IEEE Signal Processing - May 2018 - 83

activity of N brain sources S (t). The computation of the statistical couplings directly between the X(t) time series produces an M # M -dimensional functional network at the scalp
level. Scalp-EEG-based networks were widely used in the past
[5]. However, interpretation of connectivity from sensor-level
recordings is very difficult, as these recordings are severely
corrupted by the effects of field spread and volume conduction
[6]-[8]. Ideally, if each electrode measures only the neuronal
activity below it, then any statistical coupling measured from
signals recorded from two electrodes X 1 and X 2 would
reflect the connectivity between two physically distinct brain
regions S 1 and S 2 [Figure 1(a)].
Unfortunately, this ideal situation cannot always be assumed
for EEG recordings. The biophysics of the forward problem of
EEG shows that each scalp electrode, to a certain degree, measures the activity arising from all brain sources, depending on
1) the source-to-sensor distance and 2) the orientation of the
equivalent dipoles associated with these sources. Therefore,
scalp EEG signals correspond to a complex mixture of overlapping signals arising from distinct brain regions. A direct
consequence is that statistical couplings measured in the electrode space (whatever the signal processing method used to
this end) cannot be interpreted in a straightforward manner
as a brain connectivity measure between the underlying cortical regions [Figure 1(b)].
Several methods have been proposed to manage the volume-conduction problem when computing connectivity at the
scalp level, such as the use of a spatial filter prior to computing connectivity (Laplacian montages), the computation of the
time-lagged connectivity that would reflect a propagation process between distant areas, and the use of measures less sensitive to volume conduction, such as the imaginary part of the
coherence. However, none of the proposed methods has shown
itself to be capable of completely overcoming the limitations of
the volume-conduction and the field-spread problems. See [8]
for more details concerning these approaches.

From EEG signals to cortical network
The computation of the statistical couplings between EEG
cortical sources reconstructed from the M channels is one of
the best methods so far for alleviating the volume-conduction
problem, as the connectivity is computed at the level of the
sources S (t). This can produce a network (at the cortical level)
of N # N sources. Practically, this network is often reduced
to R # R brain regions, where R represents the number of
regions of interest (ROIs), which can vary depending on the
segmentation parameters for the cortical surface (this issue
will be considered in the following sections). The key idea of
the EEG source-connectivity method is the reconstruction of
functional networks at the neocortical level from scalp recordings (see Figure 2).
EEG data can be recorded during task-related or task-free
paradigms, and the recordings can be performed on medical
patients as well as healthy subjects. Signals are preprocessed
using, e.g., artifact removal and filtering techniques. The
resulting signals constitute the input to the source connectivity

(a)

(b)

FIGURE 1. An illustration of the volume-conduction problem for interpreting scalp-level connectivity. X1 and X2 represents the electrodes, S1 and
S2 represent the brain sources, the black arrow represents the measured
functional connectivity between X1 and X2, and the white arrows represent
the pathway of electrical activity from S1 and S2. (a) Ideally, each electrode
measures brain activity below the electrode, and, thus, the connectivity between electrodes reflects the connectivity between distinct brain
regions. (b) In practice, both brain sources S1 and S2 contribute to signals
recorded at each electrode. Due to this mixing phenomenon, the statistical
couplings measured in the electrode space cannot be directly interpreted
in terms of brain connectivity between the underlying cortical regions.

method. Figure 2(b) details the necessary elements required
to reconstruct the EEG sources. A lead field matrix is needed
and can be computed from a multiple-layer head model and the
position of the scalp electrodes. Figure 2(b) also illustrates the
boundary element method, which is classically used in the case
of realistic multiple-layer head models (the skin, skull, cerebrospinal fluid, gray matter, and white matter layers). Using
segmented MRI data, the source distribution is constrained
to a field of current dipoles homogeneously distributed over
the cortex and normal to the cortical surface. The dynamics
of the reconstructed sources are then estimated by solving the
inverse problem, which consists of estimating the remaining
free parameter, i.e., the moment of the dipoles. A source space
with defined ROIs is most often used given a number of regional time series (68 ROIs extracted from a Desikan atlas [20] in
this example).
Figure 2(c) and (d) details the subsequent steps that occur
once the regional time series are reconstructed. The functional connectivity can be estimated by computing the statistical couplings between these time series. This produces an
adjacency matrix that represents the pairwise functional connections between all of the ROIs. Finally, once the nodes and
edges have been defined, network topological properties can
be studied by graph theory-based analysis. These quantitative
metrics can be used for cognitive research or with a clinical
perspective, such as in the localization of abnormal epileptic networks or the computation of biomarkers of cognitive
decline in neurodegenerative diseases. The full pipeline from
EEG recordings to cognitive/clinical markers of brain functions and dysfunctions involves four main steps, which are
detailed in the following sections.

IEEE Signal Processing Magazine

May 2018

Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018