Predicting human resting-state functional correlation from structural correlation
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 populations, 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 computational 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 connectivity (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 connectivity impractical; (ii) that indirect connections and interregional distance accounted for some of the variance in functional connectivity 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.
Predicting human resting-state functional connectivity
from structural connectivity
C. J. Honey
, O. Sporns
, L. Cammoun
, X. Gigandet
, J. P. Thiran
, R. Meuli
, and P. Hagmann
Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405;
Signal Processing Laboratory 5, Ecole Polytechnique Fe´de´ rale de
Lausanne, CH-1011 Lausanne, Switzerland; and
Department 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 兩 diffusion MRI 兩 neuroanatomy 兩
cerebral cortex 兩 brain networks
opulations of neurons in the mammalian cerebral cortex are
continuously active during purposeful behavior, as well as
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
to reflect the patterns of interaction between neuronal populations.
A set of functionally connected regions is referred to as a ‘‘func-
tional network.’’ Some functional networks are most commonly
detected when participants are not performing any demanding task
(in the resting state); others are observed in the context of task-
focused behavior; and some networks persist across both behavioral
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
robust across participants and cognitive states. It has been suggested
that the more persistent functional networks may be involved with
ongoing organizational processe s in the brain (9, 10), and that
disruptions in reliably pre sent correlations are indicative, and
potentially diagnostic, of neuropathology (11, 12).
Because the propensity for 2 areas to interact should vary in
proportion to the density and efficacy of the projections connecting
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-
ity? Second, how does the structure-function relationship vary as we
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 feature s 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-
nectivity (SC) maps were constructed using streamline tractography
and resting state functional connectivity (rsFC) maps were based on
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
SC-rsFC relationship would be mediated by distance and by indirect
anatomical connections, although only partially, and that this effect
would also be observed in our model. Finally we expected that rsFC
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
reagents/analytic tools; C.J.H., O.S., and P.H. analyzed data; and C.J.H., O.S., and P.H. wrote
The authors declare no conﬂict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2009 by The National Academy of Sciences of the USA
February 10, 2009
cellation [supporting information (SI) Fig. S1A], 66 cortical regions
(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
the low-resolution surface partition, and is composed of 998 regions
of interest (ROIs) of approximately equal area (⬇1.5 cm
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
found by the tractography algorithm that link those ROIs. rsFC was
calculated using pairwise Pearson’s correlation coefficients of
BOLD time series obtained for each ROI by averaging across voxels
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
evolution is governed by a set of differential equations. The strength
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
further details for each of these steps. All correlations we report are
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
strengths across all region-pairs were found to be highly significantly
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
data averaged across participants (Fig. S2), the SC-rsFC correlation
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-
and low-resolution correlations in individual participants and in the
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
true-positive rates vary as this threshold is adjusted. The area under
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
threshold. This percentage is improved in the computational model,
but still too low for practical inference. For the threshold at which
80% of structural connections are correctly detected, only ⬇28% of
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
decrease with the distance between those regions. This effect could
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-
range (20), the structure-function relationship we report here could
result artifactually if both SC and rsFC are spatially autocorrelated,
but for entirely unrelated reasons. To rule out this possibility we first
Fig. 1. Overall SC-rsFC relationships. (A) Scatter plot
(single acquisition, 20 min) of rsFC against SC at high
resolution for participant B, showing edges with non-
zero SC. (B) Scatter plot (single run, 16 min) of simulated
rsFC against SC (from participant B) at high resolution,
showing edges with nonzero SC. (C) The probability den-
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
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0811168106 Honey 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
equivalent to calculating a partial correlation between SC and rsFC,
controlling for interregional fiber distance. Although the SC-rsFC
relationship is weaker when we control for distance, it remains
highly significant in all participants in both high- and low-resolution
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
model, 29% of the variance in rsFC is explained by the combination
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 SC
is the direct SC between regions a and b). When
we consider only region pairs linked by a shortest path of 2 edge s,
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
linkage does induce some of the rsFC seen between regions lacking
Within the computational model, indirect connections were also
observed to induce functional connectivity. When considering
participant-averaged rsFC matrices, the correlation between sim-
ulated rsFC and empirical rsFC at direct links in the high-resolution
network was at r ⫽ 0.46, and for indirectly connected nodes was at
r ⫽ 0.37, indicating that the model was capturing network-level
influence s 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 value s. For individual
participants at the high re solution, reliability across scans ranged
from r ⫽ 0.38 to r ⫽ 0.69, and reliability across two 10-min windows
within the first scan ranged from r ⫽ 0.39 to r ⫽ 0.61. Unexpectedly
low reliability is also observed in our computational model: across
two consecutive 8-min windows within a single run, the simulated
rsFC reliability ranged from r ⫽ 0.69 to r ⫽ 0.80 for individual maps
at the high resolution.
