Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 148

We should note that the spatial distribution of potentials on the head surface is
reference invariant 4 , since if the reference potential shifts up or down the whole “po-
tential landscape” shifts by the same amount. It is important to keep in mind that the
absolute locations of the potential maxima or minima on the scalp do not necessarily
reflect the location of the underlying generators. This is due to the propagation of
the intracranial signals by volume conduction. One has to realize this fact in order to
avoid confusion in the interpretation of EEG data.
One possibility to obtain reference-free waveforms, which exploits the reference
invariance of topography, is the computation of the so-called current source density
(CSD) waveforms. The CSD or Laplacian derivation is obtained by estimation of the
2nd spatial derivative across the electrode montage ( Sect. 4.1.3) . In this way, CSD
derivations are intrinsically based on spatial gradients in the electric field at the scalp.
This procedure eliminates to some extent the problem of reference-dependance in-
herent to voltage waveforms and it also minimizes contributions of volume conduc-
tion within the plane of the scalp, thus effectively working as spatial “sharpening”
(high-pass) filters. However this kind of reference is not proper for methods rely-
ing on estimation of correlation matrix between the channels of the process, i.e., for
the MVAR model. The Laplacian operator disturbs the correlation structure of the
multivariate set of signals, and hence the phase dependencies.
It is important to note that the changes in the topography of the electric field at the
scalp can only be caused by changes in the configuration of the underlying intracra-
nial sources (excluding artifacts such as eye movements, muscle activity, etc.). 5 Map-
ping of electrical brain activity in itself does not constitute an analysis of the recorded
data but it is a prerequisite to extracting quantitative features of the scalp recorded
electrical activity. In the second step, in order to find the differences between experi-
mental conditions or between groups of subjects, the derived topographical measures
must be subjected to statistical tests.
Due to volume conduction, potentials measured on the scalp are spatially blurred.
The linear superposition of electric fields allows to assume that each electrode
records a signal which is a linear mixture of all the underlying sources of electri-
cal activity (not only from the brain, but also from muscle, cardiac, eye movement
etc.). Successful separation of the signals from different sources gives possibilities
of more correct functional interpretation of the different components of recorded
brain responses. In general there are three approaches to the problem of separating
the sources. Two of them operate in the sensor space and will be discussed in this
paragraph, the third approach is the solution of the inverse problem. Methods of so-
lutions to the inverse problem are beyond the scope of signal processing, therefore
they will not be considered here. The methods operating in the sensor space do not
require an explicit head model. They include: principal component analysis (PCA,
see Sect. 3.6.1) and blind source separation (BSS), most often implemented as in-
4 Please note that this does not hold for maps of power.
5 The opposite need not be the case, since there is an infinite number of current source configurations
inside the volume conductor that give the same distribution of potentials on the surface.