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Y. Zhang
constant “e” at the end of the equation, which represents the error of the model at the
particular voxel and timepoint. This term is added to account for the variation that
does not result from the variation in the known X factors. The model is considered
optimized when error is minimized—an e-value of 0 would be ideal; however such
a case never really occurs in practice. Instead, B values are chosen in such a manner
that the ‘e’-value of the equation is minimized in accordance with the shifting X
factors, resulting in an optimized model.
At this point, we have modeled the intensity of a single voxel at a single point in
time. Considering the number of timepoints and large number of possible factors, it
becomes easier to rewrite this model in matrix form. We will then rewrite this as:
y xβ + e
(5.44)
where y is a t × 1 matrix of the greyscale intensity of the volume at the t timepoints,
x is a j × t matrix representing the timecourse of the j regressors within the model
(known as the Design Matrix), β is the j × 1 matrix of static regressor coefficients,
and e is the t × 1 matrix representing the appropriately distributed error of the system
at any given time point. This is the essence of fMRI analysis—a GLM is established
and T- or F-tests are applied to identify specific voxels or regions of activity that are
significantly different from their baseline value. An example of this construction can
be seen in Fig. 5.8.
For many years, MRI stood as a singular imaging platform that was unable to
be a part of simultaneous data acquisition due to the use of strong magnetic fields.
More recent technological advances, however, have been enabling simultaneous
EEG-fMRI. This advent of MRI-capable EEG devices has brought with it the
search for algorithmic methods to capitalize on the temporal features of EEG and
spatial features of fMRI. At the time of writing, a number of methods are available
which can be broadly split into Asymmetrical Methods and Symmetrical Methods
depending on how they treat the information from each modality. A broad overview
of the topic can be seen in Fig. 5.9.
5.3.2.2 Asymmetrical Methods
Asymmetrical Methods were among the first devised which, in accordance with their
name, place a stronger value on one modality over another. This typically takes the
form of one modality generating the actual observed results while the secondary
method provides a guiding influence. Once more, these approaches will split into
categories to allow for a clearer analysis investigation.
fMRI-Constrained EEG
fMRI-informed EEG is perhaps the most fundamental of the multimodal approaches.
Under this architecture, static fMRI maps are used to constrain EEG source localization results. The most straightforward method of combination is to restrict the source
Y. Zhang
constant “e” at the end of the equation, which represents the error of the model at the
particular voxel and timepoint. This term is added to account for the variation that
does not result from the variation in the known X factors. The model is considered
optimized when error is minimized—an e-value of 0 would be ideal; however such
a case never really occurs in practice. Instead, B values are chosen in such a manner
that the ‘e’-value of the equation is minimized in accordance with the shifting X
factors, resulting in an optimized model.
At this point, we have modeled the intensity of a single voxel at a single point in
time. Considering the number of timepoints and large number of possible factors, it
becomes easier to rewrite this model in matrix form. We will then rewrite this as:
y xβ + e
(5.44)
where y is a t × 1 matrix of the greyscale intensity of the volume at the t timepoints,
x is a j × t matrix representing the timecourse of the j regressors within the model
(known as the Design Matrix), β is the j × 1 matrix of static regressor coefficients,
and e is the t × 1 matrix representing the appropriately distributed error of the system
at any given time point. This is the essence of fMRI analysis—a GLM is established
and T- or F-tests are applied to identify specific voxels or regions of activity that are
significantly different from their baseline value. An example of this construction can
be seen in Fig. 5.8.
For many years, MRI stood as a singular imaging platform that was unable to
be a part of simultaneous data acquisition due to the use of strong magnetic fields.
More recent technological advances, however, have been enabling simultaneous
EEG-fMRI. This advent of MRI-capable EEG devices has brought with it the
search for algorithmic methods to capitalize on the temporal features of EEG and
spatial features of fMRI. At the time of writing, a number of methods are available
which can be broadly split into Asymmetrical Methods and Symmetrical Methods
depending on how they treat the information from each modality. A broad overview
of the topic can be seen in Fig. 5.9.
5.3.2.2 Asymmetrical Methods
Asymmetrical Methods were among the first devised which, in accordance with their
name, place a stronger value on one modality over another. This typically takes the
form of one modality generating the actual observed results while the secondary
method provides a guiding influence. Once more, these approaches will split into
categories to allow for a clearer analysis investigation.
fMRI-Constrained EEG
fMRI-informed EEG is perhaps the most fundamental of the multimodal approaches.
Under this architecture, static fMRI maps are used to constrain EEG source localization results. The most straightforward method of combination is to restrict the source