Biomedical Engineering Reference
In-Depth Information
12.1.2 Volume Conductor Models
An exact model of the conducting properties of the human head is a necessary
(although not sufficient) condition for accurately localizing brain activity based on
the EEG. As outlined in Chapter 5, head modeling is part of the forward problem of
source analysis, which implies that head model errors or inaccuracies cannot neces-
sarily be detected by an inspection of the solution of the inverse problem or its asso-
ciated goodness-of-fit. The typical effect of an inaccurate head model is a
mislocalization of brain activity.
12.1.2.1 Spherical Head Models
Spherical head models (see Chapter 5) have been the traditional approach to EEG
source localization and have been in use since well before EEG-MRI integration was
an option. By using a spherical head model, one makes the assumption that the head
has the shape of a sphere, with electrodes located on the surface of that sphere. Elec-
trode locations on the sphere can be obtained by radial projection of the actual elec-
trode locations. Head conductivities are usually modeled as being piecewise
isotropic, with concentric subspheres delineating regions of different conductivities.
Usually, three or four differently conducting compartments are modeled, mimick-
ing the skull, everything outside the skull (often called the skin), and everything
inside the skull (the brain), and, optionally, a cerebrospinal fluid layer surrounding
the brain. Thus, the brain is also assumed to be of spherical shape.
When source localization results obtained using spherical head models are over-
laid onto MR images and compared with independently obtained information
about the true source locations, localization errors in the centimeter range can be
observed [8]. Discrepancies are larger in “nonspherical” parts of the head (e.g., the
temporal lobes) than they are in “spherical” parts, such as the central sulcus area.
Forward calculations using spherical head models can be performed quickly and
with high numerical accuracy.
Using MRI, the parameters governing a spherical head model can be fitted to
the segmented skin and skull, although in practice they are usually fitted to the elec-
trodes, and predefined percentages of the outer sphere's radius are employed for the
outside and the inside of the skull.
Modifications and extensions of the isotropic concentric three-sphere model
include the use of eccentric spheres [9], of anisotropic conductivities for the skull
(which is known to conduct better tangentially than radially) [10], of ellipsoids
instead of spheres [11], and of individually adapted spherical models per sensor
[12]. The geometric properties of these extensions can be obtained from an analysis
of the MRI.
12.1.2.2 Realistically Shaped Head Models
The sphere and ellipsoid ansatz can be overcome altogether by using tessellated sur-
faces or volumes: The boundary element method (BEM) can be used for modeling
the same compartments of isotropic conductivities (outside the skull, skull, inside
the skull) as used by the isotropic sphere models, but with BEM the compartment
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