. HCP data
HCP data underwent the initiative’s minimal preprocessing pipelines
( Glasser et al., 2013 ). In brief, structural MRI data underwent gradient
nonlinearity and b0 distortion correction, followed by co-registration
between the T1-weighted and T2-weighted data using a rigid-body
transformation. Bias eld correction was performed by capitalizing on
the inverse intensities from the T1- and T2-weighting. Processed data
were nonlinearly registered to MNI152 space and the white and pial
surfaces were generated by following the boundaries between dierent
tissues ( Dale et al., 1999 ; Fischl, 2012 ; Fischl et al., 1999b , 1999a ). The
white and pial surfaces were averaged to generate a mid-thickness sur-
face, which was used to generate the inated surface. The spherical sur-
face was registered to the Conte69 template with 164k vertices ( Van Es-
sen et al., 2012 ) using MSMAll ( Glasser et al., 2016; Robinson et al.,
2014 ) and downsampled to a 32k vertex mesh. The dMRI data under-
went b0 intensity normalization, and EPI distortions were corrected by
leveraging reversed phase-encoded directions. The dMRI data was also
corrected for eddy current distortions and head motion. The rs-fMRI
data preprocessing involved corrections for EPI distortions and head
motion, and fMRI data were registered to the T1-weighted data and
subsequently to MNI152 space. Magnetic eld bias correction, skull re-
moval, and intensity normalization were performed. Noise components
attributed to head movement, white matter, cardiac pulsation, arterial,
and large vein related contributions were automatically removed using
FIX ( Salimi-Khorshidi et al., 2014 ). The minimal preprocessing with FIX-
denoising pipeline of the HCP performs a high-pass ltering with a cuto
of 2,000 s full width at half maximum ( Glasser et al., 2013 ). Prepro-
cessed time series were mapped to standard grayordinate space, with a
cortical ribbon-constrained volume-to-surface mapping algorithm. The
total mean of the time series of each left-to-right/right-to-left phase-
encoded data was subtracted to adjust the discontinuity between the
two datasets and they were concatenated to form a single time series
data.
2.3.2. MICA-MTL
MICA-MTL data were processed similarly as the HCP data. In brief,
T1-weighted data were deobliqued, reoriented, skull stripped, and
cortical surfaces were generated using FreeSurfer ( Dale et al., 1999 ;
Fischl, 2012 ; Fischl et al., 1999b , 1999a ). The dMRI data was processed
using MRtrix ( Tournier et al., 2019 , 2012 ) including correction for sus-
ceptibility distortions, head motion, and eddy currents. The rs-fMRI
data were processed using AFNI and FSL ( Cox, 1996 ; Jenkinson et al.,
2012 ). The rst ve volumes were discarded to allow for magnetic
eld saturation, followed by reorientation, motion and distortion correc-
tion, skull stripping, and nuisance variable removal using FIX ( Salimi-
Khorshidi et al., 2014 ). Functional time series were mapped to each
individual’s cortical surface using boundary-based registration and sub-
sequently to the 32k vertex Conte69 template.
2.4. Structural connectome generation and manifold identification
Structural connectomes were generated from preprocessed dMRI
data using MRtrix ( Tournier et al., 2019 , 2012 ). Dierent tissue types
of cortical and subcortical grey matter, white matter, and cerebrospinal
uid were segmented using T1-weighted image for anatomical con-
strained tractography ( Smith et al., 2012 ). Multi-shell and multi-tissue
response functions were estimated ( Christiaens et al., 2015 ) and con-
strained spherical-deconvolution and intensity normalization were per-
formed ( Jeurissen et al., 2014 ). The initial tractogram was generated
with 40 million streamlines, with a maximum tract length of 250
and a fractional anisotropy cuto of 0.06. Spherical-deconvolution in-
formed ltering of tractograms (SIFT2) was applied to reconstruct whole
brain streamlines weighted by cross-section multipliers ( Smith et al.,
2015 ). To build a structural connectome, the reconstructed cross-section
streamlines were mapped onto the Schaefer atlas with 200 parcels
( Schaefer et al., 2018 ). Connectome data were log-transformed to re-
duce connectivity strength variance ( Fornito et al., 2016 ; Goñi et al.,
2014 ).
The principal eigenvectors explaining spatial shifts in the structural
connectome, referred to as structural connectome gradients were esti-
mated using the BrainSpace toolbox ( https://github.com/MICA-MNI/
BrainSpace ) ( Margulies et al., 2016 ; Vos de Wael et al., 2020 ). A cosine
similarity matrix was constructed from the group averaged structural
connectome to capture the similarity of connections among dierent
brain regions. We capitalized on diusion map embedding, a non-linear
manifold learning algorithm, to identify low dimensional manifolds ( i.e.,
principal components) ( Cox, 1996 ). In this manifold, strongly intercon-
nected brain regions that have many and/or strong connections are
closely located, while regions with little and/or weak inter-connectivity
are farther apart. Diusion map embedding algorithm is robust to noise
and computationally ecient compared to other non-linear manifold
learners ( Tenenbaum et al., 2000 ; Von Luxburg, 2007 ). The algorithm
is controlled by two parameters 𝛼and t, where 𝛼controls the inuence
of the density of sampling points on the manifold ( 𝛼= 0, maximal in-
uence; 𝛼= 1, no inuence) and t controls the scale of eigenvalues of
the diusion operator. We followed recommendations and xed 𝛼at
0.5 and t at 0, a choice that retains the global relations between data
points in the embedded space ( Hong et al., 2019 ; Margulies et al., 2016 ;
Paquola et al., 2019 ; Vos de Wael et al., 2018 ).
2.5. Dynamic functional connectivity analysis
Dynamic functional connectivity analysis was performed using a
multivariate autoregressive HMM approach, which models distinct brain
states via a multivariate Gaussian distribution and which infers model
parameters via variational Bayes ( https://github.com/OHBA-analysis/
HMM-MAR ) ( Vidaurre et al., 2017 ). The number of brain states was de-
termined according to the following six steps: (1) For each participant,
we divided the functional time series into ten non-overlapping segments
and (2) applied k-means clustering to 9/10 time series segments with k
ranging from 2 to 20. (3) For each k, we calculated the ratio of between-
cluster variance to total variance, and the optimal number of brain states
for the given time series was determined as the minimum value at which
the explained variance exceeded 90% of total variance ( Kodinariya and
Makwana, 2013 ; Park et al., 2018b ). (4) We repeated steps 1–3 for a to-
tal of 10 times with dierent time segments within a participant, and (5)
also repeated steps 1–4 for all participants. (6) Finally, we determined
the optimal number of brain states for HMM training as the most fre-
quently observed number of k across time segments and participants. We
trained HMM using the concatenated time series across participants. To
mitigate circularity ( Kriegeskorte et al., 2009 ), we used dierent time
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
segments for HMM training and brain state estimation. For each par-
ticipant, we concatenated 50% of the time series from session 1 and
the other 50% from session 2. Then, we concatenated this reconstructed
time series across all participants to train the HMM. The trained model
was applied to the rest of the time series to estimate distinct brain states.
HMM estimates specic states, where a state k is characterized by a mul-
tivariate Gaussian distribution with a mean distribution of whole-brain
activity ( 𝜇k
) and covariance matrix ( Σk
) ( Vidaurre et al., 2018 , 2017).
Specically, time series data x in the hidden state s at time t follows the
multivariate Gaussian distribution N as follows:
𝑥
𝑡
|𝑠
𝑡
= 𝑘 ∼𝑁
(𝜇𝑘
, Σ𝑘
)(1)
Here, 𝜇k
is a vector of mean blood oxygen level-dependent (BOLD) acti-
vation, which is here referred to as functional mean patterns of activa-
tion (fMPA), and Σk
is the covariance matrix when state k is active. In
addition, HMM estimates transition probabilities between brain states
and allows representing the frequency of transitions ( Vidaurre et al.,
2018 , 2017). Meta-states, i.e., communities of functional states, were
estimated to simplify the transition structure ( Vidaurre et al., 2017 ), by
applying the Louvain community detection algorithm ( Blondel et al.,
2008 ) to the transition probability matrix. To avoid eects related to
random HMM initialization, HMM training, estimating brain states, and
meta-state estimation were repeated 100 times. The most frequently ob-
served meta-state structure across iterations was selected.
2.6. Association between functional dynamics and structural connectome
organization
Structure-function coupling was rst assessed by spatial associations
( i.e., linear product moment correlation coecients) between structural
gradients and dierences in fMPA ( ΔfMPA) within and between meta-
states. Specically, we calculated ΔfMPA as the average of dierences in
fMPA between all possible pairs of transitions within or between meta-
states:
Δ𝑓 𝑀𝑃 𝐴
{
𝑆→𝑇
}
=
1
𝐴
𝑁
∑
𝑖 =1
𝑀
∑
𝑗=1
𝑓 𝑀𝑃 𝐴
𝑆
𝑖
− 𝑓 𝑀𝑃 𝐴
𝑇
𝑗
(2)
Here, i and j are individual states within meta-states S and T; N and
M are the numbers of individual states in the meta-states; and A is
the number of possible pairs of state transitions ( i.e., transitions within
meta-state: 𝐴 =
𝑁
𝐶
2
, transitions between meta-states: 𝐴 = 𝑁 ⋅𝑀). The
signicance of the correlation was assessed using 1,000 spin tests, which
randomly rotate ΔfMPA and hence preserve the spatial autocorrelation
( Alexander-Bloch et al., 2018 ). A null distribution was constructed, and
the real correlation strength was deemed signicant if it belonged to
the 5
th
percentile. To evaluate whether the above structure-function as-
sociations were robust above and beyond inter-regional variations of
cortical morphology, we correlated ΔfMPA with MRI-derived cortical
thickness and folding measures (derived from FreeSurfer). In addition,
we controlled for cortical thickness and folding when correlating ΔfMPA
with structural connectome gradients, to establish that structural gradi-
ents explain dynamic functional shifts above and beyond the eects of
cortical morphology.
