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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5835_Библиотеки_им_академика_М_И_Перельмана.pdf
variation and translation for malignant cases between precompressed and
postcompressed are obviously smaller than benign ones. Hence, we will present
some useful features for the lesion strain analysis in the following section.
7.3.4 Strain Features
As discussed earlier, the elasticity of tissue can be utilized as a framework for classi
-
fication of breast lesions into two different classes: benign cases and malignant
174 3-D Breast Ultrasound Strain Imaging
(b)
(a)
Figure 7.9 Sample segmentation results for a benign case in strain imaging framework: (a) the
precompressed image slices (numbers: 57, 66, 70, and 79), and (b) the postcompressed image slices.
(b)
(a)
Figure 7.10 Sample segmentation results for a malignant case in strain imaging framework: (a)
the precompressed image slices (numbers: 64, 68, 80, and 91), and (b) the postcompressed
image slices.
cases. This classification can be achieved by a powerful classifier, SVM, which can
utilize the deformation features of the two kinds of breast lesions. Thus, our imme-
diate goal should be to develop a strategy by which we can quantify tissue deforma-
tions in compression framework. The most straightforward and direct way would
be to compute the change in quantified values in precompressed and post-
compressed modes. We thus approach this in four different ways, utilizing features
of volume, enveloped cuboids enveloping the 3-D tumors, silhouette change, and
movement of lesions due to compression. These features are the ones mentioned
earlier in the chapter: volume difference (V
d
), shape difference (S
d
), contour differ-
ence (C
d
), and shift distance (M
d
).
7.3.4.1 Normalized Volume Difference
Because the volume of the precompressed lesion changes as a result of the probe
pressure, the purpose of this feature is to compare volumes between the
precompressed and postcompressed lesions. If the lesion is hard, then its volume in
the postcompressed images should be similar to that of the precompressed images.
Of course, the volume difference of a large lesion will be larger than that of a small
lesion. Hence, the volume difference should be normalized by the lesion volume.
The volume difference feature is mathematically expressed as:
V
d
=
−Vol Vol
Vol
pre post
pre
(7.8)
where Vol
pre
and Vol
post
are the lesion volumes in the precompressed and
postcompressed datasets, respectively. The volume of the lesion is mathematically
expressed as:
()
Vol Area
Lesion
=
∈
∑
R
i
R
i
(7.9)
where R
i
is the lesion region in the image slice i, and Area(R
i
) is the number of pixels
in region R
i
. For example, the tumor area is 15 pixels in Figure 7.11(c), and the
tumor area is 13 pixels in Figure 7.11(d). Then we calculate the volumes of a tumor
by summing up the tumor area sizes of every image slice. If the volume of the tumor
is 210 pixels in Figure 7.11(a) and the volume of the tumor is 197 pixels in Figure
7.11(b), then the number of difference pixels of these two tumors in Figures 7.11(a)
and (b) is 13 pixels, and the volume difference is 13/210 = 0.0619.
7.3.4.2 Normalized Shape Difference
When a tumor is compressed, its height will become smaller but its width and length
will become larger. If a tumor is soft, then the differences of height, width, and
length will be larger than those of a hard tumor. In a hard tumor, the height, width,
and length will remain at values similar to the precompressed values. Actually, the
ratios of width–height (WH) and length–height (LH) can be used to represent the
simple shape information. Hence, the shape difference of the precompressed and
postcompressed tumors can be defined by these two ratios:
7.3 Proposed Architecture of the 3-D Strain Imaging System 175
S
WH WH
WH
LH LH
LH
d
=
−−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
max ,
post pre
pre
post pre
pre
(7.10)
where WH
pre
and WH
post
are the width–height ratios for precompressed and
postcompressed tumor, respectively; LH
pre
and LH
post
are the length–height ratios
for precompressed and postcompressed tumor, respectively. To compute the length,
height, and width of a tumor efficiently, we use a cube to cover the 3-D breast
tumor, as shown in Figure 7.12. Thus, the information of length, height, and width
can be obtained directly form this cube.
