RECHERCHE
Timescales of spontaneous fMRI fluctuations
relate to structural connectivity in the brain
John Fallon 1, Phillip G. D. Ward 1,2, Linden Parkes
1,3, Stuart Oldham1,
Aurina Arnatkevi˘ci ¯ut˙e
1, Alex Fornito1, and Ben D. Fulcher
2,4
1Turner Institute for Brain and Mental Health, School of Psychological Sciences, and Monash Biomedical Imaging,
Monash University, Victoria, Australia
2Australian Research Council Centre of Excellence for Integrative Brain Function, Melbourne, Australia
3Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, Pennsylvanie,
19104 Etats-Unis
4School of Physics, University of Sydney, NSW, Australia
un accès ouvert
journal
Mots clés: Structure–function relationship, Time series analysis, Structural connectivity, Resting-
state fMRI, Interspecies comparison
ABSTRAIT
Intrinsic timescales of activity fluctuations vary hierarchically across the brain. This variation
reflects a broad gradient of functional specialization in information storage and processing,
with integrative association areas displaying slower timescales that are thought to reflect
longer temporal processing windows. The organization of timescales is associated with
cognitive function, distinctive between individuals, and disrupted in disease, but we do not
yet understand how the temporal properties of activity dynamics are shaped by the brain’s
underlying structural connectivity network. Using resting-state fMRI and diffusion MRI data
depuis 100 healthy individuals from the Human Connectome Project, here we show that the
timescale of resting-state fMRI dynamics increases with structural connectivity strength,
matching recent results in the mouse brain. Our results hold at the level of individuals,
are robust to parcellation schemes, and are conserved across a range of different timescale-
related statistics. We establish a comprehensive BOLD dynamical signature of structural
connectivity strength by comparing over 6,000 time series features, highlighting a range of
new temporal features for characterizing BOLD dynamics, including measures of stationarity
and symbolic motif frequencies. Our findings indicate a conserved property of mouse and
human brain organization in which a brain region’s spontaneous activity fluctuations are
closely related to their surrounding structural scaffold.
RÉSUMÉ DE L'AUTEUR
Reflecting structural and functional differences across brain regions, the spontaneous
dynamics of neural activity vary correspondingly. Dynamical timescales are thought to be
organized hierarchically, with slower timescales in integrative association areas, consistent
with longer durations of information processing. In the mouse brain, this variation in BOLD
dynamical properties follows the variation in structural connectivity strength, with more
strongly connected regions exhibiting slower dynamics. Here we show a consistent variation
in human cortex that holds at the level of individuals, and characterize a range of BOLD
properties that vary strongly with structural connectivity strength. Our results indicate a
conserved property of mouse and human brain organization in which a brain area’s
spontaneous activity fluctuations are closely related to its structural connectivity strength.
Citation: Fallon, J., Ward, P.. G. D.,
Parkes, L., Oldham, S., Arnatkevi ˘ci ¯ut ˙e,
UN., Fornito, UN., & Fulcher, B. D. (2020).
Timescales of spontaneous fMRI
fluctuations relate to structural
connectivity in the brain. Réseau
Neurosciences, 4(3), 788–806.
https://doi.org/10.1162/netn_a_00151
EST CE QUE JE:
https://doi.org/10.1162/netn_a_00151
Informations complémentaires:
https://doi.org/10.1162/netn_a_00151
Reçu: 22 Novembre 2019
Accepté: 8 Juin 2020
Intérêts concurrents: Les auteurs ont
a déclaré qu'aucun intérêt concurrent
exister.
Auteur correspondant:
Ben D. Fulcher
ben.fulcher@sydney.edu.au
Éditeur de manipulation:
Michael Cole
droits d'auteur: © 2020 Massachusetts
Institute of Technology Published
under a Creative Commons Attribution
4.0 International (CC PAR 4.0) Licence
La presse du MIT
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
t
/
/
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
t
.
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
INTRODUCTION
Structural connectivity:
The set of physical connections
between all pairs of neural elements
(par exemple., brain regions).
Functional hierarchy:
The organization of brain regions by
the abstraction and complexity of
their function, from unimodal to
multimodal areas.
The brain’s complex spatiotemporal dynamics unfold on an intricate web of axonal connec-
tion: the connectome (Fornito, Zalesky, & Bullmore, 2016; Sporns, Tononi, & Kötter, 2005).
These pathways facilitate information transfer between brain regions, manifesting in a com-
plex relationship between connectome structure and neural dynamics. Reflecting the pairwise
(region–region) nature of structural connectivity, existing studies have overwhelmingly com-
pared pairwise measurements of anatomical connectivity to pairwise statistical relationships
between neural activity time series, or functional connectivity, often using simulations of net-
work dynamics to better understand how the observed relationships may arise (Abdelnour,
Dayan, Devinsky, Thesen & Raj, 2018; Abdelnour, Voss, & Raj, 2014; Deco & Jirsa, 2012;
Deco et al., 2014; Deco et al., 2013; Finger et al., 2016; Ghosh, Rho, McIntosh, Kötter, & Jirsa,
2008; Goñi et al., 2014; Hagmann et al., 2008; Hermundstad et al., 2013; Hinne, Ambrogioni,
Janssen, Heskes, & van Gerven, 2014; Honey, Kötter, Breakspear, & Sporns, 2007; Honey et al.,
2009; Miši´c et al., 2016; Skudlarski, Jagannathan, & Calhoun, 2008; van Den Heuvel, Mandl,
Kahn, & Hulshoff Pol, 2009; Wang et al., 2019).
Structural connectivity is highly informative of functional connectivity, consistent with the
connectome as a physical substrate constraining interregional communication dynamics. Comment-
jamais, our understanding of pairwise structure–function relationships remains disconnected
from our understanding of how a brain area’s structural connectivity properties shape its lo-
cal activity dynamics. The structural connectivity profile of a region’s incoming and outgoing
axonal connections characterizes its function (Passingham, Stephan, & Kötter, 2002). Plus loin-
plus, the activity dynamics of brain areas follow a functional hierarchy, with rapid dynamics
in “lower” sensory regions and slower fluctuations in “higher” regions associated with integra-
tive processes (Gao, van den Brink, Pfeffer, & Voytek, 2020; Hasson, Chen, & Honey, 2015;
Honey et al., 2012; Kiebel, Daunizeau, & Friston, 2008; Murray et al., 2014; Stephens, Honey,
& Hasson, 2013). The spatial variation of intrinsic timescales has been measured using ECoG
(Honey et al., 2012), MEG (Demirta¸s et al., 2019; Keitel & Gross, 2016; Mahjoory, Schoffelen,
Keitel, & Gross, 2019), TMS–EEG (Rosanova et al., 2009), and fMRI (Baria, Baliki, Parrish, &
Apkarian, 2011; Baria et al., 2013; Cocchi et al., 2016; Huang, Liu, Mashour, & Hudetz, 2018;
Lee & Xue, 2017; Stephens et al., 2013; Watanabe, Rees, & Masuda, 2019), and may func-
tionally correspond to a variation in temporal receptive windows (timescales over which new
information can be actively integrated with recently received information [Hasson et al., 2015;
Hasson, Lequel, Vallines, Heeger, & Rubin, 2008; Watanabe et al., 2019]). Spatial variation in
intrinsic activity fluctuations may form a key basis for the brain’s functional hierarchical organ-
ization, shaped by variation in the brain’s microcircuitry (Burt et al., 2018; Fulcher, Murray,
Zerbi, & Wang, 2019; García-Cabezas et al., 2017). This organization is thought to be im-
portant for behavior and cognition (Cavanagh, Wallis, Kennerley, & Hunt, 2016; Gollo, 2019;
Hasson et al., 2015; Runyan, Piasini, Panzeri, & Harvey, 2017) and its disruption has clini-
cal implications; Par exemple, differences in intrinsic timescales are associated with symptom
severity in autism (Watanabe et al., 2019). While much is known about the structure–function
relationship at the level of pairs of brain regions, and how structural and functional connec-
tivity architecture shape cognitive function and are affected in disease (Fornito, Zalesky, &
Breakspear, 2015; Li et al., 2009; Penke et al., 2012; van den Heuvel & Sporns, 2019), rel-
atively little is known about how structural connectivity affects the information-processing
dynamics of individual brain areas. En particulier, we do not yet understand the role structural
connections play in the organization of timescales.
Neurosciences en réseau
789
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
t
/
/
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
t
.
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
hctsa:
A software package for highly
comparative time series analysis that
implements an interdisciplinary
library of thousands of time series
features.
Weighted in-degree:
The aggregate strength of axonal
inputs to a brain area.
Interspecies conservation:
Properties of brain organization that
are maintained across species are
likely to provide a functional
advantage.
Neurosciences en réseau
Recent work has provided statistical evidence for a relationship between regional tract-
tracing estimates of anatomical connectivity and rs-fMRI dynamics in the mouse brain (Sethi,
Zerbi, Wenderoth, Fornito, & Fulcher, 2017). This work took a comprehensive, data-driven ap-
proach, comparing over 7,000 properties of regional BOLD dynamics (using the hctsa software
package; Fulcher & Jones, 2017; Fulcher, Little, & Jones, 2013) with three key structural con-
nectivity properties—degree, betweenness, and clustering coefficient—measured in each of
184 zones du cerveau. The tract-traced connectivity measurement available in mouse (Oh et al.,
2014) also allowed the role of directed and weighted connectivity information to be inves-
tigated. The weighted in-degree, kw
dans, showed the strongest correlation to BOLD dynamics,
particularly with its autocorrelation properties (including the Fourier spectral power in differ-
ent frequency bands). Par exemple, relative high-frequency power ( f > 0.4 Hz) was found to
be negatively correlated to weighted in-degree, kw
dans (ρV = −0.43, partial Spearman correlation
controlling for region volume). The results suggest that structural connectivity may play a role
in the spatial patterning of intrinsic timescales: Brain areas with a greater aggregate strength of
axonal input (highest kw
dans) display slower timescales of spontaneous activity fluctuations, con-
sistent with the predictions of model simulations (Chaudhuri, Knoblauch, Gariel, Kennedy, &
Wang, 2015; Cocchi et al., 2016; Gollo, Zalesky, Hutchison, van den Heuvel, & Breakspear,
2015). Despite the low sampling rate of rs-fMRI, recent work has shown a strong correlation
between timescales estimated from EEG and fMRI (Watanabe et al., 2019), suggesting that a
similar trend may hold at much faster timescales. When ignoring edge directionality, Sethi et al.
