Biomedical Engineering Reference
In-Depth Information
can be used to simulate deformation induced by the tumor in the atlas and obtain
ϕ
a
, followed by the use of a deformable image registration method to get
ϕ
b
, and
therefore also the desired deformation map:
ϕ
f
(
X
A
)=
ϕ
b
◦
ϕ
a
(
X
A
)
=
ϕ
b
(
ϕ
a
(
X
A
))
.
(2)
The behavior of the biomechanical model is controlled by a number of parameters,
such as the location of the tumor, its size, and the extent of peri-tumor edema. We
will collectively refer to these variables as Θ. The values of these parameters are
not known for real tumor cases, and therefore they must be estimated for each
new tumor case. This inverse estimation problem is solved via a statistical model
that exploits the relationship between
ϕ
f
and the mass-effect model parameters.
The overall procedure for deformable image registration between the normal brain
image of an atlas and a patient's tumor-bearing image can be summarized as
follows:
1. A readily available deformable brain image registration approach (such
as HAMMER [52]) is used to obtain an approximation of the desired
deformation map
ϕ
f
between the atlas image (with no tumor) and the
patient's tumor-bearing image. The resulting deformation map will be
inaccurate in and around the tumor area (denoted by
M
A
in the atlas image
in Figure 12).
2. Although the approximation of
ϕ
f
obtained in Step 1 is incorrect in region
M
A
, the pattern of this deformation outside
M
A
can guide the estimation of
the mass-effect model parameters Θ. This is achieved here via a statistical
model, which is trained on examples of the map
ϕ
f
ϕ
c
for different
values of the tumor parameters. These deformation maps are obtained
through the use of HAMMER to register the atlas to brain images of normal
subjects, followed by tumor mass-effect simulations on the images of these
normal subjects. The details of the statistical model training and estimation
stages are provided in Sections 4.4.1 and 4.4.2, respectively.
=
ϕ
d
◦
3. With the estimated biomechanical tumor model parameters, a simulation
of tumor mass effect is performed on the atlas images to obtain an estimate
of the deformation map
ϕ
a
and to generate an atlas image with a simulated
tumor.
4. A deformable image registration approach, such as HAMMER, is then
used to obtain an estimate of the deformation map
ϕ
b
between the atlas
image with the simulated tumor and the image of the real tumor patient.
5. The composition of the obtained deformation maps in Steps 3 and 4 pro-
vides an estimate of the desired deformation map
ϕ
f
. The estimate of the