176 3-D Breast Ultrasound Strain Imaging
YY
ZZ
XX
15 pixels 13 pixels
197 pixels210 pixels
(a) (b)
(c) (d)
Figure 7.11 (a) Precompressed images. (b) Postcompressed images. (c) An image slice of the
precompressed lesion. (d) An image slice of the postcompressed lesion.
Length = l
Width = w
Width = w
Height = h
Height = h
Length = l
(a) (b)
pre
pre
pre
post post
post
Figure 7.12 Dimensions of a tumor in the strain imaging framework. (a) Precompressed tumor
dimensions are given as l
pre
, w
pre
, and h
pre
. (b) Postcompressed tumor dimension are given as l
post
,
w
post
, and h
post
. The filled shapes are represented as tumors in the breast.
7.3.4.3 Normalized Contour Difference
This feature is used to compare the contours between the precompressed and
postcompressed lesions. The initial contours of precompressed and postcompressed
lesions can be obtained by using the level set segmentation framework. These con-
tours should be registered first because of the movement caused by the pressure of
the probe. To simplify the alignment between two contours, a reference point
should first be defined. A pure spatial alignment technique is used in this chapter.
The centers of gravity are used as the basic reference points for the alignment of two
lesion contours. For each pixel (x, y, z) inside the lesion, the center of gravity
(
xyz,,
) can be defined as
()
(
)
(
)
(
)
xyz
x
N
y
N
z
N
xy zxy zxy z
,, , ,
,,,,,,
=
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
∈∈∈
∑∑∑
RRR
(7.11)
where N is the total number of pixels in the tumor region R. Then, the contour dif-
ference is defined as:
()
C
ARR
d
di
i
i
=
∑
,
reg
Vol
pre
(7.12)
where R
i
is the lesion region in ith precompressed image slice;
R
i
reg
is the lesion
region in ith registered postcompressed image slice; A
d
is the number of different
pixels in these two registered regions; and Vol
pre
is the lesion volume in the
precompressed dataset. The value as a number carries a quantification significance
compared to other similar scenarios.
For example, in Figure 7.13, image slice B in the postcompressed dataset is reg-
istered to image slice A in the precompressed dataset. The center of gravity in slice A
is at the (5,5) position, and the center of gravity in slice B is at the (5,3) position.
Before alignment of these two image slices, the area in slice A is 12 pixels [see Figure
7.13(a)], and the area in slice B is 11 pixels [see Figure 7.13(b)]. In the alignment
process, we consider only the spatial transition of two reference points; therefore,
the number of difference pixels is 5 while the alignment of reference points is com-
7.3 Proposed Architecture of the 3-D Strain Imaging System 177
(a) (b) (c)
Center of gravity
Difference
pixels
Figure 7.13 Computation of alignment and difference pixels in the strain imaging framework.
Image slice B in the postcompressed dataset is aligned with image slice A in the precompressed
dataset. (a) Precompressed slice A, (b) postcompressed slice B, and (c) alignment of these two
images and determination of the contour difference.
pleted, as shown in Figure 7.13(c). Suppose that the total volume of the
precompressed tumor is 210 and the total number of different pixels between two
aligned tumors is 64. In such a case, the contour difference is 64/210 = 0.3048.
7.3.4.4 Shift Distance
The shift distance uses the concept of the motion estimation in video compression
[41] to find the motion of the contours. At first, the centers of gravity of two lesions
have to be aligned as done for the computation of the contour difference feature. For
speed reasons, we compute the motion vectors for the contour pixels rather than for
each pixel in the image. The contour of the current image slice will be equally
divided into eight sections and eight points can be obtained. These points are
so-called “cutting points” because they radially cut the breast lesion contour into
different sections. It is this cutting point that needs to have a motion vector.
