Complementary contributions of concurrent EEG and fMRI connectivity for predicting structural connectivity

Accepted Manuscript Complementary contributions of concurrent EEG and fMRI connectivity for predicting structural connectivity Jonathan Wirsich, Ben Ridley, Pierre Besson, Viktor Jirsa, Christian Bénar, JeanPhilippe Ranjeva, Maxime Guye PII:

S1053-8119(17)30702-4

DOI:

10.1016/j.neuroimage.2017.08.055

Reference:

YNIMG 14286

To appear in:

NeuroImage

Received Date: 5 May 2017 Revised Date:

1053-8119 1053-8119

Accepted Date: 21 August 2017

Please cite this article as: Wirsich, J., Ridley, B., Besson, P., Jirsa, V., Bénar, C., Ranjeva, J.-P., Guye, M., Complementary contributions of concurrent EEG and fMRI connectivity for predicting structural connectivity, NeuroImage (2017), doi: 10.1016/j.neuroimage.2017.08.055. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Complementary contributions of concurrent EEG and fMRI connectivity for predicting structural connectivity

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Jonathan Wirsicha,b,c, Ben Ridleya,b, Pierre Bessona,b, Viktor Jirsac, Christian Bénarc, JeanPhilippe Ranjevaa,b, Maxime Guyea,b

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Aix Marseille Université, CNRS, CRMBM 7339, 13385 Marseille, France

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AP-HM, CHU Timone, Pôle d’Imagerie, CEMEREM, 13385 Marseille, France

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Aix Marseille Université, Inserm, UMR_S 1106, INS, Institut de Neurosciences des Systèmes,

Corresponding author: Jonathan Wirsich

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13385 Marseille, France

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CRMBM UMR 7339, Faculté de Médecine, 27 Boulevard Jean Moulin, 13385 Marseille,

E-mail: [email protected] Phone: +33 4 91 38 84 68

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Keywords:

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connectome, multimodal, network theory, brain connectivity

Abbreviations

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dMRI Diffusion Magnetic Resonance Imaging Euclidian Distance

FC

Functional Connectivity

IH RSN SC SI

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ED

Interhemispheric

Resting State Network

Structural Connectivity Search Information

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ACCEPTED MANUSCRIPT Abstract

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While averaged dynamics of brain function are known to estimate the underlying structure, the exact relationship between large-scale function and structure remains an unsolved issue in network neuroscience. These complex functional dynamics, measured by EEG and fMRI, are thought to arise from a shared underlying structural architecture, which can be measured by diffusion MRI (dMRI). While simulation and data transformation (e.g. graph theory measures) have been proposed to refine the understanding of the underlying function-structure relationship, the potential complementary and/or independent contribution of EEG and fMRI to this relationship is still poorly understood.

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As such, we explored this relationship by analyzing the function-structure correlation in fourteen healthy subjects with simultaneous resting-state EEG-fMRI and dMRI acquisitions. We show that the combination of EEG and fMRI connectivity better explains dMRI connectivity and that this represents a genuine model improvement over fMRI-only models for both group-averaged connectivity matrices and at the individual level. Furthermore, this model improves the prediction within each resting-state network. The best model fit to underlying structure is mediated by fMRI and EEG-δ connectivity in combination with Euclidean distance and interhemispheric connectivity with more local contributions of EEG-γ at the scale of resting state networks.

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This highlights that the factors mediating the relationship between functional and structural metrics of connectivity are context and scale dependent, influenced by topological, geometric and architectural features. It also suggests that fMRI studies employing simultaneous EEG measures may characterize additional and essential parts of the underlying neuronal activity of the resting-state, which might be of special interest for both clinical studies and the investigation of resting-state dynamics.

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1 Introduction

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Human behavior and cognitive function are widely viewed as fast dynamic processes taking place in a restricted parameter space bounded by relatively static brain architecture (Bullmore and Sporns, 2009). This implies that averaged functional activity should display patterns constrained by and as such able to be mapped back to the anatomical substrate. Directly correlating functional and structural connectivity metrics demonstrates that the relationship between functional networks and their structural substrates is substantial, but not complete (Honey et al., 2009). Ideally, the unexplained difference represents the contribution of the dynamical behavior of brain systems as they oscillate through various brain states i.e. the ‘true’ functional dynamics, as opposed to measurement error and methodological limitations of non-invasive methods of brain measurements. The contribution of such error could be potentially reduced by taking advantage of multimodal measurements which could contribute complementary information to the estimation of brain function and structure.

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Non-invasive methods permit assessment of the dynamic evolution of neural activity via hemodynamic (fMRI) (Achard et al., 2006) or electrophysiological signals (MEG/EEG) (Brookes et al., 2011b) as well as the static structure of white matter tracts extracted by diffusion MRI (dMRI) (Hagmann et al., 2008). Attempts to characterize the macroscopic interareal relationships revealed by these methods has produced the field of connectomics, which describes this complex architecture as maps of connections between different brain regions (Sporns et al., 2005). A large body of work now exists discussing the putative common and distinct properties of functional and structural large-scale brain networks (Damoiseaux and Greicius, 2009). Small world architecture (Achard et al., 2006), for example, has been proposed for both functional and structural networks. Distinct features of dMRI networks include a ‘rich club’ clique of structurally highly connected core nodes (van den Heuvel and Sporns, 2011). Functional brain networks are thought to break down into communities representing the averaged dynamics of spontaneous oscillations whose implicit structure is referred to as resting-state networks (RSNs) (Damoiseaux et al., 2006; Yeo et al., 2011) which are variably (Misic et al., 2016) but closely (Greicius et al., 2009) linked to structure.

