IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 29, NO. 2, FEBRUARY 2010
513
Classification of Benign and Malignant Breast Tumors
by 2-D Analysis Based on Contour Description and
Scatterer Characterization
Po-Hsiang Tsui, Member, IEEE, Yin-Yin Liao, Chien-Cheng Chang, Wen-Hung Kuo, King-Jen Chang, and
Chih-Kuang Yeh*, Member, IEEE
Abstract—Ultrasound B-mode scanning based on the echo
intensity has become an important clinical tool for routine breast
screening. The efficacy of the Nakagami parametric image based
on the distribution of the backscattered signals for quantifying
properties of breast tissue was recently evaluated. The B-mode and
Nakagami images reflect different physical characteristic of breast
tumors: the former describes the contour features, and the latter
reflects the scatterer arrangement inside a tumor. The functional
complementation of these two images encouraged us to propose
a novel method of 2-D analysis based on describing the contour
using the B-mode image and the scatterer properties using the
Nakagami image, which may provide useful clues for classifying
benign and malignant tumors. To validate this concept, raw data
were acquired from 60 clinical cases, and five contour feature
parameters (tumor circularity, standard deviation of the normalized radial length, area ratio, roughness index, and standard
deviation of the shortest distance) and the Nakagami parameters
of benign and malignant tumors were calculated. The receiver
operating characteristic curve and fuzzy c-means clustering were
used to evaluate the performances of combining the parameters in
classifying tumors. The clinical results demonstrated the presence
of a tradeoff between the sensitivity and specificity when either
using a single parameter or combining two contour parameters
to discriminate between benign and malignant cases. However,
combining the contour parameters and the Nakagami parameter
produces sensitivity and specificity that simultaneously exceed
80%, which means that the functional complementation from the
B-scan and the Nakagami image indeed enhances the performance
in diagnosing breast tumors.
Manuscript received October 01, 2009; revised November 10, 2009; accepted
November 10, 2009. Current version published February 03, 2010. This work
was supported in part by the Academia Sinica under Grant AS-98-TP-A02 and
in part by the National Science Council of China under Grant 97-2627-B-007008. Asterisk indicates corresponding author.
P.-H. Tsui is with the Division of Mechanics, Research Center for Applied
Sciences, Academia Sinica, Taipei 11529, Taiwan (e-mail: [email protected].
edu.tw).
Y.-Y. Liao is with the Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu 30013, Taiwan
(e-mail: [email protected]).
C.-C. Chang is with the Division of Mechanics, Research Center for Applied
Sciences, Academia Sinica, Taipei 11529, Taiwan, and also with the Institute of
Applied Mechanics, National Taiwan University, Taipei 106, Taiwan (e-mail:
[email protected]).
W.-H. Kuo and K.-J. Chang are with the Department of Surgery, National
Taiwan University Hospital, Taipei 100, Taiwan (e-mail: [email protected].
edu.tw; [email protected]).
*C.-K. Yeh is with the Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu 30013, Taiwan
(e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMI.2009.2037147
Index Terms—Backscattered statistics, breast tumor, contour
analysis, Nakagami distribution, ultrasound.
I. INTRODUCTION
REAST cancer is a public health problem worldwide.
X-ray mammography is the main imaging methodology
used to diagnose breast cancer due to its high sensitivity and
resolution, which aid early detection [1]. However, mammography does not reveal soft tissues and has a lower sensitivity
for dense breasts [2], [3], and thus its use in screening breasts
is often complemented by pulse-echo ultrasound B-mode
imaging. Ultrasound imaging provides advantages including
noninvasiveness, the use of nonionizing radiation, real-time
display, and comparatively low cost and good penetration
ability compared to mammography, making it convenient and
suitable for routine breast screening.
Ultrasound imaging can differentiate between cysts and solid
masses [4], [5] and detect masses that are not visible in X-ray
mammography of dense breasts [5]. Since the early 1990s,
there has been significant progress in the use of ultrasound
imaging for classifying benign and malignant tumors [6]–[9].
