Predicting human resting-state functional connectivity
from structural connectivity
C. J. Honeya, O. Spornsa,1, L. Cammounb, X. Gigandetb, J. P. Thiranb, R. Meulic, and P. Hagmannb,c
aDepartment of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405;bSignal Processing Laboratory 5, Ecole Polytechnique Fe ´de ´rale de
Lausanne, CH-1011 Lausanne, Switzerland; andcDepartment of Radiology, University Hospital Center and University of Lausanne, CH-1011 Lausanne, Switzerland
Edited by Marcus E. Raichle, Washington University, St. Louis, MO, and approved December 9, 2008 (received for review November 4, 2008)
In the cerebral cortex, the activity levels of neuronal populations
are continuously fluctuating. When neuronal activity, as measured
using functional MRI (fMRI), is temporally coherent across 2 pop-
ulations, those populations are said to be functionally connected.
Functional connectivity has previously been shown to correlate
with structural (anatomical) connectivity patterns at an aggregate
level. In the present study we investigate, with the aid of compu-
tational modeling, whether systems-level properties of functional
networks—including their spatial statistics and their persistence
across time—can be accounted for by properties of the underlying
anatomical network. We measured resting state functional con-
nectivity (using fMRI) and structural connectivity (using diffusion
spectrum imaging tractography) in the same individuals at high
resolution. Structural connectivity then provided the couplings for
a model of macroscopic cortical dynamics. In both model and data,
we observed (i) that strong functional connections commonly exist
between regions with no direct structural connection, rendering
the inference of structural connectivity from functional connectiv-
ity impractical; (ii) that indirect connections and interregional
distance accounted for some of the variance in functional connec-
tivity that was unexplained by direct structural connectivity; and
(iii) that resting-state functional connectivity exhibits variability
within and across both scanning sessions and model runs. These
empirical and modeling results demonstrate that although resting
state functional connectivity is variable and is frequently present
between regions without direct structural linkage, its strength,
persistence, and spatial statistics are nevertheless constrained by
the large-scale anatomical structure of the human cerebral cortex.
computational model ? diffusion MRI ? neuroanatomy ?
cerebral cortex ? brain networks
during resting and sleep (1). Activity levels are modulated across
time by the internal dynamics of each neuronal population and by
signals received from cortical, subcortical, and peripheral elements
of the nervous system. In the past decade, there has been intense
interest in the patterns of correlated activity [‘‘functional connec-
tivity’’ (2)] in the human brain, because these patterns are believed
A set of functionally connected regions is referred to as a ‘‘func-
tional network.’’ Some functional networks are most commonly
(in the resting state); others are observed in the context of task-
states (3–6). A set of regions including posterior medial, anterior
medial, and lateral parietal cortices comprise the default mode
network (DMN) (7, 8), a functional network that is particularly
that the more persistent functional networks may be involved with
ongoing organizational processes in the brain (9, 10), and that
disruptions in reliably present correlations are indicative, and
potentially diagnostic, of neuropathology (11, 12).
Because the propensity for 2 areas to interact should vary in
opulations of neurons in the mammalian cerebral cortex are
continuously active during purposeful behavior, as well as
them, it is widely assumed that the repertoire of functional config-
urations assumed by the cerebral cortex is reflective of underlying
anatomical linkage (13- 18). However, the nature of this structure-
function relationship is only beginning to be revealed. A general
correspondence between functional connectivity (measured using
functional MRI) and structural connectivity (measured using dif-
fusion tractography) has previously been demonstrated in adjacent
gyri in a single axial slice (19) and across the cortex in a 66-region
parcellation (20). However, several questions remain. First, given
that structural and functional connectivity are correlated, is it
possible to infer structural connectivity from functional connectiv-
increase the distance between neuronal populations, and what are
the contributions of indirect structural connections to functional
connectivity? Third, to what extent does functional connectivity
vary across time, and which anatomical features distinguish persis-
tent functional networks from those that are more transient? To
address these questions, we compared structural and functional
connectivity maps to one another. We then used the structural
connectivity maps as couplings in a computational model of the
large-scale dynamics of the cerebral cortex (21, 22), and from these
dynamics we extracted simulated blood-oxygenation level depen-
dent (BOLD) signals and functional connectivity, which could be
quantitatively compared against empirical observations.