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The averaged dynamics of brain function can estimate parts of the underlying structure but the exact relationship between large-scale brain function and structure remains an unsolved problem in systems neuroscience (Park and Friston, 2013). Low but significant relationships between structural connectivity (SC) and hemodynamic functional connectivity (FCfMRI)(Honey et al., 2009) as well as electrophysiological functional connectivity (FCM/EEG) as accessed by both EEG (Deligianni et al., 2016) and MEG (Meier et al., 2016) have been demonstrated. To better characterize this function-structure correlation, a transformation of the structural connectivity matrix to better estimate the contribution of indirect structural connections to functional connectivity is a common approach. Proposed methods include network communication theory (Goni et al., 2014) or the use of generative models (Betzel et al., 2016). As an alternative to simply fitting the data to a (non-)linear stochastic model, it has been shown that in order to realistically model the dynamic functional repertoire of the resting-state only a sparse set of structural parameters are necessary (Deco et al., 2009; Hansen et al., 2015). 4

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The approaches for exploring the function-structure relationship described above are all limited to the transformation of structural connectivity only and usually rely on matrices averaged over subjects which might miss the contribution of dynamics in each recording. From a functional perspective, data from hemodynamic and electrophysiological measurements could be combined to give a fused estimate of dynamic brain function (Rosa et al., 2010). Indeed, multimodal connectomic analyses applied to simultaneous EEG-fMRI acquisitions have shown a relationship between EEG- and fMRI-derived connectivity (Deligianni et al., 2014). Furthermore, the same resting-state networks have been demonstrated in both fMRI and MEG resting-state data (Brookes et al., 2011b) and estimates of connectivity from both modalities are closely related (Tewarie et al., 2016). As electrophysiological and hemodynamic data are subject to different artifacts, and given that they are partly distinct in terms of their overlap with structural connectivity (Engel et al., 2013), we hypothesize that combining the two functional modalities in a linear model should improve the characterization of the relationship of function to underlying structure beyond what is possible in either modality alone, in terms of better predicting structural connectivity from functional connectivity. Such graph-analytical approaches based on whole brain connectivity to characterize the function-structure relationship are generally understudied (Sui et al., 2014).

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Several additional factors influence the function-structure relationship such as individual variation in subjects. Previous work on the function-structure relationship has been mostly based on averaged connectivity matrices, an approach which would be ill-suited to potential single subject usage (such as clinical applications), and which fails to account for the individual states of intrinsic dynamic connectivity. Individual function-structure correlation is known to be lower compared to correlations on averaged matrices (van den Heuvel et al., 2013). Also the functional and structural connectivity architectures of the brain are strongly influenced by geometric constraints, such as distance rules (Ercsey-Ravasz et al., 2013; Honey et al., 2009; Roberts et al., 2016), likely due to the energetic costs of maintaining brain activity (Tomasi et al., 2013). Higher level topological features are thought to be involved in costly deviations from such geometric constraints. One example is the rich club, a set of core nodes more interconnected and geometrically more widespread than would be predicted by energy minimization alone (Roberts et al., 2016; van den Heuvel and Sporns, 2011). As such, here we sought to investigate the multimodal relationships of function and structure in order to improve the goodness of fit between modalities. In particular, we wanted to better understand the extent to which unexplained variability in previous function-structure studies is driven by variability intrinsic to non-neuronal noise and missing neuronal information in any given single modality (SI Figure 1). We hypothesize that both these forms of variability can be reduced by adding additional modalities to the acquisition. Further estimation of the function-structure relationship might be improved by explicitly modelling the known intrinsic geometric and topological properties (e.g. RSNs) of the brain as a functional and structural network defining a restricted parameter space. Minimizing this methodological error should help to better estimate the real variability of functional measurements linked to functional states that cannot be directly inferred by structure. Thus, to examine multimodal function-structure relationship of brain connectivity using for the first time concurrent EEG, fMRI and dMRI in the same individuals, in order to evaluate 5

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(using a linear model) if 1) source-reconstructed EEG adds to the prediction of structure 2) if this extends to the individual level, and how such contributions may be mediated by 3) intrinsic connectivity architecture and 4) large scale topological features.

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2 Materials and Methods 2.1 Subjects

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Seventeen healthy subjects provided informed consent, as per the rules of the local ethics committee (Comité de Protection des Personnes (CPP) Marseille 2), to participate in one session of resting-state acquisition alongside 3D T1 MRI and diffusion MRI. Three participants were excluded due to moderate movement (>20% of resting state data would need scrubbing (Power et al., 2012), resulting in a final group which had at least 16min12s out of total 21min of clean resting state signal for each subject), thus final group size was 14 subjects (five females, mean age: 30.9, std: 8,6, Min/Max age: 20/55).

2.2 Acquisition

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Subjects were scanned using a Siemens Magnetom Verio 3T MRI-Scanner (Siemens, Erlangen, Germany). Subjects were wearing a 64 channel EEG-cap (BrainCap-MR 3-0, Easycap, Hersching, Germany) according to the 10-20 system with one ECG channel and a reference at the mid-frontal FCz position. The participant’s head was fixed with foam to avoid movement, and EEG was acquired using a MR-compatible EEG-amplifier (BrainAMP MR – Brain Products, Munich, Germany, sampling rate 1000Hz). The amplifier was placed as far as possible from the scanner and the connector cables were fixed with sandbags to avoid distortions due to mechanical vibrations of the scanner. A BOLD-sensitized EPI T2*-weighted sequence was used to record 350 fMRI images with a TR of 3.6 s (2.0 × 2.0 × 2.5 mm, TE = 27 ms, 50 slices, FA = 90°, total fMRI time series of 21 min). The subjects were asked to keep their eyes closed and not to fall asleep during fMRI acquisition. An angular gradient set of 64 directions with a TR of 10.7 s was used for dMRI acquisition (2.0 × 2.0 × 2.0 mm, TE = 95 ms, 70 slices, b weighting of 1000 s/mm2). Anatomical T1-weighted images were recorded using a MPRAGE-sequence (TR = 1900 ms, TE = 2.19 ms, 1.0 × 1.0 × 1.0 mm, 208 slices).

