Image Processing Reference
In-Depth Information
for which the flux-locked loop acquired a lock [19, p. 265]. Although the choice of
a reference value in EEG and the DC line in MEG do not influence the analysis of
potential/field topographic maps, they do impact inverse solution algorithms that
assume zero net source in the head, i.e., zero baseline. In general, the simple average
reference across the electrodes is used, and it has been shown to be a good approx-
imation to the true reference signal (Reference 10, Subsection 8.2.2).
Even if the reference value (baseline) is chosen correctly, both conventional
EEG and MEG face obstacles in measuring the slowly changing DC component
of the signal in the low-frequency range (
[0.1]Hz). In the case of EEG, the
problem is due to the often-used coupling of the electrodes via capacitors, so
that any DC component (slowly changing bias) of the EEG signal is filtered out.
That leaves the researcher with nonzero frequency components of the signal,
which often correspond to the most informative part of the signal as in the case
of conventional ERP or frequency domain analysis. The DC-EEG component
can be registered by using sensors with direct coupling and special scalp elec-
trodes that are gel-filled to eliminate changes of electrical impedance at the
electrode-skin interface that can cause low-frequency noise in the EEG signal.
Although the MEG system does not require direct contact between sensors and
skin, it is nevertheless subject to 1/
f
<
sensor noise, which interferes with the
measurement of the neuronal DC fields. In the last decade, DC-MEG has been
methodically refined by employing controlled brain-to-sensor modulation allow-
ing the monitoring of low-frequency magnetic fields. Formalized DC-E/MEG
techniques make it possible to perform E/MEG studies, which rely on the shift
of DC and low-frequency components of the signal, components that occur, for
example, during epileptic seizures, hyperventilation, changes in vigilance states,
and cognitive or motor tasks.
f
8.2.2
F
M
ORWARD
ODELING
The analysis of E/MEG signals often relies on the solution of two related prob-
lems. The forward problem concerns the calculation of scalp potentials (EEG)
or magnetic fields near the scalp (MEG), given the neuronal currents in the brain,
whereas the inverse problem involves estimating neuronal currents from the
observed E/MEG data. The difficulty of solving the forward problem is reflected
in the diversity of approaches that have been tried (see Mosher et al. [
20
] for an
overview and unified analysis of different methods).
The basic question posed by both the inverse and forward problems is how
to model any neuronal activation so that the source of the electromagnetic field
can be mapped onto the observed E/MEG signal. Assuming that localized and
synchronized primary currents are the generators of the observed E/MEG sig-
nals, the most successful approach is to model the
i
th source with a simple
equivalent current dipole (ECD)
q
[21], uniquely defined by three factors: loca-
i
tion represented by the vector
r
, strength
q
, and orientation coefficients
θ
. The
i
i
i
orientation coefficient is defined by projections of the vector
q
into
L
orthogonal
i
Cartesian axes:
θ
=
q
/
q
. However, the orientation coefficient may be expressed
i
i
i
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