(2017) found weaker but statistically significant relationships between (undirected) weighted
degree, kw, and rs-fMRI dynamics. This suggests that a similar relationship may hold in hu-
mans, where the directionality of connections cannot be measured through noninvasive MRI
methods like diffusion-weighted imaging.
We know of only two investigations into how structural connectivity properties relate to
BOLD dynamics in the human cortex, and both have reported weak relationships between
structural connectivity strength and (un) low-frequency rs-fMRI fluctuations, Pearson’s r = 0.12
(Lee & Xue, 2017); et (b) the log-linear slope of the Fourier power spectrum, r = 0.22 (Baria
et coll., 2013). These weak correlations may be due to both studies measuring BOLD for a short
duration (less than 300 volumes at a sampling rate TR = 2.5 s) in a small sample of individuals:
30 (Baria et al., 2013) et 36 (Lee & Xue, 2017). Cependant, neither study controlled for region
volume, which correlates strongly with the autocorrelation properties of the BOLD signal,
because of the averaging of more voxelwise signals in larger areas (Afyouni, Forgeron, & Nichols,
2019; Sethi et al., 2017). The Human Connectome Project (HCP) dataset alleviates many of
these issues, containing a large rs-fMRI dataset collected at a high sampling rate, TR = 0.72 s,
across 1,200 time points (Van Essen et al., 2013).
Here we characterize the rs-fMRI signature of structural connectivity in the human cortex
using data from the HCP. We aimed to investigate whether more strongly connected regions
are associated with slower timescales of BOLD activity in the human cortex, as they are in the
mouse brain (Sethi et al., 2017). Following the results in mouse, we use relative low-frequency
pouvoir (RLFP) to estimate the prominence of slow BOLD fluctuations ( F < 0.14 Hz), and show
that this measure is strongly correlated with other measures of timescale obtained from the
decay of the autocorrelation function with time lag (Murray et al., 2014; Watanabe et al., 2019).
Consistent with predictions from mouse, RLFP increases with structural-connectivity strength
in human cortex, ρV = 0.53 (partial Spearman correlation adjusting for region volume, p = 2 ×
10−3). Our results hold at both the group and the individual level, and across different cortical
parcellations, reflecting a robust interspecies conservation of how structural connectivity and
regional activity dynamics are related.
790
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
t
/
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
.
t
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
RESULTS
Methods Summary
We investigated whether a brain area’s structural connectivity strength is related to its sponta-
neous BOLD dynamics, as illustrated schematically in Figure 1. Our methods are summarized
briefly here (and detailed in Methods). We used an HCP dataset of 100 healthy, unrelated
participants (54 male, 46 female; 22–35 years old; Van Essen et al., 2013). Our main anal-
ysis focuses on the left hemisphere of the 68-region Desikan-Killiany atlas (Desikan et al.,
2006; analysis of the right hemisphere yielded similar results; see below). Structural connec-
tivity was estimated from the diffusion data using MRtrix3 (Tournier, Calamante, & Connelly,
2012) and the FMRIB Software Library (Jenkinson, Beckmann, Behrens, Woolrich, & Smith,
2012), performing tractography with 10 million streamlines using FACT, ACT, and SIFT-2, yield-
ing a 34 × 34 left-hemisphere connectome. Following work in mouse (Sethi et al., 2017), we
summarized the structural connectivity of each brain area as its node strength, s, estimated
as the total number of diffusion MRI-reconstructed streamlines attached to it (equivalent to
weighted degree, kw). rs-fMRI data were processed after regressing standard nuisance signals
(including the global signal) and were high-pass filtered at 8 × 10−3 Hz, yielding a 34 × 1200
(region × time) fMRI data matrix.
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
t
/
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
t
.
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
Autocorrelation function:
The correlation between lagged
versions of a time series, as a
function of the time lag.
Based on our previous findings in mouse (Sethi et al., 2017), we summarized BOLD dy-
namics in a given brain region as the relative low-frequency power, RLFP ( f < 0.14 Hz). Note
that frequencies f < 8 × 10−3 Hz were removed through high-pass filtering (see Methods). As
we used RLFP to understand how the frequencies, or timescales, underlying a given BOLD
time series are distributed, we verified that RLFP gives highly correlated results to other com-
mon estimates of timescales from time series data: (a) a fitted exponential decay timescale to
the autocorrelation function (Murray et al., 2014; Pearson’s r = 0.98 across all brain regions,
averaged across subjects, p = 5 × 10−26); and (b) the area under the autocorrelation function
before it passes zero (Watanabe et al., 2019; r = 0.995, p = 8 × 10−28). RLFP is also highly
correlated to the similarly constructed metric, fALFF (Yu-Feng et al., 2007; Zou et al., 2008;
relative power in the range 0.01 < f < 0.08 Hz), which has been widely used to characterize
human fMRI (r = 0.997, p = 2 × 10−37). Thus, while we focus our main results on RLFP here,
very similar quantitative results were obtained using similar timescale-related statistics.
Figure 1. Schematic showing how we investigate the relationship between a region’s structural
connectivity properties to their resting-state dynamics. We summarize each cortical region as its
structural connectivity strength, s, and its relative low-frequency power, RLFP ( f < 0.14 Hz). Note
that, for the purposes of schematic visualization, edge weights and node strength colors represent
relative strength, from low (blue) to high (red).
Network Neuroscience
791
FMRI timescales relate to structural connectivity in the brain
Relationships between the structural properties of a cortical region and its univariate dynam-
ics were estimated as Spearman correlation coefficients, ρ. Region volume, which varies from
49 to 4,570 voxels in the Desikan-Killiany atlas (Desikan et al., 2006), is a major confound,
correlating strongly with RLFP, ρ = 0.61 (p = 2 × 10−4; see Figure S1A), as in the mouse brain
(Sethi et al., 2017). To control for region volume, we computed partial Spearman correlation
coefficients, denoted here as ρV.
Node Strength Is Correlated With Power-Spectral Properties of Resting-State BOLD Dynamics
We first investigated the group-level relationship between connectivity strength, s, and relative
low-frequency power, RLFP, by summarizing each brain region as the mean of each quantity
across all 100 participants. As shown in Figure 2A, there is a strong correlation between s
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
t
/
/
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
t
.
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
Figure 2. Group-level connectivity strength, s, is positively correlated with relative low-frequency
power of BOLD dynamics, RLFP ( f < 0.14 Hz) after correcting for region volume. (A) Rank residuals
of relative low-frequency power (RLFP) and node strength, s, across 34 left-hemisphere cortical
regions of the Desikan-Killiany atlas (Desikan et al., 2006), after regressing out region volume. The
plot reveals a positive relationship, partial Spearman’s ρV = 0.53 (p = 2 × 10−3). (B) The group-
averaged Fourier power spectra for three colored brain areas in A are plotted: medial orbitofrontal
area (low s, blue), pars triangularis (moderate s, red), and superior parietal (high s, green), shown up
to a maximum of 0.3 Hz. RLFP corresponds to the shaded area under the curve below 0.14 Hz. (C)
As A, but for 100 left-hemisphere cortical regions from a custom 200-region parcellation generated
by randomly dividing each hemisphere into 100 approximately equal-sized regions (Fornito et al.,
2011). (D) Spatial maps of node strength and low-frequency power across 180 left-hemisphere
cortical areas of the Glasser et al. (2016) parcellation, with the relative variation of each metric
shown using color, from low (blue) to high (red).
Network Neuroscience
792
FMRI timescales relate to structural connectivity in the brain
and RLFP in the left hemisphere of the cortex, ρV = 0.53 (controlling for region volume, p =
2 × 10−3). Similar results were observed in the right hemisphere, ρV = 0.57 (p = 6 × 10−4; see
Figure S3). The positive correlation indicates that human cortical areas with greater aggregate
structural connectivity display stronger low-frequency fluctuations, matching the relationship
characterized in the mouse brain (Sethi et al., 2017). Note that RLFP is strongly correlated
with region volume, ρ = 0.61 (Figure S1A), and the s–RLFP relationship is stronger when
region volume is not controlled for, ρ = 0.74 (p < 2 × 10−6; see Figure S1B).
