Multimodal Integration: fMRI, MRI, EEG, and MEG - Advance Image Processing in Magnetic Resonance Imaging - page 241

which the solution was presented as unregularized (just minimum norm;
Equation 8.8) with and . The simplest way to account for
fMRI data is to use a thresholded fMRI activation map as the inverse solution
space, but this was rejected [1] due to its incapability to account for fMRI-silent
sources, which is why the idea to incorporate variance information from fMRI
into was further elaborated [108] by the introduction of relative weighting for
fMRI-activated voxels via constructing a diagonal matrix ,
where for fMRI-activated voxels and for voxels which are
not revealed by fMRI analysis. A Monte Carlo simulation showed that
(which corresponds to the relative fMRI weighting) leads to a good compro-
mise with the ability to find activation in the areas which are not found active by
fMRI analysis and to detect active fMRI spots (even superficial) in the DECD
inverse solution. An alternative formulation of the relative fMRI weighting in the
DECD solution can be given using a subspace regularization (SSR) technique [145],
in which an E/MEG source estimate is chosen from all possible solutions describing
the E/MEG signal, and is such that it minimizes the distance to a subspace defined
by the fMRI data (Figure 8.2). Such a formulation aids an understanding of the
mechanism of fMRI influence on the inverse E/MEG solution: SSR biases under-
determined the E/MEG source locations toward the fMRI foci.

WC
Q

= λ WC

X

=

S ε

C S

WW
Q

= = {} ν ii

fMRI

ν ii = 1 νν

ii

=∈,
0

0[]

ν 0 =. 01

90 %

FIGURE 8.2 Geometrical interpretation of subspace regularization in the MEG/EEG source
space. (A) The cerebral cortex is divided into source elements q1, q2,…,qK, each represent-
ing an ECD with a Fixed orientation. All source distributions compose a vector q in K-
dimensional space. (B) The source distribution q is divided into two components q a ∈ S a ≡
range(G T ), determined by the sensitivity of MEG sensors and q 0 ∈ null G, which does not
produce an MEG signal. (C) The f MRI activations define another subspace S f MRI . (D) The
subspace-regularized f MRI-guided solution q SSR

∈ M is closest to S f MRI , minimizing the
distance ||Pq SSR ||, where P (an N × N diagonal matrix with P ii = 1/0 when the i th f MRI
voxel is active/inactive) is the projection matrix into the orthogonal complement of S f MRI .
(Adapted from Figure 1 of Ahlfors, S.P. and Simpson, G.V. (2004). Geometrical inter-
pretation of fMRI-guided MEG/EEG inverse estimates. NeuroImage. 22(1): 323-332. With
permission.)