2.7. Associations of functional dynamics with network topology
To assess structural network topology underpinnings of distinct func-
tional dynamic states, we stratied ΔfMPA in terms of rich-club tax-
onomy, a topological measure sensitive to core-periphery organization
of the network ( Gria and van den Heuvel, 2018 ; van den Heuvel
et al., 2012 ). The rich-club is a set of highly interconnected high-
degree nodes. It has been shown to play an important role in infor-
mation integration between dierent brain networks and aggregates
most long-range connections of the human brain ( de Reus and van den
Heuvel, 2013 ; Gria and van den Heuvel, 2018 ; Liang et al., 2018 ;
Shu et al., 2018 ; van den Heuvel et al., 2012 ; Zhao et al., 2017 ). In
contrast, peripheral nodes show shorter, more local connections and
serve in more specialized, segregated functions ( de Reus and van den
Heuvel, 2013 ; Gria and van den Heuvel, 2018 ; Liang et al., 2018 ;
Shu et al., 2018 ; van den Heuvel et al., 2012 ; Zhao et al., 2017 ). The
weighted rich-club coecient 𝜑
w
(k) was calculated from the group rep-
resentative structural connectome, dened using a distance-dependent
thresholding ( Betzel et al., 2019 ), using the Brain Connectivity Toolbox
( https://sites.google.com/site/bctnet/ ) ( Rubinov and Sporns, 2010 ).
The 𝜑
w
(k) was calculated across dierent levels of degree (k) rang-
ing from 1 to the maximal degree and was normalized against 1,000
randomly rewired networks with similar degree distribution. Degree
levels in which (i) the normalized rich-club coecient exceeded one
( i.e., 𝜑
w
norm
(k) > 1) and (ii) where there were signicant dierences
between real and randomized networks (p < 0.05, permutation test cor-
rected) were considered as the rich-club regime. The rich-club nodes
were dened as nodes exceeding the k
th degree level in the rich-club
regime (here, k = 28). Remaining nodes were classied into feeder nodes,
which had more than 10% connections with rich-club nodes, and lo-
cal nodes, which had less than 10% connections ( Hong et al., 2019 ).
The magnitude of ΔfMPA within and between meta-states was quanti-
ed according to the rich-club taxonomy and they were compared us-
ing two-sample t-tests across rich-club, feeder, and local nodes. Find-
ings were corrected at a false discovery rate < 0.05 ( Benjamini and
Hochberg, 1995 ).
Structural connectivity distance provides an index of network hierar-
chy complementary to rich-club taxonomy, given the observation that
backbone hubs often host longer-range connections to distributed tar-
gets than local nodes that mostly travel along short-range paths ( Avena-
Koenigsberger et al., 2019 ; van den Heuvel et al., 2012 ). To assess the
relationship between functional dynamic transitions and structural con-
nectivity distance, we stratied ΔfMPA according to connectivity dis-
tance ( Larivière et al., 2019b ; Oligschläger et al., 2019 ). Connectivity
distance, thus, indicates a given brain area’s average geodesic distance
to its structurally connected regions ( Oligschläger et al., 2019 ). Geodesic
distance was dened as the shortest path connecting two points along
the cortical surface, following prior procedures ( Ecker et al., 2013 ;
Hong et al., 2018 ; Margulies et al., 2016 ). It represents the physical dis-
tance between the two cortical points when travelling through the corti-
cal sheet, and does not depend on network topology. The multiplication
between the geodesic distance and the binarized structural connectome
was performed, and the row-wise mean was calculated to compute the
connectivity distance ( Hong et al., 2019 ; Oligschläger et al., 2019 ). The
connectivity distance was partitioned into 10 bins and the magnitude of
ΔfMPA was quantied according to each bin.
2.8. Role of network communication
In addition to the rich-club taxonomy and connectivity distance
measures, we leveraged network communication models that deter-
mine how a structural connectome can implement functional sig-
naling and information transfer ( Avena-Koenigsberger et al., 2019 ,
2018 ; Goñi et al., 2014 ) to associate functional dynamics to models
of structurally-governed communication ( Avena-Koenigsberger et al.,
2018 ; Goñi et al., 2014 ). The metrics of mean rst-passage time and path
length measuring network diusivity ( Avena-Koenigsberger et al., 2018 )
were calculated from the weighted structural connectivity matrix using
the Brain Connectivity Toolbox ( https://sites.google.com/site/bctnet/ )
( Rubinov and Sporns, 2010 ). Mean rst-passage time quanties the ex-
pected length of a random walk between two nodes, indicating a diu-
sion mechanism ( Avena-Koenigsberger et al., 2018 ; Goñi et al., 2013 ).
Path length, on the other hand, is dened as the shortest weighted
path between the source and target; nodes with low path lengths con-
tribute to globally ecient communication ( Avena-Koenigsberger et al.,
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
2018 ; Goñi et al., 2014 ; Rubinov and Sporns, 2010 ). To assess dier-
ences in communication mechanisms of the brain regions showing large
changes in brain activity during meta-state transitions, we quantied
mean rst-passage time and path length in the brain regions, which
showed a strong (top 5%) magnitude of ΔfMPA within and between
meta-states, and computed communication metrics on resultant subma-
trices. We repeated calculating mean rst-passage time and path length
in the brain regions that showed the top 10, 15, and 20% magnitude
of ΔfMPA within and between meta-states to assess the consistency of
the ndings. To conrm ndings using alternative parameters, we ad-
ditionally stratied changes in ΔfMPA with respect to search informa-
tion and path transitivity ( Avena-Koenigsberger et al., 2018 ; Goñi et al.,
2014 ). Search information quanties the amount of information needed
to access the path connecting from a source node to a target node
( Avena-Koenigsberger et al., 2018 ; Goñi et al., 2014 ). Similar to mean
rst-passage time, higher search information indicates the diuse prop-
erty of the network by implying that it requires a large amount of in-
formation to reach the target node through the shortest path ( Avena-
Koenigsberger et al., 2018 ; Goñi et al., 2014 ). Path transitivity captures
the density of local detours along the given shortest path, indicating high
path transitivity represents the existence of many closed loops along
the path enabling a signal to return to the shortest path after detouring
( Avena-Koenigsberger et al., 2018 ; Goñi et al., 2014 ).
2.9. Functional dynamic transitions in terms of cortical hierarchy
Finally, we contextualized functional dynamic transitions within a
prior model of neural organization formulated in non-human primates
that subdivides the cortex into four levels: idiotypic (level-1), unimodal
association (level-2), heteromodal association (level-3), and paralimbic
(level-4) cortices ( Mesulam, 1998 ). Hierarchical weights of the fMPA
patterns for each state were quantied with respect to Mesulam hier-
archy for each brain state. The discretized fMPA was interpolated with
30 bins and the point that exhibited maximum fMPA value was selected
as the mean hierarchical level. For each hierarchical level, we calcu-
lated the following topological parameters and communication metrics:
(i) the proportion of rich-club nodes (relative to all nodes on that hi-
erarchical level), (ii) the average connectivity distance, and (iii) ratio
between signal diusion to routing in terms of structurally-governed
communication. For diusion/routing communication ratio, we calcu-
lated the ratio between mean rst-passage time and path length. The
linear product moment correlation between the rst structural gradi-
ent (sG1) and ΔfMPA and mean hierarchical level between all pairs of
brain states were computed. Then, the magnitude of structure-function
coupling ( i.e., correlation between sG1 and ΔfMPA) was quantied ac-
cording to the mean hierarchical level to assess the relationship between
cortical hierarchy and structure-functional dynamic coupling.
2.10. Sensitivity and reproducibility analyses
a) Matrix thresholding. We repeated structural gradient estimation based
on structural connectomes with dierent levels of density (un-
thresholded, 25, 50, and 75% density).
b) Spatial scale. To evaluate the impact of spatial scale, we repeated our
analyses across dierent granularities of the Schaefer atlas ( i.e., 100,
300, or 400 regions) ( Schaefer et al., 2018 ).
c) Reproducibility in HCP. We assessed reproducibility by performing
the same analyses on the independent Replication subset from the
HCP. Structural gradients, functional brain states, and the correla-
tion between structural gradients and ΔfMPA as well as morpho-
logical associations were computed and compared to those in the
Discovery cohort.
d) Reproducibility in another dataset. We furthermore replicated our nd-
ings in a locally scanned cohort (MICA-MTL, n = 47).
3. Results
3.1. Cortex-wide structural connectome gradients
We computed whole brain structural connectomes from all partic-
ipants, using an established parcellation scheme (See Supporting Infor-
mation for replication across partitioning schemes and spatial scales)
( Schaefer et al., 2018 ). Using non-linear dimensionality reduction tech-
niques, we derived structural connectome gradients ( Vos de Wael et al.,
2020 ). The rst two gradients (sG1, sG2) were selected, as these ex-
plained 44.5% of connectome variance and corresponded to the clearest
elbow in the scree plot ( Fig. 1 A). For additional information, the third
to fth gradients (sG3, sG4, sG5) are shown in Fig. S1A but will not be
further discussed. While sG1 dierentiated a sensorimotor from a me-
dial prefrontal anchor, sG2 extended from the ventral to dorsal visual
systems. Structural gradients were consistent across dierent levels of
density in structural connectomes, which showed mean product moment
correlations across spatial maps of 0.95 with SD 0.03 (p < 0.001) (Fig.
S1B).
3.2. Dynamic functional connectivity analysis
Dynamic changes in functional states were estimated using an HMM
( Fig. 1 B). HMM provided the fMPA and associated connectivity matrix
for each brain state (Fig. S2A), as well as transition probabilities be-
tween states. Meta-states were estimated to simplify the transition struc-
ture ( Vidaurre et al., 2017 ) via Louvain community detection ( Fig. 1 C)
( Blondel et al., 2008 ). This approach identied two functional meta-
states fM1 and fM2, each with distinct spatial activation and connec-
tivity patterns. fM1 showed high activation in sensorimotor and lat-
eral prefrontal regions while fM2 showed activations in default and
frontoparietal networks ( Fig. 1 D). Spatial correlations in activation pat-
terns between both meta-states were low (mean ± SD r = 0.24 ± 0.10),
while states falling within each meta-state showed moderate to high
correlations to one another (mean ± SD r = 0.32 ± 0.17 for fM1 and
r = 0.36 ± 0.19 for fM2). Directly comparing the top 1% connections
between meta-states, fM1 had stronger connections in visual and so-
matosensory networks, and fM2 showed stronger connections in fron-
toparietal and default-mode networks (Table S1). Furthermore, the cor-
relation between fMPA of meta-states and meta-analysis maps of diverse
cognitive domains ( Margulies et al., 2016 ), derived using Neurosynth
( Yarkoni et al., 2011 ), revealed distinct cognitive term associations be-
tween meta-states; fM1 was characterized by ‘motor’ terms while fM2
related to higher-order cognitive terms such as ‘autobiographical mem-
ory’ and ‘social cognition’ (Fig. S2B). Collectively, these ndings support
that fM1 reects a low-level sensorimotor state whereas fM2 is more in-
volved in higher-order transmodal functions.