To better understand these findings, we selected three representative brain regions: the
medial orbitofrontal region (low s = 1.4 × 105), pars triangularis (moderate s = 4.6 × 105),
and superior parietal cortex (high s = 1.7 × 106), as annotated in Figure 2A. The Fourier
power spectrum for each of these brain areas is plotted in Figure 2B, with the RLFP region
shaded ( f < 0.14 Hz). Differences in spectral power are clearest at low frequencies, especially
near the peak power around 0.02 Hz. As the total power is normalized to unity, increased
relative power around 0.02 Hz results in lower relative power at higher frequencies. Accord-
ingly, the relationship with s is not sensitive to the precise RLFP frequency range, but is re-
produced (with opposite sign) at higher frequency bands of the same extent: ρV = −0.53
(0.14–0.28 Hz), ρV = −0.56 (0.28–0.41 Hz), ρV = −0.53 (0.41–0.55 Hz), and ρV = −0.53
(0.55–0.69 Hz). The brain region that deviated most from the overall trend was the insula (cor-
responding to the point in bottom right of Figure 2A), which has surprisingly low RLFP given
its strong structural connectivity across the brain (after correcting for region volume), perhaps
because of its vicinity to large blood vessels making it more susceptible to physiological noise
(Di, Kannurpatti, Rypma, & Biswal, 2012). The common statistical summary of univariate
BOLD dynamics, fALFF (Zou et al., 2008), is algorithmically very similar to RLFP and is simi-
larly correlated with s: ρV = 0.54. Other common measures of timescales derived from the de-
cay of the autocorrelation function also yielded similar results, including the decay timescale
of Murray et al. (2014), ρV = 0.48, and the area-based measure of Watanabe et al. (2019),
ρV = 0.51.
The relationship between s and RLFP does not depend strongly on cortical parcellation. A
similar relationship was found when randomly dividing each hemisphere into approximately
100 equal-sized regions (Fornito et al., 2011), shown in Figure 2C for the left hemisphere,
ρV = 0.53 (p = 1 × 10−8). We also found a significant positive relationship when using the
180-region Glasser et al. (2016) parcellation of the left cortex, ρV = 0.43 (p = 3 × 10−9; see
Figure S2), and when resampling the same number of voxels from each brain region (circum-
venting the need to correct for variation in region volume), ρ = 0.43 (p = 0.01; see Figure S1D).
Spatial maps of both properties, at the higher spatial resolution of the Glasser et al. (2016) par-
cellation, are shown in Figure 2D.
Regional Structure–Function Relationships Extend Across Individuals
Having demonstrated a robust group-level relationship between node connectivity strength, s,
and Fourier spectral characteristics of rs-fMRI time series, we next investigated whether these
results could be detected at the level of individual subjects. We measured the partial correlation
coefficient, ρV , between s and RLFP for each individual, plotted as a distribution across all 100
individuals in Figure 3. After false discovery rate multiple-hypothesis correction (Benjamini &
Hochberg, 1995), 43% of participants individually displayed a significant correlation (pcorr <
0.05: ρV > 0.40). The group-level s–RLFP relationship (annotated red in Figure 2) was stronger
than the individual correlation for 91% of participants, consistent with a concentration of
meaningful signal (and thus a reduction in measurement noise) through group averaging. À
investigate whether interindividual variation in s–RLFP correlation, ρV, is driven by in-scanner
Neurosciences en réseau
793
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
/
/
t
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
t
.
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
/
/
t
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
.
t
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
Chiffre 3. Many individuals exhibit a significant relationship between node strength, s, and rel-
ative low-frequency power, RLFP. The histogram of partial Spearman correlation coefficients, ρV ,
between RLFP and s (correcting for variations in region volume) computed separately for each of
100 individuals. The group-level result, ρV = 0.54, is shown as a vertical red line.
motion, we computed the Pearson correlation between ρV and mean framewise displacement
across individuals. We found a weak and nonsignificant relationship, r = 0.10 (p = 0.3),
suggesting that motion is not driving our results.
Diverse Properties of BOLD Dynamics Are Informative of Node Strength
Our results demonstrate that Fourier spectral properties of rs-fMRI, and related measures of au-
tocorrelation timescales (Murray et al., 2014; Watanabe et al., 2019), are strongly correlated
with connectivity strength, s. But the time series analysis literature is vast and interdisciplinary
(Fulcher, 2018); could other statistical summaries of BOLD time series exhibit stronger rela-
tionships to s? To investigate this possibility, we used the hctsa toolbox (Fulcher & Jones, 2017)
to perform a comprehensive data-driven comparison of the performance of 6,062 different
time series features. The performance of each feature was measured as ρV (computed for each
individual and then averaged across individuals). As we are interested in the magnitude of the
correlation (not the sign), we took |ρV | as the quantity of interest, plotting its distribution across
tous 6,062 time series features in Figure 4. While 3,768 individual time series features exhibit a
statistically significant partial correlation to s (|ρV | > 0.39, pcorr < 0.05), RLFP is among those
with the highest |ρV | (in the top 16% of all hctsa features). However, the distribution reveals
a tail of alternative time series features with higher |ρV |. Interestingly, these high-performing
features recapitulate a familiar set of time series analysis methods that have previously been
used to analyze BOLD dynamics, as well as some unexpected new features. Here we sum-
marize some notable features, labeling them by their name in hctsa (Fulcher & Jones, 2017);
for further descriptions of these and other features, see the Supporting Information (and see
Supplementary File 1 for a full list).
Network Neuroscience
794
FMRI timescales relate to structural connectivity in the brain
Wiener–Khinchin theorem:
The power spectrum of a stationary
random process is equivalent to the
Fourier transform of its
autocorrelation function.
Automutual information function:
The mutual information between
lagged versions of a time series,
as a function of the time lag.
Symbolic string:
An ordered set of symbols.
Figure 4. RLFP has amongst the strongest correlations to connectivity strength, s, in a compar-
ison to 6,062 time series features. We plot a histogram of absolute partial Spearman correlation
coefficients, |ρV |, between each of 6,062 rs-fMRI time-series features and connectivity strength s
(controlling for region volume). The features were computed using the hctsa toolbox (Fulcher &
Jones, 2017; Fulcher et al., 2013). RLFP (|ρV | = 0.53) is shown in red, and the 5% FDR-corrected
statistical-significance threshold (|ρV | > 0.39) is shown in green.
Neuroimaging time series have most commonly been summarized as a measure of timescale,
derived from the Fourier power spectrum or linear autocorrelation function (which are
related via a spectral decomposition, cf. the Wiener–Khinchin theorem; Baria et al., 2013;
Chaudhuri et al., 2015; Lee & Xue, 2017; Murray et al., 2014; Watanabe et al., 2019). Notre
highly comparative time-series analysis highlights many qualitatively similar features. One ex-
ample is SP_Summaries_fft_linfitloglog_mf_a2, ρV = −0.59, which estimates the
powerlaw exponent of the Fourier power spectrum (as a linear fit in a log-log plot, fitted af-
ter excluding the lower and upper quarter of frequencies), reminiscent of Hurst exponent es-
timation from neural time series (Il, 2011). Another interesting high-performing feature is
an information-theoretic analogue of the first zero-crossing of the autocorrelation function:
the first minimum of the automutual information function (Kantz & Schreiber, 2004; Lizier,
2014) computed after differencing the time series: IN_AutoMutualInfoStats_diff_20_
kraskov1_4_fmmi, ρV = −0.63. This incremental differencing step, a common time-series
transformation used to stabilize the mean (Hyndman & Athanasopoulos, 2018), also emerged
in a range of symbolic motif features. Symbolic motifs count the frequency of a particular set of
consecutive symbols in a time series that has been converted to a symbolic string using a simple
coding rule, Par exemple, coding stepwise increases as “U” (en haut) and decreases as “D” (down).
Motifs associated with small movements are consistent with slow fluctuations and showed
positive correlations with s (par exemple., the “AABB” pattern: SB_MotifThree_ diffquant_aabb,
ρV = 0.62), whereas motifs associated with rapid changes exhibited strong negative correla-
tion (par exemple., the “up-down-up-up” pattern: SB_MotifTwo_diff_uduu, ρV = −0.62). Le
symbolization process may help to capture informative structure in noisy rs-fMRI time series.
Increased durations of rs-fMRI recording have allowed dynamic functional connectivity
analyses to characterize changes in functional connectivity across the recording period
(Hutchison et al., 2013). Our data-driven analysis highlighted a range of univariate analogues
of this concept, flagging a range of high-performing features measuring time series stationarity.
Par exemple, SY_SlidingWindow_sampen_ent10_2, ρV = −0.65, measures how local
Neurosciences en réseau
795
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
/
/
t
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
.
t
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
SampEn (sample entropy):
A measure of time series
predictability that measures the
tendency of temporal patterns to
repeat themselves.
estimates of the entropy metric, SampEn(2, 0.1) (Richman & Moorman, 2000), vary across the
time series. hctsa also highlighted novel features derived from visibility graphs, which represent
each fMRI time point as a node and constructing network edges using visibility rules (Lacasa,
Luque, Ballesteros, Luque, & Nuño, 2008; Sannino, Stramaglia, Lacasa, & Marinazzo, 2017).
Par exemple, s is highly correlated to a simple outlier metric of the visibility graph degree
distribution, NW_VisibilityGraph_norm_ol90, ρV = 0.66.
Our results demonstrate the usefulness of hctsa in determining the most informative time
series analysis methods for a given problem in an automated, data-driven manner. hctsa pro-
vides new understanding of how rs-fMRI dynamics relate to structural connectivity strength by
flagging an ensemble of time-series features that both encapsulate conventional approaches
to analyzing BOLD dynamics and introduce novel ones.
DISCUSSION
In this work, we show that the variation of intrinsic fMRI timescales across human cortical ar-
eas is related to the variation of structural connectivity strength, matching a regional structure–
function relationship previously observed in the mouse brain. This interspecies consistency is
observed despite major differences in measurement between mouse (axonal tract tracing and
rs-fMRI in 18 anesthetized mice) and human (DWI and rs-fMRI in 100 awake participants).