In models and in data the observed reliability is lower than would
be expected based on the sample size (at least 200 time points per
window) and distributions of rsFC. Some of the empirical variability
is likely because of acquisition and registration artifacts. However,
we note that both empirical (30) and simulated rsFC time series
exhibit very long-range temporal autocorrelations (or, equivalently,
substantial power in very low frequencies), which effectively reduce
the number of independent measurements captured within a time
window. The values of rsFC measured in this study, as well as more
generally in the field, may therefore not reflect a static underlying entity.
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 pre sent
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
mediated by the strength of the anatomical connections between pairs.
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
parietal cortex are observed in tracer studies (32), and the weakness
of this connection in the DSI data likely reflects the difficulty of
tracking fibers perpendicular to bundles such as the superior
Fig. 2. Role of distance. (A) Scatter plot of interregional rsFC against the inverse
of the inter-regional ﬁber distance. (B) Scatter plot of residuals from (A) plotted
against SC, at the low resolution. (C) Three-dimensional scatter plot, showing the
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. PNAS
February 10, 2009
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 scale s
(22, 33). Advances in diffusion imaging (34–36) now enable us to
empirically examine this structure-function relationship in individ-
ual humans at high spatial resolution across the cerebral cortex, and
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.
Earlier work had shown that interhemispheric rsFC is diminished
in cases of callosal agene sis (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
(20). The robust SC-rsFC relationship we now report at high spatial
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
thresholding maps of rsFC. The difficulty of inferring SC from rsFC
arises because (i) rsFC can result from mechanisms other than
direct SC, and (ii) the base rate of direct SC between 2 randomly
selected ROIs at the high resolution is very low. This difficulty is not
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.
Because interregional distance can be expected to influence sources
Fig. 3. Computational model of functional connectivity. (A) Scatter plot of empirical rsFC versus simulated rsFC obtained from the nonlinear model, down-sampled
to the low resolution. (B) Comparison of SC, rsFC (empirical), and rsFC (nonlinear model) for 2 single-seed regions, the posterior cingulate in the right hemisphere (rPC)
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
cingulated/precuneus, medial orbitofrontal cortex and lateral parietal cortex in both hemispheres we selected a cluster of 5 ROIs at positions that most closely matched
the coordinates of peak foci of the DMN (31). These 30 ROIs served as the seeds from which SC and rsFC were determined. (D) Structural connectivity within the DMN.
We selected the top 200 most correlated ROIs within the DMN (see Fig. S5D) and plotted all structural connections among them.
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0811168106 Honey et al.
of rsFC that are neuronal [e.g., the strength of SC, and activation
spread across the cortical surface (27)] as well as nonneuronal [e.g.,
cardiac, vascular, acquisition and preproce ssing 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 re semble s the empirically observed fall-off. It is
therefore not necessary to invoke mechanisms beyond the topology
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-
nectivity of the cerebral cortex is fundamental to its small-world (20,
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).
Our third finding is that rsFC exhibits unexpectedly low reliability
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 re sult from a combination of the two (see SI Appendix).
It is clear, however, that the proportion of the variance in rsFC that
is explained by SC must be understood in light of the fact that fMRI
rsFC is not static on the time scales used in this and other re sting-
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
independent imaging modalities provides a degree of mutual meth-
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 bundle s running
perpendicular to major fasciculi, as well as the reliable detection of
very long fiber bundles, remains a technical challenge. Functional
MRI is subject to susceptibility artifacts, especially in baso-temporal
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
substantially reconfigure (41) within a few hundred milliseconds. In
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 que stions for future inquiry.
Extraction and Topology of Structural Networks.
protocol was reviewed and approved by the Institutional Review Board at the
University of Lausanne. After obtaining written informed consent in accordance
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-
tion T1-weighted gradient echo sequence was acquired in a matrix of 512 ⫻ 512 ⫻
128 voxels of isotropic 1-mm resolution.