3.3. Structural connectome gradients relate to dynamic functional
transitions
To assess structure-function correspondence, we computed product
moment correlations between structural connectome gradients sG1 and
sG2 and dynamic activity changes ( ΔfMPA) within the two meta-states
fM1 and fM2, and between them. Activity changes for all transitions
involving fM1 were correlated with sG1 but not sG2, with signicance
determined using non-parametric spin tests that adjust for shared spa-
tial autocorrelations ( Fig. 2 and Fig. S3) ( Alexander-Bloch et al., 2018 ;
Vos de Wael et al., 2020 ). Indeed, sG1 correlated with transitions within
fM1 (r = -0.5778, p < 0.001), from fM1 to fM2 (r = 0.3827, p < 0.05),
and from fM2 to fM1 (r = 0.4635, p < 0.005). Conversely, no signi-
cant relationship was found in transitions within fM2 (r = 0.0758, p >
0.4). Although sG2 by itself did not signicantly correlate with these
transitions, model t ( i.e., adjusted R
2
) generally improved when incor-
porating both sG1 and sG2 into a common model via linear regression
( + 4.1% variance explained for transitions within fM1; + 2.4% from fM1
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Fig. 1. Structural gradients and dynamic functional connectome proles. (A) Manifolds estimated from the structural connectome. Systematic dMRI ber tracking
generated a cortex-wide structural connectome, on which non-linear dimensionality reduction identied principal components describing connectivity variance.
The rst two components (sG1 and sG2) corresponded to the clearest elbow in the scree plot. (B) Dynamic functional analysis leveraged Hidden Markov Models
(HMM) that decompose the time series into a set of states and their transition probabilities. (C) Transition probabilities were clustered using a community detection
algorithm to identify functional meta-states (fM1 and fM2). Line widths represent transition probability strengths, thresholded at 0.2. (D) The functional mean
patterns of activation (fMPA) for two meta-states (fM1, fM2) and their dierences at the level of the whole brain and functional networks are shown in the upper
row. Signicant dierences in fMPA between fM1 and fM2 are indicated with an asterisk. Corresponding connectivity matrices and dierences in edges with top
1% weights for the two meta-states are shown in the bottom row. Abbreviations : dATN, dorsal attention network; FPN, frontoparietal network; DMN, default-mode
network; VN, visual network; LBN, limbic network; SMN, sensorimotor network; vATN, ventral attention network.
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Fig. 2. Associations between structural gradients and functional dynamic transitions. (A) The ΔfMPA with respect to sG1 and sG2 were reported in the upper row.
The color indicates the magnitude of ΔfMPA. The ΔfMPA for transitions within and between meta-states are reported in the bottom row. (B) The correlation between
sG1 and ΔfMPA. Permutation-based correlation values across 1,000 spin tests are shown in the histogram, with the real correlation value indicated via a red line.
(C) Linear t of ΔfMPA using both sG1 and sG2, incorporated via linear regression model.
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
to fM2; + 27.1% from fM2 to fM1; and + 127.4% within fM2). For tran-
sitions within fM1 and from fM2 to fM1, both sG1 and sG2 showed sig-
nicant contributions for model tting (within fM1: p < 0.001/0.0035
for sG1/sG2; from fM2 to fM1: p < 0.001/ < 0.001). On the other hand,
only sG1 showed signicance for the transitions between fM1 to fM2 (p
< 0.001/0.2059), and only sG2 showed signicance for the transitions
within fM2 (p = 0.2859/0.0285).
3.4. Morphological structures are not relevant to functional dynamic
transitions
To assess contributions of regional morphological variations, we also
correlated MRI-derived measures of cortical thickness and folding to
ΔfMPA. We observed weak and non-signicant associations with corti-
cal thickness ( Fig. 3 A). Although the association between cortical fold-
ing and activity changes within fM1 and from fM2 to fM1 reached signif-
icance, correlations were overall relatively weak ( Fig. 3 B). Importantly,
the correlations between structural gradients and ΔfMPA were robust
after correcting gradient values for cortical thickness and folding, both
for the model based on sG1 only ( Fig. 3 C) and for the model based on
both sG1 and sG2 ( Fig. 3 D), suggesting that structural connectome orga-
nization contains information about neural dynamics above and beyond
the information provided by local variation in cortical morphology.
3.5. Connectome topology analysis
The above ndings suggest a reasonably strong structure-function
correspondence for functional transitions involving states anchored in
sensorimotor systems ( i.e., within fM1, from fM1 to fM2, and from fM2
to fM1). However, there was no comparable prediction for states that
are linked to more transmodal regions. These ndings are broadly in
line with previous ndings showing stronger structure-function cou-
pling in unimodal than transmodal cortices ( Park and Friston, 2013 ;
Vázquez-Rodríguez et al., 2019 ). To understand the underlying mecha-
nism of exibility in more transmodal states, we next evaluated the rela-
tionship to network topology parameters describing long distance com-
munication between regions ( Avena-Koenigsberger et al., 2019 , 2018 ).
Contemporary views of cortical organization have highlighted that the
cortex is organized by an apparent rich-club structure, in which cer-
tain hub regions are more densely connected to themselves than to the
rest of the brain ( Avena-Koenigsberger et al., 2019 , 2018 ; Bullmore and
Sporns, 2009 ; van den Heuvel et al., 2012 ). We identied the rich-club
following established procedures ( Fig. 4 A). Rich-club nodes were lo-
cated at backbone structures and surrounded by feeder nodes, and local
nodes were located near sensorimotor areas ( Fig. 4 A ). Notably, high
ΔfMPA was observed in local nodes for the transitions within fM1 and
from fM2 to fM1, while no dierences were found within fM2 and from
fM1 to fM2, indicating that the transitions in sensorimotor-dominated
states primarily occurred in the locally-connected brain regions and
those in transmodal states occurred uniformly across either local or hub
nodes.
As a complementary information to rich-club taxonomy, we
stratied ΔfMPA according to structural connectivity distance
( Larivière et al., 2019b ; Oligschläger et al., 2019 ). Stratifying dy-
namic functional changes ( ΔfMPA) with respect to connectivity
distance, we observed that transitions within fM1 or from fM2 to fM1
more frequently involved short-range connections, while those within
fM2 or from fM1 to fM2 involved long-range connections ( Fig. 4 B).
Shifts in ΔfMPA according to connectivity distance indicate that
marked transitions occurred along with the short-range connections for
low-level brain states, while transitions for the higher-order brain state
increasingly used long-range connections. Our results indicate that
transitions involving sensorimotor states traverse along the path with
short distances, while those in transmodal states engage long-range
connections across network hubs.
We furthermore derived mean rst-passage time and path length
from the structural connectome to assess structurally-governed network
communication ( Avena-Koenigsberger et al., 2018 ; Goñi et al., 2014 ).
Interestingly, higher mean rst-passage time was observed in transitions
within fM1 and from fM2 to fM1 compared to transitions from fM1 to
fM2 and within fM2. Similarly, higher path length was observed within
fM1, and it monotonically decreased in transitions between meta-states
and within fM2 ( Fig. 4 C). This analysis indicates dierent functional
states are associated to dierent structural communication mechanisms.
Specically, communication in functional states localized in low-level
sensory areas is better explained by network diusion. On the other
hand, functional states in transmodal regions are better explainable by
routing along shortest paths. Results for mean rst-passage time and
path length were consistent when considering those brain regions of
the top 10, 15, and 20% ΔfMPA within and between meta-states (Fig.
S4). To further validate our ndings using dierent graph parametriza-
tion methods, we calculated search information and path transitivity.
Higher search information was observed in transitions within fM1 and
monotonically decreased in transitions between meta-states and within
fM2. In contrast, higher path transitivity was observed within fM2 and
in transitions from fM1 to fM2 compared to fM1 (Fig. S5), suggesting
consistent results with mean rst-passage time and path length.
3.6. Cortical hierarchy and functional dynamic transitions
To assess how the dynamic uctuations of brain function change ac-
cording to contemporary views of cortical hierarchy ( Fig. 5 A), we rst
computed the mean hierarchical level for each brain state based on hi-
erarchical system proposed by Marcel Mesulam ( Mesulam, 1998 ). Brain
states in fM1 had a tendency for lower mean hierarchical levels than
those in fM2 (mean ± SD = 1.70 ± 1.10 vs. 2.61 ± 1.14; t = -1.50,
one-tailed p = 0.08). Although the dierence was not statistically sig-
nicant, this suggest that both meta-states may be involved in dier-
ent hierarchical levels, where dynamic functional states in fM1 were
anchored in lower levels of the hierarchy, while those in fM2 were an-
chored in higher levels ( Fig. 5 B). We aimed to understand the specic
features of cortical topology that underpinned this relationship by cal-
culating the proportion of rich-club nodes, connectivity distance, and
diusion/routing communication ratio ( i.e., ratio between mean rst-
passage time and path length) within each of the four levels of the hier-
archy. Conrming the dierentiation of our structure-function relation-
ships across the hierarchy, we observed a higher proportion of rich-
club nodes and longer connectivity distance in higher-order regions,
together with lower diusion/routing communication ratio ( Fig. 5 C).
Importantly, beyond the location of states in the hierarchy, the magni-
tude of structure-function coupling ( i.e., correlation between sG1 and
ΔfMPA) was strong when dynamic states changed within the low hi-
erarchical levels, between low- and high-level hierarchies, while the
coupling appeared weakest for dynamic transitions between high level
states ( Fig. 5 D). Together, this result supports our nding that structure-
function correspondence is strong when dynamic transitions involve
sensorimotor states and that correspondence decreases when transitions
are anchored in transmodal states.
3.7. Sensitivity and replication experiments
Repeating the above analysis across spatial scales ( i.e., 100, 300, and
400 parcels), ndings were highly consistent at parcel resolutions > 100
(Fig. S6–8). Correlations between sG1 and ΔfMPA became somewhat
weaker at the lowest resolution of 100 parcels, indicating that more
granular parcellations may be more ecient for the study of associa-
tions between structural connectivity and functional dynamics. To as-
sess reproducibility, we performed the same analyses on the initially
held out Replication dataset from the HCP. We observed virtually iden-
tical patterns of structural connectome gradients, functional meta-states,
and structure-function associations (Fig. S9–10). Finally, main ndings
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Fig. 3. Morphological associations. (A) Correlations between cortical thickness and ΔfMPA, showing scatter plots and spin test histograms. (B) Correlations between
cortical folding and ΔfMPA. (C) Correlations between ΔfMPA and sG1, corrected for cortical morphology. (D) Linear model between ΔfMPA and sG1 and sG2,
corrected for cortical morphology.
