Combining EEG and MRI Techniques - Quantitative EEG Analysis Methods and Clinical Applications - page 328

erties of the corresponding source vector J . However, the smallest unit of brain
activity that is visible outside the head is not a cortical point source but an extended
cortical patch. The dense 2- to 3-mm discretization of the cortical sheet (correspond-
ing to “point sources” that actually are 2- to 3-mm patches) is necessary to sample
the variation of surface orientations with sufficient resolution. The extension of cor-
tical excitation that actually produces an EEG signal above noise is typically larger
by a factor of 5 to 10, and so is the spatial resolution of the inverse methods used.
The effects of this discrepancy can best be seen when cortical surface normals
are taken into account and cortical source orientations are fixed. In such a case,
MNLS will reconstruct activity only in parts of the cortex where locations and sur-
face normals match the measured field distribution. Because the variation of normal
orientations within the range of matching locations is rather wide, a fragmented
source constellation is reconstructed. Such a constellation might show activity on
opposing walls of a gyrus or sulcus but not on the crown, and it is hard to tell
whether these distinct activities are distinct sources or an artifact of using point
sources and cortical surface normals.
The use of extended sources (cortical patches) instead of point sources in the
lead field matrix and the model term promises to remove this ambiguity. The size of
the patches should match the resolving power of the inverse method or the size of the
actual extension of cortical excitation, whatever is larger (see Figure 12.7).
Patch-based source models have also been proposed as extensions of dipole fit
methods, where only one or a few patches are active simultaneously [29, 30], and it
is certainly advantageous to perform an exhaustive search optimization for one or a
few cortical patches instead of dipoles [31]. Cortical patches can also be used as the
basis of CDR:
The relation between N J point sources J and N P cortical patches U can be
expressed by the N P ×

N J weighting matrix P , whose columns represent the shape of
the patch in terms of the point sources J [32]:

JPU = (12.6)

To capture the variability of possible source constellations, it is important that
overlapping patches are used. When using cortical patches, further spatial coupling
is unnecessary, so that B N P . Favorably, fixed orien-

tations (cortical normals) are used such that each patch is centered around the loca-
tion of the respective point source, yielding N P =

= 1. The dimension of W is N P ×

N V . Such a cortical patch
models the joint activity of sources with a variety of orientations along the folded
gray matter sheet.
Exchanging J for U yields the model term U T WU , while the data term is modi-
fied according to (12.6)

N J =

Φ −=− KJ Φ KPU (12.7)

We obtain a new CDR formulation that can be used with any inverse method. In
the MNLS case,

T T

U = arg min Φ − KJ + λ U WU = arg min Φ − KPU + λ U WU (12.8)