Electrophysiological Brain Connectivity: Theory and Implementation

Abstract

We review the theory and algorithms of electrophysiological brain connectivity analysis. This tutorial is aimed at providing an introduction to brain functional connectivity from electrophysiological signals, including electroencephalography (EEG), magnetoencephalography (MEG), electrocorticography (ECoG), stereoelectroencephalography (SEEG). Various connectivity estimators are discussed, and algorithms introduced. Important issues for estimating and mapping brain functional connectivity with electrophysiology are discussed.

Fig. 1

Levels involved in estimating neural connectivity from EEG and MEG. On the left models of brain reality. On the right, inferences made about this reality. Identifying neural connectivity is the ultimate objective. This is defined by the interactions (κ) between the activities of neural sources (ι). These in turn, determine the observed time series (ν) at the sensors. From these time series one can obtain measures of statistical dependence (δ). The attempt to use δ as a proxy for κ is known as “sensor level connectivity”. “Source level connectivity” solves the inverse problem to estimate κ. Estimated quantities at sensor and source levels are denoted as $\widehat{\delta }$, $\widehat{\iota }$, $\widehat{\kappa }$.

Fig. 2.

Venn diagrams depicting directed information decomposition. The terms T_x→y, denote Transfer Entropy, the terms T_ik→j, denote Joint Transfer Entropy, I_xy→z the Interaction Information, U_x→y the Unique Information, S_xy→z and R_xy→z the Synergetic and Redundant joint information of variables x and y on variable z. Reproduced from [107].

Fig. 3

Schematic diagram of EEG/MEG source imaging (From [116]).

Figure 4.

A computer simulation example to illustrate sensor and source connectivity issues. Four dipoles were placed upon the cortical surface. The forward field was generated by a BEM forward model. Activation is coded by a heat scale (red to yellow) and connectivity by a cool scale (blue to white). The projection to the scalp produces a very blurred activation and connectivity matrix due to volume conduction. On the right these same quantities are shown for four example inverse solutions - MNE, e-Loreta, ENET-SSBL, and BC-VARETA showing the appearance of “leakage” of both activation and connectivity estimates.

Fig. 5.

Top left: Functional connectivity patterns estimated in a subject during the performance of finger tapping movement, after the EMG onset. Each pattern is represented with arrows moving from one cortical area toward another. The color and size of the arrows code the level of strength of the functional connectivity observed between ROIs. The labels indicate the names of the ROIs employed. Bottom right: outflow patterns in all the ROIs obtained for the same connectivity pattern depicted in top left. The figure summarizes in red hues the behavior of a ROI in terms of reception of information flow from other ROIs, by adding all the value of the links arriving on the particular ROI from all the others. The information is represented with the size and the color of a sphere, centered on the particular ROI analyzed. The larger the sphere, the higher the value of inflow or outflow for any given ROI. The blue hues codes the outflow of information from a single ROI towards all the others. (From [134])

Fig. 6

Example of a spontaneous 8 sec EEG epoch and the decomposition of the data into microstates. The Upper part shows the bandpass (2-20Hz) filtered EEG. In the lower part, we see the four microstate classes estimated in the individual subject and the GFP of the above EEG data, color labelled based on the assignment of the individual time points to the best-fitting microstate class.

Fig. 7

Comparison of epileptic networks obtained on MEG-ICA and intracerebral EEG, with data recorded simultaneously (courtesy of S. Medina, methods in [251], [261], [262]).

Fig. 8

Identifying epileptic networks from ictal signals in a patient. Dynamic seizure imaging is applied to the seizures recorded in the EEG of this patient prior to surgery to identify the nodes of the ictal network. ADTF analysis was then applied to combined source space signals to determine the driving IC (left). The identified IC is in good accord with clinical findings, i.e. SOZ electrodes and surgical resection (right). (From [145])

Fig. 9

Altered directed resting-state connectivity in left and right temporal lobe epilepsy (TLE) measured by high density EEG in the absence of spikes. Main outflow in the posterior cingulate in controls (A) and ipsilateral medial temporal lobe in patients (B, C) (From [149]).