This is because modern ultrasound scanners exhibit higher
image quality and resolution, which improves the ability to
describe the tumor growth that differs markedly between benignancy and malignancy. Benign lesions form the so-called
pseudocapsule that prevents the tumor growth from invading
the surrounding normal tissues. In this condition, benign tumors have well-defined contours with rounder and smoother
shapes and margins [10], [11]. In contrast, malignant tumors
(without the pseudocapsule) tend to invade the surrounding
tissues, resulting in sonographic features of poorly defined
and irregular contours, such as spiculation, angular margins,
microlobulations, posterior shadowing, duct extension, and
tissue architectural distortion. For these reasons, the main role
of conventional B-mode scanning in breast screening is to
clearly depict the tumor contour features and to derive effective
contour parameters for distinguishing between benign and
malignant tumors [10], [12].
Contour analysis cannot describe all the tumor properties due
to the absence of information on the interior scatterers of the
tumor. In soft tissues at diagnostic imaging frequencies ( 20
MHz), the strongest scatterers are composed of mesenchymal
B
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cells [13]. Specifically in breast tissues, scatterers include arterioles, mammary ducts, and lobules—any connective tissue
structure rich in collagen and elastin fibers and muscle cells [14].
There is evidence that the sizes, shapes, structures, and arrangements of cells differ between malignant and benign tumors [15],
[16]. Thus, the characteristics of scatterers in benign and malignant tumors may be different. However, there is also literature demonstrating that backscattered echoes vary with the size,
density, arrangement, and other properties of scatterers in tissues [17]–[20]. In other words, information about the scatterer
properties of the tumor may be extracted from the backscattered
signals.
The backscattered signal has a statistical nature when the resolution cell of the transducer has a large number of randomly
distributed scatterers. In this case, the probability density function (pdf) of the echo envelope would obey the Rayleigh distribution [21], and the speckle pattern in ultrasound image is normally called fully developed speckle. The Rayleigh-distributed
envelope is not a general case. The reason is that the number
of scatterers may not be large enough. Moreover, the scatterers
may not be randomly located, because there may be periodic
structures or clustering in the spatial distribution of scatterers
[22]. Therefore, non-Rayleigh models are necessary for better
explaining the backscattering behaviors, which are determined
by the scatterer properties [23]. Among all the possibilities, the
Nakagami statistical distribution has recently received considerable attention because the corresponding Nakagami parameter
estimated from the backscattered echoes can be used to identify various backscattering distributions in medical ultrasound,
thereby providing the ability to characterize biological tissues
[24]. It has been shown that using the Nakagami parameter with
B-mode scanning improves the classification of breast tumors
[25]–[27]. Combining the Nakagami parameter with additional
techniques such as frequency diversity and compounding [28],
[29], a multiparameter approach [30] and the Nakagami compounding distribution [31] can also improve its effectiveness in
discriminating between benign and malignant breast tumors.
The routine use of imaging tools by physicians and radiologists for visually identifying the properties of breast tumors
in clinical applications has led to the development and evaluation of the ultrasonic Nakagami parametric image. The concept of Nakagami imaging originated from the suggestion of
Shankar [32] and some other preliminary studies [33], [34]. We
recently proposed a standard criterion for constructing the Nakagami image [35] and confirmed its feasibility in breast tumor
monitoring [36]. We found that the Nakagami image is able to
classify cysts, tumors, and fat in breasts. Moreover, due to the
Nakagami parameter only being dependent on the shape of the
statistical distribution of the backscattered signal (i.e., raw data),
the Nakagami image is less affected by different operators and
system factors that are associated with changes in the signal
amplitude (e.g., system gain or dynamic range) in a condition
of using the same ultrasound system. Therefore, the Nakagami
image is not subject to the shadow effect that frequently occurs
beneath high-attenuation breast masses in B-mode images [36].
It is interesting to compare the application of B-mode and
Nakagami imaging in breast screening. These methods are
based on a standard pulse-echo measurement technique, but
they reflect different physical and physiological characteristics
of breast tumors. The grayscale B-mode image is derived
from the intensity of the backscattered echoes, which reflects
the echogenicities of scatterers and impedance mismatches
between interfaces. Moreover, the B-mode image also exhibits
an outstanding spatial resolution. Thus, the B-mode image
supplies information about the exterior of the imaged region for
describing the tumor growth by contour analysis. In contrast,
although the resolution of the Nakagami image is not as good as
that of the B-mode image, the Nakagami image is based on the
statistical distribution of the backscattered signals, and hence
reflects the arrangements of scatterers in a scattering medium.