2.3 Post processing

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2.3.1 Brain parcellation

T1-weighted images were processed with the Freesurfer suite (v5.3, http://surfer.nmr.mgh.harvard.edu/) performing non-uniformity and intensity correction, skull stripping and grey/white matter segmentation. The cortex was parcelated into 148 regions according to the Destrieux atlas (Destrieux et al., 2010; Fischl et al., 2004).

2.3.2 fMRI processing The fMRI timeseries were timesliced and spatially realigned using the SPM12 toolbox (revision 6685, http://www.fil.ion.ucl.ac.uk/spm/software/spm12). The subjects T1 image and Destrieux atlas were coregistered to the fMRI images. Average CSF and white matter signal from manually defined ROIs (Marsbar Toolbox 0.43, http://marsbar.sourceforge.net) were extracted and were regressed out of the BOLD timeseries along with 6 rotation and translation motion parameters and global gray matter signal (Goni et al., 2014; van den Heuvel et al., 2013). Subsequently data was filtered by wavelet analysis using the Brainwaver 7

ACCEPTED MANUSCRIPT toolbox (version 1.6, http://cran.r-project.org/web/packages/brainwaver/index.html) (Achard et al., 2006). Timeseries were scrubbed according to the DVAR criteria (threshold 0.5) and framewise displacement (threshold 0.5) defined by Power et al. (2012). Finally, the Pearson correlation of the remaining wavelet coefficients of scale two (equivalent to a frequency band 0.04-0.09 Hz) was used to build a functional connectivity matrix (FCfMRI).

2.3.3 EEG processing

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We used the Brain Vision Analyzer 2 software (Brain Products, Munich, Germany) for correction of gradient artifact induced by the scanner via template subtraction and adaptive noise cancelation, with 70Hz low-pass filtering and downsampling to 250Hz (Allen et al., 2000). ECG channel peaks were extracted in order to construct cardiac pulse artifact templates of the average waveform over 100 pulses, which were used for subtraction of the EEG-signal (Allen et al., 1998). We used ICA to manually reject eye movement artifacts and high-pass filtered the signal at 0.3 Hz. Then data was segmented into periods of 3.6s (one fMRI volume acquisition). The segments with obvious movement artifacts were semi-automatically excluded from further analysis. The remaining segments then were analyzed with Brainstorm software (Tadel et al., 2011), which is documented and freely available for download online under the GNU general public license (http://neuroimage.usc.edu/brainstorm, version: January 2016). Electrode positions were manually coregistered to the T1 image and a forward model of the skull was calculated using the T1 image of each subject using the OpenMEEG BEM model (Gramfort et al., 2010; Kybic et al., 2005). EEG data reconstructed into source space using the Tikhonov-regularized minimum-norm with the Tikhonov parameter set to λ = 10% of maximum singular value of the lead field (Baillet et al., 2001). Source timeseries were averaged to the regions of the Destrieux atlas and connectivity matrices were calculated for each segment by taking the imaginary coherence of delta, theta, alpha, beta and gamma frequency bands between each region (Nolte et al., 2004). We chose this connectivity measure to provide the least overlap with information derived from FCfMRI compared to envelope-derived connectivity (Engel et al., 2013) (this is equivalent to maximizing area c III. in the schema of SI Figure 1). The final EEG connectivity matrices were obtained by averaging the band specific connectivity of all segments (FCδ, FCθ, FCα, FCβ and FCγ).

2.3.4 Diffusion MRI processing and tractography Affine registration of dMRI data was carried out with the FSL software (FMRIB Software Library 5.0, http://www.fmrib.ox.ac.uk/fsl/) in order to correct for motion and eddy currents. We used the MRtrix software (Brain Research Institute, Melbourne, Australia, Version 0.2.12, http://www.brain.org.au/software/) for whole-brain fiber tracking. Mean diffusivity maps and FA were calculated by fitting the diffusion tensors to each voxel. For voxels with FA > 0.7 we estimated fiber orientation distribution (FOD) with the help of constrained spherical convolution (Tournier et al., 2007). Sampling of FOD at each step was used to generate a probabilistic fiber tracking (150.000 fibers of minimum length 20mm) (Behrens et al., 2003). Default tracking parameters were used. Fiber seeds were randomly placed in a 1mm dilated white matter mask and tracking was stopped upon reaching a voxel outside the mask or violating the default stop criteria (step size 0.2mm, minimum radius of 8

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2.3.5 Extraction of resting-state networks

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curvature of 1 mm, FOD cutoff 0.1). T1 were coregistered with dMRI by extracting CSF maps from T1 and b0 images (SPM) and rigidly and non-linearly registering T1-CSF map to b0-CSF map (Symmetric Group-Wise Normalization: SyGN algorithm, ANTs 2.1.0, http://picsl.upenn.edu/software/ants/ (Avants et al., 2011; Avants et al., 2010)). ROIs of the Destrieux atlas previously defined on T1 were realigned with dMRI using the obtained transformation. Structural connectomes were constructed by counting the connecting tracks between each regional pair. To better characterize whole brain functional connectivity from structure, and to account for by indirect links between regions along the shortest path we used the previously proposed metric search information, which weights the shortest path by connection strengths with a correction for strength of connections branching off along the shortest path. See SI figure 2 for an illustration of the metric or Goñi et al. (2014) for a detailed description. In the following, connectomes based on this measure will be referred to as SCSI.

