Biomedical Engineering Reference
In-Depth Information
c
U
f
−
µ
f
. The likelihood that
U
d
U
f
where
a
=
V
−
µ
c
−
V
c
a
=
is
generated with tumor model parameters Θ
j
is defined as
f
b
j
,
L
j
≡
where
j
=
V
d,j
U
d
−
µ
d,j
for
j
=1
, ..., n
m
. The estimate of the tumor model parameters is given by
b
T
j
=1
n
m
L
j
Θ
j
ˆ
Θ=
.
n
m
L
j
j
=1
4.5. Registration Results
Results of applying the approach described above are reported here for two
tumor cases. The first is an MR image of a patient with a glioma and a large region
of peri-tumor edema. The second is a simulated tumor image obtained by applying
the mass-effect model described in Section 4.3 to anMR image of a normal subject.
Both images are registered to an anatomical brain atlas that is composed of a T1-
weighted MR scan of a normal subject and an associated manual segmentation
of 106 cortical and subcortical brain structures. Both subject's images are also
T1-weighted MR scans. The atlas image dimensions are 256
×
×
256
198, and
the voxel size is 1
×
1
×
1 mm. The real and simulated tumor images are both of
dimension 256
1.5 mm.
The FE tumor mass-effect model simulations comprise the most computa-
tionally intensive step of the presented approach. In order to make the statistical
training step tractable, tumor simulations were performed on
n
s
=20MR brain
images of normal subjects. For each subject
n
m
=64simulations were performed,
with two values of each of the six model parameters covering the range expected
for the real tumor case. The parameter values were
r
t
∈
[3
,
5] mm,
r
e
∈
[20
,
27]
mm,
P
×
256
×
124 and voxel size 0.9375
×
0.9375
×
∈
[2
,
5] kPa, and corners of a cube in the atlas for the simulated tumor
center locations.
The simulations were carried out using the FE software ABAQUS [96]. The
average time needed to perform one simulation was about 35 minutes on a 900-
MHZ processor Origin 300 SGI processor machine with 4Gb of RAM. For the
results reported here, all principal components of the displacement
U
c
were re-
tained and
m
d
j
=1,
j
=1
, ..., n
m
, was used.
Modeling the statistical properties of shape and deformation over the whole
of the atlasl domain except for
M
A
requires the use of a very high-dimensional
space to represent these shapes or deformations. Beside the limitation imposed by