Biomedical Engineering Reference
In-Depth Information
3.
VOXEL-BASED MORPHOMETRIC ANALYSIS
3.1. Deformation-Based Methods
This is the most popular family of methods, and it derives directly from the
principles described above, namely that the shape transformation from a template
to an individual anatomy is a quantitative measure of the individual anatomy. A
variety of methods that rely on the analysis of shape transformations have been
presented in the literature. Many of these methods deal directly with the defor-
mation fields generated at each voxel in the template image. Examples of this
approach include Bookstein's work on landmark-based morphometrics [23], the
work of Grenander [40], Miller [24], and earlier studies by our group focusing on
sex differences in the corpus callosum [25, 41].
Quantities that are derived from shape transformations have been studied in
the literature and proposed for morphometric analysis. A deformation field that
maps one image to another may be treated as a discrete vector field. Taking
the gradients of this field at each element produces a Jacobian matrix field in
which each element is a tensor. The use of this tensor field in shape analysis is
sometimes called Tensor-Based Morphometrey (TBM) [27]. The determinant of
this Jacobian field has also been suggested for mophometric analysis [66]. This
scalar field describes local differences in the volume of structures relative to their
corresponding structures in the template image.
3.2. The VBMMethod Used by the SPM Software
An alternative to the approach of measuring a deformation field that accurately
maps a template to an individual has been adopted by the SPMgroup [67] and used
in several studies (e.g., [68]). The main rationale behind that method is that one
does not necessarily need to accurately match all images in a study to the template.
A coarse match, which removes some but not all variability across subjects, is
used to spatially normalize images into a stereotaxic coordinate system. Then,
residual differences in tissue types encountered in the vicinity of an image voxel
are assumed to reflect underlyingmorphological differences across individuals and
groups. For example, if a particular brain disease causes a selective loss of tissue
in a particular region of the brain, the residual density, after spatial normalization,
of brain tissue in a diseased population will be lower than that in a population
of healthy controls. This approach is a reasonably effective approach when the
tissue atrophy is spread over a large region of the brain, in which case accurate
registration should not be critical. However, for diseases that affect brain tissue
relatively focally, this approach is limited. Moreover, some of the morphological
characteristics of interest are removed by the spatial normalization transformation,
and therefore they are never measured by the residual density. This is in contrast to
deformation-based methods. Even more importantly, the amount of information