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Resting-state networks (RSN) play a central role in the functional organization of the brain and it has been shown that RSN connectivity is correlated to structure in both humans and primates (Greicius et al., 2009; Vincent et al., 2007; Wang et al., 2013). Mišić et al. (2016) recently found out that RSNs differ in the strength of their function-structure correlation. To better understand the role of RSNs in the context of EEG-fMRI-dMRI models we split our connectivity matrices into four resting-state modules (Moussa et al., 2012; Zalesky et al., 2014) (Figure 1 step c). Resting-state networks were extracted from the fMRI connectivity matrices according to the method proposed by Zalesky et al. (2014) via the Brain Connectivity toolbox (default parameters, version 2016-01-16, www.brain-connectivitytoolbox.net, (Rubinov and Sporns, 2010)): Firstly, we applied the Louvain algorithm 250 times (Blondel et al., 2008) to decompose each connectivity matrix (FCfMRI) into nonoverlapping modules defined by higher correlation of inter-module connections compared to intra-module connections. Then for each subject a consensus matrix was built from the resulting 250 modularizations (Lancichinetti and Fortunato, 2012). Finally, another consensus matrix was built from the modules of all 14 subjects combined. Note that a finer modular parcelation of seven RSN networks would have been also possible by changing the parameters of the Louvain and the consensus algorithm (Misic et al., 2016). This option was not pursued in order to avoid small modules with insufficient data points to be included into the regression model. The parameter is limited by the coarse parcellation scheme which was chosen to aid integration of EEG, given its low spatial resolution.

2.4 Statistical Methodology 2.4.1 Model improvement when using EEG to inform the function-structure relationship The following analyses were performed on the weights of the upper triangle of the undirected connectivity matrix only. First, we confirmed that the extracted connectivity matrices were, as in previous studies, correlated between each pair of modalities (dMRIfMRI, dMRI-EEG and EEG-fMRI) in terms of a direct pairwise correlation of the matrix weights. Note that the search information metric used here on structural data is negatively 9

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correlated to functional connectivity (Goni et al., 2014). Secondly, to investigate the benefit of adding source space derived EEG connectivity above and beyond a pairwise FCfMRI-SCSI correlation, we split the fourteen subjects into two equally sized groups of seven in order to train and test a linear regression model in separate datasets. By doing so, we can assess the generalizability of the coefficients from our linear model. Given prior evidence of significant correlation between FCfMRI and SCSI (Goni et al., 2014), here we focused on the added value of EEG derived regression coefficients - beyond the two MRI-derived methods - in terms of cross-validated predictability in a linear model. Since adding new parameters can arbitrarily improve estimation in a linear regression model, to determine model improvement statistically it is necessary to construct a null model. As such we compared the combined EEG-fMRI linear model with a model of fMRI and pseudo-EEG connectivity matrices with equivalent spatial structural properties. To generate these surrogate data we used the approach of Prichard et al. (1994), by randomizing the phases of the Fourier transform. As we are interested in a null model for static connectivity rather than a null model of temporal dynamics we apply the graph Fourier transform to our connectivity matrix rather than transforming the EEG timecourses. This graph Fourier transform is defined by taking the Fourier transform of the Eigenvectors (Sandryhaila and Moura, 2013). We applied the transformation for the Eigenvectors of each source reconstructed EEG matrix and randomized their phases (Eigenvector size n = 148 per the number of regions of the Destrieux atlas, we analyzed each EEG band separately). The result was then back transformed by the inverse Fourier transformation and new matrices were created by reversing the Eigenvalue decomposition with these phase-randomized Eigenvectors. This procedure created connectivity matrices uncorrelated with the original signal but with preserved connectivity matrix spatial structure (such as interhemispheric connections and ordering in resting state networks). Please see SI figure 4 for a representative EEG connectivity matrix and a corresponding pseudo matrix; for more detail please refer to Tewarie et al. (2016).

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Subsequently, a permutation procedure was used to test for model improvement: generating an averaged test and training connectivity matrix (for each modality) for each of the 1716 possible combinations produced by randomly splitting the subjects into a training and a test set of seven subjects. For the training matrix of each permutation, EEG-pseudoconnectivity matrices for each frequency were generated by averaging 250 phase randomized EEG matrices (approach described in the previous paragraph). Regression coefficients calculated on FCfMRI and FCEEG (based on original or pseudo-EEG) averaged training matrices in order to predict SCSI were then applied to the averaged test matrices. Specifically, coefficients of the linear regression model (predicting Log(SCSI) by FCfMRI, FCδ, FCθ, FCα, FCβ, and FCγ) and null model (predicting Log(SCSI) by FCfMRI, FCδ-pseudo, FCθ-pseudo, FCαpseudo, FCβ-pseudo and FCγ-pseudo) were defined on the averaged training set and then used on the averaged test set. A p-value was defined according to the ratio between the number of times the correlation of the pseudo model was higher than the correlation of the real data divided by the number of iterations (n=1716). This out-of-sample procedure is a conservative means of ensuring out-of-sample validity as compared to obtain a test statistic by repetitively generating surrogate data only for the average connectome of the 14 subjects. To assure that FCfMRI significantly contributes to SCSI prediction we repeated this procedure by randomizing FCfMRI in the null model and keeping all EEG connectivity matrices constant.

