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INVESTIGACIÓN

Using structural connectivity to augment
community structure in EEG
conectividad funcional

Katharina Glomb 1, Emeline Mullier1, Margherita Carboni2,3, Maria Rubega4,
Giannarita Iannotti3, Sebastien Tourbier1, Martin Seeber3,
Serge Vulliemoz2, and Patric Hagmann1

1Connectomics Lab, Department of Radiology, University Hospital of Lausanne and University of Lausanne,
Lausanne (CHUV-UNIL), Vaud, Suiza
2EEG and Epilepsy, Neurología, University Hospitals of Geneva and University of Geneva, Geneva, Suiza
3Functional Brain Mapping Lab, Department of Fundamental Neurosciences, University of Geneva, Geneva, Suiza
4Department of Neurosciences, University of Padova, Padova, Italia

un acceso abierto

diario

Palabras clave: Conectividad cerebral, EEG, Resting state, Structure-function-relationship

ABSTRACTO

Recientemente, EEG recording techniques and source analysis have improved, making it feasible to
tap into fast network dynamics. Todavía, analyzing whole-cortex EEG signals in source space is
not standard, partly because EEG suffers from volume conduction: Conectividad funcional
(FC) reﬂecting genuine functional relationships is impossible to disentangle from spurious FC
introduced by volume conduction. Aquí, we investigate the relationship between white
matter structural connectivity (CAROLINA DEL SUR) and large-scale network structure encoded in EEG-FC.
We start by conﬁrming that FC (power envelope correlations) is predicted by SC beyond the
impact of Euclidean distance, in line with the assumption that SC mediates genuine FC.
We then use information from white matter structural connectivity in order to smooth the
EEG signal in the space spanned by graphs derived from SC. Thereby, FC between nearby,
structurally connected brain regions increases while FC between nonconnected regions
remains unchanged, resulting in an increase in genuine, SC-mediated FC. We analyze the
induced changes in FC, assessing the resemblance between EEG-FC and volume-conduction-
free fMRI-FC, and ﬁnd that smoothing increases resemblance in terms of overall correlation
and community structure. This result suggests that our method boosts genuine FC, un
outcome that is of interest for many EEG network neuroscience questions.

RESUMEN DEL AUTOR

en este estudio, we combine high-density EEG recorded during resting state with white matter
connectivity obtained from diffusion MRI and ﬁber tracking. We leverage the additional
information contained in the structural connectome towards augmenting the source-level
EEG functional connectivity. En particular, it is known—and conﬁrmed in this study—that the
activity of brain regions that possess a direct anatomical connection is, on average, más
strongly correlated than that of regions that have no such direct link. We use the structural
connectome to deﬁne a graph and smooth the source-reconstructed EEG signal in the space
spanned by this graph. We compare the resulting “ﬁltered” signal correlation matrices with
those obtained from fMRI and ﬁnd that such “graph ﬁltering” improves the agreement
between EEG and fMRI functional connectivity structure. This suggests that structural
connectivity can be used to attenuate some of the limitations imposed by volume conduction.

Citación: Glomb, K., Mullier, MI.,
Carboni, METRO., Rubega, METRO., Iannotti, GRAMO.,
Tourbier, S., … Hagmann, PAG. (2020).
Using structural connectivity to
augment community structure in EEG
conectividad funcional. Red
Neurociencia, 4(3), 761–787.
https://doi.org/10.1162/netn_a_00147

DOI:
https://doi.org/10.1162/netn_a_00147

Supporting Information:
https://doi.org/10.1162/netn_a_00147

Recibió: 5 Noviembre 2019
Aceptado: 12 Puede 2020

Conflicto de intereses: Los autores tienen
declaró que no hay intereses en competencia
existir.

Autor correspondiente:
Katharina Glomb
katharina.glomb@gmail.com

Editor de manejo:
Richard Betzel

Derechos de autor: © 2020
Instituto de Tecnología de Massachusetts
Publicado bajo Creative Commons
Atribución 4.0 Internacional
(CC POR 4.0) licencia

La prensa del MIT

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Combining structural and functional connectivity in EEG

EEG source imaging:
The projection of EEG signals
recorded on the scalp into the gray
matter by means of mathematical
modelos.

Conectividad funcional:
Statistical relationship (Por ejemplo,
correlation or coherence) entre
time series recorded from pairs of
regiones del cerebro (parcels).

Structural connectivity:
Using speciﬁc imaging techniques,
pathways of axon bundles
connecting brain regions (parcels)
over large distances are traced and
summarized in SC matrices.

INTRODUCCIÓN

Electroencephalography (EEG) measures neural signals directly (Buzsáki, Anastassiou, & Koch,
2012) on a timescale of milliseconds, fast enough to be relevant for neural events. In MEG
and fMRI, the study of functional connectivity (FC) with the tools of whole-brain network neu-
roscience has yielded a multitude of important and interesting insights (see Bassett & despreciar,
2017, para una revisión). Concurring ﬁndings show that FC between regions of interest (ROI)/
sources located in the gray matter is in part shaped by anatomical connections of the structural
conectividad (CAROLINA DEL SUR; obtained from dMRI and ﬁber tracking), such that the strength of SC (ﬁber
count, density) is predictive to some degree of the strength of FC (correlation, coherencia, etc.;
Abdelnour, Dayán, Devinsky, Thensen, & Raj, 2018; Atasoy, Donnelly, & Pearson, 2016;
Cabral et al., 2014; Damoiseaux & Greicius, 2009; Deco et al., 2013; Glomb, Ponce-Alvarez,
Gilson, Ritter, & decoración, 2017; Goñi et al., 2014; Hagmann et al., 2008; Honey et al., 2009;
Meier et al., 2016; Tewarie et al., 2019, 2014; Vincent et al., 2007). This ﬁnding has been
shown to extend to EEG data on the source level (es decir., signals recorded on the scalp projected
into the gray matter) using analytical (Chu et al., 2015; Wirsich et al., 2017) and modeling
approaches (Bhattacharya, Coyle, & Maguire, 2011; de Haan, Mott, van Straaten, Scheltens,
& estampar, 2012; Finger et al., 2016; Pons, Cantero, Atienza, & Garcia-Ojalvo, 2010; Ponten,
Daffertshofer, Hillebrand, & estampar, 2010; van Dellen et al., 2013). The main hurdle when try-
ing to understand EEG network architecture and dynamics is signal leakage due to volume
conduction, which obscures genuine functional relationships between sources in the brain:
Additionally to the low spatial resolution (Buzsáki et al., 2012; Schoffelen & Bruto, 2009;
Srinivasan, Invierno, Ding, & Núñez, 2007) and signal-to-noise ratio intrinsic to the EEG signal,
the interaction of the electric ﬁeld with the tissue creates “sham” functional connections whose
strengths depend on the Euclidean distance between locations. In order to circumvent these
problemas, it has been suggested that zero-lag statistical dependencies should be removed al-
together from FC analysis since signal leakage is instantaneous, resulting in measures such as
imaginary coherence (Nolte et al., 2004) and phase lag index (estampar, Nolte, & Daffertshofer,
2007). Contrary to this, it has been pointed out that zero-lag statistical dependencies still carry
meaningful information about ongoing activity (Pascual-Marqui et al., 2017; Tognoli & Kelso,
2009; Uhlhaas et al., 2009), and may therefore be particularly important for data recorded
during resting state. Además, approaches exist that orthogonalize the time series, remov-
ing common dependencies between sources (Brookes, lana rica, & Barnes, 2012; Colclough,
Brookes, Herrero, & lana rica, 2015; Hipp, Hawellek, Corbetta, Siegel, & ángel, 2012; Wens
et al., 2015).

en este estudio, we propose an approach that incorporates additional information from SC
into EEG functional connectivity on the source level. We ﬁrst replicate the previous ﬁnding
(Chu et al., 2015; Finger et al., 2016; Siems, Pape, Hipp, & Siegel, 2016; Wirsich et al., 2017)
that SC partially shapes FC in EEG, beyond the impact of Euclidean distance induced by vol-
ume conduction. Después, we use additional information in the SC to augment the EEG
functional signal by applying a low-pass ﬁlter (or smoothing procedure) in the space spanned
by the SC graph. The underlying motivation is that both SC and FC decay with increasing
Euclidean distance. From an evolutionary standpoint, it makes sense for functionally related
regions to be close together (Tomasi, Wang, & Volkow, 2013). Como resultado, it is impossible
to disentangle the contributions of volume conduction and genuine FC mediated by SC to a
statistical dependency measured between two brain regions. Sin embargo, if one assumes that
genuine FC is mediated by SC, and therefore genuine FC is higher between brain regions that
are directly anatomically connected, increasing the impact of SC would also increase the con-
tribution of genuine FC relative to FC generated by volume conduction. A similar approach has

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Combining structural and functional connectivity in EEG

previously been shown to improve source estimation in EEG (Hammond, Scherrer, & Warﬁeld,
2013).

