Theory of the EEG Inverse Problem - Quantitative EEG Analysis Methods and Clinical Applications - page 122

same technique, in which brain localization inference is based on the scalp distribu-
tion of electric potentials (commonly known as topographic scalp maps).
We must emphasize from the outset that this topographic-based method is, in
general, not correct. In the case of EEG recordings, scalp electric potential differ-
ences are determined by electric neuronal activity from the entire cortex and by the
geometrical orientation of the cortex. The cortical orientation factor alone has a
very dramatic effect: An electrode placed over an active gyrus or sulcus will be influ-
enced in extremely different ways. The consequence is that a scalp electrode does not
necessarily reflect activity of the underlying cortex.
The route toward EEG-based neuroimaging must rely on the correct use of the
physics laws that connect electric neuronal generators and scalp electric potentials.
Formally, the EEG inverse problem can be stated as follows: Given measurements of
scalp electric potential differences, find the three-dimensional distribution of the
generators, that is, of the electric neuronal activity.
However, it turns out that in its most general form, this type of inverse problem
has no unique solution, as was shown by Helmholtz in 1853 [3]. The curse of
nonuniqueness [4] informally means that there is insufficient information in the
scalp electric potential distribution to determine the actual generator distribution.
Equivalently, given scalp potentials, there are infinitely different generator distribu-
tions that comply with the scalp measurements. The apparent consequence is that
there is no way to determine the actual generators from scalp electric potentials.
This seemingly hopeless situation is not very true. The general statement of
Helmholtz applies to arbitrary distributions of generators. However, the electric
neuronal generators in the human brain are not arbitrary, and actually have proper-
ties that can be combined into the inverse problem statement, narrowing the possi-
ble solutions. In addition to endowing the possible inverse solutions with certain
neuroanatomical and electrophysiological properties, we are interested only in those
solutions that have “good” localization properties, because that is what

neuroimaging is all about: the localization of brain function.
Several solutions are reviewed in this chapter, with particular emphasis on the
general family of linear imaging methods.

5.2 EEG Generation

Details on the electrophysiology and physics of EEG/MEG generation can be found
in publications by Mitzdorf [5], Llinas [6], Martin [7], Hämäläinen et al. [8],
Haalman and Vaadia [9], Sukov and Barth [10], Dale et al. [11], and Baillet et al.
[12]. The basic underlying physics can be studied in [13].

5.2.1 The Electrophysiological and Neuroanatomical Basis of the EEG
It is now widely accepted that scalp electric potential differences are generated by
cortical pyramidal neurons undergoing postsynaptic potentials (PSPs). These neu-
rons are oriented perpendicular to the cortical surface. The magnitude of experi-
mentally recorded scalp electric potentials, at any given time instant, is due to the
spatial summation of the impressed current density induced by highly synchronized