In both species, brain areas with a greater aggregate strength of structural connectivity exhibit
slower rs-fMRI BOLD fluctuations, consistent with a hierarchical gradient of intrinsic timescales
(Hasson et al., 2015; Honey et al., 2012; Kiebel et al., 2008; Murray et al., 2014). Our results
are robust to cortical parcellation, hold at the level of individuals, and are not driven by mo-
tion. We also introduce a highly comparative time-series analysis approach to the problem
que, in a data-driven way, recapitulates conventional BOLD signal analysis approaches and
highlights a range of promising new temporal features, including symbolic and stationarity-
related measures, for characterizing BOLD dynamics. This study expands the investigation of
the brain’s structure–function relationship to the level of individual regions (rather than pairs of
régions), providing a more complete picture of how the brain’s intricate axonal scaffold shapes
spontaneous brain dynamics. Continuing investigations of the structure–function relationship
at the level of individual areas will allow us to better understand how the brain’s local circuits
shape its dynamics and relate these results to hypotheses about the principles governing the
brain’s spatiotemporal organization.
Our results in mouse and human indicate that areas that are more strongly connected to the
rest of the brain have slower average timescales. This relationship is consistent with a hierarchy
of timescales in which more highly connected areas (putatively high in the hierarchy) serve
a more integrative function, integrating diverse information over longer timescales than the
fast dynamics and behavioral responses associated with lower sensory areas (Chaudhuri et al.,
2015; Gollo et al., 2015; Honey et al., 2012; Kiebel et al., 2008; Murray et al., 2014; Sethi et al.,
2017; Stephens et al., 2013). While many previous studies have reported interareal variation in
intrinsic timescales (Baria et al., 2011; Baria et al., 2013; Cocchi et al., 2016; Demirta¸s et al.,
2019; Honey et al., 2012; Huang et al., 2018; Stephens et al., 2013; Watanabe et al., 2019), à
our knowledge, only two prior human studies have related this variation to structural connec-
tivité (Baria et al., 2013; Lee & Xue, 2017). Both studies found weak relationships, r = 0.12
(Lee & Xue, 2017) and r = 0.22 (Baria et al., 2013), using hand-picked dynamical proper-
ties of rs-fMRI time series in small sample sizes, and without correcting for regional volume
variation. The much stronger correlation reported here, ρV = 0.53 (after correcting for region
volume), may be due to the high-quality imaging data (1,200 volumes at a sampling period of
Neurosciences en réseau
796
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
/
/
t
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
t
.
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
0.72 s) in a larger sample of 100 individuals. As we discuss later, the low temporal resolution
of fMRI is a major limitation of studying timescales, but on these fMRI data, we demonstrate
that RLFP, fALFF (Zou et al., 2008), and measures of the decay of the autocorrelation function
(Murray et al., 2014; Watanabe et al., 2019), are all highly intercorrelated. Given this connec-
tion, recent work indicates a significant and strong correlation between timescales estimated
from simultaneously recorded EEG and fMRI (γ band, adjusted r2 = 0.71) (Watanabe et al.,
2019), suggesting that our results may also reflect similar differences at faster timescales. Future
multimodal research could probe intrinsic processing timescales to provide a more complete
temporal picture of how timescales are structured across the cortex in different species, et
its implications for cognition and disease.
While fMRI is most frequently characterized in terms of pairwise correlations (functional
connectivité), our results highlight the utility of characterizing local brain dynamics. AUDACIEUX
dynamics are distinctive to individuals (Keitel & Gross, 2016), play a role in cognitive func-
tion (Hasson et al., 2015), and are disrupted in disease (Watanabe et al., 2019). They are also
involved in brain organization, being related to the functional and structural connections of
an area, and may provide an indirect measure of its information-processing capabilities (Baria
et coll., 2011; Baria et al., 2013). Summarizing the activity dynamics of individual brain ar-
eas also yields spatial maps that can be related to other datasets straightforwardly, tel que
macroscale maps of microstructural variation (Fulcher et al., 2019; Huntenburg, Bazin, Bazin,
& Margulies, 2017). While univariate analysis of the BOLD signal is promising, a common
problem in analyzing univariate time series is selecting an appropriate analysis method or
summary statistic to compute (Fulcher, 2018). The neuroimaging literature has most commonly
focused on linear autocorrelation properties, measured directly from either the autocorrelation
function or the Fourier power spectrum. hctsa circumvents the need for subjectivity or manual
exploration across a vast time series analysis literature (Fulcher & Jones, 2017; Fulcher et al.,
2013), providing a data-driven means of selecting the most relevant types of time-series features
for a given problem. By comparing the behavior of thousands of diverse time-series analysis
méthodes, hctsa finds interpretable features that vary most strongly with structural connectiv-
ity strength, s. These features recapitulate conventional timescale-based metrics commonly
used in the literature, and also include a range of novel features related to symbolic motifs,
stationarity, and visibility graphs. The common theme of applying incremental differencing,
a transformation commonly used to stabilize the mean (Hyndman & Athanasopoulos, 2018),
suggests that applying this transformation to BOLD data could enhance the informative signal
that can be extracted from it. We also note the prominent performance of time-series station-
arity properties, suggesting a fruitful avenue in further characterizing this property, which may
loosely be considered a univariate analogue of dynamical functional connectivity (Hutchison
et coll., 2013). Given the large number of time series analysis methods suited to long, low-noise
recordings, we expect that hctsa will be especially useful in discovering informative time-series
features from data streams with higher sampling rates than fMRI, such as those measured using
ECoG, MEG, and EEG.
This study highlights the ability of direct interspecies comparisons to accumulate evidence
for common properties of brain organization. Organizational properties that are shared across
scales and species (van den Heuvel, Bullmore, & Sporns, 2016) are strong candidates for being
under evolutionary selection pressure for serving an important functional advantage. These
range from the properties of networks abstracted from the brain’s physical structure—like rich-
club connectivity and modularity—through to hierarchical gradients (Burt et al., 2018; Fulcher
et coll., 2019) and the patterning of gene expression with structural connectivity (Arnatkevici ¯ut˙e,
Fulcher, Pocock, & Fornito, 2018; Fornito, Arnatkevici ¯ut˙e, & Fulcher, 2019; Fulcher & Fornito,
Neurosciences en réseau
797
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
/
t
/
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
.
t
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
2016). The current study adds a regional relationship between structure and function to this set
of conserved relationships; future work is needed to establish whether a similar pattern holds
across other species, such as C. elegans and nonhuman primates (Shen et al., 2019), où
both structural connectivity and large-scale brain dynamics have been measured.
Relative to rapidly sampled electrophysiological recordings, it can be harder to interpret
changes in the power spectrum of a sparsely sampled and noisy fMRI signal in terms of relative
timescales. Timescales can be quantified in terms of a natural intrinsic frequency of oscillation,
estimated from prominent peaks in the power spectrum in EEG (Chiang, Rennie, Robinson,
Van Albada, & Kerr, 2011), MEG (Mahjoory et al., 2019), and ECoG (Zhang, Watrous, Patel, &
Jacobs, 2018). Our coarser estimate of timescale, in terms of power in frequency bands, does
not correspond to variations in the power spectrum peak position (voir la figure 2), but rather the
relative contribution of low-frequency (relative to high-frequency) fluctuations ( f ∼ 0.14 Hz) à
signal variance. Our analysis of frequency bands across the full power spectrum is motivated
by evidence of meaningful neural signal in fMRI at frequencies f > 0.1 Hz (Kalcher et al.,
2014; Liao et al., 2013; Niazy, Xie, Miller, Beckmann, & Forgeron, 2011). Given the strong cor-
respondence between RLFP and measures of how the autocorrelation decays with time lag on
the fMRI data analyzed here, we are encouraged by recent work demonstrating a close cor-
respondence between autocorrelation-based timescale measurements made in EEG and fMRI
(Watanabe et al., 2019), suggesting that fMRI signals may be informative of neural dynamics
at faster timescales.
Understanding how time-series properties vary across cortical areas has important practi-
cal implications for how functional connectivity is estimated and interpreted. We first draw
attention to the strong variation of time-series properties with region volume (as more voxel-
wise time series are averaged into a region-level time series), and the strong conservation of
this relationship between mouse and human (Sethi et al., 2017). This confound of parcella-
tion is not typically acknowledged or addressed, but is crucial to account for by performing
partial correlations using region volume as a regressor, or using parcellations containing re-
gions of equal volume. Our results also suggest that different brain areas may have different
intrinsic Fourier spectral properties (and hence distinctive autocorrelation functions). As these
differences affect the estimation of functional connectivity, future work should leverage recent
statistical developments (Afyouni et al., 2019; Cliff, Novelli, Fulcher, Shine, & Lizier, 2020;
James, Parc, & Kim, 2019) to better account for regional variations in BOLD autocorrelation
when estimating and performing inference on functional connectivity.
We quantified connection weights in our connectomes using streamline count for consis-
tency with many other studies in the human connectomics literature. This measure is concep-
tually closer to the normalized connection weight measure used in our prior study of the mouse
(Sethi et al., 2017). It is well known that streamline count and other tensor-based metrics, tel
as mean tract fractional anisotropy, are only indirect proxies for the actual number (or integrity)
of axons connecting two regions (Jones, Knösche, & Tourneur, 2013). Exploring how regional
dynamics relate to other properties of axonal connectivity measured with more biologically
informative metrics would be a fruitful avenue for future work. While fMRI data-processing
pipelines have been shown to have a large impact on resulting functional connectivity esti-
mates (Parkes, Fulcher, Yücel, & Fornito, 2018), it will be important for future work to take
similar care in understanding how preprocessing steps affect the univariate properties of fMRI
data.
Neurosciences en réseau
798
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
/
t
/
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
.
t
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
Critical point:
A point in parameter space about
which the dynamical repertoire of a
system changes qualitatively.