We use an fMRI-FC acquired completely independently of the EEG dataset in order to deter-
mine whether our ﬁltering procedure leads to improvements in terms of macroscopic network
structure encoded in the FC. Numerous studies have shown that the macroscopic network
structure is, on a coarse level, similar between fMRI and EEG (Britz, Van De Ville, & Michel,
2010; Coito, Michel, Vulliemoz, & Plomp, 2019; Liu, Ganzetti, Wenderoth, & Mantini, 2018;
Musso, Brinkmeyer, Mobascher, Warbrick, & Winterer, 2010). These networks have been
demonstrated to be relevant on several spatial and temporal scales of different recording tech-
niques (Brookes et al., 2011; Kucyi et al., 2020; Liu, Farahibozorg, Porcaro, Wenderoth, &
Mantini, 2017). We hypothesize that, if our ﬁltering procedure indeed strengthens genuine FC
mediated by SC, we should see that the network structure encoded in the EEG-FCs becomes
more similar to that encountered in fMRI, a recording technique that is not impacted by vol-
ume conduction; we quantify this by testing whether the EEG-FCs computed from ﬁltered time
courses are more similar to fMRI-FC than the original, unﬁltered signals, both overall and by ex-
plicitly analyzing the FC matrices’ community structure. Our results suggest that incorporating
information from the SC by means of graph ﬁltering leads to a large-scale network structure in
EEG-FC that is more similar to known canonical resting-state networks, making our approach a
possible alternative to other methods that aim at correcting for volume conduction, especially
for the study of large-scale functional networks.

RESULTADOS

SC Provides Additional Predictive Power for EEG-FC

Our goal is to use the structural connectivity matrix to boost functional connectivity that is
mediated by white matter anatomical connections in source-level EEG resting-state time series
recorded from N = 18 subjects (ver figura 1 for an illustration of our approach).

One of our main assumptions is that genuine FC is in part mediated by SC (Chu et al., 2015;
Finger et al., 2016; Wirsich et al., 2017). To test this assumption, we ﬁrst show that SC can
predict FC beyond the common dependence of FC and SC on Euclidean distance. We test
this assumption by ﬁtting a stepwise general linear model (GLM) in order to quantify how well
the following measures predict EEG-FCs computed as envelope correlations from three typical
EEG frequency bands (alfa: 8–13 Hz, beta: 13–30 Hz, gamma: 30–40 Hz), averaged over
all subjects:

(1) SC in the form of search information Goñi et al. (2014), referred to as SCSI, a measure
that is derived from ﬁber counts and that is nonzero for all connections, yielding a con-
nectivity matrix that is dense just like the FC matrix (see Figure S1 in the Supporting
Información); the intuitive interpretation of search information is that it measures how
“hidden” the shortest path between two ROIs is. Note that search information and ﬁber
count are roughly inversely proportional.
(2) Euclidean distance (ED) between ROI centers.
(3) Relative regional variance (es decir., the variance of each ROI time course, normalized such
that the maximum variance in each subject equals 1) as an estimate of signal-to-noise
ratio.

(4) ROI size (number of voxels in the parcellation).

The third and fourth predictors are control variables for possible confounds. Tenga en cuenta que
in each case, we predict a dependent univariate variable—the EEG-FC—with an independent

763

Graph ﬁltering/smoothing:
A weighted average of a network
node’s signal and the signals of its
neighbors as deﬁned by the graph.

Envelope correlations:
A type of functional connectivity that
considers correlations of slow
ﬂuctuations only.

Parcellation:
A partition of the brain into
functionally and anatomically more
or less homogeneous brain regions,
or parcels.

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Combining structural and functional connectivity in EEG

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Illustration of general approach.

Cifra 1.
(A) Brain regions are given by the Lausanne 2008
parcellation (Hagmann et al., 2008) (fila superior). Diffusion MRI and ﬁber tracking reveal ﬁber bundles
that exist between these regions, and are summarized in the structural connectivity matrix (abajo
izquierda; brain regions from above are color coded). The graph used for ﬁltering is deﬁned by nodes
corresponding to the parcellation’s brain regions (color coded) and edges corresponding to the ﬁber
bundles in the SC matrix (bottom right; lengths of edges are approximately inversely proportional
to the weight in the structural connectivity matrix). (B) The graph deﬁned by parcellation and SC
does not change over time. EEG signals that do vary over time are conceptualized as activation
strengths of the nodes of the graph. Signals are thought to propagate along the ﬁber bundles, eso
es, the edges, to neighboring nodes.

univariate variable, such that each pair of brain regions is a sample (es decir., tenemos (N×N−N)/2
muestras). We analyze how well the independent variables can predict the FC in two different
maneras: Por un lado, we use each variable as the only predictor variable (plus intercept;
blue bars in Figure 2; “single-variable model”). En el otro, we test their predictive power
when they are entered progressively into a GLM that includes ﬁrst-order interaction terms (o-
ange curves in Figure 2; “full model”). The latter case allows us to quantify the additional
predictive power that each variable has, given all other predictors. This is important because
the predictors are not independent of each other; most prominently, there is a three-way de-
pendence between SC, Euclidean distance, and FC, such that both SC and FC decay with
increasing Euclidean distance.

Figure 2A shows the results in terms of explained variance for the EEG-FCs and for compar-
ison, for an fMRI-FC (average pairwise correlations over 88 subjects; see the Methods section
for details; see Table S1 in the Supporting Information for detailed results of the GLM analysis).
The correlation between the average EEG-FCs and the fMRI-FC is around 0.50 for all three
bands (alfa, beta, gamma).

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Combining structural and functional connectivity in EEG

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Cifra 2. Predicting functional from structural connectivity. (A) Stepwise general linear model results for EEG alpha, beta, and gamma band,
and for fMRI, using Euclidean distance (ED), relative regional variance (RRV), structural connectivity (CAROLINA DEL SUR; search information), and ROI size
(number of voxels) as predictors. Only signiﬁcant predictors are shown, in the order in which they were entered into the model (see the
Methods section for details). Blue bars: Variance explained when variables are used as the only predictor in separate “single-variable” GLMs.
Orange curves and crosses: Cumulative explained variance achieved when using all variables up to the variable corresponding to this data
punto (es decir., the variable in question and all variables to the left of the data point). (B) Comparison between average EEG-FC values for pairs that
are connected by SC (“SC+”) and those that are not (“SC-”). The samples that are compared are matched in their ED distribution to control
for the fact that pairs that are connected tend to be closer together than those that are not. Stars mark signiﬁcant differences according to the
Wilcoxon signed-rank test at alpha = 0.05 (Bonferroni-corrected for multiple comparisons).

Figure 2A shows that ED is the strongest predictor in both EEG and fMRI. This is true for both
the single-variable models (greatest explained variance as indicated by blue bars) and the full
modelo (as indicated by the fact that they are the variables that are entered ﬁrst into the model).
Sin embargo, the variance explained by ED is much higher in EEG than in fMRI, a saber 0.55 en
EEG (alpha band; other bands are similar, full list is in Table S1 in the Supporting Information)
y 0.18 in fMRI. This is due to the effect of volume conduction, which introduces spurious
correlations dependent on ED in the case of EEG-FC.

When using SCSI as the only predictor, we ﬁnd that the dependency of FC on SCSI is very
similar in both modalities (r2 of SCSI alone 0.14 in both modalities). In both cases, FC values
are high between close-by pairs of brain regions (small ED; see Figure S2A in the Supporting
Información). For fMRI, there are also highly correlated pairs that are separated by an inter-
mediate distance, and close-by pairs that are barely or not at all correlated. A diferencia de, para
EEG, all faraway pairs of ROIs have low correlations and all close-by pairs have high corre-
laciones. We checked for which connections the prediction of FC by SCSI was worst, eso es,

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Combining structural and functional connectivity in EEG

had the largest residuals (Figure S2B in the Supporting Information). We found that for fMRI,
the largest errors occur on the secondary diagonal, replicating the well-known result that in-
terhemispheric connections are underestimated in the SC. In EEG, this does not contribute as
much to the unexplained variance, as the FC between homotopic regions is low compared
with FC between close-by pairs of regions. En resumen, while the variance explained by the
SCSI is the same in both modalities, the structure of this dependency is different.

In both cases, SCSI explains an additional 3–4% of the variance (Table S1 in the Supporting
Información) after regressing out Euclidean distance. For fMRI, some connections with inter-
mediate distances remain underestimated after adding SCSI as a predictor, again related to
interhemispheric connections (Figure S2B, right panel). For EEG, the most severely underesti-
mated FC values are related to small distances, indicating that neither Euclidean distance nor
SCSI can by themselves account for some of the large EEG-FC values between nearby pairs
of regions. Note that the actual contribution of SCSI is likely to be higher than 3–4%, as SC
strength is itself dependent on Euclidean distance (two regions that are close together are more
likely to be connected by white matter tracts; furthermore, short tracts are more easily traced
by ﬁber tracking algorithms; jones, 2010). En efecto, because of this mutual dependence, el
actual contribution of SCSI cannot be estimated using this approach.

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Además, a signiﬁcant positive interaction term between ED and SCSI contributes to the
prediction in both fMRI and EEG. The correlation between these two variables (ED and SCSI)
es 0.48, in line with previous ﬁndings (Wirsich et al., 2017). Since SC and SCSI are negatively
correlacionado (see the Methods section), this translates to two interpretations: ED has less of an
impact on the FC between ROI pairs that have a strong SC connection (high weight in the SC
matrix); and the strength of the SC connection has less of an impact on the FC between ROI
pairs that are far apart from each other (high ED).

