IEEE Signal Processing - May 2018 - 94

recordings. Some studies could obtain a good matching with
intracerebral invasive recordings [38], [43], [52].
For neurodegenerative and psychiatric disorders, the main
challenge is to develop methods that establish a relationship
between 1) the degree of cognitive deficit and 2) the alterations
within the functional connectivity of brain networks. To have
direct clinical impact, these new methods should be noninvasive, easy to use, and widely available in clinics. This is already
the case with EEG (MEG is still more research oriented). These
disorders share a common feature, i.e., they are characterized by
disturbances in large-scale neuronal networks. In this context,
EEG source connectivity methods seem to have the potential to
not only identify dysfunctional networks but also open new perspectives in terms of neuromarkers for cognitive impairment.
Results reported so far and synthetized in this article show that
this objective is reachable, provided that appropriate data processing is applied to sufficiently large databases [49].

field potentials (recorded by intracerebral electrodes) and EEG
signals (recorded by scalp electrodes) are random signals,
i.e., they take random values at any given time, they cannot
be predicted, and they can be characterized only statistically.
Nevertheless, at a given time t, the relationship between the
neuronal sources and the sensors is fully determined by biophysical factors, i.e., the position and orientation of equivalent
dipoles, the source/sensor distance, and the volume-conductor
properties (conductivity of the various layers). Typically, for
EEG, the equation X (t) = GS (t) + N (t) describes the relationships between the cortical sources S (t) and the signals
collected at scalp electrodes X (t). In this equation, S (t) is the
random fraction of the EEG signal. G is the lead field matrix
that describes the deterministic quasi-instantaneous projection of signal sources on the scalp electrodes. N (t) is the measurement noise inherent in any acquisition procedure.

Limitations and future directions

Volume-conduction effects are prominent in the electrode
space. Connectivity analysis at the source level was shown to
reduce the effect of volume conduction, as connectivity methods are applied to local time series (analogous to local field
potentials) generated by cortical neuronal assemblies modeled
as current dipole sources. Nevertheless, these so-called mixing
effects can also occur in the source space but can be reduced
by an appropriate choice of connectivity measures. Inverse
methods are characterized by their own spatial resolution, i.e.,
their ability to separate spatially closed sources, which depends
on methodological assumptions. Therefore, one should be cautious when interpreting brain connectivity measures even when
they are performed at the source level, since the hypothesis that
part of the measured coupling is also caused by the mixing of
sources cannot be ruled out.

In this section, we review some recent developments based on
EEG source connectivity, which is considered to have great
potential for brain research. This field is not yet mature, and it
lacks a complete validation procedure. However, this absence of
validation is not insuperable and should not prevent us from
increasing our research efforts in this field. For instance, progress will certainly be made with future developments such as the
simultaneous recording of intracerebral and scalp EEG data that
will be further used as a ground truth to evaluate proposed algorithms, at least in patients with drug-resistant epilepsy. Some
limitations and future directions are summarized hereafter.

Dipole models
EEG signals reflect a mixing of activities generated by neuronal sources arranged as assemblies. As described by bioelectromagnetic models [19] and experimental studies [20], it is
known that synaptic activation leads to the formation of a sink
and a source at the neuronal level that can then be viewed as
elementary current dipoles. In the case where neurons are geometrically aligned (as with pyramidal cells organized in palisade in cortical structures), the dipole contributions tend to
sum up instead of cancel out. These biophysical considerations
explain why summed postsynaptic potentials (PSPs)-either
excitatory or inhibitory-generated at the level of pyramidal
cells located in the cerebral cortex are the major contributors
to EEG signals recorded distantly from sources (typically with
electrodes positioned on the head). These issues explain why
the dipole model is the most suitable for solving the inverse
problem. Nevertheless, more efforts to overcome some of the
limitations of the dipole model (mainly the spatial limitations)
will certainly improve EEG forward/inverse solutions. Note
that from a biosignal processing viewpoint, the generation
mechanisms of EEG signals are considered to be random
(nondeterministic) processes.
Moreover, the generation of action potentials and PSPs in
neuron networks results from complex nonlinear processes
that cannot be analytically described. Consequently, local
94

Volume-conduction effects

Functional and effective connectivity measures
Every functional/effective connectivity measure has its own
strengths and weaknesses. False functional couplings can be
generated by some connectivity methods when applied to
mixed signals, such as estimated brain sources. To address this
issue, various methods were developed based on the rejection
of zero-lag correlation. In particular, unmixing methods,
known as leakage correction, have been reported that force the
reconstructed signals to have zero cross-correlation at lag zero
[53]. Although handling this problem theoretically helps interpretation, a quite recent study showed that the current correction methods also produce erroneous human connectomes
under very broad conditions [54].

Graph theory
Over the past decade, graph theory has become a wellestablished approach in the network neuroscience field [1]. It
provides complementary information to source connectivity
methods by quantifying structural, functional, and/or statistical
aspects of identified brain networks. This field is moving very
fast, so we stress the need for more validation studies regarding
the use of graph theory-based approaches in the context of

IEEE Signal Processing Magazine

May 2018

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