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Author : Mr. Shao Fan & Mr. Chen Hongjun
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Figure
1. Protocol of lumpectomy by
the use of Mammotome
The problem is that after the
tumor tissue is totally removed, even the experienced doctor can hardly tell
where the margin is from the ultrasound images. To remove the margin with full
confidence, we need to develop a reliable method to keep track of the tumor
margin or predict the margin deformation during the tissue aspiration. To model
the soft-tissue deformation, biomechanical models, such as Finite Element Method
(FEM), are widely used. Despite its accuracy in modeling the biomechanical
deformation, there are three factors that put it in disadvantage over its
application in our lumpectomy surgery. Firstly, the underlying breast tissue is
composed of several layers of tissue and the biomechanical properties of the
underlying breast tissue are varied over different patients, which relate to
their age and size. Thus, in vivo measurement for the tissue properties ts
required, which is more difficult albeit possible by recent technological
advances, and adds more complexity in the operation procedure. Secondly, the
cutting process by the vacuum-assisted biopsy probe adds another complexity in
the modeling, where we have to model the suction of tissue into hollow chamber,
the tissue cutting and the retrieval of the tissue. Thirdly, to allow real-time
performance of the modeling, biomechanical model requires optimization and yet
it still demands high computation power. Therefore, in this project, two more
reasonable methodologies are investigated, i.e. statistical shape model and
image registration.
The statistical shape model can
alleviate the drawbacks faced by biomechanical model, though it may relax the
prediction accuracy. The statistical shape model is built based on a number of
training samples from which the deformation is known. The statistics of the
shape deformation is examined by the principal component analysis (PCA), and the
prediction is conducted based on the principal eigenvector that reflects the
large percentage of the statistical variations.
a) Statistical Shape Model in
Spatial Domain
Assume vector
is
the collection of points defining the shape and vector
represents
the deformation of the shape as illustrated in Figure 2.
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Figure
2. Shape deformation
represents by vector
.
Let vector
be
the concatenation of matrix
and
.
Thus the PCA is parameterized by the model mean
and the covariance matrix,
Then
can
be parameterized as follows,
where V is the matrix of M
eigenvectors,
and is the corresponding weight vector for the principal modes. Let the
eigenvector
be
decomposed into:
from which it follows that
and
where Vs and Vq
are the component of V. Based on the observed shape
and
the statistical knowledge of the deformation, we are able to estimate the
displacement vector
.
Subsequently, the unknown location of the deformed shape can be predicted
[1]. In this project, however, building a statistical (margin) shape model in
spatial domain is not easy. One of the difficulties is how to correctly
determine the landmarks correspondence from the ultrasound images of poor
quality.
b) Statistical Shape Model in
Frequency Domain
To overcome the difficulty in finding the landmarks correspondence, we
express the shape in frequency domain by means of Spherical Harmonics (SH).
According to the theory of SH, any spherical function
can
be decomposed as a linear sum of its harmonics:
where the coefficients
can
be used to reconstruct an approximation of the underlying object at different
levels. Therefore, any shape that is single-valued on R (i.e. convex-shaped
object) can be represented as
Here N denotes the highest
truncated degree which controls the shape detail, coefficients
is
now called the shape descriptors. By bijectively mapping each point on object
surface to the unit sphere, the non-convex shape can also be well expressed by
spherical harmonics [2].
Similar analysis on statistics of
and
in
spatial domain is then applied to shape descriptors
.
The shape deformation is characterized by the change of shape descriptors thus
the difficult in finding the landmarks correspondence can be avoided.
Nevertheless, there are some big challenges in building a reliable statistical
model to fulfill the project tasks. The most serious problem is that to make
sure the training data conform to a normal distribution, huge amount of data
need to be collected and analyzed carefully (e.g. outline
the margin surface manually) afterwards. From our experience, limited
sets of data can not model the tissue deformation well due to the irregular
shape of breast cancer. Besides, the problem of difficulty in determining
the margin surface after the tumor tissue is totally gone is still there (though
not urgent) when we build the model.
Rather than describing the margin
surface according to the remained tumor during the tissue aspiration, we can use
image registration to keep track of the margin deformation. The basic idea
arises from the fact that the contents appeared outside the margin surface keep
consistent though deformed during the whole surgery process.
A wide range of methods have been
developed for registration, each suited to certain types of data and problems.
These methods mainly rely on internal anatomic point, contour and surface
landmarks, or voxel similarity. Internal landmark based registration techniques
are limited since they require a specific segmentation. Contour and surface
based registration methods also rely on accurate segmentation of anatomical
structures. However, due to poor quality of ultrasound images, segmentation of
ultrasound volumes has been proven a very difficult task. Hence, voxel
similarity-based methods seem to be more suited to ultrasound volume
registration. As they require no segmentation, they are expected to be fully
automatic.
A few voxel similarity-based
methods have been proposed for ultrasound registration. According to the
literature, three main similarity measures were used: mutual information measure
[3], correlation coefficient on intensity values [4] or on gradient images [5],
and intensity values using optical flow hypothesis [6]. Besides, texture
information was also used to measure the similarity as proposed in [7]. Though
the most suitable method to our project is still under investigation, we prefer
the image registration methodology to statistical shape modeling.
References
[1] C.
Davatzikos, D. Shen, A. Mohamed, and S. K. Kyriacou, A framework for predictive
modeling of anatomical deformations, IEEE Trans. Medical Imaging, Vol. 20, No.
8, pp 836-843, 2001.
[2] C.
Brechbühler, G. Gerig and O. Kübler, Parametrization of closed surfaces
for 3-D shape description, Computer Vision and Image Understanding, Vol. 61, No.
2, pp 154-170, 1995.
[3] R. Shekhar
and V. Zagrodsky, Mutual
information based rigid and nonrigid registration of ultrasound volumes,
IEEE Trans. Medical Imaging, Vol. 21, No. 1, pp 9-22, 2002.
[4] G. Xiao, M.
Brady, J. A. Noble, M. Burcher, and R. English, Nonrigid registration of 3-d free-hand ultrasound images of
the breast, IEEE Trans. Medical
Imaging, Vol. 21, No. 4, pp 405-412, 2002.
[5] R. Rohling,
A. Gee, and L. Berman, Automatic
registration of 3d ultrasound images, Ultrasound
in Medicine and Biology, Vol. 24, pp 841-854, 1998.
[6] I.
Pratikakis, C. Barillot, and P. Hellier, Robust
multiscale non-rigid registration of 3D ultrasound images,
in Int. Conf. on Scale-Space and Morphology in Computer Vision, pp
389-397,
[7] F. Rousseau,
R. Fablet and C. Barillot, Robust statistical registration of 3D ultrasound
images using texture information, in: IEEE Int. Conf. on Image Processing, pp 581-584
The project is funded by National Medical Research Council (NMRC) and started in August 2002. The participants include Tan Tock Seng Hospital and Nanyang Technological University.
Publications related to Soft Tissue Study.
We would be glad if you could sign our guest book.
For more information, please contact the principal investigator:
A/P Ng Wan Sing
School of Mechanical & Aerospace Engineering
Nanyang Technological University
Nanyang Avenue, Singapore 639798
Fax:(65) 6791 1859