Structural connectivity was measured noninvasively in 5 individ-
ual participants using diffusion spectrum imaging (DSI). Resting
neural activity was then recorded in the same participants on two
separate occasions using functional MRI (fMRI). Structural con-
the Pearson correlations between the BOLD time series in all
possible pairs of 998 cortical regions.
We hypothesized that, in both empirical and simulated data,
more strongly connected region-pairs would exhibit stronger signal
correlations, but that underlying SC would not be necessary for the
observation of strong rsFC (19). We expected, further, that the
anatomical connections, although only partially, and that this effect
would be most reliable where SC is strongest.
We report results using 2 cortical parcellations, called the ‘‘low
resolution’’ and the ‘‘high resolution.’’ In the low-resolution par-
Author contributions: C.J.H., O.S., and P.H. designed research; C.J.H., O.S., L.C., X.G., R.M.,
and P.H. performed research; C.J.H., O.S., L.C., X.G., J.P.T., R.M., and P.H. contributed new
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
1To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2009 by The National Academy of Sciences of the USA
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(33 per hemisphere) of varying size are identified and matched
across participants using an automated landmark-based algorithm
(23). The high-resolution parcellation (Fig. S1B) is a refinement of
of interest (ROIs) of approximately equal area (?1.5 cm2) (L.C.,
X.G, J.P.T, K. Q Do, P. Maeder, R.M., P.H., unpublished data).
SC between two ROIs was derived from the number of fibers
calculated using pairwise Pearson’s correlation coefficients of
within an ROI. Both SC and rsFC were calculated at the high
resolution (998 ROIs) and then down-sampled by averaging across
ROIs within each of the 66 predefined anatomical regions. For
comparison with experimental data, we simulated a nonlinear
neural mass model (21, 22) composed of 998 nodes, whose time
of connections between nodes was determined by the empirical
high-resolution SC, and simulated functional connectivity was then
calculated from the simulated BOLD time series. See Methods for
P ? ? 1e-3.
Overall Structure-Function Relationship
Low Resolution (66 Regions). As described previously (20), after
averaging low-resolution data across participants, the SC and rsFC
correlated (r ? 0.66). When excluding ROI-pairs with absent or
inconsistent structural connections (see Methods), this correlation
strengthens to r ? 0.82.
High Resolution (998 ROIs). Because of interparticipant variability in
cortical morphology, averaging data at the high resolution did not
produce as much of a de-noising effect as at the low resolution. For
was r ? 0.36 and increased to r ? 0.53 when excluding absent or
inconsistent structural connections. For individual participants, the
SC-rsFC correlations ranged from r ? 0.39 to 0.48 (Fig. 1A).
Computational Model (998 Nodes). A comparison of empirical SC
(from participant B) and simulated rsFC derived from a single run
of the computational model is shown in Fig. 1B. For individual
participants, the SC-rsFC correlations (single simulation) ranged
from r ? 0.32 to 0.44 when excluding absent connections. For data
averaged across participants, the overall correlation between SC
and simulated rsFC was r ? 0.46 and increased to r ? 0.52 when
excluding absent or inconsistent structural connections. For high-
model, see Table S1.
Inference of Structure from Function. When structural connections
are present, the relationship between the strength of SC and rsFC
is robust in both the empirical data and computational model.
When direct structural connectivity is absent, however, the rsFC
values will still vary over a wide range (Fig. 1 C and D), a finding
consistent with ref. 19. Thus, although the presence of strong SC at
an edge is predictive of strong rsFC, the reverse inference is less
reliable. When inferring SC by thresholding rsFC, one obtains, for
each given threshold value, some number of false-positives and
some number of true-positives. The receiver-operating character-
istic (ROC) curves in Fig. 1E show how the false-positive and
the ROC curve is greater for the modeled data than the empirical
data (0.95 versus 0.79). However, in both cases, thresholding of
rsFC yields highly inaccurate prediction of SC. For example, in the
empirical data, the threshold at which 80% of structural connec-
tions are correctly detected is one at which more than 40% of the
unconnected region pairs are incorrectly detected (see Fig. 1E).
