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Y. Zhang
not distorted by the conductive properties of tissues, since the magnetic permeability
of biological tissue is similar to that of empty space. As a result, MEG signals are not
affected by the volume conduction problem and the modelling of the volume conductor is not needed. A detailed description and formulation of the forward problem
for MEG is provided in [37]. Methods pertaining to solving the inverse problem are
similar for both EEG and MEG.
While insensitive to radial sources, the resistance of MEG measurements to the
blurring and distortion effects of volume conduction allows for better spatial resolution and accuracy. On the other hand, EEG signals are capable of capturing both
“radial” and “tangential” sources, yet the resolution suffers due to volume conduction problem. These features are clearly complementary, making methods for the
data integration analysis of these two modalities highly desirable. Owing to the fact
the MEG and EEG signals are generated by the same underlying current sources,
the integration analysis of MEG and EEG is made straightforwardly by combining the forward models of each individual method. Let us define a vector j of the
unknown dipole strengths of the current source, with the electric and magnetic lead
field matrices of G and B, respectively, and the vectors of the corresponding recorded
scalp potentials v and magnetic values m. The combined forward expressions is then
written in a concatenated form as:
G
B
j
v
m
(5.40)
A scaling procedure is implemented by normalizing the rows of G and B to their
respective norms and performing the same scaling operation on the measurement
vectors v and m [6]. The resulting linear system is presented as:
y A j + n
(5.41)
where y is the measurement vector representing the combined normalized electric and magnetic values, A is the combined normalized lead field matrix, and n
is the measurement noise vector. This formulation is analogous to the EEG forward
problem presented above, such that the same inversion scheme, with the same limitations, discussed for EEG can be applied to this system. Using a computer simulation
study, the EEG + MEG integration analysis was demonstrated to be able to achieve
significantly superior localization performance (in terms of residual error and temporal accuracy) in comparison to the separate unimodal analyses of EEG and MEG [6].
Further, EEG + MEG analysis results showed the best correspondence with the spatial
pattern of neural activity obtained by functional MRI results [77] (see Fig. 5.6).
Y. Zhang
not distorted by the conductive properties of tissues, since the magnetic permeability
of biological tissue is similar to that of empty space. As a result, MEG signals are not
affected by the volume conduction problem and the modelling of the volume conductor is not needed. A detailed description and formulation of the forward problem
for MEG is provided in [37]. Methods pertaining to solving the inverse problem are
similar for both EEG and MEG.
While insensitive to radial sources, the resistance of MEG measurements to the
blurring and distortion effects of volume conduction allows for better spatial resolution and accuracy. On the other hand, EEG signals are capable of capturing both
“radial” and “tangential” sources, yet the resolution suffers due to volume conduction problem. These features are clearly complementary, making methods for the
data integration analysis of these two modalities highly desirable. Owing to the fact
the MEG and EEG signals are generated by the same underlying current sources,
the integration analysis of MEG and EEG is made straightforwardly by combining the forward models of each individual method. Let us define a vector j of the
unknown dipole strengths of the current source, with the electric and magnetic lead
field matrices of G and B, respectively, and the vectors of the corresponding recorded
scalp potentials v and magnetic values m. The combined forward expressions is then
written in a concatenated form as:
G
B
j
v
m
(5.40)
A scaling procedure is implemented by normalizing the rows of G and B to their
respective norms and performing the same scaling operation on the measurement
vectors v and m [6]. The resulting linear system is presented as:
y A j + n
(5.41)
where y is the measurement vector representing the combined normalized electric and magnetic values, A is the combined normalized lead field matrix, and n
is the measurement noise vector. This formulation is analogous to the EEG forward
problem presented above, such that the same inversion scheme, with the same limitations, discussed for EEG can be applied to this system. Using a computer simulation
study, the EEG + MEG integration analysis was demonstrated to be able to achieve
significantly superior localization performance (in terms of residual error and temporal accuracy) in comparison to the separate unimodal analyses of EEG and MEG [6].
Further, EEG + MEG analysis results showed the best correspondence with the spatial
pattern of neural activity obtained by functional MRI results [77] (see Fig. 5.6).