A simple prediction from the hypothesis that FC is shaped by SC is that ROI pairs that are
connected via white matter tracts should exhibit stronger FC than those that are not (Chu et al.,
2015). In order to control for the common dependence of FC and SC on Euclidean distance,
we compare average FC values over subsamples of pairs of ROIs that are matched in their
Euclidean distance distribution. Figure 2B shows that even in those matched subsamples, allá
is indeed a signiﬁcant difference between the mean FC values (Wilcoxon signed-rank test at
alfa = 0.05, Bonferroni-corrected for multiple comparisons) between structurally connected
and unconnected ROI pairs.

Graph Filtering Increases Resemblance Between EEG-FC and fMRI-FC

Building on the ﬁnding that SC shapes EEG-FC beyond the impact of ED, we use the fact that
the EEG data live on a graph deﬁned by the SC (Cifra 1). En el siguiente, we perform spatial
smoothing, or low-pass ﬁltering, in graph space. This means that the activity in one node of
the graph—an ROI—is smoothed by computing a weighted average of the ROI’s activity and
the activity of its nearest neighbors, eso es, nodes with which it is anatomically connected:

ˆxi(t) = xi(t) + G ∑N

j=1 cijxj

(t).

Aquí, cij is the entry in the SC that corresponds to the pair of regions i and j, and G is the
scalar “ﬁlter weight” that scales how much impact node i’s neighbors j have on the activity of i.
This will increase the effect shown in Figure 2B: Connected nodes’ activity will become more
similar and unconnected nodes’ activity will become less similar. Since spurious correlations
depend only on Euclidean distance, but not on the SC per se, this would correspond to an
increase of genuine FC relative to spurious FC.

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Combining structural and functional connectivity in EEG

Cifra 3. All SCs from which graphs for ﬁltering are derived. From left to right: (1) SC derived
from ﬁber tracking, averaged over subjects (log is used only for visualization purposes); (2) CAROLINA DEL SUR
derived from Euclidean distances by using the distances as negative exponents; (3) SC derived from
Euclidean distances (as SC 2), but masking the distances by using present connections as in SC 1;
(4) SC derived from Euclidean distances (as SC 2), but keeping only shortest distances such that the
density is the same as in the left and middle right panels.

We ﬁlter the single epoch, source-level activity xi(t) of each ROI using the above formula
and compute FC matrices from the ﬁltered data ˆxi(t) como antes (envelope correlations in alpha,
beta, and gamma frequency bands). We use four different graphs (Cifra 3, from left to right):

(1) The SC (number of ﬁbers) sí mismo, averaged across subjects according to Betzel, Griffa,

Hagmann, and Miši´c (2019). This graph has a connection density of 25%.

(2) A graph derived from Euclidean distances, setting connection weights with exp (−k ∗ ED),

where the weight k just serves to scale the distribution such that the multiplication of the
graph weights with the ﬁlter weights will result in effective weights in the same range as
for the other SCs. This is a dense graph and will be referred to as “ED full.”

(3) A graph derived from Euclidean distances, but exactly matching the SC in terms of ex-
isting and absent ﬁbers. This means that the connections are the same as for SC 1, pero
the weights are set as in SC 2 instead of the ﬁber count. This graph will be referred to as
“ED match.”

(4) A graph derived from Euclidean distances, but preserving the density of SCs 1 y 3. Este
means keeping the connections that correspond to the smallest EDs up to a threshold,
which leads to the same connection density as in SC 1 (and SC 3). We include this graph
because otherwise, if matrices 1 o 3 outperform matrix 2, this could just be due to the
difference in connection density. This graph will be referred to as “ED dens.”

After ﬁltering, EEG-FCs are computed as for the unﬁltered data. As expected, the ﬁltered FCs
become more similar to their respective SCSI (Pearson correlation between EEG-FCs and SCSI),
and the difference in average correlation between structurally connected versus unconnected
ROI pairs increases (see Figures S3 and S4 in the Supporting Information).

To validate our results, we compare our EEG-FCs with fMRI-FC (obtained by averaging over
88 subjects; see the Methods section for details) by computing the Pearson correlation between
the two matrices for each subject. The goal is to assess whether the changes in FC induced
by graph ﬁltering result in a change in the network/community structure encoded in the FC
that is in line with known functional networks (Britz et al., 2010; Coito et al., 2019; Liu et al.,
2018; Musso et al., 2010). We obtain a comparison for each ﬁlter weight G and each of the
four graphs described above and shown in Figure 3.

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Combining structural and functional connectivity in EEG

Cifra 4. Correlation between EEG and fMRI functional connectivity. (A) Fit (z-transformed cor-
relation) between the EEG-FCs (beta band) computed from time courses with different ﬁlter weights
(GRAMO) and the fMRI-FC. The shaded regions mark the 95% intervalo de confianza. (B) Boxplots summariz-
ing results of the Wilcoxon signed-rank test comparing individuals’ maximum ﬁts (shown in panel
A) across versions of the SC as well as to the baseline correlation between unﬁltered EEG-FCs and
fMRI-FCs. Black bars mark signiﬁcant differences. Red lines mark the median, each black dot marks
the value for one subject. Note that we did not compare the medians, but the individual differences
(see the Methods section).