Because structurally unconnected pairs are about 30 times as
numerous as connected pairs within our high-resolution data, only
?6% of inferred structural connections would be genuine at this
but still too low for practical inference. For the threshold at which
the inferred SC would correspond to the true structural couplings
that underlie the model dynamics.
The Role of Distance. On average, both structural connectivity (24,
25) and functional connectivity (26) between cortical regions
result from a combination of factors, including (i) spatial autocor-
relation of cortico-cortical connectivity, (ii) spatial autocorrelation
of subcortico-cortical projections, (iii) activation spread along the
surface of the cortex via local circuitry (27, 28), (iv) spatial blurring
of the BOLD signal because of vascular drainage, and (v) MRI
acquisition or data preprocessing artifacts (29).
Because most of the structural connectivity we observe is short-
result artifactually if both SC and rsFC are spatially autocorrelated,
(single acquisition, 20 min) of rsFC against SC at high
resolution for participant B, showing edges with non-
rsFC against SC (from participant B) at high resolution,
sities of rsFC values between structurally connected and
unconnected region pairs, data for participant B at the
high resolution. (D) Same as (C), but for simulated rsFC.
(E) ROC curves, indicating the signal detection perfor-
mance when inferring SC by thresholding empiricial
(green) and simulated (dark blue) rsFC maps at the high
Overall SC-rsFC relationships. (A) Scatter plot
www.pnas.org?cgi?doi?10.1073?pnas.0811168106Honey et al.
confirmed that average rsFC is linearly related to the inverse of the
fiber distance between regions (r ? 0.67) (Fig. 2A, low resolution).
Then, after regressing rsFC on fiber distance, we checked that
structural connectivity is robustly related to the residuals of that
rsFC-fiber distance relationship (r ? 0.47) (Fig. 2B). This is
controlling for interregional fiber distance. Although the SC-rsFC
relationship is weaker when we control for distance, it remains
analyses. A bivariate linear regression using SC and (inverse) fiber
distance to predict rsFC can explain 69% of the variance in
participant-averaged rsFC at the low resolution, and 30% at the
high resolution (see Table S1 and Fig. 2C). In the computational
of SC and inverse fiber distance at high resolution.
Indirect Connections and Network Effects. We next sought to exam-
ine the potential role of multisynaptic anatomical structures in
explaining the presence of rsFC between ROIs without direct SC.
We assigned indirect connections to region-pairs that were not
directly connected, but for which there existed at least one 2-edge
path connecting them. For each such region pair ij, the indirect
structural connection had strength equal to the sum of all of the
multiplicatively weighted SC paths from i to j (i.e., Indirect SCij?
?wikwkjwhere wabis the direct SC between regions a and b). When
we consider only region pairs linked by a shortest path of 2 edges,
the Pearson correlation between the indirect-SC values and rsFC
values was found to r ? 0.29 for the average data at the high
resolution (Fig. S3). This effect could not be accounted for by the
Euclidean distance between region pairs, and was significant in
each individual. These data suggest that indirect cortico?cortical
Within the computational model, indirect connections were also
observed to induce functional connectivity. When considering
participant-averaged rsFC matrices, the correlation between sim-
network was at r ? 0.46, and for indirectly connected nodes was at
r ? 0.37, indicating that the model was capturing network-level
influences of SC on rsFC. In the low-resolution networks, the
correlation between simulated and empirical rsFC increased to r ?
0.70 for directly linked pairs (Fig. 3A), but dropped to r ? 0.23
between indirectly linked edges.
Reliability of rsFC. As rsFC was acquired from each participant on
two separate occasions (20- and 15-min scans), we were able to
examine the reliability of rsFC. Reliability was operationalized as
the correlation between 2 sets of rsFC values. For individual
participants at the high resolution, reliability across scans ranged
low reliability is also observed in our computational model: across
two consecutive 8-min windows within a single run, the simulated
at the high resolution.
be expected based on the sample size (at least 200 time points per
is likely because of acquisition and registration artifacts. However,
we note that both empirical (30) and simulated rsFC time series
the number of independent measurements captured within a time
window. The values of rsFC measured in this study, as well as more
We also note that ROI pairs with SC exhibit significantly less
variability in empirical rsFC (both across and within sessions) than
do ROI pairs without SC (see SI Appendix, Fig. S4). In the present
data we cannot distinguish whether rsFC between these ROIs is
more persistent because it is stronger (and therefore, statistically,
less subject to sampling variability in finite samples), or whether it
is stronger because it is more persistent (that is, because the
underlying interaction is more stable). In either case, the effect is
SC and rsFC in the DMN. On an area-by-area basis (Fig. 3B and Fig.
