Journal of Medical and Biological Engineering, 30(5): 307-312
307
Classification of Benign and Malignant Breast Tumors by
Ultrasound B-scan and Nakagami-based Images
Yin-Yin Liao1
Po-Hsiang Tsui2
Chih-Kuang Yeh1,*
1
Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu 300, Taiwan, ROC
2
Department of Medical Imaging and Radiological Sciences, Chang Gung University, Taoyuan 333, Taiwan, ROC
Received 15 Sep 2009; Accepted 19 Nov 2009; doi: 10.5405/jmbe.30.5.06
Abstract
The B-scan shows the intensity of reflected echoes and is clever at a clear description of tumor contour to provide
knowledge of morphology. Nakagami image reflects the statistical distribution of local backscattered signals, which is
associated with the arrangements and concentrations of scatterers in tumors. In this study, we explored the clinical
performance of combining B-scan-based tumor contour analysis and Nakagami-image-based tumor scatter
characterization in classifying benign and malignant breast tumors. To confirm this concept, raw data obtained from 60
clinical cases were acquired. The B-scan images were used to calculate the standard deviation (SD) of the shortest
distance for contour feature analysis. The Nakagami images were applied to estimate the average Nakagami parameters
in the region of interests (ROI) in tumors. Overall, malignant tumors were highly irregular in tumor contour, whereas
they had lower average Nakagami parameters in scatter characterization. The receiver operating characteristic (ROC)
curve and fuzzy c-means (FCM) clustering were used to estimate the performances of combining two parameters in
classifying tumors. The clinical results showed that there would be a tradeoff between the sensitivity and specificity
when using a single parameter to differentiate benign and malignant tumors. The ROC analysis demonstrated that the
SD of the shortest distance had a diagnostic accuracy of 81.7%, sensitivity of 76.7%, and specificity of 86.7%. The
Nakagami parameter had a diagnostic accuracy of 80%, sensitivity of 86.7%, and specificity of 73.3%. However, the
combination of the SD of the shortest distance and the Nakagami parameter concurrently allows both the sensitivity
and specificity to exceed 80%, making the performance to diagnose breast tumors better.
Keywords: Breast tumor classification, Nakagami image, Contour and scatterer characterization
1. Introduction
Breast cancer is the most common cancer in women
worldwide. Ultrasound imaging has advantages including
nonionizing radiation, noninvasiveness, real-time display, and
comparatively low cost and good penetration ability compared
to mammography, which make it convenient and suitable for
routine and frequent breast screening. Malignant breast tumors
without pseudocapsule will tend to invade the surrounding
tissues, resulting in the sonofeatures of poorly defined and
irregular contours, such as spiculation, microlobulations,
angular margins, posterior shadowing, and tissue architectural
distortion [1-4]. For these reasons, the major purpose of the
conventional B-scan in breast screening is to clearly portray
the tumor contour features and to take effective contour
parameters for classifying between benign and malignant
tumors [5-8]. Nevertheless, it is hardly to find an effective
* Corresponding author: Chih-Kuang Yeh
Tel: +886-3-5715131 ext. 34240; Fax: +886-3-5718649
E-mail: [email protected]
contour feature that is suited for all the tumor shapes, and the
contour analysis is insufficient to describe all the tumor
properties for lack of information from the interior of the
tumor.
Fortunately, previous studies have confirmed that the
information about the scatterer properties inside tumors may be
extracted from the backscattered signals. It is worth noting that
the backscattered signals are treated as random signals. Thus,
modeling the probability density function (pdf) of the
backscattered signals by some appropriate statistical
distributions can help us understand the backscattering
behaviors, which are demonstrated by the scatterer properties.
Among all possibilities, the Nakagami statistical distribution
has recently received considerable attention. The parameter of
the Nakagami distribution estimated from the backscattered
echoes can identify various backscattering distributions in
medical ultrasound, having the ability to characterize biological
tissues [9,10]. It has been shown that the Nakagami parameter
can be used to assist conventional B-scan when classifying
breast masses [11,12]. Then the ultrasonic Nakagami
parametric image was developed and evaluated, and the
concept of it originated from the suggestion of Shankar [13]
J. Med. Biol. Eng., Vol. 30. No. 5 2010
308
and some preliminary studies [14,15]. Recently, we further
proposed a standard criterion for constructing the Nakagami
parametric image, and we established that it is able to classify
cyst, tumor, and fat in breasts [16]. However, the resolution of
the Nakagami image is as poor as that of the B-scan.
Obviously, the B-scan and the Nakagami images are in
different physical dimensions, and functionally complementary.