Figure 4A shows that correlations between the two matrices obtained from the two modal-
ities increase as hypothesized (results are shown for beta band; alpha and gamma are similar
[not shown]). The graph that reaches the highest maximum correlations between EEG-FC and
fMRI-FC is the one in which Euclidean distance and SC are combined by masking the weights
derived from Euclidean distances with the nonzero connections given by the SC (“ED match;"
Wilcoxon signed-rank test comparing the correlation coefﬁcients of each subject, pag < 0.05 Bonferroni corrected). The mean correlation increases from 0.42 to 0.51 at a ﬁlter weight of G = 100, corresponding to a 23% increase (increase computed based on the Fisher z-transformed values as shown in Figures 4A and 4B: 0.46 and 0.56, respectively), while the increase when using the SC itself is only from 0.42 to 0.44 (Fisher z-transformed values: increase from 0.46 to 0.48). Figure 5 shows the original EEG-FC (beta band) and the EEG-FC derived from ﬁltered data with G = 100. In order to better interpret these results, we use a control SC in which connections are randomized while preserving the degree distribution and density (Figure S5 in the Supporting Information; see the Methods section for details). In this case, the ﬁt between EEG-FC and fMRI-FC increases from 0.42 to 0.44 when using the SC itself, an increase that is almost the same that is achieved with the original matrix, and that remains signiﬁcant (Figure S5B in the Supporting Information; Wilcoxon signed-rank test, p < 0.05 Bonferroni corrected). The remaining three versions of the graph lead to statistically identical increases, that is, in this case, there is no advantage of using the SC-derived mask on the Euclidean distances (“ED match”) over using the full set of Euclidean distances (“ED full”) or the shortest Euclidean distances only (“ED dens”). Note that since randomizing the Euclidean distances is not readily possible (as the resulting geometry would need to be consistent), “ED dens” and “ED full” are identical for the randomized and the original SC. Network Neuroscience 768 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 6 1 1 8 6 7 4 2 8 n e n _ a _ 0 0 1 4 7 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Combining structural and functional connectivity in EEG Figure 5. Comparison between FCs. (A) fMRI-FC (B) and (C) EEG-FCs (beta band) before (B) and after (C) graph ﬁltering with “ED match” and G = 100. All correlations are z-transformed. Taken together, increases in ﬁt due to the SC alone can mostly be attributed to the degree distribution (which is preserved in the random SC). Using a graph in which the real SC is used to mask Euclidean distance-derived weights leads to a signiﬁcant advantage compared with purely Euclidean distance-derived graphs. We further repeat the analysis using FC matrices computed from white Gaussian noise (WGN-FCs; see the Methods section) in order to test how far our results can be explained purely by linear dependencies imposed by the graphs used as ﬁlters. We ﬁnd that the correlation between WGN-FCs that were ﬁltered with the SC and the fMRI-FC reaches a maximum of 0.26 (Figure S6A in the Supporting Information), indicating that ﬁltering white noise with the SC does not explain the association between fMRI-FC and EEG-FCs, where the correlation is 0.42 without any ﬁltering (Figure 4A). The correlation between WGN-FCs and fMRI-FC reaches a value of r = 0.49 (z-transformed value: 0.53) when using only Euclidean distances (dense ED) with G = 500. This is comparable to the optimal ﬁt of r = 0.51 (z-transformed value: 0.56) obtained with empirical EEG-FCs at G = 100 (ED match), but at G = 100, the empirical EEG-FCs clearly outperform the WGN-FCs (r = 0.35). We also checked whether the ﬁt to fMRI can be explained by the fact that EEG-FCs become more similar to WGN-FCs as the ﬁlter weight is increased. At G = 500, the ﬁltered EEG-FCs are very similar to the FCs obtained from ﬁltered WGN (average r = 0.91 [z-transformed value: 1.5], Figure S6B in the Supporting Information). At G = 100, this correlation is r = 0.69 for ED match (z-transformed value: 0.85). As a further comparison, we use the orthogonalization approach described in Colclough et al. (2015) to correct for leakage in the unﬁltered data (Figure S7). We ﬁnd that the correla- tion between fMRI-FCs and EEG-FCs decreases for each subject (Table S3). Furthermore, we repeat our analyses using coherence and imaginary part of coherence (Figures S8 and S9), the latter of which is assumed to remove zero-lag correlations resulting from volume conduction (Nolte et al., 2004). We ﬁnd no advantage of these measures over correlations between power envelopes. Speciﬁcally, the correlation between fMRI-FCs and EEG-FCs computed using this measure is not higher than when using the power envelope correlations (Figure S8A). Network Neuroscience 769 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 6 1 1 8 6 7 4 2 8 n e n _ a _ 0 0 1 4 7 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Combining structural and functional connectivity in EEG High-Quality SCs Are Necessary to Achieve an Increase in Fit We perform the same analysis with two additional SC matrices from different cohorts (see the Methods section for details). The ﬁrst one is obtained from a small cohort with relatively lower quality than the “primary” SC used in the main analysis above, that is, diffusion tensor imag- ing (DTI) was used instead of diffusion spectrum imaging (DSI), as well as a smaller number of subjects (N = 20). The second one consists of the 45 subjects of the Human Connectome Project’s (HCP) “retest” dataset, data of very high quality. When using the lower quality data (Figure S10 in the Supporting Information), there is no additional beneﬁt of using the SC ma- trix as a mask on the matrix of Euclidean distances (ﬁt between EEG-FC and fMRI-FC is the same for “ED full” and “ED match”). However, when using the high-quality HCP SC matrices (Figure S11), ED match performs signiﬁcantly better than the three other graphs, as is the case for the primary SC matrix. This also shows that our results do not depend on the fMRI data and the dMRI data stemming from the same subjects. Figure S12A (in the Supporting Information) illustrates that the primary matrix used in this study, as well as the HCP matrix, possesses a higher density of interhemispheric connections than the DTI-derived matrix (primary: 12%, HCP: 20%, DTI: 9%, see Figure S12). This may be because interhemispheric ﬁbers are found more consistently in the DSI-based datasets (primary and HCP) than in the DTI-based one, but could also be attributed to variations in the tractog- raphy techniques (deterministic versus probabilistic, seeding from white matter versus seeding from gray matter/white matter interface). The absence of some interhemispheric connections leads to high errors in the resulting ﬁltered EEG-FC for the DTI SC matrix (Figure S12B). This shows that our method relies in part on the improvement of interhemispheric FC, an effect that can only be achieved with high-quality diffusion data. Graph Filtering Increases Resemblance Between EEG and fMRI Community Structure In the following, we explore the effect of graph ﬁltering on the EEG-FC structure. To this end, we use FCs averaged over all subjects. First, we consider seed correlations. In order to make correlations comparable, we resample average FCs such that FC values are normally distributed around mean 0 and with a standard deviation of 1. Figure 6 shows the normalized correlations between two seed regions and all other ROIs in the parcellation (i.e., one row/column of the EEG-FC) before and after ﬁltering with the best SC identiﬁed above (“ED match,” G = 100; beta band). We choose these regions because they exhibit the largest overall change in connection weights with other regions (all changes in Figure S13 in the Supporting Information). In both cases, the correlations to the corresponding region on the other side of the brain are increased. In general, the correlation structure of many regions changes considerably (Figure S13), but these changes are hard to interpret on a ROI-by-ROI basis. Therefore, to investigate this further, we extract the community structure (Network communities) of the average EEG-FCs before and after ﬁltering by assessing the probability of any two regions to be assigned to the same community (Figure 7, top row and bottom left). We apply the same procedure to the average fMRI-FC (Figure 7, bottom right). As the ﬁlter weight (G) increases, more values in the “community matrices” tend towards 0 or 1, indicating that the variability in clustering outcomes decreases. Interestingly, also the community assignments derived from the fMRI-FC show some variability, especially for certain frontal and temporal regions. Figure 8A shows one example of community assignments. The main difference between EEG and fMRI is that EEG community structure is dominated by the lobe architecture, whereas in fMRI, we see the robust clustering of frontal with middle temporal and posterior cingulate cortices, reminiscent Network communities: A partition of a network into sets of nodes (here: brain regions) that are more connected (as quantiﬁed by functional/structural connectivity) to each other than to other parts of the network. Network Neuroscience 770 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 6 1 1 8 6 7 4 2 8 n e n _ a _ 0 0 1 4 7 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Combining structural and functional connectivity in EEG Figure 6. Surface renderings of FC before and after ﬁltering. EEF-FC (beta band; correlation) values were resampled from a standard normal distribution in order to linearize them and make them comparable. (A) Seed correlations of region left rostral middle frontal before (top panel) and after (bottom panel) graph ﬁltering. (B) Same as panel A, but for region right superior parietal. of the default mode network (Laird et al., 2009), as well as the symmetry across hemispheres between temporal regions. We quantify the similarity between the community structures in EEG-FCs and fMRI-FCs by taking the rank correlation between each row/column of the “community matrices” (examples for λ = 1.1 in Figure 7). We compute this measure depending on two parameters: (a) the res- olution parameter λ, which controls the spatial resolution of the Louvain algorithm and thus the number of communities; and (b) the ﬁlter weight G. Figure 9A shows the averaged (over ROIs) similarity in community structure. There is a region where the average rank correlation is ∼0.45, that is, for ﬁlter weights between 200 and 1,000 and λ = 1.075. At the same time, Figure 9B shows that with increasing λ, the number of communities also increases: The over- all maximum in average rank correlation is 0.60 at λ = 1.3 and G = 800 (Figure S14), but at this point, we have 27 communities. Because of the coarseness of the parcellation used here, and according to the literature (Yeo et al., 2011), we seek to partition the cortex into as few communities as possible while also achieving a good agreement between the community structures of EEG-FCs and fMRI-FCs. Choosing λ = 1.1 (row indicated in Figures 9A and 9B), the number of communities is 5 and the agreement with the fMRI community structure is 0.45 (at G = 200, 300, or 400; see Figures 9C). The same ﬁt can be achieved at λ = 1.125 and G = 300, but at this point we have 6.5 communities on average. Similarly, without ﬁltering, the correlation is 0.42, but the number of communities is 6. Thus, λ= 1.1 and G = 200, 300, or 400 represents the optimal trade-off between number of communities and community agreement in comparison to other ﬁlter weights, including G = 0. Since Figure 8A provides only an example partition, we plot on the cortex rows/columns of the community matrices in Figure 7 in order to analyze the community structure across all iterations of the clustering, that is, the probability of a speciﬁc ROI to be coassigned to Network Neuroscience 771 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 6 1 1 8 6 7 4 2 8 n e n _ a _ 0 0 1 4 7 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Combining structural and functional connectivity in EEG 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 6 1 1 8 6 7 4 2 8 n e n _ a _ 0 0 1 4 7 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 7. Results of Louvain clustering (“community matrices”). Each matrix shows, for each pair of ROIs, the fraction of repetitions of Louvain clustering (200 rounds, λ = 1.1) that assigned both ROIs to the same community. λ = 1.1 and G = 400 (upper right matrix) are the parameter settings from a region of the parameter space where the agreement between EEG and fMRI community structures were found to be maximal (Figure 9; main text). the same community as each of the other ROIs. We call this the “community behavior” of this ROI. In Figure 8B, we show three ROIs that exhibit a switch in community membership pertaining to three major communities found by the Louvain algorithm: the frontal community, the somatosensory/motor network, and one of the two temporal communities; we do not show the occipital network as it is quite stable. Figure 8B, left panel, shows how the “community behavior” of an example frontal ROI (right lateral orbitofrontal ROI) differs between unﬁltered and ﬁltered EEG-FCs. The most Network Neuroscience 772 Combining structural and functional connectivity in EEG 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 / Figure 8. Effect of ﬁltering on community structure. (A) One result of Louvain clustering commu- nity assignments. For EEG, λ = 1.1, G = 400 for the ﬁltered version. In the legend, * marks com- munities only present in EEG. (B) Surface renderings of the rows/columns of the matrices shown in Figure 7 corresponding to three example ROIs that tend to switch community membership because of ﬁltering. Colors reﬂect the ROIs’ network membership according to the example in panel A. Left: right lateral orbitofrontal ROI; middle: right paracentral lobule; right: right fusiform area. / / / / 4 3 7 6 1 1 8 6 7 4 2 8 n e n _ a _ 0 0 1 4 7 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 conspicuous change that is introduced by the ﬁltering is the establishment of a coherent frontal network that includes orbitofrontal regions, as in fMRI. This can be observed in Figure 8A (blue network) as well as examining the changes in single ROIs displayed in Figure 9D. Figure 8B, middle panel, shows an example from the somatosensory/motor network (right paracentral lobule). This ROI shows a marked improvement in its agreement with fMRI. Namely, before ﬁltering, this ROI is grouped with frontal regions (dark blue network in Figure 8A). Afterwards, it becomes a member of the somatosensory/motor network (orange network in Figure 8A), as is the case in fMRI. However, in contrast to fMRI, a symmetrical network is not established. When using the SC graph for the smoothing procedure, this network is robustly expressed in a certain area of the parameter space (Figures S15 and S16 in the Supporting Information), however, the overall correspondence between EEG-FCs and fMRI-FCs and com- munity structures is much lower at this point (average rank correlation: 0.22). While the visual network is well established even without any ﬁltering (Figure 8A, cyan network, and Figure 9D), temporal regions are mostly grouped because of their anatomical proximity. Figure 8B, right panel, shows how the community behavior of an example tem- poral region (right fusiform area) changes due to ﬁltering. Despite there being a qualitative improvement in that the region switches to a temporal network and decouples from visual Network Neuroscience 773 Combining structural and functional connectivity in EEG 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 6 1 1 8 6 7 4 2 8 n e n _ a _ 0 0 1 4 7 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 9. Quantitative comparison between community structure in EEG and fMRI. (A) Agreement between community structure of EEG-FC and fMRI-FC as measured by average rank correlations between “community matrices” (Figure 7). The black box marks the λ that is shown in panel C. (B) Average number of communities found by the Louvain clustering algorithm. The red box marks the λ that is shown in panel C. (C) Rank correlations and number of communities for λ = 1.1 (marked in the same colors in panels A and B). (D) Rank correlations between rows/columns of “community matrices” (Figure 7) of EEG-FC and fMRI-FC, for λ = 1.1 (marked with colored boxes in panels A and B). regions, there are also many spurious coassignments with other temporal regions that, in total, explain why this region shows no improvement due to ﬁltering. DISCUSSION In this study, we show that additional information in the SC can be used to selectively increase the FC between brain regions that are connected via white matter ﬁbers, leading to a large-scale functional network structure that is more in accordance with canonical resting-state networks (Liu et al., 2017; Yeo et al., 2011). We ﬁrst show that the strength of FC between pairs of regions that are connected via SC is higher than between those pairs that are not, conﬁrming the assumption that both volume conduction and SC contribute to Euclidean distance-dependent functional connectivity. Second, we ﬁnd that using a graph that combines SC and Euclidean distances to smooth functional EEG signals in nearest neighbor graph space results in a higher agreement between fMRI-FC and EEG-FC structure. SC Is Outperformed by Graphs (Partially) Derived from Euclidean Distance The result that a combination of SC and Euclidean distance performs best was contrary to our initial expectation that SC (ﬁber counts) would give the largest improvement because Network Neuroscience 774 Combining structural and functional connectivity in EEG of strengthening of FC between distant pairs of ROIs. SC is correlated with Euclidean dis- tance with r = 0.48, and there exist many pairs of regions that are both nearby in terms of Euclidean distance and strongly connected according to the SC (Figure S2A in the Supporting Information). Thus, strong connections exist between these pairs in all four versions of the graph, and ﬁltering based on any of the four graphs increases the strength of these connections (Figure S4). The increase in ﬁt to the fMRI-FC common to all graphs indicates that despite the fact that these connections are already strong in the EEG-FCs, they are still underestimated compared with fMRI-FC. This is consistent with our rationale that strengthening these connec- tions corresponds to boosting genuine FC mediated by white matter connections. Furthermore, the GLM analysis showed that the third-strongest predictor for fMRI-FC was an interaction between SC and Euclidean distance, explaining why, beyond the commonalities across graphs based on Euclidean distance, the graph containing information from both SC and Euclidean distances outperforms all other graphs. A trivial explanation for the increase in agreement between EEG-FC and fMRI-FC is that graph ﬁltering removes pairwise nonlinear relationships that are only present in EEG but not in fMRI. Indeed, Messé, Rudrauf, Giron, and Marrelec (2015) showed that a generative model of fMRI-FC that takes into account only linear relationships between structurally connected pairs outperformed all other models that included nonlinearities. In order to investigate this possibility, we simulated white Gaussian noise (WGN) and applied the same ﬁltering proce- dure, obtaining WGN-FC matrices. We found that at G = 100, where the best ﬁt (r = 0.51) between EEG-FCs and fMRI-FCs is reached, the ﬁt of WGN-FCs to fMRI-FCs is 0.35 (Figure S6A in the Supporting Information), despite the EEG-FCs being quite similar to ﬁltered WGN-FCs (average maximum correlation: 0.69, Figure S6B). This suggests that making EEG-FCs more similar to linearly related WGN cannot fully account for the increase in ﬁt between EEG-FC and fMRI-FC. However, at high G values (G > 500), the WGN-FCs did show a ﬁt to the fMRI-
FCs that was just as good as that obtained through our ﬁltering procedure with the empirical
EEG-FCs, namely around 0.5, which is also the correlation between fMRI-FC and Euclidean
distancia. En este punto, the correlation between WGN-FCs and EEG-FCs reaches ∼0.9. Este
indicates that indeed, imposing an interesting graph structure on white Gaussian noise is able
to account for about 25% of the variability in fMRI-FC. This result is in line with Messé et al.
(2015). Importantly though, our ﬁltering procedure identiﬁes a range of G where only about
half of this variance is explained by WGN, suggesting that some interesting nonlinearities are
Preservado.