The motion estimation is block based, and a small block containing each cutting
point will find the most similar block in the postcompressed image slice. To reduce
the number of searched blocks in the postcompressed image slice, a search window
could be defined to limit the searching region. The motion estimation technique [42]
is used to find the motion vector of these eight blocks for each image slice. For a
block at (m, n), if the most similar block in the postcompressed image slice is at (m +
i, n + j), then the motion vector for the block (m, n)is(i, j), as shown in Figure 7.14,
and the distance between these two blocks is defined as
dis =+ij
22
. Thus, shift
distance of the breast lesion can be defined as
()
()
M
d
A
kG
k
=
∈
avg dismax
(7.13)
178 3-D Breast Ultrasound Strain Imaging
Nw+2
Nw+2
(,)mn
(,)minj++
Search window in the
postcompressed image
NN ijblock in the search in the postcompressed image shifted by ( , )×
( ) block in the
precompressed image
NN×
Figure 7.14 Demonstration of the matching process. The current block and the most similar
block in a search window of the postcompressed sliced image.
where G represented eight blocks in each image slice and A represented all slices in
the postcompressed 3-D dataset. Only eight blocks on the contour need to find their
most similar blocks. The maximum of these eight distances will be assigned as the
shift distance of this slice. Then, the shift distance of this sequence will be the aver-
age of the shift distances of all slices in the sequence. Once the four features are
determined, our goal is to use a classifier that can distinguish the benign and malig-
nant breast lesions.
7.4 Experimental Protocol, Data Analysis, and Results
7.4.1 2-D and 3-D Experimental Protocols
Two sets of protocols were used for experimentation with the datasets. Protocol A
used the 3-D ultrasound acquisition method, whereas protocol B used conventional
2-D images. With the 2-D strain imaging method, only one precompressed and one
postcompressed image slice were used for feature analysis. These slices were
obtained from the middle slice of images that contained tumor information. Four
strain features—contour difference, shift distance, volume difference, and shape
difference—are adopted for all lesion cases. In our experiments, we used 100
pathology-proven cases for the 2-D and 3-D strain method, including 60 benign
breast tumors and 40 malignant ones, to evaluate the classification accuracy of the
proposed method.
Three data analysis methods—ROC curves, Student’s t-test, and the Chi-square
test, are used to analyze these four features. An SVM [42–44] is also used to com-
bine all four features to classify whether a tumor is malignant or not. The major rea-
son to adopt an SVM classifier is that the SVM was found to be better than the
Bayesian classifier, which is a classic linear classification method, for continuous
ultrasound strain images [28]. This research is our previous study for continuous
ultrasound strain images; the statistical significance have been proven especially in
accuracy and specificity (87.0% versus 77.0%, 88.3% versus 70.0%, and p-value
<0.01). According to a study by Chang et al. [45], the classification ability of the
SVM at gray-scale ultrasound was equal to that of a neural network model, whereas
the SVM had a much shorter training time (1 versus 189 seconds). Because of its
performance, the SVM has become an effective tool for pattern recognition,
machine learning, and data mining.
7.4.2 Segmentation Results
The level set method is first used to extract the contours of the 100 pathology-
proven cases. Then these contours are used for the 2-D and 3-D strain image analy-
sis to obtain four strain features. According to the experiments, most benign lesions
usually have larger values for the four strain features than the malignant lesions.
Unfortunately, some misdiagnoses may result due to the effects of speckle noise and
tissue-related texture, which cannot be reduced by the preprocessing. This effect
will result in an incomplete lesion contour and directly affect the accuracy of the
strain feature analysis. In this situation, some feature values of benign cases are
smaller compared to those of malignant cases. These cases would be misdiagnosed
7.4 Experimental Protocol, Data Analysis, and Results 179
by the proposedCAD system. In Figures 7.9 and 7.10, we show segmentation results
for both precompressed and postcompressedimages forbenign andmalignant cases.
7.4.3 Classification Strategy Using ROC Curves and SVM
We used ROC curve analysis for demonstrating the performance of our CAD sys-
tem. The performances of the four strain features can be evaluated by examining the
ROC area index, A
z
. In addition, to improve validation of the classification results,
discriminant analysis was applied in combination with jack-knifing. Jack-knifing
means that each case was classified using an individual discriminant function
trained with all cases except this one [46, 47].