S5), correlations between simulated and empirical rsFC were
highest for many regions located in the posterior medial cortex,
including the precuneus and posterior cingulate cortex, and the
medial orbitofrontal cortex. Using previously published focal co-
ordinates of the DMN (31) within the precuneus/posterior cingu-
late, the medial prefrontal cortex, and the lateral parietal cortex as
seed points, we extracted a subset of ROIs most strongly correlated
with ROIs located in the DMN (see Fig. S5D). Figs. 3 C and D
portray the relationship of SC to rsFC within the DMN. We find
strong SC linking the 2 medial portions of the precuneus/posterior
cingulate and medial prefrontal cortex, both interhemispherically
and along the medial walls of the cerebral cortex. Lateral parietal
cortex is linked through parieto-frontal pathways, while anatomical
links to medial parietal cortex are less dense (see Fig. 3D).
Connections between lateral and medial aspects of the posterior
of this connection in the DSI data likely reflects the difficulty of
tracking fibers perpendicular to bundles such as the superior
of the inter-regional fiber distance. (B) Scatter plot of residuals from (A) plotted
relationship between SC, rsFC, and inverse fiber distance. The superimposed
plane shows the fit of the bivariate linear model. Points above the plane of
best-fit are light blue, points below are dark blue.
Honey et al.
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longitudinal fasciculus. Consistent with the structural DSI data
supplied to the model, the simulated rsFC seeded in the DMN
reproduces empirical rsFC patterns along the medial axis, but
largely fails to include lateral parietal cortex.
Computational work has suggested that the underlying anatomical
architecture of the cerebral cortex, including its cluster structure,
shapes resting-state functional connectivity on multiple time scales
(22, 33). Advances in diffusion imaging (34–36) now enable us to
empirically examine this structure-function relationship in individ-
to compare a variety of systems-level features of resting-state
functional connectivity against the predictions of computational
models informed by the underlying anatomical network.
in cases of callosal agenesis (37), is related to callosal integrity in
healthy individuals (38), and is almost entirely abolished acutely
after callosotomy (39, 40). Structural and functional connectivity
were also shown to be correlated in adjacent cortical regions in a
single axial slice (19) and across 66 regions of the cerebral cortex
resolution provides further evidence that functional connectivity is
reflective, at least in part, of interactions between distant neuronal
populations. However, because anatomically unconnected edges
exhibit a wide range of rsFC values, one cannot simply infer SC by
arises because (i) rsFC can result from mechanisms other than
direct SC, and (ii) the base rate of direct SC between 2 randomly
simply a reflection of the practical limitations of fMRI, because
inference was nearly as difficult within our computational
mode—in which SC provided the exact coupling matrix—as in
Our second finding is that both SC and rsFC tend to decrease
with interregional distance [consistent with previous studies of SC
(24, 25) and rsFC (26)] and that a significant portion of the rsFC
variance unexplained by SC alone is explained when distance
information is combined with SC information in a bivariate model.
and the precuneus in the left hemisphere (lPCUN). The plot displays SC and rsFC values for the seed regions in relation to all 66 regions within the corresponding
low-resolution matrices. (C) Mapping of SC, rsFC (empirical), and rsFC (modeled) within the DMN. Warmer colors indicate stronger SC and rsFC. Within the posterior
We selected the top 200 most correlated ROIs within the DMN (see Fig. S5D) and plotted all structural connections among them.
Computational model of functional connectivity. (A) Scatter plot of empirical rsFC versus simulated rsFC obtained from the nonlinear model, down-sampled
www.pnas.org?cgi?doi?10.1073?pnas.0811168106Honey et al.
of rsFC that are neuronal [e.g., the strength of SC, and activation
cardiac, vascular, acquisition and preprocessing artifacts (29)], we
cannot definitively determine the origin of this distance-related
residual variability in rsFC. We note, however, that although our
computational model incorporates only topological (and not ex-
plicitly spatial) coupling, it exhibits a distance-associated decrease
in rsFC that resembles the empirically observed fall-off. It is
of cortico-cortical projections in explaining the distance effects.
