Estimation of the effective and functional human cortical connectivity with structural equation modeling and directed transfer function applied to high-resolution EEG

Laura Astolfi, Febo Cincotti, Donatella Mattia, Serenella Salinari, Claudio Babiloni, Alessandra Basilisco, Paolo Maria Rossini, Lei Ding, Ying Ni, Bin He, Maria Grazia Marciani, Fabio Babiloni

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Different brain imaging devices are presently available to provide images of the human functional cortical activity, based on hemodynamic, metabolic or electromagnetic measurements. However, static images of brain regions activated during particular tasks do not convey the information of how these regions are interconnected. The concept of brain connectivity plays a central role in the neuroscience, and different definitions of connectivity, functional and effective, have been adopted in literature. While the functional connectivity is defined as the temporal coherence among the activities of different brain areas, the effective connectivity is defined as the simplest brain circuit that would produce the same temporal relationship as observed experimentally among cortical sites. The structural equation modeling (SEM) is the most used method to estimate effective connectivity in neuroscience, and its typical application is on data related to brain hemodynamic behavior tested by functional magnetic resonance imaging (fMRI), whereas the directed transfer function (DTF) method is a frequency-domain approach based on both a multivariate autoregressive (MVAR) modeling of time series and on the concept of Granger causality. This study presents advanced methods for the estimation of cortical connectivity by applying SEM and DTF on the cortical signals estimated from high-resolution electroencephalography (EEG) recordings, since these signals exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. To estimate correctly the cortical signals, we used a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from individual MRI, a distributed source model and a regularized linear inverse source estimates of cortical current density. Before the application of SEM and DTF methodology to the cortical waveforms estimated from high-resolution EEG data, we performed a simulation study, in which different main factors (signal-to-noise ratio, SNR, and simulated cortical activity duration, LENGTH) were systematically manipulated in the generation of test signals, and the errors in the estimated connectivity were evaluated by the analysis of variance (ANOVA). The statistical analysis returned that during simulations, both SEM and DTF estimators were able to correctly estimate the imposed connectivity patterns under reasonable operative conditions, that is, when data exhibit an SNR of at least 3 and a LENGTH of at least 75 s of nonconsecutive EEG recordings at 64 Hz of sampling rate. Hence, effective and functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high-resolution EEG techniques and linear inverse estimation with SEM or DTF methods. We conclude that the estimation of cortical connectivity can be performed not only with hemodynamic measurements, but also with EEG signals treated with advanced computational techniques.

Original languageEnglish (US)
Pages (from-to)1457-1470
Number of pages14
JournalMagnetic Resonance Imaging
Issue number10 SPEC. ISS.
StatePublished - Dec 2004

Bibliographical note

Funding Information:
This work was supported in part by the grant NSF BES-0411898.

Copyright 2018 Elsevier B.V., All rights reserved.


  • Directed transfer function
  • High-resolution EEG
  • Structural equation modeling


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