Our findings suggest that the brain may exploit timescales to efficiently store, processus, et
transfer information, with these timescales coupled to the underlying structural connectivity
properties of a brain area (Baria et al., 2011) in the same way in the mouse brain and human cor-
tex. An intriguing possibility is that the relationship reported here reflects a causal role of long-
range structural connectivity in shaping the intrinsic activity timescales of a brain area, as has
been demonstrated in simulations of network-coupled dynamical systems (Chaudhuri et al.,
2015; Cocchi et al., 2016; Gollo et al., 2015). This is consistent, Par exemple, with greater ag-
gregate inputs to a brain region pushing it towards its critical point where dynamical timescales
are slower (Cocchi, Gollo, Zalesky, & Breakspear, 2017). Our results could also be explained
by a hierarchical gradient of microstructural variation (Burt et al., 2018; Fulcher et al., 2019),
along which both structural connectivity strength and spontaneous dynamics vary (Demirta¸s
et coll., 2019; Mahjoory et al., 2019; Wang et al., 2019). In this view, timescales vary hierar-
chically (because of variations in cortical microstructure or subcortical inputs), but may not
be causally modulated by cortico-cortical structural connections. Regional variations in per-
fusion, perhaps to support the increased metabolic demands of highly connected hub areas
(Liang, Zou, Il, & Lequel, 2013), could also manifest in corresponding spatial differences in
BOLD dynamics (Aso, Urayama, Fukuyama, & Murai, 2019; Di et al., 2012). In the absence
of experiments that can causally manipulate structural connectivity, computational modeling
will continue to play a crucial role in distinguishing between possible mechanistic explana-
tions of the statistical relationships characterized here, towards an understanding of the general
and specific mechanisms through which intrinsic timescales may be shaped. Given the cog-
nitive importance of how differences in local neural dynamics, including their timescales, sont
organized across the cortex (Huang et al., 2018; Watanabe et al., 2019), understanding the
physical mechanisms shaping variations in BOLD dynamics could lead to novel new treat-
ments that aim to rectify abnormal timescales in the brain, Par exemple, using a transcranial
stimulation magnétique (TMS) protocol (Gollo, 2019) tailored to an individual’s structural con-
nectivity profile. Integrating data across species and scales to elucidate common relationships,
and using theoretical modeling approaches to propose possible mechanisms underlying those
motifs, will be key to understanding how the brain’s organization allows it to efficiently pro-
cess and integrate information.
DATA AND METHODS
Code for reproducing our analyses is at https://github.com/NeuralSystemsAndSignals/
humanStructureFunction (Fallon, 2020). Data to support the findings of this study are
available from the HCP at https://db.humanconnectome.org.
Acquisition et prétraitement des données
MRI data were downloaded from the Human Connectome Project (HCP, Van Essen et al.,
2013). We selected the HCP 100 unrelated participants dataset (54 males, 46 females) for de-
tailed analysis (Van Essen et al., 2013), as in previous work (Parkes, Fulcher, Yücel, & Fornito,
2017). All participants were healthy and aged between 22 et 35 years and provided written
informed consent; ethics was approved by the Institutional Review Board of Washington Uni-
versity. We used the minimally preprocessed data of which full details can be found elsewhere
(Glasser et al., 2013); a broad overview is provided here.
Diffusion-weighted imaging. UN 3 T Siemens Skyra scanner with a customized head coil (100 mT/m
maximum gradient strength and a 32-channel head coil) located at Washington University,
St. Louis, was used to acquire all neuroimaging data. Diffusion data were acquired using a
Neurosciences en réseau
799
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
/
t
/
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
.
t
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
spin-echo EPI sequence with the following parameters: TR/TE = 5,520/89.5 ms, slice thick-
ness = 1.25 mm, 111 slices, 1.25 mm isotropic voxels. Three gradient shells of 90 diffusion-
weighted directions and six b0 images were collected with right-to-left and left-to-right phase
encoding polarities for each of the three diffusion weightings (1,000, 2,000, et 3,000 s/mm2).
For additional imaging parameters see Glasser et al. (2013). The diffusion data had been prepro-
cessed using the HCP diffusion pipeline (Glasser et al., 2013), which included normalization
of b0 image intensity across runs, correction for EPI susceptibility, and eddy-current-induced
distortions, gradient-nonlinearities, subject motion, and application of a brain mask.
Subsequent processing of the diffusion data used MRtrix3 (Tournier et al., 2012) and FM-
RIB Software Library (Jenkinson et al., 2012). Tractography was conducted using Fibre As-
signment by Continuous Tracking (FACT), a deterministic measure (Mori, Crain, Chacko, &
Van Zijl, 1999; Mori & Van Zijl, 2002). This deterministic measure was selected over proba-
bilistic methods because it is less prone to false positive connections (Thomas et al., 2014),
which have been shown to be more detrimental to network construction than false negative
relations (Zalesky et al., 2016). A total of 10 million streamlines were generated with a
step size of 0.125 mm. Streamlines terminated when the curvature exceeded 45°, when the
fractional anisotropy value was less than 0.1, or if the length was greater than 250 mm.
In order to further improve the biological accuracy of the structural networks, Anatomically
Constrained Tractography (ACT) and Spherically Informed Filtering of Tractograms (SIFT-2)
were applied to the tractography data. ACT delineates the brain into different tissue types (par exemple.,
cortical gray matter, subcortical gray matter, white matter, CSF). This information is then used
while tractography is being conducted to ensure streamlines are beginning, traversing, et
terminating in anatomically correct locations (R.. E. Forgeron, Tournier, Calamante, & Connelly,
2012). Another issue hampering tractography is that the density of reconstructed connections
does not reflect the underlying diffusion data (R.. E. Forgeron, Tournier, Calamante, & Connelly,
2013). SIFT-2 addresses this limitation by modeling the expected density of connections as cal-
culated from the diffusion signal before comparing this prediction to the connection densities
obtained in tractography. Streamlines are then weighted by a cross-sectional area multiplier
determined by this model fit (R.. E. Forgeron, Tournier, Calamante, & Connelly, 2015). This same
model of diffusion density was also used to dynamically choose streamline seeding points
during tractography (R.. E. Smith et al., 2015).
Our main cortical parcellation was the 68-region Desikan–Killiany atlas (Desikan et al.,
2006; 34 regions per hemisphere). To demonstrate robustness of our results, we also compared
two additional parcellations: (un) Glasser et al.’s 360-region HCP parcellation (180 regions per
hemisphere; Glasser et al., 2016), et (b) a custom built 200-node parcellation (100 régions
per hemisphere), which was formed by randomly dividing each hemisphere into 100 approx-
imately equal-sized cortical regions (Fornito et al., 2011). These parcellations were generated
on the FreeSurfer-extracted surfaces for each subject and then projected to volumetric space.
As in the mouse (Sethi et al., 2017), we focused our analysis on a single hemisphere. Un-
alyzing ipsilateral connectivity also has the advantage of avoiding errors associated with re-
constructing long-range contralateral connections using diffusion tractography (Reveley et al.,
2015). Ipsilateral structural connectivity within the left hemisphere was represented as a
weighted, undirected 34 × 34 adjacency matrix, Aij, where each entry captures the number
of streamlines with termination points within 5 mm of either regions i or j. A group-weighted
structural connectome, Gij, was constructed by retaining interregional connections that were
present in more than 75% of participants (van den Heuvel & Sporns, 2011), and setting edge
weights to the average value across participants (where zero entries were not included in the
Neurosciences en réseau
800
je
D
o
w
n
o
un
d
e
d
F
r
o
m
h
t
t
p
:
/
/
d
je
r
e
c
t
.
m
je
t
.
t
/
/
e
d
toi
n
e
n
un
r
t
je
c
e
–
p
d
je
F
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
un
_
0
0
1
5
1
p
d
t
.
F
b
oui
g
toi
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
average). The resulting adjacency matrix had an edge density of 25%, and edge weights vary-
ing from 322 à 7.6 × 104. Following Sethi et al. (2017), each brain region was summarized as
its connectivity strength, s, calculated by summing all streamlines connected to a region (after
applying ACT and SIFT-2).
Resting-state fMRI (rs-fMRI) data were downloaded from the HCP database
Resting-state fMRI.
(Van Essen et al., 2013). Images were obtained using a gradient-echo, echo planar image (EPI)
sequence with the following parameters: TR/TE = 720/33.1 ms, slice thickness = 2.0 mm, 72
slices, 2.0 mm isotropic voxels, frames per run = 1,200. We used the volumetric EPI data from
the first rs-fMRI session (left-right phase encoding), processed and denoised using ICA-FIX
(S. M.. Smith et al., 2013).
Subsequent processing of the rs-fMRI data was performed. D'abord, the rs-fMRI time series were
linearly detrended. Alors, to provide more stringent control over nuisance signals we regressed
the rs-fMRI data against mean white matter (WM) and mean cerebrospinal fluid (CSF) aussi
as the global signal (GS) using fsl_regfilt. Specifically, gray matter (GM), WM, and CSF
probability masks were generated using SPM8’s New Segment routine. The WM and CSF masks
were thresholded and binarized, retaining only voxels with > 99% probability. The GM mask
was thresholded and binarized to retain only voxels with > 50% probability. The binary GM
mask was then subtracted from the binary WM and CSF masks to ensure no gray matter voxels
were present in the estimation of the WM and CSF nuisance signals. Estimating the GS was
done by taking the union of two whole-brain masks created using FSL’s bet function applied
to the spatially normalized EPI and T1-weighted images (Parkes et al., 2018). All nuisance
time series were extracted by taking the mean over all voxels in the respective masks. Enfin,
we removed low-frequency ( F < 8 × 10−3 Hz) fluctuations using a high-pass filter as a hard
threshold at 8 × 10−3 Hz, applied to the EPI data via a fast Fourier transform. Once processed,
EPI time series were summarized at the level of brain regions by averaging voxel time series
over all voxels within each parcel.