The information from the B-scan and the Nakagami images
may be treated as two independent and uncorrelated vectors
mathematically, implying that the two-dimensional analysis
based on a combination of the B-scan and the Nakagami
images should be more useful at classifying benign and
malignant breast tumors. In this study, the B-mode image was
used to manually track the tumor contour for calculating the
contour parameters. The Nakagami image was used to
calculate the average Nakagami parameter inside the tumor for
the scatterer characterization. Receiver operating characteristic
(ROC) curve and Student‟s t-test were used to estimate the
performance of each proposed feature. Fuzzy c-means (FCM)
was the cluster method applied to investigate the diagnostic
performance based on combining the contour parameter and
the Nakagami parameter.
2. Materials and methods
2.1 Data acquisition
The ultrasound radio-frequency (RF) signals are acquired
using a commercial ultrasound scanner (Model 3000, Terason,
Burlington, MA, USA), with the raw RF data digitized at the
sampling rate varied with transmission frequency. The applied
probe is a wideband linear array with a central frequency of 7.5
MHz and 128 elements. The axial resolution is 0.4 mm, and
lateral resolution is 0.4 to 0.6 mm depending on frequency and
sector depth. The study was approved by the Institutional
Review Board of National Taiwan University Hospital, and the
patients all signed informed consent forms. We collected 60
female patients, their ages ranged from 18 to 67 years. The 30
benign (fibroadenoma) and 30 malignant (invasive carcinoma)
breast masses in different patients were identified for further
follow-up medical procedure, including operation or invasive
diagnostic examination. We invited a physician with more than
10 years‟ clinical experience to sketch manually the tumor
contours for subsequent analyses.
2.2 Scatterer characterization by Nakagami imaging
The pdf of the ultrasonic backscattered envelope R under
the Nakagami statistical model is given by
f (r ) 
2 m m r 2 m 1
 ( m ) m
 m 
exp   r 2 U ( r ),
  
(1)
where r means the possible values for the random variable R of
the backscattered envelopes. (．) and U(．) are the gamma
function and the unit step function, respectively. Let E(．)
denote the statistical mean, then scaling parameter Ω and
Nakagami parameter m associated with the Nakagami
distribution can be respectively obtained from
  E(R 2 )
(2)
and
m
[ E ( R 2 )] 2
E[ R 2  E ( R 2 )] 2
.
(3)
Nakagami parameter m is a shape parameter determined by the
pdf of the backscattered envelope. It varies from 0 to 1
corresponding to the change of the envelope statistics from
pre-Rayleigh to Rayleigh distribution, and the backscattered
statistics conform to post-Rayleigh distributions when it is
larger than 1. More specifically, the Nakagami image is based
on the Nakagami parameter map, which is constructed by using
a square sliding window to process the uncompressed envelope
image. The appropriate sliding window is suggested as a square
with a side length equal to three times the pulse length of the
incident ultrasound [17]. A pseudocolor scale was applied to
demonstrate the information in the Nakagami image. The
Nakagami parameters smaller than 1 were assigned blue
shading that changed from dark to light with increasing value,
signifying the backscattered envelope that conformed to
various pre-Rayleigh statistics. Values equal to 1 were shaded
white to specify a Rayleigh distribution, and those larger than 1
were assigned red shading from dark to light with the
increasing value, demonstrating backscattered statistics with
various degrees of a post-Rayleigh distribution. The average
Nakagami parameter inside the tumor contour was calculated.
2.3 Contour feature extraction by B-scan
Most benign lesions tend to exhibit a wider shape. Also,
some studies have used an ellipse to roughly describing the
mass shape [18,19]. In order to consider the shape and
orientation of tumor growth, the equivalent best-fit ellipse is
regarded as a baseline. As observed in Fig. 1, the gray line
represents the tumor contour and its centroid at the point (h,
k), with the maximum path passing the centroid of the tumor
contour defined as the major axis (semimajor axis a) the
minor axis passing through the centroid and perpendicular to
the major axis (semiminor axis b), and θ the angle between
the X-axis and the major axis. The parametric form of an
ellipse may be specified by the following:
x (t )  h  a cos t cos   b sin t sin  ,
(4)
y (t )  k  b sin t cos   a cos t sin  ,
(5)
where t may be restricted to the interval angle (0 < t < 2π). An
ellipse in general position can be expressed parametrically
as the path of a point (x(t), y(t)), as shown by the red line in
Fig. 1.
