Biomedical Engineering Reference
In-Depth Information
diffeomorphisms [24], and by P. Thompson's work on tensor mapping [27], among
several other investigators. One of the first applied studies was performed by our
group by focusing on sex differences in the corpus callosum [25, 41].
In addition to allowing the mophometric analysis of brain structure, the avail-
ability of shape transformations from an anatomical brain template to various brain
images provides an additional important benefit. Through the inverse of such shape
transformations, information defined on the domains of individual brain images
can now be mapped onto the domain of the template. Thus the template acts
as a stereotactic space where structural, functional, and pathological information
from large databases of brain images can be collected and used for construction
of statistical atlases of normal and pathological variability. Through the use of
multivariate statistical analysis methods, it is also possible to discover correlates
between all variables stored in the atlas and to link this information to normal,
pathological and aging processes.
Despite the mathematical subtleties involved in the morphometric analysis
via shape transformations, the basic principle is simple and follows three standard
measurement steps, similar to the steps one would perform in order to measure,
for example, the lengths of objects:
1. A measurement unit is first selected to be used as reference; this might be
the meter or the yard in standard length measurements; and the measure-
ment unit is a typical brain image in shape measurements and is referred
to as the template.
2. The template is stretched over the extent of an individual's brain, so that
homologous features are mapped to each other; the shape transformation
quantifies exactly this stretching, and is analogous to stretching the meter
or the yard over the full length of an object, if one seeks to obtain a length
measurement.
3. Inter-individual comparisons are performed by comparing respective shape
transformations, exactly as one would compare a 2.3-m object to a 2.8-m
object. Of course, obtaining and comparing three- or four-dimensional
shape transformations is far more complicated than obtaining and com-
paring scalar length measurements, but the fundamental principle is the
same.
This chapter is dedicated to describing an approach for extracting shape trans-
formations based on medical images and the use of these shape transformations
to obtain voxel-based morphometric measurements of the anatomy in the images.
The selection of a suitable template that acts as a standard unit of measurement is
an important decision that affects subsequent steps. This active research topic is
not dealt with here, but the interested reader may wish to refer to recent articles
on the topic [42, 43].