In contrast to the B-mode image, the Nakagami image supplies
information about the interior of the imaged region, such as
the distribution of the scatterers inside a breast tumor. Because
the B-mode and Nakagami images reflect different physical
characteristics, they are functionally complementary, and the
information therefrom may be treated as two independent and
uncorrelated vectors mathematically. This implies that a 2-D
analysis (i.e., contour features and scatterer properties) based
on a combination of these images should be able to improve the
classification of benign and malignant breast tumors.
To validate the previously mentioned new concept, raw data
obtained from 60 clinical cases were acquired in a hospital to
construct the B-mode image to calculate contour feature parameters and the Nakagami image to estimate the average Nakagami
parameters inside tumors. The receiver operating characteristic
(ROC) curve was plotted to evaluate the ability of each parameter to classify tumors, and fuzzy c-means (FCM) clustering was
applied to explore the diagnostic performances of combining the
contour parameters and the Nakagami parameter. In the next
sections, we describe the materials and methods and present
experimental results that allow a discussion of the advantages
and potential of 2-D breast tumor analysis based on the B-mode
image and the recently proposed Nakagami image in clinical applications.
II. MATERIALS AND METHODS
A. Data Acquisition
The study was approved by the Institutional Review Board of
National Taiwan University Hospital and the patients signed informed consent forms. Breast ultrasound images were collected
with a commercial portable ultrasound scanner (Model 2000,
Terason, Burlington, MA), with the raw RF data digitized at
a sampling rate of 30 MHz. The probe comprised a wideband
linear array (Model 10L5, Terason) with a central frequency of
7.5 MHz and 128 elements. In order to estimate the pulse length
of the incident wave, two-way pulse-echo testing of the transducer was carried out. We placed both the transducer and a steel
reflector in a water bath and adjusted the distance between the
transducer and reflector to be the focal length of the transducer
(focal length is adjustable for Terason system). Then, we acquired the echo signal from the reflector for estimating the pulse
length. The pulse length of the incident wave was approximately
0.7 mm. On the other hand, the specification showed that the
beamwidth was between 0.4 and 0.6 mm.
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TSUI et al.: CLASSIFICATION OF BENIGN AND MALIGNANT BREAST TUMORS BY TWO-DIMENSIONAL ANALYSIS
There are some considerations for the used ultrasound machine. Note that the pulselength and beamwidth of the transducer determine the size of the resolution cell, which is a key
factor for scatterers characterization based on the envelope statistics analysis by the Nakagami parameter [37]. A smaller resolution cell (i.e., smaller pulselength and beamwidth) makes the
backscattered statistics, and the corresponding Nakagami pais much
rameter vary with the scatterer concentration when
smaller than 1, where is the wave number, and means the
radius of the scatterer. Contrarily, a large resolution cell tends
to contain more than ten scatterers for various scatterer concentrations, which leads to Rayleigh distribution for the envelopes
of different scatterer concentrations. In this condition, the Nakagami parameter has no ability to characterize tissues. Consequently, some factors able to diminish the resolution cell and enhance the transducer focusing, such as increasing frequency and
bandwidth, beamforming adjustments, or multifocusing settings
should be considered when using the Nakagami parameter to
quantify the envelope statistics. Lower frequencies, rough transducer focusing, or acoustic attenuation that would accompany
the frequency downshift to increase the size of the resolution
cell may limit the performance of the Nakagami image in tissue
characterization.
We recruited 60 volunteer female patients aged 18–67 years.
A sonographer performed the ultrasound scanning, and breast
tumors were identified as benign or malignant according to
biopsy reports. There were 30 benign (fibroadenoma) and 30
malignant (invasive carcinoma) tumors. Each image acquisition
protocol involved obtaining a total of 128 scan lines of the
backscattered echoes. The interval between each scan line was
0.3 mm. Each scan line was demodulated using the Hilbert
transform to obtain the envelope image, and the B-mode image
was obtained based on the logarithm-compressed envelope
image with a dynamic range of 40 dB. Finally, a physician with
more than ten years of clinical experience manually tracked the
tumor contours for subsequent analyses.