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
/
t
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
.
t
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
BOLD Time-Series Analysis
For each brain region (34 left-hemisphere regions for our default parcellation) in each subject,
we extracted a BOLD time series. Following Sethi et al. (2017), we focused our main analysis
on the power across frequency bands of the discrete Fourier transform of each BOLD time
series. BOLD time series were linearly detrended and normalized to unit variance using a z-
score before applying a fast Fourier transform. Variance normalization ensures that the total
power in the Fourier power spectrum is unity; the power in a given frequency band represents
relative power and is unitless. In this work, we refer to relative low-frequency power (RLFP) as
the proportion of power contained in the lowest 20% of frequencies ( f < 0.14 Hz), as in Sethi
et al. (2017).
For initial comparison to some commonly used time series metrics, we took an imple-
mentation of fALFF based on the REST toolkit (Song et al., 2011; see SP_fALFF in the code
repository), and our implementations of the autocorrelation function decay timescale and area
are taken from CO_AutoCorrShape from the hctsa toolbox, available at https://github.com/
benfulcher/hctsa (Fulcher & Jones, 2017; Fulcher et al., 2013). To more comprehensively in-
vestigate how the power in specific frequency bands of the Fourier power spectrum com-
pares to alternative univariate time series properties, we compared across the full set of time
series features in hctsa (v0.96; Fulcher & Jones, 2017). This software was used to extract
Network Neuroscience
801
FMRI timescales relate to structural connectivity in the brain
over 7,000 features from each rs-fMRI time series. Following standard procedures (Fulcher &
Jones, 2017), we filtered features that returned special values (features that are inappropriate
for these data) or were approximately constant across all brain regions (features that provide
no meaningful information). We then restricted our analysis to 6,062 well-behaved features
that were not filtered from any participant.
To investigate the dependence of our results to variations in region volume (Sethi et al.,
2017), we estimated the volume of each region in our parcellation by summing the number
of 0.7-mm isotropic voxels in a region using the T1-weighted image. Region volume was con-
trolled for by computing a partial Spearman correlation. We used Spearman rank correlations
because of the frequently nonnormally distributed nodal properties, particularly region volume
and node strength.
ACKNOWLEDGMENTS
The author would like to thank Leonardo Gollo and Dan Lurie for thoughtful comments on a
draft manuscript.
AUTHOR CONTRIBUTIONS
John Fallon: Formal analysis; Writing - Original Draft. Phillip Ward: Supervision; Formal anal-
ysis; Methodology; Writing - Review & Editing. Linden Parkes: Data curation; Formal analysis;
Writing - Review & Editing. Stuart Oldham: Data curation; Formal analysis; Writing - Review
& Editing. Aurina Arnatkeviciute: Data curation; Formal analysis; Writing - Review & Editing.
Alex Fornito: Supervision; Writing - Review & Editing. Ben David Fulcher: Conceptualization;
Formal analysis; Methodology; Supervision; Writing - Review & Editing.
FUNDING INFORMATION
Ben David Fulcher, National Health and Medical Research Council (AU), Award ID: 1089718.
Alex Fornito, Sylvia and Charles Viertel Charitable Foundation (http://dx.doi.org/10.
13039/100008717).
SUPPORTING INFORMATION
Supporting information for this article is available at https://doi.org/10.1162/netn_
a_00151. Code for reproducing our analyses is at https://github.com/NeuralSystemsAndSignals/
humanStructureFunction (Fallon, 2020). The authors highly comparative time series anal-
ysis was performed using the hctsa toolbox, available at https://github.com/benfulcher/
hctsa (Fulcher & Jones, 2017; Fulcher et al., 2013).
REFERENCES
Abdelnour, F., Dayan, M., Devinsky, O., Thesen, T., & Raj, A. (2018).
Functional brain connectivity is predictable from anatomic net-
work’s Laplacian eigen-structure. NeuroImage, 172, 728–739.
Abdelnour, F., Voss, H. U., & Raj, A. (2014). Network diffusion ac-
curately models the relationship between structural and func-
tional brain connectivity networks. NeuroImage, 90, 335–347.
Afyouni, S., Smith, S. M., & Nichols, T. E.
(2019). Effective de-
grees of freedom of the Pearson’s correlation coefficient under
autocorrelation. NeuroImage, 199, 609–625.
Arnatkevici ¯ut˙e, A., Fulcher, B. D., Pocock, R., & Fornito, A. (2018).
Hub connectivity, neuronal diversity, and gene expression in the
Caenorhabditis elegans connectome. PLoS Computational Biol-
ogy, 14(2), e1005989.
Network Neuroscience
802
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
/
t
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
t
.
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
Aso, T., Urayama, S., Fukuyama, H. & Murai, T. (2019). Axial varia-
tion of deoxyhemoglobin density as a source of the low-frequency
time lag structure in blood oxygenation level-dependent signals.
PLoS ONE, 14(9), 1–25.
Baria, A. T., Baliki, M. N., Parrish, T., & Apkarian, A. V. (2011). Ana-
tomical and functional assemblies of brain BOLD oscillations.
Journal of Neuroscience, 31(21), 7910–7919.
Baria, A. T., Mansour, A., Huang, L., Baliki, M. N., Cecchi, G. A.,
Mesulam, M. M., & Apkarian, A. V. (2013). Linking human brain
local activity fluctuations to structural and functional network
architectures. NeuroImage, 73(C), 144–155.
Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discov-
ery rate: A practical and powerful approach to multiple testing.
Journal of the Royal Statistical Society: Series B (Methodological),
57(1), 289–300.
Burt, J. B., Demirtas, M., Eckner, W. J., Navejar, N. M., Ji, J. L.,
(2018). Hierarchy of transcrip-
Martin, W. J., … Murray, J. D.
tomic specialization across human cortex captured by structural
neuroimaging topography. Nature Neuroscience, 27, 889.
Cavanagh, S. E., Wallis, J. D., Kennerley, S. W., & Hunt, L. T. (2016).
Autocorrelation structure at rest predicts value correlates of sin-
gle neurons during reward-guided choice. eLife, 5, 1096.
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. Neuron, 88(2),
419–431.
Chiang, A., Rennie, C., Robinson, P., Van Albada, S., & Kerr, C.
(2011). Age trends and sex differences of alpha rhythms including
split alpha peaks. Clinical Neurophysiology, 122(8), 1505–1517.
Cliff, O. M., Novelli, L., Fulcher, B. D., Shine, J. M., & Lizier, J. T.
(2020). Exact inference of linear dependence between multiple
autocorrelated time series. arXiv:2003.03887.
Cocchi, L., Gollo, L. L., Zalesky, A., & Breakspear, M. J.
(2017).
Criticality in the brain: A synthesis of neurobiology, models and
cognition. Progress in Neurobiology, 158, 132–152.
Cocchi, L., Sale, M. V., Gollo, L. L., Bell, P. T., Nguyen, V. T.,
Zalesky, A., … Culham, J. C. (2016). A hierarchy of timescales ex-
plains distinct effects of local inhibition of primary visual cortex
and frontal eye fields. eLife, 5, e15252.
Deco, G., & Jirsa, V. K.
(2012). Ongoing cortical activity at rest:
Criticality, multistability, and ghost attractors. Journal of Neuro-
science, 32(10), 3366–3375.
Deco, G., McIntosh, A. R., Shen, K., Hutchison, R. M., Menon, R. S.,
Everling, S., … Jirsa, V. K. (2014). Identification of optimal struc-
tural connectivity using functional connectivity and neural mod-
eling. Journal of Neuroscience, 34(23), 7910–7916.
Deco, G., Ponce-Alvarez, A., Mantini, D., Romani, G. L., Hagmann,
P., & Corbetta, M. (2013). Resting-state functional connectivity
emerges from structurally and dynamically shaped slow linear
fluctuations. Journal of Neuroscience, 33(27), 11239–11252.
Demirta¸s, M., Burt, J. B., Helmer, M., Ji, J. L., Adkinson, B. D.,
Glasser, M. F., … Murray, J. D. (2019). Hierarchical heterogeneity
across human cortex shapes large-scale neural dynamics. Neu-
ron, 101(6), 1181–1194.
Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C.,
Blacker, D., Killiany, R. J. (2006). An automated labeling system
for subdividing the human cerebral cortex on MRI scans into gy-
ral based regions of interest. NeuroImage, 31(3), 968–980.
Di, X., Kannurpatti, S. S., Rypma, B., & Biswal, B. B. (2012). Cali-
brating bold fMRI activations with neurovascular and anatomical
constraints. Cerebral Cortex, 23(2), 255–263.
Fallon, J. (2020). Main structure-function analysis for publication.
GitHub, https://github.com/NeuralSystemsAndSignals/human
StructureFunction. https://doi.org/10.5281/zenodo.3920347
Finger, H., Bönstrup, M., Cheng, B., Messé, A., Hilgetag, C. C.,
Thomalla, G., … König, P.
(2016). Modeling of large-scale
functional brain networks based on structural connectivity from
DTI: Comparison with EEG derived phase coupling networks and
evaluation of alternative methods along the modeling path.
PLoS Computational Biology, 12(8), e1005025.
Fornito, A., Arnatkevici ¯ut˙e, A., & Fulcher, B. D. (2019). Bridging the
gap between connectome and transcriptome. Trends in Cognitive
Sciences, 23(1), 34–50.
Fornito, A., Zalesky, A., Bassett, D. S., Meunier, D., Ellison-Wright,
(2011). Genetic influences
I., Yücel, M., … Bullmore, E. T.
on cost-efficient organization of human cortical functional net-
works. Journal of Neuroscience, 31(9), 3261–3270.