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2.4.2 Model improvement at the individual level

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To investigate the contribution of individual differences in underlying connectivity and noise sources, we also analyzed the contribution of EEG at a subject level. In detail, we wanted to test if our trimodal model approach scales down to the single subject and if the coefficients are comparable to the coefficients extracted from mean matrices (see approach in section 2.4.1). To do so, we applied the linear model coefficients to the individual matrices of all fourteen subjects on a one by a one basis using the coefficients derived from the average matrices of the remaining thirteen, to observe if the resulting function-structure correlation was greater compared to direct correlation between individual FCfMRI-SCSI. To further investigate if any improvement in prediction is only due to using coefficients from a model based on average matrices, we compared all possible pairs (91) of individual subjects using the coefficients of one subject in a linear model of the other subject. The resulting correlation was both compared to the baseline FCfMRI-SCSI correlation of that subject and to a linear model including FCfMRI, SCSI and the before described pseudo-EEG data generated from the subjects original EEG data. Finally, we investigated subject-specific connectivity to analyze the added value of EEG, by fitting the individual FCEEG and FCfMRI to the individual SCSI, and cross-validated (5000 iterations) the regression coefficients in each subject by picking 70% of the connections and testing on the remaining 30%. These results then were compared to a model including pseudo-EEG matrices.

2.4.3 Contributions of intrinsic connectivity, geometric and topological factors

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We tested if EEG improves estimation of function-structure correlation when considering only the internal connections of each RSN (namely default mode, visual, somatomotor and fronto-insular network and excluding interconnections between those networks) separately by training on 70% (randomly selected) intraconnections and testing on the remaining 30%, 5000 times for each subject. We then compared the model fits to the correlations from an intra-RSN model based on averaged matrices.

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Finally, in a whole-brain model taking into account all connections, intra-RSN connections were marked in the form of four binary connectivity matrices. To better account for geometrical constraints we also added Euclidian distance (mm) between region centers to the linear model. As well we added binary dummy variables to account for discrepancies in the estimation of interhemispheric (IH) connectivity between dMRI and fMRI (Deco et al., 2014). In addition to FCfMRI , Euclidian distance, interhemispheric connections and RSN participation, our final model also included the interaction terms of each frequency band of FCEEG, inspired by Tewarie et al. (2016), as well as all interactions between fMRI, EEG, interhemispheric connections, Euclidian distance and RSNs. Since it is unlikely that all parameters contribute significantly to the model, we first applied a stepwise regression starting from an empty model with the goal of reducing dimensionality. To avoid overfitting to the average matrix of our subject group, we split our subjects into a test and a training group of 7 subjects each. Subjects were permuted (1716 iterations for all possible assignments) during each step of the optimization and the parameters were retained based on the Akaike information criterion (AIC) of Log(SCSI) prediction result of the averaged test matrix.

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3 Results 3.1 Pairwise correlation of modalities and contributions of EEG

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The extracted connectivity matrices were, as in previous studies, correlated between each pair of modalities (dMRI-fMRI, dMRI-EEG and EEG-fMRI, Figure 2, SI Figure 3 and Table 1). Via the permutation procedure described above we found that including EEG to predict SC significantly improves the correlation between function and structure in the test set (P=0.040, calculated from 1716 permutated average matrices of 7 subjects used for training and 7 subjects used for testing). This shows that when applied to the test set, the coefficients trained on the veridical EEG data represent a genuine model improvement as compared to using these coefficients trained on pseudo-EEG data. Equally we observed an improvement of the model when comparing to constant EEG connectivity and randomized fMRI connectivity model (P=0.048). By linearly fitting the five FCEEG matrices and the FCfMRI matrix to SCSI (averaged over all subjects) we observed a correlation of r = 0.61 (mean matrices of all subjects), a correlation higher than the bimodal FCfMRI-SCSI correlation observed in the same data (r=-0.41, Table 1) and also higher than previous whole-brain models of a completely connected average matrices reported in the literature (SCSI-FCfMRI correlation of r = -0.41 as reported in Goñi et al. (2014) / r=-0.46 as reported by our group on a different set of subjects and an altered brain parcellation (Wirsich et al., 2016)). Note that the linear relationship between the variables used in the regression model in this analysis also shows that FCEEG could be combined with SCSI to improve FCfMRI.

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3.2 Cross-subject and single-subject SC prediction

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We found that the EEG coefficients trained on thirteen subjects also increased correlation with SCSI at the individual level in all but four subjects (29%). When comparing all possible pairings (91) of individual subjects (using the coefficients calculated from one subject in the model of the other) we found that the correlation with SCSI was increased 80% of the time when using FCEEG and FCfMRI compared to correlating SCSI and FCfMRI. This value drops to 70% of the pairs when compared to pseudo-EEG models, suggesting that individual functionstructure is equally generalizable from averaged and individualized training sets. When fitting the individual FCEEG and FCfMRI to the individual SCSI mean correlation of the fitted models across all subjects was r=0.42. Including FCEEG significantly improved functionstructure correlation for all individual subject models compared to both individual bimodal FCfMRI-SCSI correlations (p<0.001) and compared to a linear model with pseudo-EEG matrices (p<0.001). This result is consistent with the previous found improvement on a group averaged level.

3.3 The role of RSNs in the trimodal function-structure relationship EEG was found to significantly improve the function-structure correlation compared to pseudo-EEG for each RSN (RSNDMN: P=0.0029, RSNVisual: P=0.020, RSNSomatomotor: P=0.0046, RSNFronto-insula: P=0.0049). The strength of correlation was significant (P<0.001) within each single RSNs (RSNDMN: r=0.47, RSNVisual: r=0.54, RSNSomatomotor: r=0.55, RSNFronto-insula: r=0.57). By taking the mean matrix over all subjects, the correlation of the linear fit increased even farther (RSNDMN: r=0.67, RSNVisual: r=0.74, Motor r=0.75, RSNFronto-insula: r=0.79, all P<0.001). 12

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3.4 Adding geometric constraints and RSNs to build a whole brain model