B. Scatterer Characterization by Nakagami Imaging
Scatterers in breast tumors were characterized based on the
estimated Nakagami parameters. Recall that the pdf of the ultrasonic backscattered envelope
under the Nakagami statistical model is given by
515
The Nakagami parameter represents a shape parameter determined by the statistics of the backscattered signal. As varies
from 0 to 1, the envelope statistics change from a pre-Rayleigh
to a Rayleigh distribution, and the statistics of the backscattered
signal conform to post-Rayleigh distributions when is larger
than 1.
The Nakagami image is constructed from the Nakagami parameter map obtained by using a sliding window to process the
uncompressed envelope image. According to a previous study
[35], we constructed the Nakagami images of the breast tumor,
, whose
using a square window with a size of
side length was three times the pulse length of the incident ultrasound. The following pseudocolor scale was designed for the
optimal display of the information in the Nakagami image: Nakagami parameters smaller than 1 were assigned blue shading
that changed from dark to light as the value increased, representing a backscattered envelope that conformed to various
pre-Rayleigh statistics; a value of 1 was shaded white to indicate a Rayleigh distribution, and values larger than 1 were assigned red shading from dark to light as the value increased,
representing a backscattered envelope that conformed to various post-Rayleigh statistics. The average Nakagami parameter
inside the tumor contour was calculated.
C. Contour Analysis by B-Mode Scanning
The features of the tumor contour, including its shape, orientation, and margin, were described using five typical parameters:
tumor circularity, standard deviation of the normalized radial
length, area ratio, roughness index, and standard deviation of
the shortest distance. The tumor circularity, standard deviation
of the normalized radial length, and area ratio are parameters related to the tumor shape (the degree of irregularity), the roughness index describes the margin (the degree of spiculation), and
the standard deviation of the shortest distance is a contour parameter we proposed to characterize the orientation of tumor
growth. These contour parameters are detailed shortly.
Tumor circularity is a gross contour feature descriptor that
has been shown to be useful for classifying breast masses [38].
We can calculate the tumor circularity as
(4)
(1)
where
and
are the gamma function and the unit step
function, respectively. The symbol means possible values for
the random variable of the backscattered envelopes. Let
denote the statistical mean, then scaling parameter and Nakagami parameter associated with the Nakagami distribution
can be, respectively, obtained from
(2)
where is the perimeter and is the area of the tumor. The
perimeter was measured by summing the number of pixels corresponding to the tumor contour, and the area was the number
of pixels inside the contour.
The standard deviation of the normalized radial length is
a measure similar to tumor circularity, reflecting the macroscopic boundary changes, but it can also indicate fine boundary
changes [11]. We first computed the radial length as
and
(3)
where
(5)
is the coordinate of the tumor centroid,
is the coordinate of the contour pixel at the th lo-
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in
tion points with the best-fit ellipse. We choose the point
to define the shortest disthe best-fit ellipse that is closest to
tance, as given by
(12)
and the mean and the standard deviation of the shortest distance
are, respectively, given by
Fig. 1. Illustration of the standard deviation of the shortest distance. The black
and red lines indicate the tumor contour and the corresponding best-fit ellipse,
respectively. The tumor centroid is denoted by “E .”
(13)
and
cation, and is the number of contour pixels. The normalized
radial length was further calculated as
(6)
is the maximum value in data set . Thus, the
where
mean and standard deviation of the normalized radial length
were, respectively, calculated as
(7)
and
(8)
The area ratio is a measure of the percentage of the tumor
lying outside the circular region defined by the mean of the
line plot [11] and is defined as
(9)
where
(10)
The roughness index is used to describe the degree of tumor
spiculation [11] and is calculated as
(11)
In order to better describe the shape and orientation of the
tumor, we further proposed using the standard deviation of the
shortest distance to classify tumors. This new parameter is based
on the best fit of the tumor shape to an ellipse, which is considered a more general tumor shape [39]. The black and red lines in
Fig. 1 indicate the tumor contour and the corresponding best-fit
ellipse, respectively. The tumor centroid and contour point are
denoted by and . For each , we can plot the linear relationship determined by itself and , as described by pink dotted
lines. Note that such a linear plotting would have two intersec-
(14)
D. Statistical Analysis
We first compared the values of each parameter between benign and malignant tumors, with tests used to calculate probability values. The ability of each parameter to discriminate between benign and malignant tumors was evaluated using the
ROC curve. The sensitivity, specificity, accuracy, and threshold
value were determined according to the closest point on the
ROC curve to (0, 1).