Fornito, A., Zalesky, A., & Breakspear, M. J.
(2015). The connec-
tomics of brain disorders. Nature Reviews Neuroscience, 16(3),
159–172.
Fornito, A., Zalesky, A., & Bullmore, E.
(2016). Fundamentals of
brain network analysis. London, United Kingdom: Academic Press.
In Fea-
ture engineering for machine learning and data analytics
(pp. 87–116). Boca Raton, FL: CRC Press.
(2018). Feature-based time-series analysis.
Fulcher, B. D.
Fulcher, B. D., & Fornito, A. (2016). A transcriptional signature of
hub connectivity in the mouse connectome. Proceedings of the
National Academy of Sciences, 113(5), 1435–1440.
Fulcher, B. D., & Jones, N. S. (2017). hctsa: A computational frame-
work for automated time-series phenotyping using massive fea-
ture extraction. Cell Systems, 5(5), 527–531.e3.
Fulcher, B. D., Little, M. A., & Jones, N. S. (2013). Highly compar-
ative time-series analysis: The empirical structure of time series
and their methods. Journal of the Royal Society Interface, 10(83),
20130048.
Fulcher, B. D., Murray, J. D., Zerbi, V., & Wang, X.-J. (2019). Mul-
timodal gradients across mouse cortex. Proceedings of the Na-
tional Academy of Sciences, 116(10), 4689–4695.
Gao, R., van den Brink, R. L., Pfeffer, T., & Voytek, B. (2020). Neu-
ronal timescales are functionally dynamic and shaped by cortical
microarchitecture. bioRxiv.
García-Cabezas, M. Á., García Cabezas, M. Á., Joyce, M. K. P., John,
Y. J., Zikopoulos, B., & Barbas, H. (2017). Mirror trends of plastic-
ity and stability indicators in primate prefrontal cortex. European
Journal of Neuroscience, 46(8), 2392–2405.
Ghosh, A., Rho, Y., McIntosh, A. R., Kötter, R., & Jirsa, V. K. (2008).
Noise during rest enables the exploration of the brain’s dynamic
repertoire. PLoS Computational Biology, 4(10), e1000196.
Glasser, M. F., Coalson, T. S., Robinson, E. C., Hacker, C. D.,
Harwell, J., Yacoub, E., … Van Essen, D. C. (2016). A multi-modal
Network Neuroscience
803
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
/
t
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
.
t
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
parcellation of human cerebral cortex. Nature, 536(7615),
171–178.
Glasser, M. F., Sotiropoulos, S. N., Wilson, J. A., Coalson, T. S.,
Fischl, B., Andersson, J. L., … Jenkinson, M. (2013). The mini-
mal preprocessing pipelines for the Human Connectome Project.
NeuroImage, 80, 105–124.
Gollo, L. L. (2019). Computational psychiatry: Exploring atypical
timescales in the brain. eLife, 8, e15252.
Gollo, L. L., Zalesky, A., Hutchison, R. M., van den Heuvel, M. P.,
& Breakspear, M. J.
(2015). Dwelling quietly in the rich club:
Brain network determinants of slow cortical fluctuations. Philo-
sophical Transactions of the Royal Society B:Biological Sciences,
370(1668), 20140165.
Goñi, J., van den Heuvel, M. P., Avena-Koenigsberger, A., de
Mendizabal, N. V., Betzel, R. F., Griffa, A., … Sporns, O. (2014).
Resting-brain functional connectivity predicted by analytic mea-
sures of network communication. Proceedings of the National
Academy of Sciences, 111(2), 833–838.
Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C. J.,
Wedeen, V. J., & Sporns, O. (2008). Mapping the structural core
of human cerebral cortex. PLoS Biology, 6(7), e159.
Hasson, U., Chen, J., & Honey, C. J. (2015). Hierarchical process
memory: Memory as an integral component of information pro-
cessing. Trends in Cognitive Sciences, 19(6), 304–313.
Hasson, U., Yang, E., Vallines, I., Heeger, D. J., & Rubin, N. (2008).
A hierarchy of temporal receptive windows in human cortex.
Journal of Neuroscience, 28(10), 2539–2550.
He, B. J.
(2011). Scale-free properties of the functional magnetic
resonance imaging signal during rest and task. Journal of Neuro-
science, 31(39), 13786–13795.
Hermundstad, A. M., Bassett, D. S., Brown, K. S., Aminoff, E. M.,
Clewett, D., Freeman, S., … others (2013). Structural foundations
of resting-state and task-based functional connectivity in the hu-
man brain. Proceedings of the National Academy of Sciences,
110(15), 6169–6174.
Hinne, M., Ambrogioni, L., Janssen, R. J., Heskes, T., & van Gerven,
M. A.
(2014). Structurally-informed Bayesian functional con-
nectivity analysis. NeuroImage, 86, 294–305. https://doi.org/
10.1016/j.neuroimage.2013.09.075
Honey, C. J., Kötter, R., Breakspear, M. J., & Sporns, O. (2007). Net-
work structure of cerebral cortex shapes functional connectivity
on multiple time scales. Proceedings of the National Academy
of Sciences, 104(24), 10240–10245.
Honey, C. J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J. P.,
Meuli, R., & Hagmann, P. (2009). Predicting human resting-state
functional connectivity from structural connectivity. Proceedings
of the National Academy of Sciences, 106(6), 2035–2040.
Honey, C. J., Thesen, T., Donner, T. H., Silbert, L. J., Carlson, C. E.,
Devinsky, O., … Hasson, U. (2012). Slow cortical dynamics and
the accumulation of information over long timescales. Neuron,
76(2), 423–434.
Huang, Z., Liu, X., Mashour, G. A., & Hudetz, A. G.
(2018).
Timescales of intrinsic BOLD signal dynamics and functional
connectivity in pharmacologic and neuropathologic states of un-
consciousness. Journal of Neuroscience, 38(9), 2304–2317.
Huntenburg, J. M., Bazin, P.-L., Bazin, P. L., & Margulies, D. S.
(2017). Large-scale gradients in human cortical organization.
Trends in Cognitive Sciences, 22(1), 21–31.
Hutchison, R. M., Womelsdorf, T., Allen, E. A., Bandettini, P. A.,
Calhoun, V. D., Corbetta, M., . . . Chang, C. (2013). Dynamic
functional connectivity: Promise,
issues, and interpretations.
NeuroImage, 80, 360–378.
Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Princi-
ples and practice. OTexts.
James, O., Park, H., & Kim, S. G. (2019). Impact of sampling rate on
statistical significance for single subject fMRI connectivity anal-
ysis. Human Brain Mapping, 5(3), 537.
Jenkinson, M., Beckmann, C. F., Behrens, T. E., Woolrich, M. W., &
Smith, S. M. (2012). FSL. NeuroImage, 62(2), 782–790.
Jones, D. K., Knösche, T. R., & Turner, R.
(2013). White matter
integrity, fiber count, and other fallacies: The do’s and don’ts of
diffusion MRI. NeuroImage, 73, 239–254.
Kalcher, K., Boubela, R. N., Huf, W., Bartova, L., Kronnerwetter, C.,
Derntl, B., … Moser, E. (2014). The spectral diversity of resting-
state fluctuations in the human brain. PLoS ONE, 9(4), e93375.
(2004). Nonlinear time series analysis
(Vol. 7). Cambridge, United Kingdom: Cambridge University
Press.
Kantz, H., & Schreiber, T.
Keitel, A., & Gross, J.
Individual human brain areas can
be identified from their characteristic spectral activation finger-
prints. PLoS Biology, 14(6), e1002498.
(2016).
Kiebel, S. J., Daunizeau, J., & Friston, K. J. (2008). A hierarchy of
time-scales and the brain. PLoS Computational Biology, 4(11),
e1000209.
Lacasa, L., Luque, B., Ballesteros, F., Luque, J., & Nuño, J. C. (2008).
From time series to complex networks: The visibility graph.
Proceedings of the National Academy of Sciences, 105(13),
4972–4975.
Lee, T.-W., & Xue, S.-W. (2017). Linking graph features of anatom-
ical architecture to regional brain activity: A multi-modal MRI
study. Neuroscience Letters, 651, 123–127.
Li, Y., Liu, Y., Li, J., Qin, W., Li, K., Yu, C., & Jiang, T. (2009). Brain
anatomical network and intelligence. PLoS Computational Biol-
ogy, 5(5), e1000395.
Liang, X., Zou, Q., He, Y., & Yang, Y. (2013). Coupling of functional
connectivity and regional cerebral blood flow reveals a physio-
logical basis for network hubs of the human brain. Proceedings
of the National Academy of Sciences, 110(5), 1929–1934.
Liao, X.-H., Xia, M.-R., Xu, T., Dai, Z.-J., Cao, X.-Y., Niu, H.-J., …
He, Y. (2013). Functional brain hubs and their test–retest reliabil-
ity: A multiband resting-state functional MRI study. NeuroImage,
83, 969–982.
Lizier, J. T. (2014). JIDT: An information-theoretic toolkit for study-
ing the dynamics of complex systems. Frontiers in Robotics and
AI, 1, 1085.
Mahjoory, K., Schoffelen, J.-M., Keitel, A., & Gross, J. (2019). The
frequency gradient of human resting-state brain oscillations fol-
lows cortical hierarchies. BioRxiv, 857656.
Miši´c, B., Betzel, R. F., de Reus, M. A., van den Heuvel,
(2016).
M. P., Berman, M. G., McIntosh, A. R., & Sporns, O.
Network Neuroscience
804
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
t
/
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
t
.