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Stepwise regression based on cross-validated AIC values, showed that the Log(SCSI) connectivity matrix is best predicted by ED, IH, FCfMRI*FCδ, FCfMRI*ED, FCfMRI, FCδ*IH, FCδ, FCδ*ED, RSNFronto-insula, IH*RSNVisual, FCγ*RSNVisual (ordered by AIC criterion selection of stepwise regression, with first variable added ED and last parameter added FCγ*RSNVisual; see also SI Table 1: e.g. pairwise SCSI-ED correlation is r=0.64). Each individual factor (fMRI, EEG, Euclidian distance, cross-hemispheric connections and RSN) contributed significantly (P<10-8, Table 2) to the cross-validated model. We fitted this model to the mean structural connectome of all fourteen subjects. With this model, we were able to provide a tight fit to underlying structure while also integrating connections usually undersampled by dMRI, such as short range connections as well as interhemispheric connections and those without a direct structural counterpart (Figure 3, r=0.80). Table 2 shows the magnitudes of the variables in the underlying fitted linear model, note that this conservative cross-validated approach will only select the most robust variables for any combination of averaged connectomes using seven subjects.

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4 Discussion

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We explored the potential of multimodal recordings to improve our understanding of the relationship between FC and SC, by simultaneously measuring the interareal covariation in spontaneous fluctuations in electrophysiological and hemodynamic signals followed by diffusion imaging to estimate axonal links among brain regions. We found that both FCEEG (imaginary coherence) and FCfMRI (Pearsons correlation) are correlated to the underlying SCSI and that a combination of these two measurements in a linear model increases the ability to predict structure, highlighting the benefit of including both functional signals. This statement holds for both group-averaged and individual connectivity. The prediction becomes even more accurate when taking into account topological and geometric parameters such as analytic measurements of network communication (Goni et al., 2014), Euclidean distance (Honey et al., 2009; Roberts et al., 2016), interhemispheric connections (Deco et al., 2014), resting-state network membership (Greicius et al., 2009) and first order parameter interactions (Tewarie et al., 2016). These multimodal results show that the correlation between structure and function is much higher than previously estimated and that including EEG provides a much better estimate of function-structure coupling beyond a hemodynamiccentric view, placing greater and more accurate constraints on the unaccounted variance in dynamics that cannot be directly linked to macroscopic brain structure. Thus, this further clarifies the space occupied by the dynamical behavior of brain systems as they oscillate through various brain states.

4.1 Bimodal relationships and the added value of concurrent EEG-fMRI and dMRI

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To establish our trimodal model we validated the bimodal relationships between FCfMRI-SCSI and FCEEG-FCfMRI. We reproduced the whole brain results from the previous FCfMRI-SCSI studies (r=0.41 in our study, r=0.41/-0.35/-0.32 for the three datasets of Goñi et al. (2014)). Deligianni et al. (2014) reported no absolute values but only that the FCEEG-FCfMRI correlation was significant across all frequency bands as also shown in our study. Furthermore, while every frequency band is correlated with BOLD, the beta-band was found to provide the highest FCEEG-FCfMRI correlation, in line with previous work comparing fMRI and MEG (Brookes et al., 2011a) (comparison of FC only in motor cortices). We observed that the gamma band provides the lowest (but significant) correlation with fMRI-derived connectivity, in line with both recent animal models (Wang et al., 2012) and human MEG data (Marzetti et al., 2013). This stands in potential contradiction to a previous EEG-fMRI study (Deligianni et al., 2014), however the apparent discrepancy could reflect differences between envelope and coherence based methods as anticipated by Engel et al. (2013). Note that direct comparisons of correlation values between studies are difficult to interpret as they depend on several methodological decisions such as brain parcellation. For example Honey et al. (2009) report a SCdMRI-FCfMRI correlation of r=0.66 for low resolution parcellation (66 regions) which drops to r=0.36 when applying high resolution parcellation to the same data (998 regions). Our results constitute a comparison of simultaneous EEG-fMRI and dMRI acquired in the same participants during the same sessions used to investigate the coupling between the connectivity estimates from each modality across the whole brain, permitting a direct comparison of pairwise relationships between modalities and specifically demonstrating the 14

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added value of source reconstructed EEG. Our results indicate a higher FC-SC correlation when comparing electrophysiological signals to SC than BOLD signals. Equally we observed that adding FCfMRI to an FCEEG-SC model will increase correlation indicating distinct contributions of FCfMRI and FCEEG. Chu et al. (2015) observed that electrophysiological connectivity decreases in the absence of direct structural connections. In contrast, strong FCfMRI correlations exist even in the absence of direct structural connections (Damoiseaux and Greicius, 2009), which is reflected in our results in terms of higher correlation values between FCEEG (all bands) and SCSI compared to FCfMRI and SCSI. This discrepancy between FCfMRI and structural connectivity is well-known (Deco et al., 2014), and our results add to this in the sense that they put - on a whole brain scale - EEG imaginary coherence closer to SCSI than FCfMRI.

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4.2 The benefit of EEG – subject, topological, geometric and large scale architectural factors

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In addition to supplementing bimodal findings this study extends previous work fitting FC to SC (Goni et al., 2014) by showing that FC-SC models can be further improved with EEG data. In particular, we show the significant added value of subject-level FCEEG when combined with distinct functional information from another modality. Adding EEG improves prediction of structure from function to a higher extent than previously reported in bimodal dMRI-fMRI (mean r=0.42 as opposed to r= 0.25 (van den Heuvel et al., 2013) and r=0.28 (Zhang et al., 2011)) , demonstrating the advantage of adding electrophysiological metrics at the individual subjects.