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Fig. 4. Connectome topology analysis. (A) ΔfMPA in terms of rich-club taxonomy. Rich-club coecients according to dierent degree levels were reported on the
left side and the magnitudes of ΔfMPA of rich-club, feeder, and local nodes were reported on the right side. The error bars represent the standard deviation of ΔfMPA
across brain regions. (B) ΔfMPA in regard to connectivity distance. The connectivity distance was reported on the left side and the magnitudes of ΔfMPA according
to the connectivity distance were reported on the right side. (C) Mean rst-passage time and path length with respect to the meta-state transitions. The error bars
indicate the standard deviation of network communication measures across transitions.
could be conrmed in the independent 3T dataset from our local site
that had slightly dierent imaging parameters as HCP (MICA-MTL) (Fig.
S11).
4. Discussion
Understanding how the structure of the cortex gives rise to ongoing
cognitive function is a key aim for systems neuroscience ( Batista-García-
Ramó and Fernández-Verdecia, 2018 ; Baum et al., 2020 ; Becker et al.,
2018 ; Ciric et al., 2017 ; Hermundstad et al., 2013 ; Honey et al.,
2009 ; Mi ŝ ic et al., 2016 ; Park and Friston, 2013 ; Rubinov et al., 2009 ;
Snyder and Bauer, 2019 ; Suárez et al., 2020 ; Vázquez-Rodríguez et al.,
2019 ; Wang et al., 2019 , 2015 ). Yet, it remains unclear how a hard-
wired neural architecture can give rise to exible ( i.e., time-varying)
neural dynamics. Our analysis established that low dimensional repre-
sentations of white matter connectivity are closely aligned with spa-
tiotemporal patterns of dynamic functional transitions between lower-
level sensorimotor states, and between lower-level and higher-order
transmodal states. Conversely, transitions between states anchored in
transmodal regions were not simply explained by structural connectome
organization. This apparent dierence may occur because transitions be-
tween transmodal states preferentially related to subnetworks that com-
municate increasingly via a routing strategy involving long-range and
globally ecient connections. In contrast, sensorimotor state changes
were primarily explicable in terms of changes through local network
diusion and implicated shorter connectivity distances. Findings were
robust across multiple sensitivity analyses and could be replicated in dif-
ferent datasets. Together, our work suggests that exible neural dynam-
ics may rely on a balance between complementary features of structural
connectome organization: Local aspects of brain structure are important
for shifts between neural states anchored in sensorimotor cortex, and a
more distributed rich club architecture support transitions between neu-
ral states anchored in transmodal cortex.
Our study capitalized on manifold learning techniques applied to
structural connectome data, an approach that has recently gained trac-
tion in the neuroimaging and network neuroscience communities, as
it oers novel perspectives on dimensions of brain organization giving
rise to human cognition ( Margulies et al., 2016 ; Vos de Wael et al.,
2020 ). While similar algorithms have been applied to microstructural
and functional connectivity data ( Burt et al., 2018 ; Huntenburg et al.,
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Fig. 5. Transition patterns in terms of cortical hierarchy. (A) Hierarchical cortical organization according to a model of the cortical hierarchy developed in non-
human primates ( Mesulam, 1998 ). (B) fMPA patterns weighted according to mean hierarchical levels. Red bars indicate the point that exhibited maximum fMPA
value. (C) Connectome topology analysis according to hierarchical levels. Proportion of rich-club nodes, connectivity distance, and network communication ratio
are reported with respect to the dierent levels of cortical hierarchy. (D) Correlation between sG1 and ΔfMPA, and mean hierarchical level for every pair of state
transitions. The magnitude of structure-function coupling is quantied according to the mean hierarchical levels on the right side, showing highest coupling in low
hierarchical levels and lowest in high levels.
2017
; Margulies et al., 2016 ; Paquola et al., 2019 ; Shine et al., 2019 ;
Vos de Wael et al., 2020 ), they remained underexplored in the analysis
of dMRI-derived connectomes. Conceptual work has advocated for the
use of gradients to capture subregional heterogeneity and multiplicity
( Haak and Beckmann, 2020 ; Margulies et al., 2016 ), yet, only few ap-
plications leveraged manifold learning on dMRI tractography data and
these were mainly restricted to individual regions ( Beckmann et al.,
2009 ; Cerliani et al., 2012 ) or specic lobes ( Bajada et al., 2017 ), of-
ten to guide subregional parcellations. In contrast, directly analyzing
the low dimensional spaces obtained from dMRI data revealed that
these gradients can serve as a powerful coordinate system to visual-
ize and contextualize functional dynamics at macroscale. Similar to
classical sensory-transmodal gradients derived from myelin sensitive
MRI, as well as resting-state functional connectivity data ( Hong et al.,
2019 ; Larivière et al., 2019a ; Margulies et al., 2016 ; Paquola et al.,
2019 ), dMRI gradients are anchored by sensory and motor systems, and
guided by spatial proximity. On the other hand, dMRI manifolds ap-
peared less specic to the transmodal and paralimbic system than rs-
fMRI and myelin sensitive measures, both of which capture spatially
distributed, potentially polysynaptic cortical systems, such as the de-
fault mode or frontoparietal network ( Hong et al., 2019 ; Larivière et al.,
2019a ; Margulies et al., 2016 ; Paquola et al., 2019 ). Our study shows
that the application of gradient methods to dMRI metrics can com-
plement graph theoretical analyses, suggesting that including both ap-
proaches in future approaches could help rene our understanding of
structure-function relationships more generally.
Having delineated the principal dimensions of cortical structural
connectivity, we used these to interrogate the capacity of this mani-
fold to describe structure-function coupling. An increasing body of prior
work studied the correspondence between brain structure and function,
using statistical analyses ( Messé et al., 2014 ; Mi ŝ ic et al., 2016 ), com-
munication models ( Goñi et al., 2014 ; Mi š i ćet al., 2015 ), biophysical
simulations ( Breakspear, 2017 ; Deco et al., 2009 ; Honey et al., 2009 ;
Wang et al., 2019 ), and articial intelligence ( Rosenthal et al., 2018 ).
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Here, we expanded from prior work assuming stationarity in brain func-
tion by inferring time-varying functional states and their transitions
( Gotts et al., 2020 ; Hansen et al., 2015 ; Vidaurre et al., 2018 , 2017)
using HMMs to describe dynamic neural changes that emerge during
wakeful rest. Our analysis highlighted a temporal hierarchy that re-
ects a division between low-level sensorimotor and higher-order trans-
modal states, replicating earlier applications of HMMs to resting-state
data ( Vidaurre et al., 2017 ). Importantly, relating these distinct func-
tional states to structural connectome manifolds, we found that they
were uniquely related to complementary features of cortical organi-
zation. Structural connectome dimensions were particularly useful in
describing transitions between low-level functional states and between
low- and high-level states. On the other hand, they could not strongly
capture transitions within the transmodal regime, a pattern that echoes
prior ndings that close relationships between structure and function ex-
ist in primary sensorimotor areas while the associations become increas-
ingly divergent in transmodal cortices ( Park and Friston, 2013 ; Vázquez-
Rodríguez et al., 2019 ). Notably, structure-function coupling was more
marked for the rst structural gradient, while the second gradient did
not reveal a signicant association with function. However, when we
incorporated both gradients into a common linear regression, the sec-
ond gradient indeed improved model performance. A potential expla-
nation for these increases is the interaction between the rst two gradi-
ents, which might come from continuously changing connectivity pat-
terns as well as potentially overlapping multiple gradients ( Haak et al.,
2018 ; Haak and Beckmann, 2020 ). Topological parameterization based
on connectivity distance and rich-club taxonomy related the dynamic
functional ndings to two important features of core-periphery distinc-
tion established by graph theoretical studies ( de Reus and van den
Heuvel, 2013 ; Gria and van den Heuvel, 2018 ; Liang et al., 2018 ;
Shu et al., 2018 ; van den Heuvel et al., 2012 ; Zhao et al., 2017 ). In fact,
dynamic transitions in the sensorimotor state-space engaged mainly
short- and intermediary-range connections, while transitions within the
higher-order meta-state increasingly occupied rich-club nodes that are
mutually interconnected by long-range connections. The dierential oc-
cupation of nodes with a more regional versus a more large-scale con-
nectivity pattern in lower versus higher-order functional states may re-
ect dierent ways they related to large-scale brain dynamics, with
nodes involved in more segregated sensorimotor states having a more
localized connectivity prole while higher-order functions are orches-
trated by nodes with a more integrated connectivity prole. This con-
clusion is consistent with our application of connectome-informed com-
munication models, which assume functional signal transmission occurs
along structural network edges ( Avena-Koenigsberger et al., 2019 , 2018 ;
Goñi et al., 2014 ). We established that sensorimotor states and their
transitions frequently involve decentralized mechanisms of network dif-
fusion, where signals diuse locally without necessarily traversing along
the shortest possible paths. In contrast, functional transitions within the
transmodal regime increasingly leverage centralized, and globally e-
cient, routing strategies to maintain long-range communication across
distributed hubs. These results, therefore, highlight that dynamic infor-
mation ow in the brain adheres to dierent modes of communication,
ranging from more decentralized network diusion processes that run
within multiple parallel hierarchies anchored on specic sensorimotor
systems towards connector nodes on the one hand, and a more central-
ized and topology-sensitive routing mechanism that enables the brain-
wide integration of the information aggregated by these hubs in a glob-
ally ecient manner, on the other ( Avena-Koenigsberger et al., 2019 ,
2018 , 2014; Goñi et al., 2014 ). Future work may determine whether
these dierent communication processes are mediated by dierent sig-
naling properties. A prior computational model of non-human primate
cortical dynamics that incorporated a gradient of synaptic excitation
suggested multiple temporal hierarchies across the cortex, with lower-
level sensorimotor areas involving fast signaling mechanisms while
higher-order cognitive areas demonstrated slow and integrated activ-
ity ( Chaudhuri et al., 2015 ). In that study, hierarchical position was
found to correlate with the number of synaptic spines representing a
plausible microcircuit substrate underlying an area’s capacity to en-
gage in integrative function. The current study adopted mean rst-
passage time and path length, as well as search information and path
transitivity, to explore structurally-governed network communication
mechanisms underlying dynamic functional states. These metrics repre-
sent a spectrum of communication processes anchored on shortest path
communication ( i.e., routing) at one extreme, and random walk pro-
cesses ( i.e., diusion) at the other extreme ( Avena-Koenigsberger et al.,
2019 , 2018 ). Communication models residing between these two ex-
tremes may include (i) communicability, which considers non-shortest
paths to characterize complex networks ( Estrada and Hatano, 2008 ), (ii)
navigation, a decentralized network communication strategy that cap-
tures long and inecient paths as well as shortest paths ( Seguin et al.,
2019 , 2018 ), and (iii) spreading models, which describe how local per-
turbations trigger global cascades ( Mi š i ćet al., 2015 ). These commu-
nication models may provide additional information for understand-
ing the correspondence of brain structure and function ( Baum et al.,
2020 ; Hermundstad et al., 2013 ; Honey et al., 2009 ; Mi ŝ ic et al., 2016 ;
Osmanl ı o ğlu et al., 2019 ; Seguin et al., 2020 ; Snyder and Bauer, 2019 ;
Suárez et al., 2020 ; Vázquez-Rodríguez et al., 2019 ) beyond our cur-
rent ndings based on diusion and routing. An interesting future di-
rection to link brain structure and functional dynamics may capitalize
on asymmetric communication measures ( Avena-Koenigsberger et al.,
2019 , 2018 ; Goñi et al., 2014 , 2013; Rubinov and Sporns, 2010 ). A
recent study estimated send-receive communication asymmetry from
undirected structural connectome data, and found that this asymmetry
recapitulated functional gradients dierentiating low-level sensory to
higher-order transmodal areas ( Seguin et al., 2019 ). It may be of interest
to explore whether the asymmetric measures can further be associated
to communication mechanisms across dierent structurally-determined
and temporal hierarchies, particularly in transmodal networks and a
higher-order dynamic state space.