It is worth mentioning that the results of both ED match and SC might be improved by
optimizing the thresholding procedure. As there is currently no consensus on how thresholding
of ﬁber count and recurrence of pairwise connections across subjects should be combined,
how the differences between long and short ﬁbers should be taken into account, y cómo
thresholding procedures should differ depending on scanning protocols (p.ej., DTI versus DSI),
ﬁber tracking algorithms (p.ej., probabilistic versus deterministic), and number of subjects, a
systematic exploration of the effect of thresholding procedure is beyond the scope of this study.
Sin embargo, the ﬁtting procedure between EEG-FC and fMRI-FC described here could be
employed as one measure to evaluate such thresholding procedures, as a higher ﬁt could be
taken to mean that the most relevant ﬁbers were correctly preserved.

Comparison to Methods That Attenuate Volume Conduction

We used envelope-based correlations, which are known to be strongly inﬂuenced by vol-
ume conduction. We opted for this measure because it is widely used (Cabral et al., 2014,

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Combining structural and functional connectivity in EEG

Hipp et al., 2012; O’Neill, Barratt, Hunt, Tewarie, & Brookes, 2015) and captures predomi-
nantly slow power modulations, which is closer to what the BOLD signal captures. También, el
graph ﬁltering does not remove zero-lag correlations.

We repeated our analyses using coherence and imaginary part of coherence (Figures S8 and
S9 in the Supporting Information), the latter of which is thought to remove zero-lag correlations
y por lo tanto, volume conduction (Nolte et al., 2004). We found that the increase in ﬁt to the fMRI-
FC was much smaller. Sin embargo, this was the case for both measures, and may therefore just
reﬂect the fact that they are less suited for comparison with BOLD-FC. This does not mean
that graph ﬁltering does not work for coherence-based measures, but that comparing with
fMRI-FC is not suitable in this case. Further research is necessary in order to clarify the effect
of FC measure on graph ﬁltering results. Cualitativamente, the results were the same with all three
measures.

We also used the method described in Colclough et al. (2015) to orthogonalize the EEG
signals, and found that this resulted in a decrease in the correlations between EEG-FCs and
fMRI-FCs for every subject, suggesting that orthogonalization removes genuine FC.

En general, these results suggest that both orthogonalization and imaginary coherence remove
zero-lag correlations relevant to large-scale network structure. This does not mean that these
methods are not useful in detecting true connectivity (Nolte et al., 2004). Some recent studies
using such measures have shown network structure partly concordant with fMRI resting-state
redes, and have added some directionality in network analysis (Coito et al., 2016, Coito
et al., 2019; Silfverhuth, Hintsala, Kortelainen, & Seppänen, 2012).

Euclidean Distance and Fiber Count Differentially Affect FC in Different Communities

Our community analysis, using Louvain clustering, revealed that EEG functional networks are
differentially affected by our ﬁltering procedure (using “ED match”). For frontal regions, robusto
improvements are observed, yielding a network that resembles that found in fMRI, apart from
missing functional connections that would constitute the hallmarks of the default mode net-
trabajar, eso es, long-range connections between frontal regions and the middle temporal, inferior
parietal, and posterior cingulate cortices. Sin embargo, note that with this coarse anatomical—
not functional—parcellation, even the fMRI community structure, does not clearly resolve the
default mode network, which is mixed with the frontoparietal network. This indicates that for
this network, “ED match” is a good choice.

For temporal regions, fMRI shows a distinct structure that is not reproduced by EEG either
with or without ﬁltering. The main difference is that there is no FC across hemispheres between
temporal regions. This shows a limitation of our approach (see below for more discussion on
limitations), because even in the SC, there are very few, if any, white matter ﬁber tracts between
the temporal lobes. This is because these ﬁbers are very long and pass through the corpus callo-
sum, making them hard to track. Beyond that, in fMRI, superior, middle, and inferior temporal
gyri belong to different networks (somatosensory/motor/auditory, default mode/frontoparietal,
limbic/visual, respectively—the resolution of this parcellation is too coarse to resolve these
systems properly), while in EEG, the anatomical architecture of the lobes determines the par-
tition into communities. This is a shortcoming that could potentially be improved by using a
more EEG-appropriate parcellation.