In this SVM experiment, the ultrasonic images were divided into five groups by
the jack-knifing procedure. At the beginning, the first group was used as the testing
group, and the remaining four groups were used to train the SVM. After training,
the SVM was then tested on the first group. Then the second group was used as
another testing group, with the remaining four groups being the training set, and
again the SVM was tested on the second group. This process was repeated until each
group had been set as a testing group. A nonlinear SVM with Gaussian radial basis
kernel was adopted asour classifier, where C and γ are 658 and 0.094, respectively.
Table 7.1 shows the mean value, standard deviation, and p-value using Stu-
dent’s t-test for 2-D and 3-D strain features in the benign and malignant lesions.
Table 7.2 lists the experimental results of 2-D and 3-D SVM. Figure 7.15 shows the
ROC analysis for all strain features using an SVM classifier on the 3-D strain
180 3-D Breast Ultrasound Strain Imaging
Table 7.1 The Mean Value, Standard Deviation and p-Value (Using Student’s t-Test) of Four
Strain Features: Volume Difference (V
d
), Shape Difference (S
d
), ContourDifference (C
d
), and Shift
Distance (M
d
), for Benign and Malignant Lesions Using 3-D and 2-D Strain Methods
Value Type
Mean
p-Value (Using t-Test)
3-D 2-D 3-D 2-D
V
d
Benign
19.43 ± 8.06% 19.08 ± 12.49% <0.0001 <0.0001
Malignant
6.62 ± 7.90% 10.07 ± 9.17%
S
d
Benign
0.289 ± 0.138 0.245 ± 0.161 <0.0001 <0.0001
Malignant
0.146 ± 0.12 0.145 ± 0.136
C
d
Benign
32.53 ± 12.01% 25.53 ± 12.73% <0.0001 <0.0001
Malignant
13.15 ± 7.98% 15.27 ± 8.21%
M
d
Benign
3.087 ± 0.425 2.979 ± 0.648 <0.0001 <0.0001
Malignant
2.352 ± 0.453 2.458 ± 0.512
Table 7.2 Classification of Breast Tumors by SVM with the Four
Strain Features for 3-D and 2-D Strain Methods
Classification
3-D Strain 2-D Strain
Benign Malignant Benign Malignant
Benign TN 55 FN 4 TN 45 FN 10
Malignant FP 5 TP 36 FP 15 TP 30
Total 60 40 60 40
method. The total ROC analyses for the 3-D and 2-D strain methods are shown in
Figure 7.16.
7.4.4 Figure of Merit for 2-D Versus 3-D: Performance Evaluation
To estimate the performances of the 2-D and 3-D strain images, five performance
indices are compared by using Chi-square test. These indices are accuracy, sensitiv-
ity, specificity, PPV, and NPV and are mathematically given as:
()( )
()
Accuracy TP TN TP TN FP FN
Sensitivity TP TP FN
Specif
=+ +++
=+
()
()
()
icity TN TN FP
PPV TP TP FP
NPV TN TN FN
=+
=+
=+
(7.14)
where TP is the number of positives correctly classified as positive; TN is the num-
ber of negatives correctly classified as negative; FP is the number of negatives falsely
classified as positive; and FN is the number of positives falsely classified as negative.
In this experiment shown in Table 7.3, accuracy of the 2-D SVM is 75.00% (75 of
100), the sensitivity is 75.00% (30 of 40), the specificity is 75.00% (45 of 60), the
PPV is 66.76% (30 of 45), and the NPV is 81.82% (45 of 55). The accuracy rate of
7.4 Experimental Protocol, Data Analysis, and Results 181
0
0
0.1
0.1
TPF
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1
1
A = 0.8855 for all strain features using SVM
z
AV= 0.8588 for
z
d
AS= 0.8193 for
z
d
AC= 0.8757 for
z
d
AM= 0.8436 for
z
d
Figure 7.15 The ROC analysis of four strain features (contour difference, shape difference, shift
distance, and volume difference) using an SVM classifier in 3-D strain imaging framework.
the 3-D SVM is 91.00% (91 of 100), the sensitivity is 90.00% (36 of 40), the speci-
ficity is 91.67% (55 of 60), the PPV is 87.80% (36 of 41), and the NPV is 93.22%
(55 of 59). The p-values that result when using the Chi-square test are 0.0026,
0.0775, 0.0143, 0.0205, and 0.0638, respectively. We can conclude that the 3-D
strain image analysis is better than the 2-D strain image analysis. In the next section,
we present some of the reasons for better performance of the 3-D method compared
to the 2-D method.