None of the results we report in this study can be fully accounted
for by interregional distance, but many are mediated by it, and the
prevalence of nearest-neighbor (i.e., lattice-like) anatomical con-
36, 41–43) and hierarchical (44, 45) properties. Another factor
contributing to the local clustering in rsFC networks is that indirect
SC induces rsFC between region pairs that lack direct anatomical
linkage. The relationship between indirect SC and rsFC is weaker
than that between direct SC and rsFC, but is highly significant.
Previous work (15) suggested that interhemispheric rsFC between
the visual cortices most likely requires polysynaptic connectivity,
and we note here that indirect cortico-cortical SC is an especially
strong predictor of rsFC between the visual cortices of each
hemisphere (see Fig. S3).
within and across scanning sessions. This phenomenon is observed
in each participant, as well as in our model, which is not susceptible
to physiological or acquisition artifacts. In empirical data, we also
observe that ROI pairs linked by SC exhibit more reliable rsFC, so
that highly interconnected systems such as the DMN are neverthe-
less quite persistent. Within our data we cannot determine whether
the shifts in rsFC reflect reconfiguration of neuronal interactions,
are the result of low-frequency signal components of unknown
origin, or result from a combination of the two (see SI Appendix).
It is clear, however, that the proportion of the variance in rsFC that
rsFC is not static on the timescales used in this and other resting-
state fMRI experiments. Studies, which compare fMRI FC against
FC in modalities with higher sampling rates (16, 46, 47) remain
crucial in determining the potential cognitive and behavioral
significance of slow correlated fluctuations in the BOLD signal.
The rsFC of some highly connected regions was matched with
high fidelity (see Fig. 3B), and this was found in particular within
the posterior medial components of the default mode network (see
Fig. 3 C and D). This is likely a consequence of the fact that there
is a dense anatomical subnetwork linking DMN member regions
(see SI Appendix) (48, 49). In future modeling work it may be
fruitful to investigate how dynamical properties of individual nodes
vary as a function of the node’s network embedding. Large-scale
cortical models will also be improved when we have access to
interregional physiological efficacies, rather than fiber strengths,
which only approximate the effective couplings between neuronal
populations. It is also important that future models include the
thalamus (50, 51) as well as the basal ganglia, which likely mediate
diverse cortico-cortical interactions. By limiting ourselves in the
present model to aggregate neural dynamics at each node, and by
only including cortico-cortical couplings, we have been able to
identify systems-level features of empirical rsFC that can be ex-
plained without recourse to subcortical input or specialized local
The robust correspondence between SC and rsFC measured in
odological validation for our SC and rsFC acquisition methods.
Nevertheless, the potential for interregional variability in the reli-
ability of these methods limits our ability to examine interregional
differences in the strength of the structure-function relationship.
While DSI tractography is often successful in resolving crossing
fibers, the detection of relatively small fiber bundles running
perpendicular to major fasciculi, as well as the reliable detection of
very long fiber bundles, remains a technical challenge. Functional
regions and near the frontal pole, and BOLD correlations can be
contaminated by vascular, respiratory, and preprocessing artifacts
(30). Preliminary conclusions about regional differences in the
strength of the SC-rsFC relationship are presented in the SI
Appendix, along with considerations of rsFC anti-correlations (see
SI Appendix and Fig. S3B) and interparticipant differences (see SI
Appendix and Table S2).
Structural connectivity of the adult mammalian brain is essen-
tially constant from day to day, but functional connectivity can
this study we confirm (19, 20, 22) at high resolution that the
organizations of SC and of rsFC are strongly interrelated: struc-
turally connected cortical regions exhibit stronger and more con-
sistent rsFC than structurally unconnected regions. However, we
also demonstrate, and capture in quantitative models, the fact that
robust functional connectivity can be found between regions not
linked by cortico-cortical projections, that spatial auto-correlation
in functional connectivity likely results from underlying anatomy,
and that functional networks continually reconfigure around the
underlying anatomical skeleton. The timescales on which rsFC
changes, and the relation of these changes to cognition, are impor-
tant questions for future inquiry.