The abilities of using two parameters to characterize tumors
were subsequently explored by FCM, which is an iterative clustering method commonly used in the pattern recognition field
[40]. Prior to FCM clustering, each parameter should be normalized according to its mean and standard deviation
(15)
This normalization stops the parametric scale and dynamic
range from influencing the FCM clustering. The FCM algorithm first assigns data points with similar characteristics to a
predefined number of classes, and then it iteratively updates
the centers of clusters and the membership grades for each data
point to move 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. Each vector is assigned to the clustering corresponding
to the maximum of its membership function values. The output
of the FCM algorithm consists of the cluster center and the
values of the membership functions for each vector.
III. RESULTS AND DISCUSSION
Fig. 2(a) and (b) shows the typical B-mode image and the
corresponding Nakagami image of a benign breast tumor (fibroadenoma), respectively. The white line is the tumor contour
that was tracked manually by the physician. The contour of the
benign tumor appears to be comparatively smooth and regular.
The region of the benign tumor in the Nakagami image appears
in red and blue shading, corresponding to local post-Rayleigh
and local pre-Rayleigh distributions of the backscattered envelopes, respectively. In this case, the average and the standard
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TSUI et al.: CLASSIFICATION OF BENIGN AND MALIGNANT BREAST TUMORS BY TWO-DIMENSIONAL ANALYSIS
Fig. 2. (a) B-mode and (b) Nakagami images of a benign breast tumor (fibroadenoma). The white line is the tumor contour that was tracked manually
by the physician.
deviation of the Nakagami parameter was 0.7 0.25. Fig. 3(a)
and (b) shows the B-mode and Nakagami images of a malignant tumor (invasive carcinoma), respectively. The contour of
the malignant tumor appears more irregular than that of the benign tumor. Moreover, the Nakagami imaging shading for the
malignant tumor differs from that for the benign one. The malignant tumor has more blue shading corresponding to a Nakagami
parameter of 0.47 0.18, suggesting that the backscattered statistics tended to be a higher degree of pre-Rayleigh distribution
than did the benign tumor.
Here, we found that the Nakagami image shadings seem to
have a slight change with image depth. We have identified two
possible reasons. The first reason may be due to the attenuation
effect, resulting in that signal information is not enough for estimating the Nakagami parameter. Second, there are some structures and interfaces in deeper locations in the breast, such as
deeper layer of superficial fascia, pectoralis muscles, ribs, and
pleura. It should be noted that these structures are resolvable
in the B-scan. However, they may be smaller or comparable to
the sliding window used to construct the Nakagami image (i.e.,
the resolution of the Nakagami image). Consequently, when the
sliding window moves onto these structures, the window not
only covers the signals from the structures but also contains
those from the background. In general, the structures contribute
stronger echoes than the background does, and therefore the statistical distribution of the backscattered envelopes acquired by
the window would tend to be pre-Rayleigh statistics, rendering
the Nakagami parameter small and that the structures have dark
blue shadings in the Nakagami image. This may be called the
subresolvable effect of Nakagami imaging [41].
To quantitatively describe the features of Nakagami imaging,
Fig. 4(a) shows the boxplots of the Nakagami parameter for
benign and malignant tumors. The average Nakagami param-
517
Fig. 3. (a) B-mode and (b) Nakagami images of a malignant breast tumor (invasive carcinoma).
eters for 30 benign and 30 malignant tumors were 0.7 and 0.58,
respectively. Indeed, the backscattered signals from the malignant tumors were more pre-Rayleigh distributed than were those
from the benign tumors. The t test between benign and malignant Nakagami parameters produced a probability value smaller
than 0.05, indicating that the Nakagami parameter can effectively distinguish between benign and malignant tumors.