182 3-D Breast Ultrasound Strain Imaging
0
0
0.1
0.1
FPF
TPF
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1
1
A 0.7603 for 2-D method using SVM=
z
A 0.8855 for 3-D method using SVM=
z
Figure 7.16 Comparison between 2-D and 3-D strain imaging method using ROC analysis. The
ROC analyses of the four strain features are computed in SVM classifier frameworks. The p-value of
the A
z
values for 3-D and 2-D methods is 0.0119 by using Z-test.
Table 7.3 Results of Performance
Indices and the p-Value of the
Chi-Square Test for the SVM Based on
the Proposed Features
Items
3-D
Strain
(%)
2-D
Strain
(%)
p-Value
(Using
Chi-Square
Test)
Accuracy 91.00 75.00 0.0026
Sensitivity 90.00 75.00 0.0775
Specificity 91.67 75.00 0.0143
PPV 87.80 66.67 0.0205
NPV 93.22 81.82 0.0638
7.5 Discussions
7.5.1 Discussion About the Level Set Framework
In this chapter, segmentation is one of the critical components for extraction of the
true irregularities in breast lesions that help with classification. Hence, we have
tried several segmentation strategies ranging from deformable models to regional
models. Though the level set does optimize in the sense that it has the ability to cap-
ture the irregularity of the lesions, in some cases even the level set is powerless.
These are misdiagnosis cases; that is, those cases in which a benign case can be con-
sidered malignant and vice versa.
These types of misdiagnosis are a result of broken islands or patches of lesions
that are not well connected to each other in ultrasound images. Such broken islands
can result from the partial volume effect during the ultrasound image acquisition
process (discussion of whichis beyond thescope ofthis chapter). Anotherreason for
such broken patches is that sometimes lesions are not concentrated at one location
like a mass, but are instead scattered around in multiple masses with a fair number
of gaps in between. Here our level set assumes that the lesion is more concentrated
as a mass and hence shows a uniform intensity in ultrasound images. Thus, when
the level set is made to run under the speed functions governed by the sigmoid
enhancer, it does capture it accurately in a majority of the cases, resulting in high
sensitivity. But when the level set is made to run in multiple concentrated masses, it
fails because of its inability to find the same uniform propagating field while propa-
gating. We anticipate working on this area in the near future, but the current system
shows very promising results on central massed regions with large noise patterns.
7.5.2 Discussion About Strain Features
Four strain features were used for classifying the lesions into benign and malignant
lesions. These strain features are the major protocols fortumor analysis and classifi-
cation in this chapter. In general, benign tumors are usually softer than malignant
tumors; a soft benign tumor becomes flatter than a stiffer malignant tumor after
compression with a probe. This is because benign tumors generally have smooth
regular borders and are loosely bound to the surrounding tissues, whereas malig-
nant tumors are usually characterized by firm desmoplastic reactions with sur-
rounding tissue. Therefore, benign tumors have larger values for all strain features
than malignant ones, as shown in Table 7.1. Although there is a little overlap in the
measured values for 3-D and 2-D between benign and malignant lesions, the p-
values (<0.0001) can prove the validity of these statistical data.
In the ROC curve analysis in Figure 7.15, all A
z
values for individual strain fea-
tures are satisfactory. Besides, combining all strain features with the SVM classi-
fier, the A
z
value can be improved to approach 0.89 (0.8855). From five
performance indices (accuracy, sensitivity,specificity,PPV,andNPV),wealsocan
prove that all strain features withthe SVMclassifier can make the five performance
values more efficacious for clinical diagnosis, as shown in Table 7.2. This is to say
that the proposed strain features are useful for our 3-D ultrasound strain imaging
framework.
7.5 Discussions 183