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

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.     

Principle of structural equation modeling for exploring functional interactivity within a putative network of interconnected brain areas

Functional neuroimaging first allowed researchers to describe the functional segregation of regionally activated areas during a variety of experimental tasks. More recently, functional integration studies have described how these functionally specialized areas, interact within a highly distributed neural network. When applied to the field of neurosciences, structural equation modeling (SEM) uses theoretical and/or empirical hypotheses to estimate the effects of an experimental task within a putative network. SEM represents a linear technique for multivariate analysis of neuroimaging data and has been developed to simultaneously examine ratios of multiple causality in an experimental design; the method attempts to explain a covariance structure within an anatomical constrained model. This method, when combined with the concept of effective connectivity, can provide information on the strength and direction of the functional interactions that take place between identified brain regions of a putative network.     

A serial functional connectivity MRI study in healthy individuals assessing the variability of connectivity measures: reduced interhemispheric connectivity in the motor network during continuous performance

To date, little data is available on the reproducibility of functional connectivity MRI (fcMRI) studies. Here, we tested the variability and reproducibility of both the functional connectivity itself and different statistical methods to analyze this phenomenon. In the main part of our study, we repeatedly examined two healthy subjects in 10 sessions over 6 months with fcMRI. Cortical areas involved in motor function were examined under two different cognitive states: during continuous performance (CP) of a flexion/extension task of the fingers of the right hand and while subjects were at rest. Connectivity to left primary motor cortex (lSM1) was calculated by correlation analysis. The resulting correlation coefficients were transformed to z-scores of the standard normal distribution. For each subject, multisession statistical analyses were carried out with the z-score maps of the resting state (RS) and the CP experiments. First, voxel based t tests between the two groups of fcMRI experiments were performed. Second, ROI analyses were carried out for contralateral right SM1 and for supplementary motor area (SMA). For both ROI, mean and maximum z-score were calculated for each experiment. Also, the fraction of significantly (P<.05) correlated voxels (FCV) in each ROI was calculated. To evaluate the differences between the RS and the CP condition, paired t tests were performed for the mean and maximum z-scores, and Wilcoxon signed ranks tests for matched pairs were carried out for the FCV. All statistical methods and connectivity measures under investigation yielded a distinct loss in left–right SM1 connectivity under the CP condition. For SMA, interindividual differences were apparent. We therefore repeated the fcMRI experiments and the ROI analyses in a group of seven healthy subjects (including the two subjects of the main study). In this substudy, we were able to verify the reduction of left–right SM1 connectivity during unilateral performance. Still, the direction of SMA to lSM1 connectivity change during the CP condition remained undefined as four subjects showed a connectivity increase and three showed a decrease. In summary, we were able to demonstrate a distinct reduction in left–right SM1 synchrony in the CP condition compared to the RS both in the longitudinal and in the multisubject study. This effect was reproducible with all statistical methods and all measures of connectivity under investigation. We conclude that despite intra- and interindividual variability, serial and cross-sectional assessment of functional connectivity reveals stable and reliable results.     

A new approach to estimating the signal dimension of concatenated resting-state functional MRI data sets

Estimating the effective signal dimension of resting-state functional MRI (fMRI) data sets (i.e., selecting an appropriate number of signal components) is essential for data-driven analysis. However, current methods are prone to overestimate the dimensions, especially for concatenated group data sets. This work aims to develop improved dimension estimation methods for group fMRI data generated by data reduction and grouping procedure at multiple levels. We proposed a “noise-blurring” approach to suppress intragroup signal variations and to correct spectral alterations caused by the data reduction, which should be responsible for the group dimension overestimation. This technique was evaluated on both simulated group data sets and in vivo resting-state fMRI data sets acquired from 14 normal human subjects during five different scan sessions. Reduction and grouping procedures were repeated at three levels in either “scan–session–subject” or “scan–subject–session” order. Compared with traditional estimation methods, our approach exhibits a stronger immunity against intragroup signal variation, less sensitivity to group size and a better agreement on the dimensions at the third level between the two grouping orders.     

Construction of a Langevin model from time series with a periodical correlation function: Application to wind speed data

A Langevin-type equation for stochastic processes with a periodical correlation function is introduced. A procedure of reconstruction of the equation from time series is proposed and verified on simulated data. The method is applied to geophysical time series–hourly time series of wind speed measured in northern Italy–constructing the macroscopic model of the phenomenon.