Diffusion spectrum was performed using a diffusion-weighted single-shot
echo planar imaging sequence (TR ⫽ 4,200 ms; TE ⫽ 89 ms) encoding 129 diffusion
directions over a hemisphere. The maximum diffusion gradient intensity was 80
mT/m, the gradient duration
was 32.5 ms, and the diffusion time ⌬ was 43.5 ms,
yielding a maximal b-value of 9,000 s/mm
. The acquisition matrix was 112 ⫻ 112,
with an in-plane resolution of 2 ⫻ 2 mm. Thirty-six contiguous slices of 3-mm
thickness were acquired in 2 blocks, resulting in an acquisition time of 18 min. The
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
and ﬁnally, ﬁber connectivity was aggregated across all voxels within each of the
998 predeﬁned ROIs. Further details are available in refs. 20 and 34.
The ﬁber strengths produced by the streamline tractography algo-
rithm were exponentially distributed and spanned several orders of magnitude.
Reasoning that interregional physiological efﬁcacies would not span such a large
range, we resampled the ﬁber strengths into a Gaussian distribution as follows:
given N raw data values x
, we generated N random samples r
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
a standard deviation of 0.1 dimensionless units. The empirical results we report in
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
so for analyses in which we compare the effects of SC absence and presence while
controlling for distance (see SI Appendix) we used Euclidean distance. The results
in Fig. 2 remain robust and signiﬁcant when Euclidean distance is used.
Extraction and Topology of Functional Networks.
The same 5
participants were scanned in eyes-closed resting state using a Siemens Trio 3T
Honey et al. PNAS
February 10, 2009
system using a gradient echo EPI sequence (TR ⫽ 2,000 ms, TE ⫽ 30 ms). An axial
plane was used with a ﬁeld of view of 211 ⫻ 211 mm (64 ⫻ 64 voxels, each 3.3 ⫻
3.3 mm in-plane). Thirty-ﬁve slices of 3-mm thickness with a 0.3-mm gap were
acquired. All participants were scanned twice on separate days (scan 1 ⫽ 20 min,
scan 2 ⫽ 15 min). Scan 1 and 2 rsFC were averaged for Fig. 3 and for some SI
Appendix data as indicated. Participants were instructed to keep their eyes closed
and to remain alert.
Signal Preprocessing and Correlations.
Raw BOLD signals were registered and
resampled onto the b
image of the diffusion scan using rigid-body registration
(SPM5, www.ﬁl.ion.ucl.ac.uk/spm). Following slice-time correction BOLD time
series were then computed for each of the 998 ROIs by averaging across all voxels
within the ROI mask. ROI BOLD time series were then piecewise-linearly de-
trended (every 50 s) and mean cortical, ventricular, and white matter signals were
regressed from each time series. The results we report are essentially unchanged
if we regress out only the white matter and ventricular signals, and not the global
mean. Finally, Pearson correlations were calculated between all ROI-pairs. Al-
though the data and ﬁgures shown in this article are based on the raw correlation
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
according to an automated landmark-based registration algorithm (23). The 998
ROIs were chosen to provide a roughly uniform tiling of the cerebral cortex (each
ROI ⬇ 1.5 cm
) 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-
lated using the ROI time series and then down-sampled to the 66-region map by
averaging across all ROIs with a region.
When averaging SC, structural connections were deemed absent overall if they
were absent in more than 3 participants (high resolution) or more than 1 partic-
ipant (low resolution). The SC map for Participant A was an average of 2 separate
DSI scans (20).
Computational Model. Neuronal population dynamics were simulated at 0.2-ms
resolution for 16 min using a system of 998 neural masses with coupling strengths
linearly proportional to the resampled ﬁber strengths at each edge. Each neural
mass represents a population of densely interconnected excitatory and inhibitory
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.
Note Added in Proof. Another article has reported correlated rsFC and SC across
the whole brain (53).
ACKNOWLEDGMENTS. We thank Van Wedeen for helpful comments. C.J.H. and
O.S. were supported by the J.S. McDonnell Foundation. P.H., L.C., X.G., J.-P.T., and
R.M. were supported by a grant for interdisciplinary biomedical research of the
University of Lausanne, the Department of Radiology of University Hospital
Center in Lausanne, the Center for Biomedical Imaging of the Geneva–Lausanne
Universities, and Ecole Polytechnique Fe´de´ rale de Lausanne, as well as grants
from the foundations Leenaards and Louis-Jeantet and the Swiss National Science
1. Gusnard DA, Raichle ME (2001) Searching for a baseline: functional imaging and the
resting human brain. Nat Rev Neurosci 2:685– 694.
2. Friston KJ (1994) Functional and effective connectivity in neuroimaging: A synthesis. Hum
Brain Mapp 2:56 –78.
3. Hampson M, Driesen NR, Skudlarski P, Gore JC, Constable RT (2006) Brain connectivity
related to working memory performance. J Neurosci 26:13338 –13343.
