Biomedical Engineering Reference
In-Depth Information
Figure 5.
Schematic representation of the mass-preserving framework of the RAVENS
analysis. A shape transformation (a) that causes contraction of the structure as it maps it to
a stereotaxic space increases the tissue density within the structure, so that the total amount
of tissue is preserved. The transformation (b) is different (e.g., it might correspond to a
result with greater error in the shape transformation). However, the total amount of tissue
is preserved under both transformations, (a) and (b). For example, integrating the tissue
density within the outlined regions gives exactly the same result, and is equal to the area of
the outlined region in the original shape. This property is lacking in direct measurements
of the shape transformation.
that is lost during spatial normalization is not controlled in any way, but might
actually vary from one image to another, depending on how similar the template is
to the respective individuals and what the limitations of the spatial normalization
algorithm are. Despite these limitations, VBM has been freely available via the
SPM software and has used quite widely and successfully, especially in studies
that do not seek subtle and spatially localized brain abnormalities.
3.3. TheMass-PreservingPrinciple forRegional VolumetricAnalysis
Morphometric analysis based solely on the shape transformation that maps a
template to an individual anatomy is affected by errors in determining the shape
transformation. If thewarpingmechanismused by a particularmethod is not able to
perfectly match the anatomy of each individual with the anatomy of the template,
then subtle structural characteristics are lost and never recovered in subsequent
stages of the analysis. These errors can be significant obstacles in studying subtle
differences between two or more individuals or time points. In order to address this
problem, we developed a mass-preserving framework for shape transformations
that is relatively more robust, for reasons that are explained below. Our approach
is shown schematically in Figure 5.
In the mass-preserving framework of RAVENS [2, 69, 70] (Regional Analysis
of Volumes Examined in Normalized Space), if the shape transformation applies
an expansion to a structure, the density of the structure decreases accordingly
to warranty that the total amount of tissue is preserved. Conversely, tissue den-