Extraction and Topology of Structural Networks. DSI Acquisition. The study
protocol was reviewed and approved by the Institutional Review Board at the
with institutional guidelines, 5 healthy right-handed male participants (age
29.4 ? 3.4 years) were scanned on an Achieva 3T Philips scanner. A high-resolu-
128 voxels of isotropic 1-mm resolution.
Diffusion spectrum was performed using a diffusion-weighted single-shot
directions over a hemisphere. The maximum diffusion gradient intensity was 80
with an in-plane resolution of 2 ? 2 mm. Thirty-six contiguous slices of 3-mm
reconstruction of the data followed ref. 52. Following diffusion spectrum and
T1-weighted MRI acquisitions, the segmented gray matter was partitioned into
66 anatomical regions according to anatomical landmarks using Freesurfer
(surfer.nmr.mgh.harvard.edu) and 998 ROIs (see Fig. S1) as described in ref. 20.
White matter tractography was performed with a custom streamline algorithm
998 predefined ROIs. Further details are available in refs. 20 and 34.
Resampling. The fiber strengths produced by the streamline tractography algo-
rithm were exponentially distributed and spanned several orders of magnitude.
range, we resampled the fiber strengths into a Gaussian distribution as follows:
from a unit Gaussian distribution. We then replaced the smallest raw data value
with the smallest randomly sampled value, the second-smallest raw data value
with the second-smallest randomly sampled value, and so on until all raw data
values are replaced. This produced a set of N resampled data values distributed
according to a standard Gaussian, which we then rescaled to a mean of 0.5 and
this article remain strongly significant when SC is not resampled (Table S3).
Fiber Distance and Euclidean Distance. The fiber distance between two ROIs is
calculated as the average length of all of the connecting fibers found using
streamline tractography. The Euclidean distance between two ROIs is calculated
using the mean Talairach coordinates of voxels comprising an ROI. We used the
fiber distance where possible, as it more closely reflects the distance along the
cortical surface. However, fiber distance is only known where SC is present, and
in Fig. 2 remain robust and significant when Euclidean distance is used.
Extraction and Topology of Functional Networks. BOLD Acquisition. The same 5
participants were scanned in eyes-closed resting state using a Siemens Trio 3T
Honey et al.
February 10, 2009 ?
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system using a gradient echo EPI sequence (TR ? 2,000 ms, TE ? 30 ms). An axial Download full-text
3.3 mm in-plane). Thirty-five slices of 3-mm thickness with a 0.3-mm gap were
scan 2 ? 15 min). Scan 1 and 2 rsFC were averaged for Fig. 3 and for some SI
and to remain alert.
Signal Preprocessing and Correlations. Raw BOLD signals were registered and
resampled onto the b0image of the diffusion scan using rigid-body registration
(SPM5, www.fil.ion.ucl.ac.uk/spm). Following slice-time correction BOLD time
within the ROI mask. ROI BOLD time series were then piecewise-linearly de-
mean. Finally, Pearson correlations were calculated between all ROI-pairs. Al-
maps, the results are essentially unchanged when the 998-ROI correlation maps
are Fisher z-transformed and normalized to zero-mean and unit variance within
each participant (Table S4).
High- and Low-Resolution Matrices. The 66 anatomical regions were defined
ROI ? 1.5 cm2) so that their borders aligned with those of the 66 anatomical
regions. BOLD and DSI-fiber counts were captured at voxel resolution and then
voxel-averaged to provide ROI-average values. BOLD correlations were calcu-
averaging across all ROIs with a region.
were absent in more than 3 participants (high resolution) or more than 1 partic-
DSI scans (20).
Computational Model. Neuronal population dynamics were simulated at 0.2-ms
linearly proportional to the resampled fiber strengths at each edge. Each neural
neurons, in which the effects of both ligand- and voltage-gated membrane
channels are accounted for. This model has previously been described in detail
(21) and used in an anatomically informed model of large-scale functional con-
nectivity in the macaque monkey (22). Further modeling details are provided in
the SI Appendix.
the whole brain (53).
R.M. were supported by a grant for interdisciplinary biomedical research of the
University of Lausanne, the Department of Radiology of University Hospital
Universities, and Ecole Polytechnique Fe ´de ´rale de Lausanne, as well as grants
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