Finalmente, for parietal regions typically belonging to a prominent somatosensory/motor net-
trabajar, improvements are achieved using “ED dens;” however, the typical symmetric network

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Combining structural and functional connectivity in EEG

including pre- and postcentral gyri is not established. This is because the pre- and postcen-
tral gyri are elongated, and therefore the Euclidean distances between ROI centers—which
were used to establish the weights in the “ED match” graph—are quite high. Por lo tanto, para
this network, SC is the better choice, even though overall SC is outperformed by all ED-based
graphs.

These observations are in line with recent ﬁndings that show that the alignment between
SC and FC, eso es, the degree to which FC is shaped by SC, differs across regions (Preti & Van
De Ville, 2019), with sensory regions—that is, the visual and somatosensory/motor cortices—
being more strongly aligned with the SC than higher cognitive areas. It may also correspond
to a cortical gradient showing different levels of local recurrent connections across functional
redes (Wang y cols., 2019).

Previous studies have shown consistent functional connectivity between certain homotopic
regiones (Hipp et al., 2012; Mehrkanoon, romper la lanza, Britz, & Boonstra, 2014), while here and
elsewhere (Cabral et al., 2014) these connections are shown to be underestimated in M/EEG-
FC. Por un lado, these ﬁndings might depend on the exact methodology (p.ej., cual
source-reconstruction algorithm is used, whether signals were orthogonalized or not). Sobre el
other hand, our ﬁnding that frontal/occipital networks are quite symmetric across hemispheres
even before ﬁltering while temporal and parietal networks are not suggests that FC might be
robust between some regions and largely absent between others.

Limitaciones

We have already mentioned two limitations of our methodology. Primero, the SC has obvious
shortcomings like the absence of many interhemispheric ﬁbers and the underestimation of long
ﬁbers, which are hard to track (Jeurissen, Descoteaux, Mori, & Leemans, 2019; jones, 2010).
Segundo, we used envelope-based correlations, which are known to be strongly inﬂuenced by
volume conduction. Although we compared with coherence and imaginary part of coherence,
a closer investigation of how graph ﬁltering impacts different measures is warranted.

Además, the standard FreeSurfer parcellation is probably not optimal for EEG. The ROIs
of this parcellation are mostly anatomically deﬁned, not taking into account the nature of the
EEG signal: Regions are highly unequal in size, resulting in a wide range of numbers of dipoles
being averaged to obtain the ROI time courses. Además, ROIs are in many cases elon-
gated, while for EEG, more spherical regions (as far as this would be anatomically/functionally
plausible) would be preferable. Finalmente, the appropriate number of ROIs is a matter of debate,
as a simple correspondence between the number of ROIs and the number electrodes is not
applicable (Farahibozorg, Henson, & Hauk, 2018). This is also in line with our ﬁnding that in
the GLM, the relative regional variance (RRV) is the second-strongest predictor of EEG-FC in
terms of added explained variance, indicating that noise is unequally distributed across ROIs.
This could be because signals from deep sources are harder to pick up than those of superﬁcial
sources (Whittingstall, Stroink, Gates, Connolly, & Finley, 2003).

On the conceptual level, it is unclear how much EEG-FC should resemble fMRI-FC, desde
BOLD and the EEG signal are related in a way that is not straightforward. Al mismo tiempo,
recent studies show that resting-state networks are quite similar across these modalities and
por lo tanto, on this level of resolution and detail, we should expect a good agreement between
the FC matrices (Coito et al., 2019; Liu et al., 2018). Still, validation should include a biophys-
ical model that simulates both genuine FC based on SC as well as volume conduction.

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Combining structural and functional connectivity in EEG

Conclusions and Future Work

Tomados juntos, we add to the thus far sparse knowledge on how SC and FC are related in EEG
source space. Developing these methods is crucial for taking full advantage of the immense
richness of the EEG signal in the temporal and frequency domain, and combining EEG with
other modalities like MEG and fMRI. We have limited our analysis to the grand-average FC, pero
our method could be used to improve signal-to-noise ratio on the single trial level, potentially
easing statistical analysis of task EEG in source space. One important conclusion from our
results is that EEG-speciﬁc parcellation schemes are necessary to guarantee that we take full
advantage of the richness of the EEG signal. Además, our results conﬁrm that it is feasible
and sensible to use dynamical models that assume functional activity to spread through white
matter ﬁbers in EEG (Bhattacharya et al., 2011; de Haan et al., 2012; Finger et al., 2016; Pons
et al., 2010; Ponten et al., 2010; van Dellen et al., 2013). On the data-analysis side, este estudio
provides a justiﬁcation and an avenue to applying more sophisticated methods like graph signal
Procesando (Shuman, Narang, Frossard, Ortega, & Vandergheynst, 2012).

MÉTODOS

EEG Data and Source Projection

Data were recorded from 21 healthy controls as part of an epilepsy study at the EEG and
Epilepsy Unit, University Hospitals of Geneva. The local ethics committee approved this study.
Three subjects were excluded because of too many movement artifacts, leaving 18 for analysis.
Since subjects were age-matched to patients (not analyzed here), 6 subjects aged less than 18
years were included (age range: 8 a 54 años, median: 29.5). Since we could not ﬁnd any
qualitative differences when excluding these subjects, we proceeded with using all 18 disponible
conjuntos de datos.

Resting-state EEG was collected with the Geodesic Sensor Net with 256 electrodes (Elec-
trical Geodesic, Cª, Eugene, EE.UU) during resting state. Electrodes on cheeks and neck were
excluded, leaving 204 electrodes for analysis. Data were downsampled to 1 kHz and artifacts
were removed by Infomax-based independent component analysis prior to source projection.
Remaining artifacts were marked manually and visually, and markers were later used to ex-
tract artifact-free intervals of varying length and number per subject (Table S3 in the Supporting
Información). Inverse solutions were computed using LAURA with LSMAC as implemented in
CARTOOL (Brunet, Murray, & Michel, 2011), employing individual head models that were
extracted from T1-weighted images (acquired as magnetization-prepared rapid gradient echo
[MPRAGE] volumes with a Siemens TrioTim 3T MRI scanner and a tﬂ3d1ns pulse sequence
with ﬂip angle = 9◦; echo time = 2.66 EM, repetition time = 1.51 s, inversion time = 0.9, voxel
size = 1 × 1 × 1 mm3 head ﬁrst supine) obtained from the same subjects in order to create
the forward model. Segmentation and ROI extraction (es decir., parcellation) was performed using
Connectome Mapper 3 (Tourbier et al., 2020). Gray and white matter were segmented from the
MPRAGE volume using FreeSurfer with the Lausanne 2008 multiscale parcellation (Hagmann
et al., 2008), whose ﬁrst scale corresponds to the Desikan atlas (Desikan et al., 2006).

Data were source projected to ∼5,000 dipole locations equally spaced on a three-dimensional
grid, where the gray matter volume extracted from the same images served as a constraint
for the dipole locations. In order to project the three-dimensional time courses of the solu-
tion points to one-dimensional ROI time courses for further analysis, the main direction of
variance was extracted using singular value decomposition (Rubega et al., 2019): All solu-
tion points were concatenated and their time courses were projected onto the ﬁrst principal
component, preserving most of the variance. This was done for each artifact-free interval

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Combining structural and functional connectivity in EEG

(Table S3 in the Supporting Information). Note that all analysis steps were done on the in-
dividual level. Since both functional (see below) and structural connectivity were computed
between ROIs, averaging of the corresponding FC and SC matrices is possible without ever
coregistering images to a common space.

MRI Data

We used three separate structural connectivity datasets in this study, one primary and two
additional datasets to check for replicability. See Figure S12 in the Supporting Information for
a comparison between the average SC matrices resulting from these datasets.

Primary structural connectivity matrices and fMRI functional connectivity matrices: 88
healthy control subjects (mean age 29.7 años, minimum 18.5 años, maximum 59.2 años;
34 hembras) were scanned in a 3-Tesla MRI scanner (Trio, Siemens Medical, Alemania) usando
a 32-channel head coil. Informed written consent in accordance with institutional guidelines
(protocol approved by the Ethics Committee of Clinical Research of the Faculty of Biology and
Medicamento, University of Lausanne, Suiza, #82/14, #382/11, #26.4.2005) was obtained
for all subjects. A large subset (70 out of 88 subjects) of the structural and functional con-
nectivity matrices obtained from these data are available on Zenodo (Griffa, Alemán-Gómez,
& Hagmann, 2019), where the processing pipelines are described in detail. Brieﬂy, for dif-
fusion imaging, a DSI sequence (128 diffusion-weighted volumes and a single b0 volume,
maximum b-value 8,000 s/mm2, 2.2 × 2.2 × 3.0mm voxel size) was applied. For resting-state
resonancia magnética funcional, a gradient echo EPI sequence sensitive to BOLD contrast (3.3-mm in-plane resolution
and slice thickness with a 0.3-mm gap, TR 1,920 EM, Resultando en 280 images per participant)
was applied. A magnetization-prepared rapid acquisition gradient echo (MPRAGE) secuencia
sensitive to white/gray matter contrast (1-mm in-plane resolution, 1.2-mm slice thickness) era
also acquired. ROI extraction (es decir., parcellation) was performed using the Connectome Mapper
(Daducci et al., 2012). Gray and white matter were segmented from the MPRAGE volume us-
ing FreeSurfer with the Lausanne 2008 multiscale parcellation (Hagmann et al., 2008), cuyo
ﬁrst scale corresponds to the Desikan atlas (Desikan et al., 2006). DSI data were reconstructed
following the protocol described in Wedeen, Hagmann, Tseng, Reese, & Weisskoff (2005).