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
Network-level structure-function relationships in human neocor-
tex. Cerebral Cortex, 26(7), 3285–3296.
signal dynamics in the mouse brain. Chaos: An Interdisciplinary
Journal of Nonlinear Science, 27(4), 047405.
Mori, S., Crain, B. J., Chacko, V. P., & Van Zijl, P. C. (1999). Three-
dimensional tracking of axonal projections in the brain by mag-
netic resonance imaging. Annals of Neurology: Official Journal of
the American Neurological Association and the Child Neurology
Society, 45(2), 265–269.
Mori, S., & Van Zijl, P. C.
(2002). Fiber tracking: Principles and
strategies–a technical review. NMR in Biomedicine: An Interna-
tional Journal Devoted to the Development and Application of
Magnetic Resonance In Vivo, 15(7–8), 468–480.
Murray, J. D., Bernacchia, A., Freedman, D. J., Romo, R., Wallis,
(2014). A hierarchy of intrinsic
J. D., Cai, X., … Wang, X.-J.
timescales across primate cortex. Nature Neuroscience, 17(12),
1661–1663.
Niazy, R. K., Xie, J., Miller, K., Beckmann, C. F., & Smith, S. M.
(2011). Spectral characteristics of resting state networks. Progress
in Brain Research Progress in Brain Research, 193, 259–276.
Oh, S. W., Harris, J. A., Ng, L., Winslow, B., Cain, N., Mihalas, S., …
Zeng, H. (2014). A mesoscale connectome of the mouse brain.
Nature, 508(7495), 207–214.
Parkes, L., Fulcher, B. D., Yücel, M., & Fornito, A.
(2017). Tran-
scriptional signatures of connectomic subregions of the human
striatum. Genes, Brain and Behavior, 25(7), 1176–663.
Parkes, L., Fulcher, B. D., Yücel, M., & Fornito, A. (2018). An evalu-
ation of the efficacy, reliability, and sensitivity of motion correc-
tion strategies for resting-state functional MRI. NeuroImage, 171,
415–436.
Passingham, R. E., Stephan, K. E., & Kötter, R. (2002). The anatomi-
cal basis of functional localization in the cortex. Nature Reviews
Neuroscience, 3(8), 606–616.
Penke, L., Maniega, S. M., Bastin, M., Hernández, M. V., Murray,
C., Royle, N., … Deary, I.
(2012). Brain white matter tract in-
tegrity as a neural foundation for general intelligence. Molecular
Psychiatry, 17(10), 1026.
Reveley, C., Seth, A. K., Pierpaoli, C., Silva, A. C., Yu, D., Saunders,
R. C., . . . Ye, F. K. (2015). Superficial white matter fiber systems
impede detection of long-range cortical connections in diffusion
MR tractography. Proceedings of the National Academy of Sci-
ences, 112(21), E2820–E2828.
Richman, J. S., & Moorman, J. R. (2000). Physiological time-series
analysis using approximate entropy and sample entropy. Amer-
ican Journal of Physiology: Heart and Circulatory Physiology,
278(6), H2039–H2049.
Rosanova, M., Casali, A., Bellina, V., Resta, F., Mariotti, M., &
Massimini, M. (2009). Natural frequencies of human corticotha-
lamic circuits. Journal of Neuroscience, 29(24), 7679–7685.
Runyan, C. A., Piasini, E., Panzeri, S., & Harvey, C. D. (2017). Dis-
tinct timescales of population coding across cortex. Nature, 548,
92–96.
Sannino, S., Stramaglia, S., Lacasa, L., & Marinazzo, D.
(2017).
Visibility graphs for fMRI data: Multiplex temporal graphs and
their modulations across resting-state networks. Network Neu-
roscience, 2015, 1–14.
Sethi, S. S., Zerbi, V., Wenderoth, N., Fornito, A., & Fulcher, B. D.
(2017). Structural connectome topology relates to regional BOLD
Shen, K., Bezgin, G., Schirner, M., Ritter, P., Everling, S., &
McIntosh, A. R. (2019). A macaque connectome for large-scale
network simulations in the virtual brain. Scientific Data, 6(1),
1–12.
Skudlarski, P., Jagannathan, K., & Calhoun, V. D. (2008). Measur-
ing brain connectivity: Diffusion tensor imaging validates resting
state temporal correlations. NeuroImage, 43(3), 554–561.
Smith, R. E., Tournier, J.-D., Calamante, F., & Connelly, A. (2012).
Anatomically-constrained tractography: Improved diffusion MRI
streamlines tractography through effective use of anatomical in-
formation. NeuroImage, 62(3), 1924–1938.
Smith, R. E., Tournier, J.-D., Calamante, F., & Connelly, A. (2013).
SIFT: Spherical-deconvolution informed filtering of tractograms.
NeuroImage, 67, 298–312.
Smith, R. E., Tournier, J.-D., Calamante, F., & Connelly, A. (2015).
SIFT2: Enabling dense quantitative assessment of brain white
matter connectivity using streamlines tractography. NeuroImage,
119, 338–351.
Smith, S. M., Beckmann, C. F., Andersson, J., Auerbach, E. J.,
Bijsterbosch, J., Douaud, G., . . . WU-Minn HCP Consortium.
(2013). Resting-state fMRI in the human connectome project.
NeuroImage, 80, 144–168.
Song, X.-W., Dong, Z.-Y., Long, X.-Y., Li, S.-F., Zuo, X.-N., Zhu,
C.-Z., … Zang, Y.-F.
(2011). Rest: A toolkit for resting-state
functional magnetic resonance imaging data processing. PLoS
ONE, 6(9), e25031.
Sporns, O., Tononi, G., & Kötter, R.
(2005). The human connec-
tome: A structural description of the human brain. PLoS Compu-
tational Biology, 1(4), e42.
Stephens, G. J., Honey, C. J., & Hasson, U. (2013). A place for time:
The spatiotemporal structure of neural dynamics during natural
audition. Journal of Neurophysiology, 110(9), 2019–2026.
Thomas, C., Frank, Q. Y., Irfanoglu, M. O., Modi, P., Saleem, K. S.,
(2014). Anatomical accuracy
Leopold, D. A., & Pierpaoli, C.
of brain connections derived from diffusion MRI tractography is
inherently limited. Proceedings of the National Academy of Sci-
ences, 111(46), 16574–16579.
Tournier, J.-D., Calamante, F., & Connelly, A. (2012). MRtrix: Diffu-
sion tractography in crossing fiber regions. International Journal
of Imaging Systems and Technology, 22(1), 53–66.
van den Heuvel, M. P., Bullmore, E. T., & Sporns, O.
(2016).
Comparative connectomics. Trends in Cognitive Sciences, 20(5),
345–361.
van Den Heuvel, M. P., Mandl, R. C., Kahn, R. S., & Hulshoff Pol,
H. E.
(2009). Functionally linked resting-state networks reflect
the underlying structural connectivity architecture of the human
brain. Human Brain Mapping, 30(10), 3127–3141.
van den Heuvel, M. P., & Sporns, O. (2011). Rich-club organization
of the human connectome. The Journal of Neuroscience, 31(44),
15775–15786.
van den Heuvel, M. P., & Sporns, O.
(2019). A cross-disorder
connectome landscape of brain dysconnectivity. Nature Reviews
Neuroscience, 20, 435–446.
Van Essen, D. C., Smith, S. M., Barch, D. M., Behrens, T. E. J.,
(2013). The WU-Minn Human
Yacoub, E., & Ugurbil, K.
Connectome Project: An overview. NeuroImage, 80, 62–79.
Network Neuroscience
805
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
t
/
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
t
.
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
FMRI timescales relate to structural connectivity in the brain
Wang, P., Kong, R., Kong, X., Liégeois, R., Orban, C., Deco, G., …
Yeo, B. T. T. (2019). Inversion of a large-scale circuit model re-
veals a cortical hierarchy in the dynamic resting human brain.
Science Advances, 5(1), eaat7854.
Watanabe, T., Rees, G., & Masuda, N.
(2019). Atypical intrinsic
neural timescale in autism. eLife, 8, 839.
Yu-Feng, Z., Yong, H., Chao-Zhe, Z., Qing-Jiu, C., Man-Qiu, S.,
Meng, L., … Yu-Feng, W. (2007). Altered baseline brain activity
in children with ADHD revealed by resting-state functional MRI.
Brain and Development, 29(2), 83–91.
Zalesky, A., Fornito, A., Cocchi, L., Gollo, L. L., van den Heuvel,
M. P., & Breakspear, M. (2016). Connectome sensitivity or speci-
ficity: Which is more important? NeuroImage, 142, 407–420.
Zhang, H., Watrous, A. J., Patel, A., & Jacobs, J. (2018). Theta and
alpha oscillations are traveling waves in the human neocortex.
Neuron, 98(6), 1269–1281.e4.
Zou, Q.-H., Zhu, C.-Z., Yang, Y., Zuo, X.-N., Long, X.-Y., Cao,
Q.-J., … Zang, Y.-F. (2008). An improved approach to detection
of amplitude of low-frequency fluctuation (ALFF) for resting-state
fMRI: Fractional ALFF. Journal of Neuroscience Methods, 172(1),
137–141.
l
D
o
w
n
o
a
d
e
d
f
r
o
m
h
t
t
p
:
/
/
d
i
r
e
c
t
.
m
i
t
.
/
/
t
e
d
u
n
e
n
a
r
t
i
c
e
-
p
d
l
f
/
/
/
/
/
4
3
7
8
8
1
8
6
7
3
7
3
n
e
n
_
a
_
0
0
1
5
1
p
d
.
t
f
b
y
g
u
e
s
t
t
o
n
0
9
S
e
p
e
m
b
e
r
2
0
2
3
Network Neuroscience
806