4. Greicius MD, Menon V (2004) Default-mode activity during a passive sensory task: uncou-
pled from deactivation but impacting activation. J Cogn Neurosci 16:1484 –1492.
5. Bartels A, Zeki S (2005) Brain dynamics during natural viewing conditions–a new guide for
mapping connectivity in vivo. Neuroimage 24:339 –349.
6. Vincent JL, et al. (2006) Coherent spontaneous activity identiﬁes a hippocampal-parietal
memory network. J Neurophysiol 96:3517–3531.
7. Raichle ME, et al. (2001) A default mode of brain function. Proc Natl Acad Sci USA
8. Greicius MD, Krasnow B, Reiss AL, Menon V (2003) Functional connectivity in the resting
brain: a network analysis of the default mode hypothesis. Proc Natl Acad Sci USA
9. Fox MD, Raichle ME (2007) Spontaneous ﬂuctuations in brain activity observed with
functional magnetic resonance imaging. Nat Rev Neurosci 8:700⫺711.
10. Guye M, Bartolomei F, Ranjeva JP (2008) Imaging structural and functional connectivity:
towards a uniﬁed deﬁnition of human brain organization? Curr Opin Neurol 24:393– 403.
11. He BJ, Shulman GL, Snyder AZ, Corbetta M (2007) The role of impaired neuronal commu-
nication in neurological disorders. Curr Opin Neurol 20:655– 660.
12. Greicius M (2008) Resting-state functional connectivity in neuropsychiatric disorders. Curr
Opin Neurol 24:424 –430.
13. Damoiseaux JS, et al. (2006) Consistent resting-state networks across healthy participants.
Proc Natl Acad Sci USA 103:13848 –13853.
14. Passingham RE, Stephan KE,Ko¨ tter R (2002)The anatomical basis of functionallocalization
in the cortex. Nat Rev Neurosci 3:606 –616.
15. Vincent JL, et al. (2007) Intrinsic functional architecture in the anaesthetized monkey
brain. Nature 447:83– 86.
16. Mantini D, Perrucci MG, Del Gratta C, Romani GL, Corbetta M (2007) Electrophysiological
signatures of resting state networks in the human brain. Proc Natl Acad Sci USA
17. Cohen AL, et al. (2008) Deﬁning functional areas in individual human brains using resting
functional connectivity MRI. Neuroimage 41:45–57.
18. Rykhlevskaia E, Gratton G, Fabiani M (2008) Combining structural and functional neuro-
imaging data for studying brain connectivity: a review. Psychophysiology 45:173–187.
19. Koch MA, Norris DG, Hund-Georgiadis M (2002) An investigation of functional and
anatomical connectivity using magnetic resonance imaging. Neuroimage 16:241–250.
20. Hagmann P, et al. (2008) Mapping the structural core of human cerebral cortex. PLoS Biol
21. Breakspear M, Terry J, Friston K (2003) Modulation of excitatory synaptic coupling facili-
tates synchronization and complex dynamics in a biophysical model of neuronal dynamics.
Network: Computation in Neural Systems 14:703–732.
22. Honey CJ, Ko¨ tter R, Breakspear M, Sporns O (2007) Network structure of cerebral cortex
shapes functional connectivity on multiple time scales. Proc Natl Acad Sci USA 104:10240 –
23. Desikan RS, et al. (2006)An automated labeling system forsubdividing the human cerebral
cortex on MRI scans into gyral based regions of interest. Neuroimage 31:968 –980.
24. Kaiser M, Hilgetag CC (2004) Modelling the development of cortical systems networks.
25. Lewis JD, Theilmann RJ, Sereno MI, Townsend J (2008) The relation between connection
length and degree of connectivity in young adults: A DTI analysis. Cereb Cortex (Epub
ahead of print).
26. Salvador R, et al. (2005) Neurophysiological architecture of functional magnetic resonance
images of human brain. Cereb Cortex 15:1332–1342.
27. Rubino D, Robbins KA, Hatsopoulos NG (2006) Propagating waves mediate information
transfer in the motor cortex. Nat Neurosci 9:1549 –1557.
28. Ermentrout GB, Kleinfeld D (2001) Traveling electrical waves in cortex: insights from phase
dynamics and speculations on a computational role. Neuron 29:33– 44.
29. Shmueli K, et al. (2007) Low-frequency ﬂuctuations in the cardiac rate as a source of
variance in the resting-state fMRI BOLD signal. Neuroimage 38:306 –320.