The standard deviation (SD) of the shortest distance is
proposed which is a new parameter based on the best fit of
the tumor shape by an ellipse. Figure 2 shows the dotted
white and solid red lines which are the tumor contour and the
equivalent best-fit ellipse, respectively. The centroid in the
tumor is denoted by „x‟. We define the shortest distance as
pˆ (i )  Oi H i , i  1, 2, ...., N
(6)
Classifications Breast Tumors by Ultrasound
Subsequently, we can have the SD of the shortest distance by
pˆ SD 
1 N 
1
  pˆ (i )  N
N  1 i 1 
N

i 1

 pˆ (i ) 
2
.
(7)
incurred. The performance of each parameter to discriminate
breast tumors was evaluated using the ROC curve. The abilities
of using two parameters to characterize tumors were explored
by FCM, an iterative clustering method in the pattern
recognition field [20]. In FCM clustering, each parameter
should be normalized according to its mean and SD
Normalized parameter 
Figure 1. The equivalent best-fit ellipse was found to roughly describe
the tumor shape and orientation.
309
parameter  mean
.
SD
(9)
Normalization could avoid the influence of parametric scale
and dynamic range on FCM clustering. FCM allots data points
with similar characteristics to a predefined number of classes.
By iteratively updating the centers of clusters and the
membership grades for each data point, the FCM algorithm
iteratively moves the cluster center to the correct position for
each data set. The iteration is based on minimizing an objective
function that represents the distance of each data point to a
cluster center, weighted by the membership grade of the
specific data point.
3. Results and discussion
Figure 2. An illustration for the SD of the shortest distance. The dotted
white and solid red lines are the tumor contour and the
equivalent best-fit ellipse, respectively. The centroid in the
tumor is denoted by „x‟.
2.4 Statistical analysis
At first, the probability value (i.e., p value) of the two-tail
t-test between each parameter of benign and malignant breast
tumors is calculated. Subsequently, accuracy, sensitivity, and
specificity are calculated by
Accuracy = (TP + TN) ⁄ (TP + TN + FP + FN)
Sensitivity = TP ⁄ (TP + FN)
Specificity = TN ⁄ (TN + FP)
(8)
where TN is the number of benign cases truly classified as
negative, TP is the number of malignant cases truly classified
as positive, FN, malignant cases falsely classified as negative
and FP, benign cases falsely classified as positive. The ROC
curve is obtained from a plot of sensitivity (y-axis) as a
function of (1- specificity) (x-axis) by varying the variable on
which the test is based over all possible values. The ROC curve
will show where the cut-off or threshold (the closest point on
the ROC curve to (0, 1)) is, when using that threshold for
finding a certain number of TP lies and how many FP will be
Figures 3(a) and (b) show the B-scan images, and the
dotted white and solid red lines signify the tumor contour
tracked manually by the physician and the equivalent best-fit
ellipse of two different benign breast tumors (fibroadenoma),
respectively. Figures 3(c) and (d) reveal the corresponding
Nakagami images. The contour of the benign tumor is depicted
to be relatively ellipse; in short, it is smooth and regular. The
region of the benign tumor in the Nakagami image had red and
blue shading, relative to local post-Rayleigh and local
pre-Rayleigh distributions of the backscattered envelopes,
respectively.
Figure 4 illustrates the B-scan and Nakagami images of
two different malignant breast tumors (invasive ductal
carcinoma), respectively. In comparison to the benign tumor,
the malignant contour is more irregular. Furthermore, the
Nakagami imaging shading for the malignant tumor is
connected with more blue shading, representing that the
backscattered statistics inclines to be a higher degree of
pre-Rayleigh distribution than those for the benign tumor.
To quantitatively describe all parameters, Fig. 5 shows the
boxplots of them for benign and malignant tumors. The
findings of the average Nakagami parameters for benign and
malignant tumors were 0.7 and 0.58, respectively. In fact, the
backscattered signals from the malignant tumor are more
pre-Rayleigh distributed than those of the benign tumor. The
t-test between benign and malignant Nakagami parameters
produced a p-value smaller than 0.05, meaning that the
Nakagami parameter indicates significant differences between
benign and malignant tumors. The average SDs of the shortest
distance of benign and malignant tumors were 6 and 11,
respectively (p < 0.05), indicating that the malignant tumor has
a more irregular contour than the benign tumor does. Benign
tumor (fibroadenoma) is made up of glandular tissues and
some local fibrous tissues or calcification [21]. Since the
benign tumor cannot infiltrate outside the breast, the tumor
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J. Med. Biol. Eng., Vol. 30. No. 5 2010
Figure 3. Two different benign tumors (fibroadenoma) obtained from (a) and (b) B-scan images as well as those derived from the Nakagami
images, (c) and (d).