Our ndings were consistent across dierent HCP subsamples and
could be replicated in an independent dataset. We also assessed the
consistency of our ndings across dierent spatial scales. Findings were
consistent at parcellations with 200 and 300 parcels. We found fairly
consistent structure-function coupling, where transitions within senso-
rimotor state and between the meta-states showed high correlations.
Unlike the main ndings based on 200 parcels, brain regions from 400
node parcellation showed non-signicant correlation between sG1 and
transitions from fM1 to fM2, and signicant correlation with transitions
within fM2. This discrepancy may be due to the parcellation approach,
which may potentially mix the fMRI signals from dierent set of ver-
tices. However, why the association between structural manifolds and
functional dynamics vary across dierent parcellation scales needs to be
investigated further.
Finally, we also re-expressed our main ndings by leveraging a well-
established model of cortical hierarchical organization developed in
non-human primates ( Mesulam, 1998 ). This model-based analysis con-
rmed that rich-club proportion, overall connectivity distance, and the
increasing use of network routing relative to diusion increases along
the putative cortical hierarchy. Similarly, this analysis also established
how the coupling between structure and dynamic functional transitions
related to hierarchical levels. Local structural constraints on functional
dynamics may be particularly strong when state transitions involve low-
level cortical systems and when transitions involve bottom-up and top-
down changes in hierarchical levels, but they may not have such a tight
grip on transitions occurring within the higher-order regime of corti-
cal hierarchy. Contemporary perspectives on brain wide information
processing often focus on the process through which sensorimotor in-
puts gain access to a global workspace that allows these information
to be processed in an explicit conscious manner ( Dehaene et al., 1998 ;
Mashour et al., 2020 ). It is possible that neural dynamics within higher
hierarchical levels increasingly engage polysynaptic mechanisms that al-
low for integrated and exible processing, which ultimately allows for
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
the implementation of adaptive control processes for which conscious
experience is argued to be important ( Mesulam, 1990 ).
In sum, our study provides a novel perspective on one of the major
questions in systems neuroscience: How does the hard-wired structure
of the cortex support dynamic functional changes that are necessary for
exible cognition? Our results suggest that this is achieved by balanc-
ing local and distant inuences in structural constraints. We established
that dynamic modes of neural function that are closely linked to lower-
level sensorimotor systems are constrained by local features of cortex. In
contrast, neural function linked to transmodal regions emerge within a
set of constraints that reect the long-range network routing. Our study,
thus, suggests that the wiring of the human brain implements local and
distal communication strategies, and that the balance of these two as-
pects of the structural connectome may be important in supporting both
specialized and integrated aspects of cognitive processing.
Declaration of Competing Interest
The authors declare no conicts of interest.
Acknowledgements
Dr. Bo-yong Park was funded by the National Research Foundation of
Korea (NRF-2020R1A6A3A03037088), Molson Neuro-Engineering fel-
lowship by Montreal Neurological Institute and Hospital (MNI) and a
postdoctoral fellowship of the Fonds de la Recherche du Quebec –Santé
(FRQ-S). Mr. Reinder Vos de Wael was funded by a studentship of the
Savoy Foundation. Dr. Casey Paquola was funded through a postdoc-
toral fellowship of the FRQ-S. Ms. Sara Larivière was funded by the
Canadian Institutes of Health Research (CIHR). Dr. Oualid Benkarim
was funded by a Healthy Brains for Healthy Lives (HBHL) postdoctoral
fellowship. Dr. Jessica Royer was supported by a Canadian Open Neuro-
science Platform (CONP) fellowship and CIHR. Dr. Raul R. Cruces was
funded through a postdoctoral fellowship of the FRQ-S. Dr. Danilo Bzdok
was supported by the Healthy Brains Healthy Lives initiative (Canada
First Research Excellence fund), and by the CIFAR Articial Intelli-
gence Chairs program (Canada Institute for Advanced Research). Dr.
Jonathan Smallwood was supported by the European Research Council
(WANDERINGMINDS-ERC646927). Dr. Boris Bernhardt acknowledges
research support from the National Science and Engineering Research
Council of Canada (NSERC Discovery-1304413), the Canadian Institutes
of Health Research (CIHR FDN-154298), SickKids Foundation (NI17-
039), Azrieli Center for Autism Research (ACAR-TACC), BrainCanada,
FRQ-S and the Tier-2 Canada Research Chairs program. Data were
provided, in part, by the Human Connectome Project, WU-Minn Con-
sortium (Principal Investigators: David Van Essen and Kamil Ugurbil;
1U54MH091657) funded by the 16 NIH Institutes and Centers that sup-
port the NIH Blueprint for Neuroscience Research; and by the McDonnell
Center for Systems Neuroscience at Washington University. Drs. Bo-yong
Park, Casey Paquola, and Boris C. Bernhardt are jointly funded through
an MNI-Cambridge collaborative award.
Data and code availability
The full imaging and phenotypic data from the Human Con-
nectome Project are provide ( https://www.humanconnectome.org/ ).
MICA-MTL data will be made available via osf.io upon publica-
tion of the paper. The codes are available at https://github.com/
MICA-MNI/BrainSpace (for manifold identication), https://github.
com/OHBA- analysis/HMM- MAR (for dynamic connectivity analysis),
and https://sites.google.com/site/bctnet/ (for calculating connectome
topology).
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi: 10.1016/j.neuroimage.2020.117429 .
References
Alexander-Bloch, A.F., Shou, H., Liu, S., Satterthwaite, T.D., Glahn, D.C., Shinohara, R.T.,
Vandekar, S.N., Raznahan, A., 2018. On testing for spatial correspondence be-
tween maps of human brain structure and function. Neuroimage 178, 540–551.
doi: 10.1016/j.neuroimage.2018.05.070 .
Allen, E.A., Damaraju, E., Plis, S.M., Erhardt, E.B., Eichele, T., Calhoun, V.D., 2012. Track-
ing whole-brain connectivity dynamics in the resting state. Cereb. Cortex 24, 663–676.
doi: 10.1093/cercor/bhs352 .
Ashourvan, A., Gu, S., Mattar, M.G., Vettel, J.M., Bassett, D.S., 2017. The energy landscape
underpinning module dynamics in the human brain connectome. Neuroimage 157,
364–380. doi: 10.1016/j.neuroimage.2017.05.067 .
Avena-Koenigsberger, A., Goñi, J., Betzel, R.F., van
den Heuvel, M.P., Gria, A., Hag-
mann, P., Thiran, J.P., Sporns, O., 2014. Using Pareto optimality to explore the topol-
ogy and dynamics of the human connectome. Philos. Trans. R. Soc. B Biol. Sci 369.
doi: 10.1098/rstb.2013.0530 .
Avena-Koenigsberger, A., Misic, B., Sporns, O., 2018. Communication dynamics in com-
plex brain networks. Nat. Rev. Neurosci. 19, 17–33. doi: 10.1038/nrn.2017.149 .
Avena-Koenigsberger, A., Yan, X., Kolchinsky, A., van den Heuvel, M.P., Hagmann, P.,
Sporns, O., 2019. A spectrum of routing strategies for brain networks. PLoS Comput.
Biol. 15, 1–24. doi: 10.1371/journal.pcbi.1006833 .
Bajada, C.J., Jackson, R.L., Haroon, H.A., Azadbakht, H., Parker, G.J.M.,
Ralph, Lambon,
M.A., Cloutman, 2017. A graded tractographic parcellation of the temporal lobe. Neu-
roimage 155, 503–512. doi: 10.1016/j.neuroimage.2017.04.016 .
Bassett, D.S., Wymbs, N.F., Porter, M.A., Mucha, P.J., Carlson, J.M., Grafton, S.T., 2011.
Dynamic reconguration of human brain networks during learning. Proc. Natl. Acad.
Sci. U. S. A. 108, 7641–7646. doi: 10.1073/pnas.1018985108 .
Batista-García-Ramó, K., Fernández-Verdecia, C.I., 2018. What we know about the brain
structure-function relationship. Behav. Sci. (Basel). 8, 39. doi: 10.3390/bs8040039 .
Baum, G.L., Cui, Z., Roalf, D.R., Ciric, R., Betzel, R.F., Larsen, B., Cieslak, M., Cook, P.A.,
Xia, C.H., Moore, T.M., Ruparel, K., Oathes, D.J., Alexander-Bloch, A.F., Shino-
hara, R.T., Raznahan, A., Gur, R.E., Gur, R.C., Bassett, D.S., Satterthwaite, T.D., 2020.