The boxplots of the five tumor contour parameters that we
explored for benign and malignant tumors are shown in Fig.
4(b)–(f). The average tumor circularities of benign and malig, which innant tumors were 25 and 30, respectively
dicates that the malignant tumor had a more irregular contour.
The roughness index and the standard deviation of the shortest
distance also differed significantly between the two tumor types,
making them suitable for classifying benign and malignant tumors. The roughness indexes were about 0.05 and 0.036 for
, and
the malignant and benign tumors, respectively
the standard deviations of the shortest distance were 11 and 6
. However, the two other contour parameters (area
ratio and standard deviation of the normalized radial length) did
not differ significantly between malignant and benign tumors
, implying that are not suitable for characterizing
breast tumors.
The differences of the Nakagami parameter and the contour
parameters between benign and malignant tumors should theoretically be attributable to scatterer properties and tumor growth,
respectively. The normal female breast mainly comprises lobules, ducts, and stroma based on the presence of fatty and connective tissues surrounding the ducts, lobules, blood vessels, and
lymphatic vessels. A previous study indicated that the speckle
would be fully developed in a normal breast B-mode image,
corresponding to the statistics of the backscattered signal conforming to the Rayleigh distribution [23], with a Nakagami parameter of 1. In contrast, a benign tumor manifests as a lump
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Fig. 4. Parameter values of the benign and malignant tumors displayed as boxplots: (a) Nakagami parameter, (b) tumor circularity, (c) standard deviation of the
normalized radial length, (d) area ratio, (e) roughness index, and (f) standard deviation of the shortest distance.
with some fibrocystic changes in the breast. The benign tumors
we collected were fibroadenomas, which comprise glandular tissues and some local fibrous tissues or calcification [42]. Because
a benign tumor cannot spread outside the breast, the tumor contour tends to be regular and smooth. However, not only local fibrosis but also duct ectasia, hyperplasia, adenosis, or some other
features of fibroadenomas may increase the echogenicities of
scatterers, making the scatterers in a tumor exhibit a higher degree of variability in scattering cross sections. This is why the
statistics of the backscattered signal of a benign tumor conform
to a pre-Rayleigh distribution, corresponding to Nakagami parameters smaller than 1.
Unlike a benign tumor, a malignant tumor is a group of cancer
cells that may invade the surrounding tissues or metastasize to
distant areas of the body. The malignant cases in this study were
invasive carcinomas. Cancer cells are able to spread to other
parts of the body via the lymphatic system and bloodstream, and
thus the tumor contour tends to be irregular. In particular, the
structure and calcification patterns may differ between malignant and benign tumors [43]–[45]. A malignant tumor exhibits
the following.
1) Increasing density and asymmetry and isolated dilated
ducts [46].
2) Calcifications with greater hardness and density based on
its intensity in an X-ray mammogram being stronger than
that of a benign tumor [44].
3) Calcifications with irregular sizes, shapes, and nonuniform
spatial distributions (e.g., branching, linear, and clustered).
4) A stronger vascular flow and angiogenesis effect [47],
[48]. These characteristics imply that an invasive malignant tumor will likely have more complex scatterer
arrangement or composition, which may further increase
the degree of variability in scattering cross section of the
scatterers, resulting in the statistics of the backscattered
signal conforming much more pre-Rayleigh distributed
(i.e., much smaller Nakagami parameters) [25], [49].
Fig. 5. ROC curves when using different parameters to classify benign and
malignant breast tumors.
We also evaluated the performance of each parameter in
distinguishing between benign and malignant tumors by performing an ROC analysis and calculating the area under the
ROC curve (AUC); the results are presented in Fig. 5 and
Table I. A larger AUC indicates that the parameter has a better
sensitivity or specificity for discriminating between benign and
malignant tumors. The AUC was highest for the standard deviation of the shortest distance, at 0.83. The tumor circularity and
the Nakagami parameter had AUCs larger than 0.75, whereas
the roughness index, the standard deviation of the normalized
radial length, and the area ratio had AUCs smaller than 0.7.