Figure 4. Two different malignant tumors (invasive ductal carcinoma) obtained from (a) and (b) B-scan images as well as those derived from
the Nakagami images, (c) and (d).
(a)
(b)
Figure 5. Each parameter of the benign and malignant tumors. The
data is expressed by boxplot. (a) Nakagami parameter; (b)
the SD of the shortest distance. Symbol „*‟ denotes p-value
smaller than 0.05. The „+‟ symbols are outliers or suspected
outliers (the points outside the end of the whiskers).
contour tends to behave regularly and be well defined.
However, local fibrosis raises the echogenicities of scatterers,
causing the scatterers in a tumor to exhibit a higher degree of
variability in scattering cross sections (Nakagami parameters
smaller than 1). In contrast with benign tumor, malignant
tumor has ability to invade the surrounding normal tissues
through the lymphatic system and bloodstream, and thus the
tumor contour tends to behave irregularly. In particular,
malignant tumors may have different structure and
calcification patterns from those of benign cases [22-24],
which may further raise the degree of variability in scattering
cross section of scatterers, contributing to a much higher
degree of pre-Rayleigh distribution for the backscattered
statistics (much smaller Nakagami parameters).
Classifications Breast Tumors by Ultrasound
We evaluated the performance of each parameter in
classifying benign and malignant tumors by performing the
ROC analysis and calculating the area under the ROC curve, as
shown in Table 1. The SD of the shortest distance had an area
under the ROC curve of 0.83, and the Nakagami parameter had
areas larger than 0.75. These results roughly suggested that the
SD of the shortest distance and the Nakagami parameter may
have good performance. We further compared the accuracy,
specificity, and sensitivity of each parameter obtained from
their ROC curves. The SD of the shortest distance had the high
accuracy (81.7%), and its specificity of 86.7% was also high,
but its sensitivity was low (76.7%). The Nakagami parameter
had a good sensitivity (86.7%) and a weaker specificity (73.3%),
and its accuracy was 80%. Namely, using a single parameter
just supplies a good sensitivity or a good specificity, depending
on the nature of the parameter.
Table 1. The performance of Nakagami parameter and the SD of the
shortest distance in classifying benign and malignant breast
tumors, respectively.
Performance
&
Parameters
m
p̂SD
Accuracy
(%)
Specificity
(%)
Sensitivity Area under the
(%)
ROC curve
80.0
73.3
86.7
0.75
81.7
86.7
76.7
0.83
Generally speaking, the multiparameter-based approach is
commonly used to enhance the sensitivity and specificity. Our
research has suggested that the parameters combined should be
independent, uncorrelated, and complementary based on
different physical meanings. Figure 6 shows the results of
FCM clustering bottomed on Nakagami parameter and the SD
of the shortest distance. The symbol „x‟ and „o‟ are the data
points corresponding to the benign and malignant tumors,
respectively. The data points were separated into two clusters
described by dotted and solid lines. We calculated the numbers
of benign and malignant data points in the regions of dotted
and solid lines to estimate the performance of using two
parameters to classify benign and malignant tumors.
Table 2 shows the combination of the Nakagami
parameter and the SD of the shortest distance produced 81.7%
in accuracy, 83.3% in specificity, and 80% in sensitivity.
Obviously, this implies that combining the Nakagami
parameter and the contour parameters effectively improves
both the sensitivity and specificity.
Table 2. The performance of combining Nakagami parameter and the
SD of the shortest distance in classifying benign and
malignant breast tumors.
Accuracy (%)
Specificity (%)
Sensitivity (%)
m
p̂SD
81.7
83.3
80.0
4. Conclusions
The two-dimensional analysis combining the contour
description by B-scan and the scatterer characterization by
the Nakagami image has been practically implemented and
provided adequate results for classifying benign and
malignant breast tumors. When using a single parameter to
discriminate benign and malignant cases, there is always a
tradeoff between the sensitivity and specificity. The tradeoff
is due to that each parameter is mainly related to its nature.
The B-scan and the Nakagami image are complementary
functionally, indeed improving the performance to classify
breast tumors. Multidimensional analysis has potential for
future development of breast tumor diagnosis using
ultrasound.
Acknowledgement
The authors thank Dr. W. H. Kuo, Department of Surgery,
National Taiwan University Hospital, Taipei, Taiwan, R. O. C.,
for supporting the clinical experiments and sketching the
tumor contours.
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Figure 6. FCM clustering for Nakagami parameter combined with the
SD of the shortest distance.
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