Development of structure–function coupling in human brain networks during youth.
Proc. Natl. Acad. Sci. U. S. A. 117, 771–778. doi: 10.1073/pnas.1912034117 .
Becker, C.O., Pequito, S., Pappas, G.J., Miller, M.B., Grafton, S.T., Bassett, D.S., Preci-
ado, V.M., 2018. Spectral mapping of brain functional connectivity from diusion
imaging. Sci. Rep. 8, 1411. doi: 10.1038/s41598-017-18769-x .
Beckmann, M., Johansen-Berg, H., Rushworth, M.F.S., 2009. Connectivity-based parcel-
lation of human cingulate cortex and its relation to functional specialization. J. Neu-
rosci. 29, 1175–1190. doi: 10.1523/JNEUROSCI.3328-08.2009 .
Benjamini, Y. , Hochberg, Y. ,
1995. Controlling the false discovery rate : a practical and
powerful approach to multiple testing. J. R. Stat. Soc. 57, 289–300 .
Bertolero, M.A., Yeo, Thomas, B.T., D’Esposito, 2015. The modular and integrative func-
tional architecture of the human brain. Proc. Natl. Acad. Sci. U. S. A. 112, E6798–
E6807. doi:
10.1073/pnas.1510619112 .
Betzel, R.F., Gria, A., Hagmann, P., Mi š i´c, B., 2019. Distance-dependent consensus
thresholds for generating group-representative structural brain networks. Netw. Neu-
rosci. 3, 475–496. doi: 10.1162/netn_a_00075 .
Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E., 2008. Fast unfold-
ing of communities in large networks. J. Stat. Mech. Theory Exp 2008.
doi: 10.1088/1742-5468/2008/10/P10008 .
Braun, U., Schäfer, A., Walter, H., Erk, S., Romanczuk-Seiferth, N., Haddad, L.,
Schweiger, J.I., Grimm, O., Heinz, A., Tost, H., Meyer-Lindenberg, A., Bas-
sett, D.S., 2015. Dynamic reconguration of frontal brain networks during exec-
utive cognition in humans. Proc. Natl. Acad. Sci. U. S. A. 112, 11678–11683.
doi: 10.1073/pnas.1422487112 .
Breakspear, M., 2017. Dynamic models of large-scale brain activity. Nat. Neurosci. 20,
340–352. doi: 10.1038/nn.4497 .
Bullmore, E., Sporns, O., 2009. Complex brain networks: graph theoretical analysis of
structural and functional systems. Nat. Neurosci. 10, 186–198. doi: 10.1038/nrn2575 .
Burt, J.B., Demirta ş , M., Eckner, W.J., Navejar, N.M., Ji, J.L., Martin, W.J., Bernacchia, A.,
Anticevic, A., Murray, J.D., 2018. Hierarchy of transcriptomic specialization across
human cortex captured by structural neuroimaging topography. Nat. Neurosci. 21,
1251–1259. doi: 10.1038/s41593-018-0195-0 .
Cerliani, L., Thomas, R.M., Jbabdi, S., Siero, J.C.W., Nanetti, L., Crippa, A., Gazzola, V.,
D’Arceuil, H., Keysers,
C., 2012. Probabilistic tractography recovers a rostrocaudal
trajectory of connectivity variability in the human insular cortex. Hum. Brain Mapp.
33, 2005–2034. doi: 10.1002/hbm.21338 .
Chai, L.R. , Khambhati, A.N. , Ciric, R. , Moore, T.M. , Gur, R.C. , Gur, R.E. , Satterth-
waite, T.D. , Bassett, D.S. , 2017. Evolution of brain network dynamics in neurode-
velopment. Netw. Neurosci. 1, 14–30 10.1162/netn_a_00001 .
Chai, L.R., Mattar, M.G., Blank, I.A., Fedorenko, E., Bassett, D.S., 2016. Functional network
dynamics of the language system. Cereb. Cortex 26, 4148–4159. doi: 10.1093/cer-
cor/bhw238 .
Chaudhuri, R., Knoblauch, K., Gariel, M.A., Kennedy, H., Wang, X.J., 2015.
A large-scale
circuit mechanism for hierarchical dynamical processing in the primate cortex. Neu-
ron 88, 419–431. doi: 10.1016/j.neuron.2015.09.008 .
Christiaens, D., Reisert, M., Dhollander, T., Sunaert, S., Suetens, P., Maes, F., 2015.
Global tractography of multi-shell diusion-weighted imaging data using a multi-
tissue model. Neuroimage 123, 89–101. doi: 10.1016/j.neuroimage.2015.08.008 .
Ciric, R., Nomi, J.S., Uddin, L.Q., Satpute, A.B., 2017. Contextual connectivity: A frame-
work for understanding the intrinsic dynamic architecture of large-scale functional
brain networks. Sci. Rep. 7, 6537. doi: 10.1038/s41598-017-06866-w .
Cox, R.W., 1996. AFNI : software for analysis and visualization of functional
magnetic resonance neuroimages. Comput. Biomed. Res. 29, 162–173.
doi: 10.1006/cbmr.1996.0014 .
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Dale, A.M., Fischl, B., Sereno, M.I., 1999. Cortical surface-based analysis: I. Seg-
mentation and surface reconstruction. Neuroimage 9, 179–194. doi: 10.1006/nimg.
1998.0395 .
Damaraju, E., Allen, E.A., Belger, A., Ford, J.M., McEwen, S., Mathalon, D.H.,
Mueller, B.A., Pearlson, G.D., Potkin, S.G., Preda, A., Turner, J.A., Vaidya, J.G., Van
Erp, T.G., Calhoun, V.D., 2014. Dynamic functional connectivity analysis reveals
transient states of dysconnectivity in schizophrenia. NeuroImage Clin. 5, 298–308.
doi: 10.1016/j.nicl.2014.07.003 .
de Reus, M.A., van den Heuvel, M.P., 2013. Rich club organization and intermodule com-
munication in the cat connectome. J. Neurosci. 33, 12929–12939. doi: 10.1523/jneu-
rosci.1448-13.2013 .
Deco, G., Jirs,
V., McIntosh, A.R., Sporns, O., Kötter, R., 2009. Key role of coupling, delay,
and noise in resting brain uctuations. Proc. Natl. Acad. Sci. U. S. A. 106, 10302–
10307. doi: 10.1073/pnas.0901831106 .
Dehaene, S., Kerszberg, M., Changeux, J.P., 1998. A neuronal model of a global workspace
in eortful cognitive tasks. Proc. Natl. Acad. Sci. U. S. A. 95, 14529–14534.
doi: 10.1073/pnas.95.24.14529 .
Ecker, C., Ronan, L., Feng, Y., Daly, E., Murphy, C., Ginestet, C.E., Brammer, M.,
Fletcher, P.C., Bullmore, E.T., Suckling, J., Baron-Cohen, S., Williams, S., Loth, E.,
Murphy, D.G.M., 2013. Intrinsic gray-matter connectivity of the brain in adults
with autism spectrum disorder. Proc. Natl. Acad. Sci. U. S. A. 110, 13222–13227.
doi: 10.1073/pnas.1221880110 .
Estrada, E., Hatano, N., 2008. Communicability in complex networks. Phys. Rev. E - Stat.
Nonlinear, Soft Matter Phys 77, 1–12. doi: 10.1103/PhysRevE.77.036111 .
Fischl, B., 2012. FreeSurfer. Neuroimage 62, 774–781.
doi: 10.1016/j.neuroimage.2012.01.021 .
Fischl, B., Sereno, M.I., Dale, A.M., 1999a. Cortical surface-based analysis: II. Ina-
tion, attening, and a surface-based coordinate system. Neuroimage 9, 195–207.
doi: 10.1006/nimg.1998.0396 .
Fischl, B., Sereno, M.I., Tootell, R.B.H., Dale, A.M., 1999b. High-resolution inter-subject
averaging and a surface-based coordinate system. Hum. Brain Mapp. 8, 272–284.
doi: 10.1002/(SICI)1097-0193(1999)8 .
Fornito, A. , Zalesky, A. , Bullmore, E. , 2016. Fundamentals of Brain Network Analysis.
Academic Press, Amsterdam .
Friston, K.J., Harrison, L., Penny, W., 2003. Dynamic causal modelling. Neuroimage 19,
1273–1302. doi: 10.1016/S1053-8119(03)00202-7 .
Glasser, M.F., Coalson, T.S., Robinson, E.C., Hacker, C.D., Harwell, J., Yacoub, E., Ugur-
bil, K., Andersson, J., Beckmann, C.F., Jenkinson,
M., Smith, S.M., Van Essen, D.C.,
2016. A multi-modal parcellation of human cerebral cortex. Nature 536, 171–178.
doi: 10.1038/nature18933 .
Glasser, M.F., Sotiropoulos, S.N., Wilson, J.A., Coalson, T.S., Fischl, B., Andersson, J.L.,
Xu, J., Jbabdi, S., Webster, M., Polimeni, J.R., Van Essen, D.C., Jenkinson, M., 2013.
The minimal preprocessing pipelines for the human connectome project. Neuroimage
80, 105–124. doi: 10.1016/j.neuroimage.2013.04.127 .
Goñi, J., Avena-Koenigsberger, A., Velez de Mendizabal, N., van den Heuvel, M.P., Bet-
zel, R.F., Sporns, O., 2013. Exploring the morphospace of communication eciency
in complex networks. PLoS One 8. doi: 10.1371/journal.pone.0058070 .
Goñi, J., van den Heuvel, M.P., Avena-Koenigsberger, A., De Mendizabal, N.V.,
Betzel, R.F., Gria, A., Hagmann, P., Corominas-Murtra, B., Thiran, J.P.,
Sporns, O., 2014. Resting-brain functional connectivity predicted by analytic mea-
sures of network communication. Proc. Natl. Acad. Sci. U. S. A. 111, 833–838.
doi: 10.1073/pnas.1315529111 .
Gotts, S.J., Gilmore, A.W., Martin, A., 2020. Brain networks, dimensionality, and
global signal averaging in resting-state fMRI: Hierarchical network structure re-
sults in low-dimensional spatiotemporal dynamics. Neuroimage 205, 116289.
doi: 10.1016/j.neuroimage.2019.116289 .