These results suggest that the standard deviation of the shortest
distance, the tumor circularity, and the Nakagami parameter are
better than the other parameters at characterizing breast tumors.
To confirm this, we compared the sensitivity, specificity, and
accuracy of each parameter obtained from their ROC curves;
the results are presented in Table II. As mentioned in Section
II, the optimal tradeoff between sensitivity and specificity of
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TSUI et al.: CLASSIFICATION OF BENIGN AND MALIGNANT BREAST TUMORS BY TWO-DIMENSIONAL ANALYSIS
TABLE I
AREAS UNDER THE ROC CURVE FOR DIFFERENT PARAMETERS
p^ : the standard deviation of the shortest distance; C : the tumor circularity;
^ : the roughness index; d^ : the standard
m: the Nakagami parameter; R
^: the area ratio.
deviation of the normalized radial length; A
TABLE II
SENSITIVITY, SPECIFICITY, AND ACCURACY OF EACH PARAMETER
IN CLASSIFYING BENIGN AND MALIGNANT BREAST TUMORS
p^ : the standard deviation of the shortest distance; C : the tumor circularity;
^ : the roughness index; d^ : the standard
m: the Nakagami parameter; R
^: the area ratio.
deviation of the normalized radial length; A
the parameter was determined by the closest point on the ROC
curve to (0, 1). For the data obtained in the present study, we
found that the standard deviation of the shortest distance had
both the highest accuracy (81.7%) and specificity (86.7%). The
tumor circularity had a sensitivity of 80.0% and an accuracy
of 73.3%, although its specificity was a little low (66.7%).
In contrast to the tumor circularity, the Nakagami parameter
exhibited a good sensitivity (86.7%) but a weaker specificity
(73.3%). Nevertheless, the accuracy of the Nakagami parameter
was 80.0%, which is better than that of the tumor circularity.
The other contour parameters, including the roughness index,
the standard deviation of the normalized radial length, and the
area ratio, were less useful because their accuracies were less
than 70%.
Overall, the results in Table II agree well with those in
Table I: the Nakagami parameter, the standard deviation of
the shortest distance, and the tumor circularity exhibited better
performances than the other parameters. More importantly,
the comparisons in Table II indicate the deficiency of using
a single parameter to distinguish between benignancy and
519
malignancy, in that only a good sensitivity or a good specificity
is obtained, depending on the nature of the parameter. Reliable
clinical diagnoses require both high sensitivity and specificity
when classifying benign and malignant tumors. In general, a
multiparameter-based approach is frequently used to enhance
the sensitivity and specificity. As mentioned in Section I,
we suggest that the parameters used in combination should
be independent, uncorrelated, and complementary based on
different physical characteristics, and thereby provide diverse
information about the tumor properties.
Fig. 6 shows the results of FCM clustering based on two parameters. The symbols “x” and “o” denote the data points corresponding to the benign and malignant tumors, respectively.
The data points were separated into the two clusters indicated
by blue and red lines, and we calculated the numbers of benign
and malignant data points therein to estimate the accuracy, sensitivity, and specificity of using two parameters to classify benign and malignant tumors; the results are presented in Table III.
Here, we discuss only cases for which the sensitivity, specificity, or accuracy were larger than 80%. We found that combining the roughness index and the tumor circularity provided
a specificity of 86.7%, which is better compared to the value of
50% for when only using the roughness index and 80% for when
only using the tumor circularity. A higher specificity makes it
easier to diagnose benign cases. However, such a combination
affects the ability to identify malignant tumors, due to the low
sensitivity of 56.7%. A similar phenomenon was also found
when we combined the standard deviation of the shortest distance, the tumor circularity, and the roughness index to classify breast tumors. The specificity was enhanced to 90% when
combining the tumor circularity and the standard deviation of
the shortest distance and to 83.3% when combining the standard deviation of the shortest distance and the roughness index.
