Biomedical Engineering Reference
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of postsynaptic potential (synchronization). If these conditions are not met, then the
total summed activity is too weak to produce nonnegligible extracranial fields.
5.3 Localization of the Electrically Active Neurons as a Small Number
of “Hot Spots”
An early attempt at the localization of the active brain region responsible for the
scalp electric potential distribution was performed in a semiquantitative manner by
Brazier in 1949 [16]. It was suggested that electric field theory be used to determine
the location and orientation of the current dipole from the scalp potential map. This
can be considered to be the starting point for what later developed into “dipole
fitting.”
Immediately afterward, using a spherical head model, the equations were
derived that relate electric potential differences on the surface of a homogeneous
conducting sphere due to a current dipole within [17, 18]. About a decade later, an
improved, more realistic head model considered the different conductivities of neu-
ral tissue, skull, and scalp [19]. Use was made of these early techniques by Lehmann
et al. [20] to locate the generator of a visual evoked potential.
Note that in the single-current dipole model, it is assumed that brain activity is
due to a single small area of active cortex. In general, this model is very simplistic
and nonrealistic, because the whole cortex is never totally “quiet” except for a sin-
gle small area. Nevertheless, the dipole model does produce reasonable results
under some particular conditions. This was shown very convincingly by Henderson
et al. [21], both in an experimentally simulated head (a head phantom) and with
real human EEG recordings. The conditions under which a dipole model makes
sense are limited to cases where electric neuronal activity is dominated by a small
brain area. Two examples where the model performs very well are in some epileptic
spike events, and in the description of the early components of the average brain
stem auditory evoked potential [14]. However, it would seem that the localization
of higher cognitive functions could not be reliably modeled by dipole fitting.
5.3.1 Single-Dipole Fitting
Single-dipole fitting can be seen as the localization of the electrically active neurons
as a single “hot spot.” Consider the case of a single current dipole located at posi-
tion
r
v
∈
R
3×1
with dipole moment
j
v
∈
R
3×1
, where
(
)
T
r
v
=
xyz
(5.1)
V
V
V
denotes the position vector, with the superscript
T
denoting vector/matrix transpo-
sition, and
(
)
T
j
v
=
j
j
j
(5.2)
x
y
z
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