Gria, A. , van den Heuvel, M.P. , 2018. Rich-club neurocircuitry: Function, evolution, and
vulnerability. Dialogues Clin. Neurosci. 20, 121–132 .
Haak, K.V., Beckmann, C.F., 2020. Understanding brain organisation in the face of
functional heterogeneity and functional multiplicity. Neuroimage 220, 117061.
doi: 10.1016/j.neuroimage.2020.117061 .
Haak, K.V., Marquand, A.F., Beckmann, C.F., 2018. Connectopic mapping with resting-
state fMRI. Neuroimage 170, 83–94. doi: 10.1016/j.neuroimage.2017.06.075 .
Han, X., Qian, X., Bernstein, J.G., Zhou, H.hui, Franzesi, G.T., Stern, P., Bronson, R.T.,
Graybiel, A.M., Desimone, R., Boyden, E.S., 2009. Millisecond-timescale optical con-
trol of neural dynamics in the nonhuman primate brain. Neuron 62, 191–198.
doi: 10.1016/j.neuron.2009.03.011 .
Hansen, E.C.A., Battaglia, D., Spiegler, A., Deco, G., Jirsa, V.K., 2015. Functional connec-
tivity dynamics: modeling the switching behavior of the resting state. Neuroimage
105, 525–535. doi: 10.1016/j.neuroimage.2014.11.001 .
Hermundstad, A.M., Bassett, D.S., Brown, K.S., Amino, E.M., Clewett, D., Free-
man, S., Frithsen, A., Johnson, A., Tipper, C.M., Miller, M.B., Grafton, S.T., Carl-
son, J.M., 2013. Structural foundations of resting-state and task-based functional
connectivity in the human brain. Proc. Natl. Acad. Sci. U. S. A. 110, 6169–6174.
doi: 10.1073/pnas.1219562110 .
Honey, C.J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., Hag-
mann, P., 2009. Predicting human resting-state functional connectivity from struc-
tural connectivity. Proc. Natl. Acad. Sci. U. S. A. 106, 2035–2040. doi: 10.1073/pnas.
0811168106 .
Hong, S.J., Valk, S.L., Di Martino, A., Milham, M.P., Bernhardt, B.C.,
2018. Multidimen-
sional neuroanatomical subtyping of autism spectrum disorder. Cereb. Cortex 28,
3578–3588. doi: 10.1093/cercor/bhx229 .
Hong, S.-J. , Vos De Wael, R. , Bethlehem, R.A.I. , Lariviere, S. , Paquola, C. , Valk, S.L. , Mil-
ham, M.P. , Martino, A.Di , Margulies, D.S. , Smallwood, J. , Bernhardt, B.C. , 2019. Atyp-
ical functional connectome hierarchy in autism. Nat. Commun. 10, 1022 .
Huntenburg, J.M., Bazin, P.L., Goulas, A., Tardif, C.L., Villringer, A., Margulies, D.S., 2017.
A systematic relationship between functional connectivity and intracortical myelin in
the human cerebral cortex. Cereb. cortex 27, 981–997. doi: 10.1093/cercor/bhx030 .
Huntenburg, J.M., Bazin, P.L., Margulies, D.S., 2018. Large-scale gradients in human cor-
tical organization. Trends Cogn. doi: 10.1016/j.tics.2017.11.002 .
Jenkinson, M., Beckmann, C.F., Behrens, T.E.J., Woolrich, M.W., Smith, S.M., 2012. Fsl.
Neuroimage 62, 782–790. doi: 10.1016/j.neuroimage.2011.09.015 .
Jeurissen, B., Tournier, J.D., Dhollander, T., Connelly, A., Sijbers, J., 2014. Multi-tissue
constrained spherical deconvolution for improved analysis of multi-shell diusion
MRI data. Neuroimage 103, 411–426. doi: 10.1016/j.neuroimage.2014.07.061 .
Khambhati,
A.N., Davis, K.A., Oommen, B.S., Chen, S.H., Lucas, T.H., Litt, B., Bassett, D.S.,
2015. Dynamic network drivers of seizure generation, propagation and termina-
tion in human neocortical epilepsy. PLoS Comput. Biol 11, 1–19. doi: 10.1371/jour-
nal.pcbi.1004608 .
Khambhati, A.N., Sizemore, A.E., Betzel, R.F., Bassett, D.S., 2018. Modeling
and interpreting mesoscale network dynamics. Neuroimage 180, 337–349.
doi: 10.1016/j.neuroimage.2017.06.029 .
Kodinariya, T.M. , Makwana, P.R. , 2013. Review on determining number of cluster in
K-Means clustering. Int. J. Adv. Res. Comput. Sci. Manag. Stud. 1, 90–95 .
Kriegeskorte, N., Simmons, W.K., Bellgowan, P.S., Baker, C.I., 2009. Circular analysis in
systems neuroscience: the dangers of double dipping. Nat. Neurosci. 12, 535–540.
doi: 10.1038/nn.2303 .
Kucyi, A. , Tambini, A. , Sadaghiani, S. , Keilholz, S. , Cohen, J.R. , 2018. Spontaneous cogni-
tive processes and the behavioral validation of time-varying brain connectivity. Netw.
Neurosci. 2, 397–417 10.1162/ netn_a_00037 .
Larivière, S., Vos de Wael, R., Hong, S.-J., Paquola, C., Tavakol, S., Lowe, A.J.,
Schrader, D.V, Bernhardt, B.C., 2019a. Multiscale structure–function gradients in the
neonatal connectome. Cereb. Cortex doi: 10.1093/cercor/bhz069 .
Larivière, S., Weng, Y., Wael, R.V. de, Frauscher, B., Wang, Z., Bernasconi, A., Bernasconi,
N., Schrader, D. V., Zhang, Z., Bernhardt, B.C., 2019b. Functional connectome
con-
tractions in temporal lobe epilepsy. bioRxiv 756494. 10.1101/756494
Lee, M.J., Park, B., Cho, S., Park, H., Kim, S.-T., Chung, C.-S., 2019. Dynamic functional
connectivity of migraine brain: a resting-state functional magnetic resonance imaging
study. Pain 160, 2776–2786. doi: 10.1097/j.pain.0000000000001676 .
Liang, X., Hsu, L.M., Lu, H., Sumiyoshi, A., He, Y., Yang, Y., 2018. The rich-club organi-
zation in rat functional brain network to balance between communication cost and
eciency. Cereb. cortex 28, 924–935. doi: 10.1093/cercor/bhw416 .
Margulies, D.S., Ghosh, S.S., Goulas, A., Falkiewicz, M., Huntenburg, J.M., Langs, G.,
Bezgin, G., Eickho, S.B., Castellanos, F.X., Petrides, M., Jeeries, E., Small-
wood, J., 2016. Situating the default-mode network along a principal gradient of
macroscale cortical organization. Proc. Natl. Acad. Sci. U. S. A. 113, 12574–12579.
doi: 10.1073/pnas.1608282113 .
Mashour, G.A., Roelfsema, P., Changeux, J.P., Dehaene, S., 2020. Conscious pro-
cessing and the global neuronal workspace hypothesis. Neuron 105, 776–798.
doi: 10.1016/j.neuron.2020.01.026 .
Messé, A., Rudrauf, D., Benali, H., Marrelec, G., 2014. Relating structure and function in
the human brain: relative contributions of anatomy, stationary dynamics, and non-
stationarities. PLoS Comput. Biol. 10, e1003530. doi: 10.1371/journal.pcbi.1003530 .
Mesulam, M.-M., 1990. Large-scale neurocognitive networks and distributed pro-
cessing for attention, language, and memory. Ann. Neurol. 28, 597–613.
doi: 10.1002/ana.410280502 .
Mesulam, M.M., 1998. From sensation to cognition. Brain 121, 1013–1052.
doi: 10.1093/brain/121.6.1013 .
Mi ŝ ic, B., Betzel, R.F., de Reus, M.A., van den Heuvel, M.P., Berman, M.G., McIntosh, A.R.,
Sporns, O., 2016. Network-level structure-function relationships in human neocortex.
Cereb. Cortex 26, 3285–3296. doi: 10.1093/cercor/bhw089 .
Mi š i ć, B., Betzel, R.F., Nematzadeh, A., Goñi, J., Gria, A., Hagmann, P., Flammini, A.,
Ahn, Y.Y., Sporns, O., 2015. Cooperative and competitive spreading dynamics on the
human connectome. Neuron 86, 1518–1529. doi: 10.1016/j.neuron.2015.05.035 .
Oligschläger, S., Xu, T., Baczkowski, B.M., Falkiewicz, M., Falchier, A., Linn, G.,
Margulies, D.S., 2019. Gradients of connectivity distance in the cere-
bral cortex of the macaque monkey. Brain Struct. Funct. 224, 925–935.
doi: 10.1007/s00429-018-1811-1 .
Osmanl ı o ğlu, Y., Tunç, B., Parker, D., Elliott, M.A., Baum, G.L., Ciric, R., Satterth-
waite, T.D., Gur, R.E., Gur, R.C., Verma, R., 2019. System-level matching of struc-
tural and functional connectomes in the human brain. Neuroimage 199, 93–104.
doi: 10.1016/j.neuroimage.2019.05.064 .
Paquola, C., Vos De Wael, R., Wagstyl, K., Bethlehem, R.A.I., Hong, S.J., Seidlitz, J., Bull-
more, E.T., Evans, A.C., Misic, B., Margulies, D.S., Smallwood, J., Bernhardt, B.C.,
2019. Microstructural and functional gradients are increasingly dissociated in trans-
modal cortices. PLoS Biol 17, e3000284. doi: 10.1371/journal.pbio.3000284 .
Park, B., Lee, M.J., Kim, M., Kim, S.-H., Park, H., 2018a. Structural and functional brain
connectivity changes between people with abdominal and non-abdominal obesity
and their association with behaviors of eating disorders. Front. Neurosci. 12, 741.
doi: 10.3389/fnins.2018.00741 .
Park, B., Shim, Mok, W., James, O., Park, 2019. Possible links between the lag
structure in visual cortex and visual streams using fMRI. Sci. Rep. 9, 4283.
doi: 10.1038/s41598-019-40728-x .
Park, B., Moon, T., Park, H., 2018b. Dynamic functional connectivity analysis reveals
improved association between brain networks and eating behaviors compared
to static
analysis. Behav. Brain Res. 337, 114–121. doi: 10.1016/j.bbr.2017.10.001 .
