Biomedical Engineering Reference
In-Depth Information
Many methods have been proposed in the literature for obtaining shape trans-
formations between a template shape and shape instances in images. This is
usually achieved through a method for deformable image registration. In Section
2 we describe recent efforts in deformable image registration by our group. Sec-
tion 3 is dedicated to explaining approaches for voxel-based morphometry and the
use of these approaches in the study of normal and pathological changes in brain
structure.
Available methods for brain image morphometry would also be very useful
in quantifying and understanding changes in brain structure due to the presence
of a brain tumor. In addition to these benefits that voxel-based morphometric
methods can provide, deformable registration between brain tumor images and
a brain template (Step 2 above) will make the construction of statistical brain
tumor atlases possible. These statistical atlases will be able to link structural and
functional information to variables such as the tumor size, type, location, and
response to therapy or the success of surgery. Such statistical brain tumor atlases
will be extremely useful in neurosurgery and radiotherapy planning and in the
study of brain tumor development and mechanisms.
The presence of tumors and their associated effects on the brain images sig-
nificantly complicate the deformable registration and make the results of current
image registration methods inaccurate in the vicinity of the tumor. In Section 4
we describe recent efforts by our group for deformable registration of brain tumor
images. Two main components have been developed to solve this deformable
registration problem. The first is a biomechanical model of brain tumor mass-
effect. The second is a statistical model that links deformation caused by tumors
to variables such as the tumor size, location, and the amount of peri-tumor edema.
These components and their integration into a method for deformable registration
of brain tumor images are described in detail in Section 4.
2.
SHAPE TRANSFORMATIONS AND DEFORMABLE REGISTRATION
OF BRAIN IMAGES
The goal of the deformable registration between two brain images is to find
the transformation that maps every point in the first image to its matching point
in the second image. Matching points should correspond to the same anatomical
feature or structure. The shape transformation found is usually required to be a
diffeomorphism — a differentiable and invertible mapping between the domains
of the two images. In mathematical terms, let
D
1
be the domain of the first image,
and let
D
2
be the domain of the second image. The sought shape transformation
is a differentiable and invertible mapping
ϕ
:
D
1
→
D
2
such that for every point
x
∈
D
1
, the point
ϕ
(
x
)
∈
D
2
corresponds to the same anatomical feature or
structure as that of point
x
.
