Biomedical Engineering Reference
In-Depth Information
As one can see, there is not much leeway for designing the model geometry, and
triangle sizes will be between 6 and 9 mm [15]. This, in turn, implies that a faithful
representation of anatomy is only one requirement of an algorithm that creates
BEM triangle meshes from MRI data. Equally important are a minimum distance
between compartment borders and a level of smoothness that allows triangles of the
required size to adequately represent the boundaries [16].
Finite element models (FEM) [17] use conductivity tensors per tetrahedral or
cubic volume element and allow us to overcome the isotropy restrictions imposed
by the BEM. However, computation times for the approximately 1 million elements
required are only now reaching practical levels [18], the definition of the tensor ori-
entations taken from, for example, diffusion tensor imaging is challenging, and for
the absolute conductivities the same literature values are still used as for the BEM
and spherical models.
12.1.3 Source Space
Large portions of prior knowledge about the sources of surface EEG are closely
related to cortical anatomy: locations and orientations of neurons, and spatial con-
nectivity (see Chapter 1). The cortex is a complexly folded two-dimensional struc-
ture. To make use of all available information from MRI for EEG source analysis
and to allow for advanced visualization, cortical triangle meshes have become a de
facto standard: The triangle mesh passes through the middle of the cortical gray
matter layers, its nodes represent potential source locations, and its edges encode
local neighborhood and allow us to compute surface normals, which represent the
orientation of neuronal current flow.
12.1.3.1 Source Locations
To constrain sources to the cortical gray matter, corresponding locations need to be
identified in the MRI. In a typical MRI, some 100,000 to 200,000 voxels represent
cortical gray matter [see Figure 12.4(a)]. If cortical voxels are taken as potential
source locations and source orientations are not taken into account, three unknown
source components per potential source location need to be computed, resulting in
300,000 to 600,000 unknowns. Because the spatial resolution of an EEG is more in
the order of a few millimeters than of a voxel (approximately 1 mm), some form of
data reduction may take place; without such data reduction, computation times
would be unjustifiably long.
As a consequence, there is basically the choice between a regular three-dimen-
sional grid with some 5- to 11-mm spacing, and a cortical source space sampled
with 2- to 3-mm resolution. When source coupling or extended sources are mod-
eled, the neighborhood relations of the source locations also need to be known.
Although this is straightforward for three-dimensional grids, the Euclidean distance
is not the correct measure for cortical sources. Functionally quite distinct areas can
be as close as two opposing walls of a sulcus while being several centimeters apart
on the two-dimensional cortical sheet. For this reason, a triangulation of the cortex
is the method of choice for defining the source space, where each vertex of the corti-
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