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Goñi et al. (2014) have proposed combining several connectivity matrices in a linear model to improve function-structure correlation. While taking topological (SI), geometric (distance), and the contributions of features of large scale brain architecture (intra-/interhemispheric edges, RSN membership) (Misic et al., 2016) into account, as well as interactions between parameters (Tewarie et al., 2016), we demonstrate a cross-validated model that is able to link function and structure to a higher extent than previously reported (Goni et al., 2014). On long timescales, intrinsic dynamics can be considered random, with the remaining static contribution to ‘functional’ modalities coming from and - given theoretically perfect measurement - predicting underlying structure. As such, Honey et al. (2007) have shown that structure can be better predicted by averaging over long time periods. Neither EEG nor fMRI perfectly capture the underlying neuronal activity (Rosa et al., 2010), though combining them enables an increase in the reliability of the estimated function-structure correlation (SI Figure 1). By perfecting the function-structure correlation it may be possible to constrain the domain in which cognitively interesting intrinsic dynamics could occur, thus providing insight and a basis for further exploration of this domain in healthy controls as well as its potential alteration in clinical condition (SI Figure 1c). Selecting the most highly-contributing model parameters facilitates identification of the most important predictors of structural connectivity. That SCSI is largely predicted by Euclidian distance and interhemispheric connectivity should come as no surprise given the geometrical relationships documented in previous work (Deco et al., 2014; Ercsey-Ravasz et al., 2013; Roberts et al., 2016). The current work highlights the importance of including these trivial parameters in the model comparing functional and structural connectivity as 15

ACCEPTED MANUSCRIPT measured by EEG, fMRI and dMRI, as each modality contributes information not available to any other single modality.

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It should be noted that when using two functional modalities (EEG and fMRI) to predict dMRI cross-validated model selection will identify parameters that add the most to dMRI prediction by contributing modality-unique information to the model. Among the variables that co-vary in terms of the information provided this approach will only take the parameter which contributes the most to predict SCSI (SI figure 1c). EEGβ and EEGα are commonly found to be most correlated with FCfMRI (Laufs et al., 2003). A close relationship between beta and alpha waves with infraslow amplitude correlations has been long recognized in electrophysiology (Ehlers and Foote, 1984) and has been supplemented by recent work showing a close relationship between infraslow BOLD and EEG signal (Hiltunen et al., 2014; Palva and Palva, 2012). Furthermore, alpha and beta-frequency EEG oscillations have been shown to correlate highly with BOLD signals in several RSNs linked to alertness (Sadaghiani et al., 2010), suggesting the possibility of redundancy in these subbands with respect to fMRI in terms of the effect of vigilance on the signals. In line with this, we observed that although FCβ and FCα are the most correlated to FCfMRI and SCSI (when compared in a pairwise manner), they are not included in the final trimodal model revealed by the stepwise analysis: since FCfMRI is already in the model further redundant information is unnecessary to predict SCSI. In contrast, FCδ was found to contribute significantly to model whole brain structure singly and by interacting with FCfMRI and Euclidian distance. This association of lower frequencies with long-range coherence is well known (Destexhe et al., 1999). The contribution of the delta-band information as compared to an fMRI only approach to predict underlying structure might also be linked to better SNR than the other EEG bands (Deligianni et al., 2014) and though reflecting the best estimation of electrophysiological connectivity. Furthermore, gamma band interactions were also found to be relevant at the modular scale of resting-state networks, where we found an interaction with the visual RSN. This locally limited result of weak gamma coherence for long distance connections is in line with the proposed role for gamma in synchronizing local circuits (Wang et al., 2012) and the important role gamma synchronization plays in the visual cortex specifically (for review see Fries (2009)). It is also worth noting that visual cortex gamma is not coupled with the BOLD response (Muthukumaraswamy and Singh, 2009). This uncoupling could be one explanation why the FCγ*RSNvisual interaction was selected in our model in parallel with FCfMRI since it provides otherwise unavailable information. High alpha coherence has also been reported in visual cortex (Guggisberg et al., 2008) but - due to the stronger correlation between FCfMRI and FCα – the matrix was not selected for the final model. From a systems neuroscience perspective, the interplay of local gamma oscillations and slow fluctuations in the large scale structure like BOLD have been previously demonstrated (Cabral et al., 2011). In summary, in addition to confirming that fMRI contributes to structure prediction on a whole brain level, we have shown that EEG contributes additional information in a subbandspecific way. In the frequency bands where EEG oscillations are closely related to fMRI through their shared relationship to alertness and vigilance fluctuations, such as alpha and beta bands the EEG will not contribute significantly to structure prediction. In contrast when focusing on EEG frequencies less influenced by vigilance, global contributions were made from delta, while the gamma-band was observed to contribute locally to the prediction of structure. Thus, the additional information provided by EEG when applied concurrently with 16

ACCEPTED MANUSCRIPT fMRI and dMRI is mediated by context and scale dependent factors at local and global levels, in addition to being influenced by topological, geometric and intrinsic architectural features.

4.3 Perspectives and limitations

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Here we investigated structure and averaged function over 21 minutes, representing a summary of the dynamic brain states instantiated by the underlying structure during that time. As such one crucial advantage of the current trimodal approach over previous studies (Meier et al., 2016) is that by simultaneously acquiring the functional modalities we do not introduce signal variance due to inter-session variation in intrinsic brain states.

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Recently the analysis of fMRI connectivity in a time resolved manner has been proposed (Zalesky et al., 2014) and such dynamics of ongoing activity have been shown to correlate with behavior such as perception (Sadaghiani et al., 2015). The validity of dynamic fMRI measures is a subject of ongoing discussion (Hindriks et al., 2016) and as such investigating the parallel dynamics of EEG-fMRI has been shown to better characterize the neurophysiological correlates of dynamic fMRI connectivity (Lewis et al., 2016). In particular, a multimodal approach as used here is not limited to the understanding of averaged function, but also opens new avenues for investigating single subject dynamic functionstructure relationships (Shen et al., 2015) by taking advantage of the added value of simultaneous EEG-fMRI recordings.

