Biomedical Engineering Reference
In-Depth Information
To evaluate the registration error in this case, 25 points were selected arbitrar-
ily in the area around the simulated tumor, and their corresponding coordinates
(found through
ϕ
d
◦
ϕ
c
, which is available in this case) were computed in the atlas
image and treated as ground truth. The errors for the direct deformable registra-
tion and that obtained by the proposed approach are also presented in Table 3.
The maximum error was reduced by 29% using the proposed approach and the
corresponding average error was reduced by 39%.
4.6. Discussion and Future Work
We have here presented an approach for the deformable registration of normal
anatomical atlases to brain tumor images. The approach utilizes a 3D biomechan-
ical FE model of tumor-induced deformation to introduce and simulate the tumor
mass-effect in the atlas image. HAMMER [52], a readily available deformable
image registration method, is then used to find the map between the atlas with
the simulated tumor and the patient's image. To solve the inverse problem of
determining the parameters of the biomechanical model, a statistical approach is
used. This approach relies on decomposition of the desired deformation map (be-
tween the atlas and the tumor-bearing patient's image) into the sum of two maps
in orthogonal subspaces, defined on the same domain, but with different statistical
properties. The first deformation map is from the atlas to another normal brain
image. The second is the deformation map from the normal brain image to one
that is deformed by the biomechanical model of tumor mass-effect. The statistical
properties of both of these deformation maps are learned via PCA from a number
of training samples. Owing to the orthogonality of the two components of the
modeled deformation map, an initial rough estimate of this deformation map is
projected on the subspace representing tumor-induced deformation and is used to
estimate the tumor mass-effect model parameters.
The results of applying the proposed approach on a real tumor case and a simu-
lated one indicate significant reduction in the registration error. These experiments
should be regarded as a proof-of-concept study. More validation experiments are
needed to assess the viability of the proposed approach for a variety of tumor cases
of different grades, types, and sizes. In addition, the sensitivity of the statistical
estimator of the model parameters to the number of used principal components and
the number of training samples also present important directions for future investi-
gations. Another possible extension to the approach presented here is to iteratively
refine the estimate of the tumor model parameters, based on the latest available
deformation map (iterate through steps 2 to 5 in the procedure in Section 4.2).
HAMMER, the used deformable registration method, was designed to deal
with images of two normal subjects. The presence of the tumor and edema in
the images present a significant challenge to the image matching, especially since
these regions may not be exactly matching in two images. An image registration
method that takes into account such differences between the images is expected to
further improve the final deformable registration result.