30. Zarahn E, Aguirre GK, D’Esposito M (1997) Empirical analyses of BOLD fMRI statistics. I.
Spatially unsmoothed data collected under null-hypothesis conditions. Neuroimage
31. Fox MD, et al. (2005) The human brain is intrinsically organized into dynamic, anticorre-
lated functional networks. Proc Natl Acad Sci USA 102:9673–9678.
32. Parvizi J, Van Hoesen GW, Buckwalter J, Damasio A (2005) Neural connections of the
posteriomedial cortex in the macaque. Proc Natl Acad Sci USA 103:1563–1568.
33. Ghosh A, Rho Y, McIntosh AR, Kotter R, Jirsa VK (2008) Noise during rest enables the
exploration of the brain’s dynamic repertoire. PLoS Comput Biol 4:e1000196.
34. Hagmann P, et al. (2007) Mapping human whole-brain structural networks with diffusion
MRI. PLoS ONE 2:e597.
35. Iturria-Medina Y, Sotero RC, Canales-Rodriguez EJ, Aleman-Gomez Y, Melie-Garcia L
(2008) Studying the human brain anatomical network via diffusion-weighted MRI and
graph theory. NeuroImage 40:1064 –1076.
36. Gong G, et al. (2008) Mapping anatomical connectivity patterns of human cerebral cortex
using in vivo diffusion tensor imaging tractography. Cereb Cortex 10.1093/cercor/bhn102.
37. Quigley M, et al. (2003) Role of the corpus callosum in functional connectivity. Am J
Neuroradiol 24:208 –212.
38. Putnam MC, Wig GS, Grafton ST, Kelley WM, Gazzaniga MS (2008) Structural organization
of the corpus callosum predicts the extent and impact of cortical activity in the nondomi-
nant hemisphere. J Neurosci 28:2912–2918.
39. Johnston JM, et al. (2008) Loss of resting interhemispheric functional connectivity after
complete section of the corpus callosum. J Neurosci 28:6453– 6358.
40. Uddin LQ, et al. (2008) Residual functional connectivity in the split-brain revealed with
resting-state functional MRI. Neuroreport 19:703–709.
41. Bassett DS, Meyer-Lindenberg A, Achard S, Duke T, Bullmore E (2006) Adaptive recon-
ﬁguration of fractal small-world human brain functional networks. Proc Natl Acad Sci USA
42. Achard S, Salvador R, Whitcher B, Suckling J, Bullmore E (2006) A resilient, low-frequency,
small-world human brain functional network with highly connected association cortical
hubs. J Neurosci 26:63–72.
43. Park C-H, Kim SY, Kim Y-H, Kim K (2008) Comparison of the small-world topology between
anatomical and functional connectivity in the human brain. Physica A 387:5958 –5962.
44. Kaiser M (2007) Brain architecture: a design for natural computation. Phil Trans R Soc A
45. Hagmann P (2005) From diffusion MRI to brain connectomics. PhD Dissertation No. 3230,
Ecole Polytechnique Fe´de´ rale de Lausanne.
46. Vanhatalo S, et al. (2004) Infraslow oscillations modulate excitability and interictal epi-
leptic activity in the human cortex during sleep. Proc Natl Acd Sci USA 101:5053–5057.
47. He BJ, Snyder AZ, Zempel JM, Smyth MD, Raichle ME (2008) Electrophysiological correlates
of the brain’s intrinsic large-scale functional architecture. Proc Natl Acad Sci USA
48. Greicius MD, Supekar K, Menon V, Dougherty RF (2009) Resting-state functional connec-
tivity reﬂects structural connectivity in the default mode network. Cereb Cortex 19:72⫺78.
49. Buckner RL, Andrews-Hanna JR, Schacter DL (2008) The brain’s default network: anatomy,
function, and relevance to disease. Ann N Y Acad Sci 1124:1–38.
50. Sotero RC, Trujillo-Barreto NJ (2008) Biophysical model for integrating neuronal activity,
EEG, fMRI and metabolism. Neuroimage 39:290 –309.
51. Izhikevich EM, Edelman GM (2008) Large-scale model of mammalian thalamocortical
systems. Proc Natl Acad Sci USA 105:3593–3598.
52. Wedeen VJ, Hagmann P, Tseng WY, Reese TG, Weisskoff RM (2005) Mapping complex
tissue architecture with diffusion spectrum magnetic resonance imaging. Magn Reson
53 Skudlarski P, et al. (2008) Measuring brain connectivity: Diffusion tensor imaging
validates resting state temporal correlations. NeuroImage 43:554 –561.
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0811168106 Honey et al.