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
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