Structural connectivity matrices were estimated for individual participants using determin-
istic streamline tractography on reconstructed DSI data, initiating 32 streamline propagations
per diffusion direction, per white matter voxel (Wedeen et al., 2008).

FMRI volumes were corrected for physiological variables, including regression of white
asunto, cerebrospinal ﬂuid, as well as motion (three translations and three rotations, estimated
by rigid body coregistration). Time courses of voxels falling into each ROI were average and
FC was computed as correlations between these ROI time courses.

Control structural connectivity matrices, small DTI cohort: 20 healthy control subjects (17
hembras, mean age: 23, age range: 20–29 years) were scanned in a 3-Tesla MRI scanner (DIS-
COVERY MR750, GE Healthcare, EE.UU) using a 32-channel head coil. For diffusion imaging,
a DTI sequence (30 diffusion-weighted directions with b-value 1,000 s/mm2 and ﬁve b0 vol-
umes, con 1 × 1 × 2.2 mm3 voxel size, TE/TR = 87/8,000 EM) was applied. A T1-weighted
(T1w) volumen (1-mm isotropic resolution) was also acquired, using an inversion-recovery-
prepared fast spoiled gradient recalled brain volume (IR-FSPGR-BRAVO) secuencia, a fast SPGR
sequence with parameters tuned to optimize brain tissue contrast. ROI extraction (es decir., parcel-
lación), diffusion signal analysis, and construction of SCs were performed using the Connec-
tome Mapper 3 (Tourbier et al., 2020). Gray and white matter were segmented from the T1w
volume using FreeSurfer and the Lausanne 2008 multiscale parcellation scheme (Hagmann

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Combining structural and functional connectivity in EEG

et al., 2008). DTI data were corrected for motion and distortions using FSL mcﬂirt (Jenkinson,
Bannister, Brady, & Herrero, 2002) and eddy_correct (andersson & Sotiropoulos, 2016), de
which ﬁber orientation distribution functions (fODFs) were estimated via constrained spheri-
cal deconvolution (orden 4). Entonces, by seeding from the white matter voxels and by the means
of fODF-driven deterministic tractography (MRtrix3 SD_STREAM, Tournier et al., 2019, a total
of 1M streamlines were reconstructed. T1w and b0 mean volumes were nonlinearly coregis-
tered using ANTs (Avants, Epstein, Grossman, & Gee, 2008)) symmetric normalization in order
to project the extracted ROIs to the DTI data space. Finalmente, by identiﬁcation of the ROIs con-
nected by ﬁbers (Hagmann et al., 2008), a graph is constructed and the structural connectivity
matrices are estimated for each individual.

Control structural connectivity matrices, Human Connectome Project Retest cohort
(Feinberg et al., 2010; Moeller et al., 2010; Setsompop & Gagoski, 2012; Van Essen et al.,
2012): The HCP Retest cohort consists of a subset of 45 HCP subjects recruited by the HCP to
undergo the HCP 3T scanning pipeline a second time. The HCP uses a customized Siemens
3T “Skyra Connectome” scanner with a 32-channel head coil, which is located at Washing-
ton University in St. luis, EE.UU, and which provides an increased gradient strength compared
with standard scanners. This allows the acquisition of multishell dMRI data (voxel size: 1.25 ×
1.25 × 1.25 mm3). Ninety diffusion weighting directions and six b0 volumes were acquired
for three different shells (with b = 1,000, 2,000, y 3,000 s/mm2, voxel size: 1.25 × 1.25 ×
1.25 mm3; Feinberg et al., 2010). An MPRAGE image is also acquired sensitive to the white/gray
matter contrast (0.7-mm isotropic resolution) and used for ROI extraction.
In this work we
used in particular the publicly available T1w- and dMRI-derived data preprocessed by the
“HCP minimal preprocessing pipelines” described in Glasser et al. (2013). This consists of
(a) the T1w images, (b) the corresponding processed FreeSurfer outputs, y (C) the fully cor-
rected dMRI images. ROI extraction (es decir., parcellation), diffusion signal reconstruction and
tractography, and construction of SCs were also performed using the Connectome Mapper 3
(Tourbier et al., 2020). Gray and white matter were segmented using the existing precom-
puted FreeSurfer outputs and the Lausanne 2008 multiscale parcellation scheme. Fiber ori-
entation distribution functions were estimated from the existing preprocessed dMRI volumes
via constrained spherical deconvolution (orden 10). Entonces, by the means of anatomically con-
strained and fODF-driven probabilistic tractography (MRtrix3 ACT iFOD2, ACT; Herrero, Tournier,
Calamante, & connelly, 2012) with seeding from the white matter interface, a total of around
200,000 streamlines were reconstructed. T1w and b0 mean volumes are nonlinearly coregis-
tered using ANTs symmetric normalization, and the extracted ROIs are projected to the dMRI
data space. Finalmente, by identiﬁcation of the ROIs connected by ﬁbers, a graph is constructed
and the structural connectivity matrices are estimated for each individual.

Functional Connectivity Measures for EEG

For our main analysis, we used power envelope correlations to measure functional connec-
tivity in alpha (8–13 Hz), beta (13–30 Hz), and gamma (30–40 Hz) bands. All data analysis
was performed in Matlab 2017a (MathWorks, Natick, EE.UU). We extracted artifact-free intervals
from the resting-state time courses by using the artifact markers mentioned above, admitting
only intervals of at least 19-s duration in order to guarantee a reliable estimation of slow en-
velope modulations (see below). Prior to extracting the FCs, for each artifact-free interval, el
data were downsampled to 250Hz in order to avoid numerical errors that can be induced if
the band of interest is much lower than the sampling rate.

Envelope correlations were computed as in Cabral et al. (2014): After zero-phase band-pass
ﬁltering (eegﬁlt from EEGLAB software package) the EEG single trial time series in the respective

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Combining structural and functional connectivity in EEG

bands, envelopes were extracted using the Hilbert transform. Envelopes were again low-pass
ﬁltered at 0.5 Hz, capturing ultraslow modulations in the respective bands. This measure was
chosen to be as closely related as possible to fMRI-FC (Pearson correlation between BOLD
time courses).

As a comparison (see the Discussion section), we computed the EEG-/fMRI-FC correla-
tions also using FCs obtained with coherence and imaginary part of coherence (icoherence;
Nolte et al., 2004. This part of the analysis was performed using functions implemented in the
Brainstorm toolbox (Tadel, Baillet, Mosher, Pantazis, & Leahy, 2011), which is documented
and freely available for download online under the GNU general public license (http://
neuroimage.usc.edu/brainstorm). Brainstorm estimates (i)coherence in a minimum
number of ﬁve windows that overlap by 50%. At a sampling rate of 250 Hz, esto resulta en
a minimum required signal length of ∼3 s. De este modo, artifact-free intervals were segmented into
epochs of ∼3 s. Since we found that these measures were more susceptible to noise intro-
duced by remaining artifacts than envelope correlations, we further rejected epochs that, en
any point, deviated from the mean by more than 6 desviaciones estandar. See Table S3 in the
Supporting Information for the number of epochs that was used for each subject.

Average Structural Connectivity Matrices

All data analysis was performed in Matlab 2017a (MathWorks, Natick, EE.UU). We used the
method introduced in Betzel et al. (2019) to obtain unbiased group-consensus SCs (promedio
number of ﬁbers) for all three datasets used in this study (primary, HCP, and DTI; see above).
The reason for using a group average rather than individual SC matrices is that ﬁber tracking
algorithms are not sufﬁciently reliable on an individual level, and information from the entire
group is necessary to identify the most likely true-positive connections.

In brief, this method takes into account the fact that interhemispheric connections are less
reliable than intrahemispheric ones. Using a single threshold on the average SC strength (es decir.,
setting all connections that have less than a certain average number of ﬁbers to 0) results in
an underestimated interhemispheric connection density compared with single subjects. El
method used here (Betzel et al., 2019) preserves both intra- and interhemispheric connection
density found in single subjects by applying separate thresholds. Además, we require a
recurrence of at least 30%. The resulting connection density in our primary SC is 25% (39%
within and 12% across hemispheres).