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More generally we observed that both EEG and fMRI contribute to predict dMRI. All three measures define the state of the art in non-invasive recording of both structure and function in the brain, but nonetheless have specific limitations in terms of information they provide. These include measuring electric potential at the scalp for non-invasive EEG, the BOLD signal which is only indirectly linked to neural activity, and the probabilistic distribution of fiber bundles estimated by the orientation implied by the diffusion-weighted signal. As such this work shows how adding modalities (in this case EEG) helps to compensate for limitations of fMRI. One intuitive example how EEG provides added value to the estimation of the function-structure relationship is when thinking about the consequences of motion artifacts on the connectivity measures of all three modalities: while FCfMRI based on Pearson’s correlation will show increased global correlation from the homogeneous global signal induced by motion (Power et al., 2012), EEG-motion artifacts will suffer from inhomogeneous signal perturbations on the electrodes (Gwin et al., 2010) resulting in a decrease of measured connectivity and local decrease in connectivity due to inhomogeneous artifacts across the white matter (Yendiki et al., 2014). This example shows that the consequences of artifacts influence different parts of the brain for each modality and an integrated framework as presented here will help to correct for those errors providing a more comprehensive view of the brain. Indeed, the added value of delta oscillations in our model may also reflect the differential sensitivity between modalities to a common artifact which might be another explanation of our finding that EEG contributes to dMRI prediction. To what extent this is due to genuine contributions of unique and veridical information from both modalities, or the mere correction of modality-specific artifacts by the other cannot be distinguished using our method and is a question for future research. Imaginary coherence provides a very conservative estimate of electrophysiological connectivity by rejecting all zero-phase coherent contributions, to correct for source leakage 17

ACCEPTED MANUSCRIPT (Nolte et al., 2004). We purposely chose the most conservative index to have the best a priori chance of contributing distinct EEG connectivity information in addition to fMRI (Engel et al., 2013). Future work might validate this approach against other approaches including phase lag index (Stam et al., 2007) or Hilbert envelopes (Brookes et al., 2012).

4.4 Conclusion

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This study demonstrates the added value of simultaneous EEG-fMRI in predicting dMRIbased structural connectivity on both a group and single-subject level. We show for the first time, that by using a trimodal model of brain connectivity in combination with intrinsic architectural properties, the contribution of non-neuronal sources to structure and function measurement is more constrained than previously thought. Furthermore, this shows that the fusion of electrophysiological and hemodynamic measurements can improve the general estimation of neuronal contributions to whole brain functional connectivity beyond the limited perspective provided by hemodynamic measurements alone.

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5 Acknowledgements

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This work was supported by the CNRS, the ANR CONNECTEPI (grant number ANR-07-NEUR0010) and the “PHRCI 2013” EPI-SODIUM (grant number 2014-27).

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Figure 1: Overview of connectivity extraction: a) transformation of EEG, fMRI and dMRI into the Detrieux atlas space, b) extraction of dMRI, fMRI and EEG connectivity, c) modularization of the atlas into resting-sate networks based on the fMRI connectivity, d) construction of resting-state and interhemispheric binary masks and map of euclidian distances (the displayed matrices are numbered (right) according to the interconnections of the four extracted RSNs: 1. DMN, 2. visual, 3. somatomotor and 4. fronto-insular). RSN brain images included in figure 1 were visualized with the BrainNet Viewer (http://www.nitrc.org/projects/bnv/, Version 1.53, (Xia et al., 2013)).

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Figure 2: Pairwise correlations between connectivity matrices derived from dMRI, fMRI and EEG beta oscillations. Note that the SI metric derived from dMRI is negatively correlated to functional connectivity.

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Figure 1: 2 columns Figure 2: 2 columns Figure 3: 1.5 columns

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Figure 3: Whole brain model of cross-validated linear regression model (predicting Log(SCSI) by FCfMRI, FCδ, ED, IH, RSNFronto-insula, FCfMRI*FCδ, FCfMRI*ED, FCδ*ED, FCδ*IH, FCγ*RSNVisual,and IH*RSNVisual) applied to the mean connectome of all subjects (r = 0.78). The figure highlights both the influence of short connections and connections which have no streamlines in tractography.

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1 Tables FCdelta FCtheta FCalpha FCbeta FCgamma log(SCSI) -0.45026 -0.41176 -0.39614 -0.5442 -0.34349 FCfMRI 0.33534 0.32489 0.32849 0.36829 0.16228 Table 1: Paired correlations of connectivity matrices between FCEEG (for all bands), FCfMRI and FCdMRI; Abbreviations: FC, functional connectivity; SC, structural connectivity; SI, search information

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FCfMRI -0.41072

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Variable t p ED 14.35 2.8*10-46 IH 14.55 1.6*10-47 FCfMRI*FCδ -7.12 1.1*10-12 FCfMRI*ED 23.44 1.4*10-118 FCfMRI -16.83 9.1*10-63 FCδ*IH 11.10 1.9*10-28 FCδ -14.34 3.1*10-46 FCδ*ED 8.63 7.1*10-18 RSNFronto-insula 9.09 1.2*10-19 IH*RSNVisual -5.85 5.1*10-09 FCγ*RSNVisual 8.59 1.0*10-17 Table 2: Variables of the linear model to predict log(FCSI), t and p-values of regression coefficients are displayed for fitting the selected variables to the connectivity matrices averaged over all subjects. The variables are in the selection order determined from our stepwise approach based on the AIC (top = selected first). Abbreviations: AIC, Akaike information criterion; ED, Euclidian distance; FC, functional connectivity; IH, interhemispheric connection; RSN, resting state network SC, structural connectivity; SI, search information

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