Park, H.J., Friston, K., 2013. Structural and functional brain networks: From connections
to cognition. Science (80-.) 342, 1238411. doi: 10.1126/science.1238411 .
Razi, A., Seghier, M.L., Zhou, Y., McColgan, P., Zeidman, P., Park, H., Sporns, O., Rees, G.,
Friston, K.J., 2017. Large-scale DCMs for resting-state fMRI. Netw. Neurosci. 1, 222–
241. doi: 10.1162/netn .
B.-y. Park, R. Vos de Wael, C. Paquola et al. NeuroImage 224 (2021) 117429
Robinson, E.C., Jbabdi, S., Glasser, M.F., Andersson, J., Burgess, G.C., Harms, M.P.,
Smith, S.M., Van Essen, D.C., Jenkinson, M., 2014. MSM: A new exi-
ble framework for Multimodal Surface Matching. NeuroImage 100, 414–426.
doi: 10.1016/j.neuroimage.2014.05.069 .
Rosenthal, G., Váš a, F., Gria, A., Hagmann, P., Amico, E., Goñi, J., Avidan, G.,
Sporns, O., 2018. Mapping higher-order relations between brain structure and func-
tion with embedded vector representations of connectomes. Nat. Commun. 9, 2178.
doi: 10.1038/s41467-018-04614-w .
Rubinov, M., Sporns, O., 2010. Complex network measures of brain
connectivity: uses and interpretations. Neuroimage 52, 1059–1069.
doi: 10.1016/j.neuroimage.2009.10.003 .
Rubinov, M., Sporns, O., van Leeuwen, C., Breakspear, M., 2009. Symbiotic re-
lationship between brain structure and dynamics. BMC Neurosci 10, 55.
doi: 10.1186/1471-2202-10-55 .
Salimi-Khorshidi, G., Douaud, G., Beckmann, C.F., Glasser, M.F., Grianti, L., Smith, S.M.,
2014. Automatic denoising of functional MRI data: combining independent com-
ponent analysis and hierarchical fusion of classiers. Neuroimage 90, 449–468.
doi: 10.1016/j.neuroimage.2013.11.046 .
Schaefer, A., Kong, R., Gordon, E.M., Laumann, T.O., Zuo, X.-N., Holmes, A.J., Eick-
ho, S.B., Yeo, B.T.T., 2018. Local-global parcellation of the human cerebral
cortex from intrinsic functional connectivity MRI. Cereb. Cortex 28, 3095–3114.
doi: 10.1093/cercor/bhx179 .
Seguin, C., Razi, A., Zalesky, A., 2019. Inferring neural signalling direction-
ality from undirected structural connectomes. Nat. Commun. 10, 4289.
doi: 10.1038/s41467-019-12201-w .
Seguin, C., Tian, Y., Zalesky, A., 2020. Network communication models improve the be-
havioral and functional predictive utility of the human structural connectome. Netw.
Neurosci 1–40. doi: 10.1162/netn_a_00161 .
Seguin, C., van den Heuvel, M.P., Zalesky, A., 2018. Navigation of brain networks. Proc.
Natl. Acad. Sci. U. S. A. 115, 6297–6302. doi: 10.1073/pnas.1801351115 .
Shine, J.M., Breakspear, M., Bell, P.T., Ehgoetz Martens, K., Shine, R., Koyejo, O.,
Sporns, O., Poldrack, R.A., 2019. Human cognition involves the dynamic integra-
tion of neural activity and neuromodulatory systems. Nat. Neurosci.
22, 289–296.
doi: 10.1038/s41593-018-0312-0 .
Shu, N., Duan, Y., Huang, J., Ren, Z., Liu, Z., Dong, H., Barkhof, F., Li, K., Liu, Y., 2018. Pro-
gressive brain rich-club network disruption from clinically isolated syndrome towards
multiple sclerosis. NeuroImage Clin. 19, 232–239. doi: 10.1016/j.nicl.2018.03.034 .
Smith, R.E., Tournier, J.D., Calamante, F., Connelly, A., 2012. Anatomically-
constrained tractography: Improved diusion MRI streamlines tractography
through eective use of anatomical information. Neuroimage 62, 1924–1938.
doi: 10.1016/j.neuroimage.2012.06.005 .
Smith, R.E., Tournier, J.D., Calamante, F., Connelly, A., 2015. SIFT2: Enabling dense quan-
titative assessment of brain white matter connectivity using streamlines tractography.
Neuroimage 119, 338–351. doi: 10.1016/j.neuroimage.2015.06.092
.
Snyder, A.Z., Bauer, A.Q., 2019. Mapping structure-function relationships in
the brain. Biol. Psychiatry Cogn. Neurosci. Neuroimaging 4, 510–521.
doi: 10.1016/j.bpsc.2018.10.005 .
Suárez, L.E., Markello, R.D., Betzel, R.F., Misic, B., 2020. Linking structure
and function in macroscale brain networks. Trends Cogn. Sci. 24, 302–315.
doi: 10.1016/j.tics.2020.01.008 .
Taghia, J., Cai, W., Ryali, S., Kochalka, J., Nicholas, J., Chen, T., Menon, V., 2018. Un-
covering hidden brain state dynamics that regulate performance and decision-making
during cognition. Nat. Commun. 9, 2505. doi: 10.1038/s41467-018-04723-6 .
Tenenbaum, J.B., Silva, V.de, Langford, J.C., 2000. A global geometric framework for
nonlinear dimensionality reduction. Science (80-.) 290, 2319–2323.
doi: 10.1126/sci-
ence.290.5500.2319 .
Tournier, J.D., Calamante, F., Connelly, A., 2012. MRtrix: diusion tractography in cross-
ing ber regions. Int. J. Imaging Syst. Technol. 22, 53–66. doi: 10.1002/ima.22005 .
Tournier, J.D., Smith, R., Raelt, D., Tabbara, R., Dhollander, T., Pietsch, M., Christi-
aens, D., Jeurissen, B., Yeh, C.H., Connelly, A., 2019. MRtrix3: A fast, exible and
open software framework for medical image processing and visualisation. Neuroim-
age 202, 116137. doi: 10.1016/j.neuroimage.2019.116137 .
van den Heuvel, M.P., Kahn, R.S., Goñi, J., Sporns, O., 2012. High-cost, high-capacity
backbone for global brain communication. Proc. Natl. Acad. Sci. U. S. A. 109, 11372–
11377. doi: 10.1073/pnas.1203593109 .
Van Essen, D.C., Glasser, M.F., Dierker, D.L., Harwell, J., Coalson, T., 2012. Parcellations
and hemispheric asymmetries of human cerebral cortex analyzed on surface-based
atlases. Cereb. Cortex 22, 2241–2262. doi: 10.1093/cercor/bhr291 .
Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E.J., Yacoub, E., Ugurbil, K., 2013.
The WU-Minn human connectome project: an overview. Neuroimage
80, 62–79.
doi: 10.1016/j.neuroimage.2013.05.041 .
Vázquez-Rodríguez, B., Suárez, L.E., Markello, R.D., Shaei, G., Paquola, C., Hagmann, P.,
van den Heuvel, M.P., Bernhardt, B.C., Spreng, R.N., Misic, B., 2019. Gradients of
structure–function tethering across neocortex. Proc. Natl. Acad. Sci. U. S. A. 116,
21219–21227. doi: 10.1073/pnas.1903403116 .
Vidaurre, D., Abeysuriya, R., Becker, R., Quinn, A.J., Alfaro-Almagro, F., Smith, S.M.,
Woolrich, M.W., 2018. Discovering dynamic brain networks from big data in rest and
task. Neuroimage 180, 646–656. doi: 10.1016/j.neuroimage.2017.06.077 .
Vidaurre, D., Quinn, A.J., Baker, A.P., Dupret, D., Tejero-Cantero, A., Woolrich, M.W.,
2016. Spectrally resolved fast transient brain states in electrophysiological data. Neu-
roimage 126, 81–95. doi: 10.1016/j.neuroimage.2015.11.047 .
Vidaurre, D., Smith, S.M., Woolrich, M.W., 2017. Brain network dynamics are
hierarchically organized in time. Proc. Natl. Acad. Sci. 114, 12827–12832.
doi: 10.1073/pnas.1705120114 .
Von Luxburg, U., 2007. A tutorial on spectral clustering. Stat. Comput. 17, 395–416.
doi: 10.1007/s11222-007-9033-z .
Vos de Wael, R., Benkarim, O., Paquola, C., Lariviere, S., Royer, J., Tavakol, S.,
Xu, T., Hong, S.-J., Valk, S.L., Misic, B., Milham, M.P., Margulies, D.S., Small-
wood, J., Bernhardt, B.C., 2020. BrainSpace: a toolbox for the analysis of macroscale
gradients in neuroimaging and connectomics datasets. Commun. Biol. 3, 103.
doi: 10.1038/s42003-020-0794-7 .
Wang, P.,
Kong, R., Kong, X., Liégeois, R., Orban, C., Deco, G., van den Heuvel, M.P.,
Yeo, B.T.T., 2019. Inversion of a large-scale circuit model reveals a cortical hierar-
chy in the dynamic resting human brain. Sci. Adv 5. doi: 10.1126/sciadv.aat7854 ,
eaat7854.
Vos de Wael, R., Larivière, S., Caldairou, B., Hong, S.J., Margulies, D.S., Jef-
feries, E., Bernasconi, A., Smallwood, J., Bernasconi, N., Bernhardt, B.C., 2018.
Anatomical and microstructural determinants of hippocampal subeld functional
connectome embedding. Proc. Natl. Acad. Sci. U. S. A. 115, 10154–10159.
doi: 10.1073/pnas.1803667115 .
Wang, Z., Dai, Z., Gong, G., Zhou, C., He, Y., 2015. Understanding structural-functional
relationships
in the human brain: A large-scale network perspective. Neuroscientist
21, 290–305. doi: 10.1177/1073858414537560 .
Yarkoni, T., Poldrack, R.A., Nichols, T.E., Van Essen, D.C., Wager, T.D., 2011. Large-scale
automated synthesis of human functional neuroimaging data. Nat. Methods 8, 665–
670. doi: 10.1038/nmeth.1635 .
Zhao, X., Tian, L., Yan, J., Yue, W., Yan, H., Zhang, D., 2017. Abnormal Rich-
Club Organization Associated with Compromised Cognitive Function in Patients
with Schizophrenia and Their Unaected Parents. Neurosci. Bull. 33, 445–454.
doi: 10.1007/s12264-017-0151-0 .