Applying the distance-dependent threshold (Betzel et al., 2019) and a recurrence thresh-
old of 0.3 to the additional datasets, DTI and HCP as described above, resulted in different
connection densities (DTI: 22% en general, 36% within and 8% across hemispheres; HCP: 50%
en general, 67% within and 34% across hemispheres). We adjusted the parameters of the distance-
dependent thresholding procedure such that the resulting average SC exhibited a density that,
for the DTI dataset, was above the density of the single subjects (18% más alto), and for the HCP
dataset such that it was below the single subject (41% más bajo). In order to still be able to take
advantage of the superior quality of the HCP data compared with the DTI data, we chose to
match the intrahemispheric connection density, allowing the interhemispheric, y por lo tanto, el
overall density, to vary. This resulted, for DTI, in an overall density of 24% (39% within and 9%
across hemispheres), and for HCP, in an overall density of 30% (39% within and 20% across
hemispheres).

Por último, the randomized SC used in one of our control analyses was obtained using the Brain
Connectivity Toolbox (Rubinov & despreciar, 2010) function randmio_und_connected() con 100

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iterations, which we used to randomly rewire the primary SC 100 veces, thereby preserving
the degree sequence.

Search Information

All data analysis was performed in Matlab 2017a (MathWorks, Natick, EE.UU). In order to cor-
relate FC and SC matrices, we have to overcome the problem that FCs are dense (Pearson
correlation of time courses can be computed for all pairs of ROIs), while ﬁber tracts only ex-
ist between a subset of ROI pairs. Aquí, we use search information as deﬁned in Goñi et al.
(2014) to derive a dense matrix SCSI from the SC. A path Πs→t is a sequence of edges (nonzero
entries in the SC) leading from node s to node t. The search information S (Πs→t) is then com-
puted as

dónde

S (Πs→t) = −log2 (cid:16)PAG(Πs→t)(cid:17) ,

PAG(Πs→t) = Πi∈Ω∗

s→t (cid:16)

Π(1)

i→t/wi(cid:17) .

s→t is the sequence of nodes on the shortest path, Π(1)

PAG(πs→t) is the probability that a signal traveling from node s to node t will take the shortest
path P(πs→t). Ω∗
i→t is the ﬁrst element
(borde) on the path from node i to node t, and wi is the weight of this edge. The intuition is
that if there exist many such sequences between two given nodes s and t, the shortest path is
“hidden” and more “information” is needed to ﬁnd it. Figure S1 in the Supporting Information
shows this matrix.

General Linear Model

We use Matlab’s function stepwiseglm() to compute coefﬁcients and p-values for a general
linear model (GLM) that computes FC from four predictors:

(1) search information derived from SC, as detailed above;
(2) Euclidean distance;
(3) relative regional variance (RRV); y
(4) ROI size.

RRV serves as a proxy for signal-to-noise ratio. Primero, we compute for each ROI and each
subject the average (over intervals) variance of this ROI’s time courses. The variances are then
scaled such that the maximum (over ROIs) variance is 1 and averaged over subjects.

Matlab’s stepwiseglm() ﬁnds the order of predictor variables in terms of their deviances, eso
es, twice the difference between the log-likelihood of that model and the full model (using all
possible predictors, es decir., four main effects and six interaction terms). A variable is added into
the model if the difference between deviances obtained by adding it is signiﬁcant (χ2 test).
Removal of a term is also possible; this can occur if predictors are linearly dependent. Cualquier
nonsigniﬁcant predictors are not included. Interactions are included only if the main effects
are signiﬁcant. For comparison, we ﬁt single-variable GLMs that use only the intercept and
one predictor variable at a time (see Figure 2A).

Smoothing in Graph Space

Cifra 1 illustrates our ﬁltering approach. We performed spatial low-pass ﬁltering, or smooth-
En g, using the space deﬁned by different versions of the structural connectivity graph. Cada
node of this weighted and undirected graph is one region of interest deﬁned by the Lausanne

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2008 parcellation scheme (Hagmann et al., 2008), yielding 68 nodos. The edges of the graph
are deﬁned by the density of white matter tracts discovered between these ROIs via dMRI.
Smoothing of node i’s signal at time t, xi(t), is then performed using the nearest neighbors of
nodo i, eso es, all nodes j 6= i that have a direct connection to i according to the connectivity
matrix C with entries cij:

ˆxi(t) = xi(t) + G ∑N

j=1 cijxj

(t).

ˆxi(t) is the resulting ﬁltered signal. G is a scalar parameter 0 ≤ G ≤ 1, 000, which tunes
the impact of the neighbors’ signal. The ﬁltering procedure was implemented using Matlab
2017a.

Statistical Analysis for Comparing EEG-FC and fMRI-FC Matrices

We compute individual FC matrices after smoothing in graph space of each subject’s EEG
node time courses. Each subject’s FC matrix, for each value of G, was correlated to the group
average fMRI-FC matrix. Since the fMRI-FC matrix was computed from a rather large sample
(88 subjects), we assume that it represents a “canonical” functional network structure. In order
to assess whether the ﬁltering procedure increases each subject’s EEG-FC similarity to this
canonical network structure, we compared the best ﬁt resulting from each of the four versions
of the graph with the baseline as well as among each other, using a Wilcoxon signed-rank
prueba. This is a paired test, comparing the differences of each subject’s individual correlations
against 0. Since there are 10 comparisons (each of the four graph versions against baseline,
and seven pairwise comparisons between graph versions), we just show a summary of the
results as boxplots; sin embargo, note that we did not compare the means or medians, pero el
individual differences.

Functional Connectivity Matrices Derived From White Gaussian Noise

In order to explore the effect that smoothing in graph space is likely to remove interesting
nonlinearities in EEG-FC, we created white Gaussian noise (WGN) time series using Matlab’s
wgn() función. We preserved the power (variance) of the original signals for each artifact-free
interval separately and computed FC in exactly the same way as for the EEG data. Además
to assessing the correlation between these WGN-FCs and fMRI-FCs, we quantiﬁed how much
ﬁltered EEG-FCs resemble WGN-FCs by computing for each ﬁlter weight the correlation be-
tween the EEG-FCs ﬁltered with this weight and all ﬁltered WGN-FCs, as a match between
the weights cannot be assumed. In Figure S6B (see the Supporting Information), el maximo
correlations to any ﬁltered WGN-FC are shown.

Analysis of Community/Modular Structure of FC Matrices

We used the Louvain community detection algorithm implemented in the Brain Connectivity
toolbox (Rubinov & despreciar, 2010) to evaluate the community structure present in the FC ma-
trices. This algorithm takes the FC (adjacency) matrix and assigns each ROI to a community.
The function takes one parameter, γ, which controls the spatial resolution and thus, indirectamente,
the number of communities that are detected, with higher values of γ leading to more and
smaller communities. We varied γ in a range of 0.9 ≤ γ ≤ 1.3, resulting in a minimum of 2
y un máximo de 35 communities (Figure S14 in the Supporting Information).

Since the community structure depends to some degree on the initial conditions (randomly
assigned module memberships of ROIs), we repeated the procedure 200 veces.
Instead of
opting for a “hard assignment” approach, we took into account the uncertainty of the cluster

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Combining structural and functional connectivity in EEG

estructuras. For each round of clustering, we determined for each pair of ROIs whether they
were assigned to the same community. This resulted in a “community matrix” that can be
interpreted as indicating the probability of a pair of ROIs to belong to the same community.
De este modo, each row/column of one of these matrices describes the “community proﬁle” of a given
ROI. In order to compare the community structures of EEG-FCs vs fMRI-FCs, we compute
the rank correlations between the community proﬁles (row/column of community matrix) de
each ROI.

SUPPORTNG INFORMATION

Supporting information for this article is available at https://doi.org/10.1162/netn_a_00147.

CONTRIBUCIONES DE AUTOR

Katharina Glomb: Conceptualización; Análisis formal; Investigación; Metodología; Software;
Validación; Visualización; Writing – Original Draft; Writing – Revisar & Editing. Emeline Mul-
lier: Conceptualización; Curación de datos; Investigación; Metodología; Software; Writing – Re-
vista & Editing. Margherita Carboni: Curación de datos; Análisis formal; Metodología; Software;
Writing – Revisar & Editing. Maria Rubega: Curación de datos; Metodología; Software; Writing –
Revisar & Editing. Giannarita Iannotti: Curación de datos; Writing – Revisar & Editing. Sebastien
Tourbier: Curación de datos; Writing – Revisar & Editing. Martin Seeber: Curación de datos; Writing –
Revisar & Editing. Serge Vulliemoz: Conceptualización; Metodología; Writing – Revisar &
Editing. Patric Hagmann: Conceptualización; Adquisición de financiación; Metodología; Project ad-
ministration; Recursos; Supervisión; Writing – Original Draft; Writing – Revisar & Editing.

INFORMACIÓN DE FINANCIACIÓN

Patric Hagmann, Katharina Glomb, Schweizerischer Nationalfonds zur Förderung der
Wissenschaftlichen Forschung (http://dx.doi.org/10.13039/501100001711), Award ID: 170873.
Maria Rubega, Ministero degli Affari Esteri e della Cooperazione Internazionale, Award ID:
PGR06121. Serge Vulliemoz, Schweizerischer Nationalfonds zur Förderung der Wissenschaft-
lichen Forschung (http://dx.doi.org/10.13039/501100001711), Award ID: 169198.

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