Nevertheless, the sensitivity was markedly reduced to 56.7%,
adversely affecting the ability to diagnose malignant tumors. It
is interesting that combining tumor contour parameters seems
to only enhance the specificity. This may be due to the contour
parameters representing the same physical characteristic (i.e.,
edge feature), resulting in information overlap after combining
the parameters. Because the Nakagami parameter corresponds
to a different physical characteristic (i.e., scatterer properties),
combining the Nakagami parameter and the contour parameters
should be effective at improving both the sensitivity and specificity, and this was confirmed by the combination of the Nakagami parameter and the standard deviation of the shortest distance exhibiting a sensitivity of 80.0%, a specificity of 83.3%,
and an accuracy of 81.7%. This strongly supports the proposed
concept of using a 2-D analysis based on contour description
and scatterer characterization. However, the results suggest that
not all of the contour parameters are suitable for combining with
the Nakagami parameter.
On the other hand, we found that the current performance is
not significantly better than those in some previous studies [34],
[50], [51]. The system characteristics and settings may be the
reasons. For instance, the transducer frequency we used is relatively lower compared to those in the previous studies. Lower
frequency means a larger size of the resolution cell and a rougher
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Fig. 6. FCM clustering for combining parameters: (a) Nakagami parameter, (b) tumor circularity, (c) standard deviation of the normalized radial length, (d) area
ratio, (e) roughness index, and (f) standard deviation of the shortest distance. Symbols “x” and “o” denote data points corresponding to benign and malignant
tumors, respectively, and the blue and red lines separate the data points into two clusters (see text).
image quality, which may affect the Nakagami imaging
performance, the description of the tumor contour, and the
corresponding calculation of the contour parameter. Moreover,
currently the tumor contour was tracked manually by a physician. This may produce some biases, which may be further
improved by automatic contour segmentation. Furthermore, the
B-mode image formation in this study was just based on the raw
data without any signal and image process. Applying additional
imaging postprocesses, such as noise reduction or contrast
enhancement, may be helpful to the contour segmentation and
the analysis of the contour parameter.
IV. CONCLUDING REMARKS
This study explored a novel method of 2-D analysis based on
describing the contour using the B-mode image and the scatterer
characterization using the Nakagami image in order to classify
benign and malignant breast tumors. From the results obtained
from clinical cases, we can make the following concluding remarks and considerations.
1) The Nakagami image is useful for distinguishing between
benign and malignant breast tumors and may represent a
new and useful imaging mode for helping physicians and
radiologists to better understand the scatterer properties of
breast tumors.
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TSUI et al.: CLASSIFICATION OF BENIGN AND MALIGNANT BREAST TUMORS BY TWO-DIMENSIONAL ANALYSIS
521
TABLE III
SENSITIVITY, SPECIFICITY, AND ACCURACY OF COMBINING TWO PARAMETER
IN CLASSIFYING BENIGN AND MALIGNANT BREAST TUMORS
2) There is a tradeoff between the sensitivity and specificity
when using a single parameter or combining contour parameters to discriminate between benign and malignant
cases. This is because, on the one hand, the performance
of each parameter depends on its nature, and on the other
hand, the contour parameters represent the same physical
characteristic, resulting in information overlap after combining them.
3) Among all of the contour parameters that we explored, the
proposed standard deviation of the shortest distance is the
most suitable for combining with the Nakagami parameter,
because this produced a sensitivity of 80.0%, a specificity
of 83.3%, and an accuracy of 81.7%. This finding supports
the concept of the B-mode and Nakagami images being
complementary functionally and indeed able to improve
the performance in classifying breast tumors.
4) Not every contour parameter can be combined with the
Nakagami parameter to enhance the diagnostic ability,
which must be considered when deciding which parameters to use.
5) Extending the 2-D analysis to a multidimensional analysis
and integrating it with texture analysis may have the poten-
tial to greatly enhance future developments in pulse-echo
ultrasound imaging.
6) The Nakagami parameter is largely affected by the size
of the transducer resolution cell. Thus, different systems
and transducers may result in different performances of
the Nakagami image in classifying benign and malignant
breast tumors.
7) A large-scale clinical experiment and the algorithm optimization should be further explored before the 2-D analysis based on the B-mode and Nakagami images is used as
a clinical tool in breast ultrasound.
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