AJR 2003; 180:257-262
© American Roentgen Ray Society
Automated Assessment of the Composition of Breast Tissue Revealed on Tissue-Thickness-Corrected Mammography
Xiao Hui Wang1,
Walter F. Good,
Brian E. Chapman,
Yuan-Hsiang Chang,
William R. Poller,
Thomas S. Chang and
Lara A. Hardesty
1 All authors: Department of Radiology, Imaging Research, Ste. 4200, University
of Pittsburgh and Magee-Womens Hospital of the University of Pittsburgh
Medical Center Health System, 300 Halket St., Pittsburgh, PA 15213-3180.
Received March 28, 2002;
accepted after revision June 28, 2002.
Supported in part by grant IMG00-000362 from the Susan G. Komen Breast
Cancer Foundation; grants CA62800, CA77850, CA80836, CA82912, and CA85241 from
the National Cancer Institute; and grant LM06236 from the National Library of
Medicine of the National Institutes of Health.
Address correspondence to X. H. Wang.
Abstract
OBJECTIVE. Variations in the thickness of a compressed breast and
the resulting variations in mammographic densities confound current automated
procedures for estimating tissue composition of breasts from digitized
mammograms. We sought to determine whether adjusting mammographic data for
tissue thickness before estimating tissue composition could improve the
accuracy of the tissue estimates.
MATERIALS AND METHODS. We developed methods for locally estimating
breast thickness from mammograms and then adjusting pixel values so that the
values correlated with the tissue composition over the breast area. In our
technique, the pixel values are corrected for the nonlinearity of the combined
characteristic curve from the film and film digitizer; the approximate
relative thickness as a function of distance from the skin line is measured;
and the pixel values are adjusted to reflect their distance from the skin
line. To estimate tissue composition, we created a backpropagation neural
network classifier from features extracted from the histogram of pixel values,
after the data had been adjusted for characteristic curve and tissue
thickness. We used a 10-fold cross-validation method to evaluate the neural
network. The averaged scores of three radiologists were our gold standard.
RESULTS. The performance of the neural network was calculated as the
percentage of correct classifications of images that were or were not
corrected to reflect tissue thickness. With its parameters derived from the
pixel-value histogram, the neural network based on corrected images performed
better (71% accuracy) than that based on uncorrected images (67% accuracy)
(p < 0.05).
CONCLUSION. Our results show that adjusting tissue thickness before
estimating tissue composition improved the performance of our estimation
procedure in reproducing the tissue composition values determined by
radiologists.
Introduction
Radiographically dense breast tissue is often cited as one of the risk
factors for breast cancer. In the early 1970s, Wolfe
[1] reported that women with
dense breast tissue have a higher risk for breast cancer than do women with
fatty breast tissue. Since then, many studies have been conducted to further
investigate the relationship between the patterns of breast tissue depicted on
mammography and the risk of breast cancer. Although some studies have
indicated that cancer risk increases with the proportion of glandular breast
tissue
[2,3,4,5,6],
the results from other studies have not supported such a relationship. One
hypothesis is that dense breast tissue may mask existing tumorous tissue
[7,8].
This masking effect may introduce a bias in case selection and, therefore,
produce a higher incidence rate among the subset of patients having denser
breast tissue. The relationship between cancer risk and tissue composition is
further confounded by the notion that the risk of developing breast cancer
increases with age, whereas breast density decreases with age. Studies of
breast cancer risk in women 50 years and older have shown no clear correlation
between breast cancer and density of tissue
[9]. Even in the study results
that provide evidence of such a relationship, the magnitude of the association
varies [10].
The inconclusive role of tissue density in contributing to the risk of
breast cancer may be partly due to the fact that the composition assessment is
generally based on subjective evaluation. This explanation is suggested by
discrepancies in tissue classification and risk assessment between
radiologists and computer-generated measurements. Indications that the
automated methods are more consistent and reproducible have been reported
[6].
Part of the ambiguity in the association between breast cancer and tissue
composition may result from variability among radiologists in subjectively
estimating tissue composition and from the different guidelines used in
various studies. The most widely used standards for tissue composition are
Wolfe's four patterns of tissue classification
[1], the Breast Imaging
Reporting and Data System (BI-RADS) standard
[11], and measures of the area
ratio of breast parenchyma
[12,13,14,15,16].
These classification criteria are substantially different, and studies with
different standards for measuring composition are unlikely to produce results
that agree on the magnitude of any association. If an association does exist
between tissue composition and cancer risk, it would be desirable to
incorporate automatic procedures for estimating tissue composition into
methods for computer-aided detection of breast abnormalities.
If the relationship between tissue density and breast cancer risk is to be
studied, a more accurate and objective method of assessing tissue density is
needed. In most reported studies that have attempted to automate such
calculations, image density was the primary parameter used for segmenting
breast tissue components [12,
14,15,16,17,18].
Because of the nonlinear characteristics of film and film digitizers,
variation in X-ray flux (e.g., heel effect), scatter, and the lack of
uniformity in the thickness of breasts during compression (which may affect as
much as 10% of the total projected breast area)
[19], pixel densities in
mammograms are not completely correlated to the composition of the
corresponding tissue volume, particularly at the peripheral area of breast
images. Procedures that correct for nonuniform tissue thickness allow the
types of breast tissue to be more accurately segmented
[12,
14] and should yield more
accurate estimates of tissue composition.
In this article, we present a procedure that corrects for variations in
breast tissue thickness in digitized mammograms, and, using the
thickness-corrected image data, automatically evaluates breast composition
with a neural network built on features extracted from the histogram of pixel
values. We compared the results from corrected and uncorrected images and
analyzed the accuracy of tissue classification.
Materials and Methods
Image Collection and Digitalization
We used an image data set of 195 mammograms (34 craniocaudal views and 161
mediolateral oblique views) collected from screening mammograms acquired in
the University of Pittsburgh Medical Center and Magee-Womens Hospital, both in
Pittsburgh, PA. As shown in Figure
1, these images represented the range of possible compositions,
from very fatty tissue to extremely dense tissue. All images were obtained
from different patients to reduce the likelihood of overfitting in the
classification mechanism caused by similarity of images from an individual
patient. The mammograms were digitized with a laser film digitizer (Lumiscan
150; Lumisys, Sunnyvale, CA) at a spatial resolution of 100 µm and contrast
sensitivity of 12 bits. To minimize the nonlinearities of gray levels induced
by the digitizer, we calibrated the digitizer to produce a linear relationship
between the digitized value and optical density over the range of 0 to
approximately 3.8. The 100-µm resolution, although required for the
detection of features such as microcalcifications, is higher than the
resolution required for the tissue characterization tasks we studied. Thus, to
reduce the computational complexity of these tasks, we used filtration to
reduce the pixel size of the full-resolution images to 400 µm.
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Fig. 1. —Bar graph shows distribution of breast tissue composition in
database of mammograms used in study. For classifications of breast tissue
composition, 1 = almost entirely fat, 2 = scattered fibroglandular densities,
3 = heterogeneously dense, and 4 = extremely dense.
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Evaluation of Tissue Composition by Radiologists
Three mammographers, each with at least 5 years of experience practicing in
a hospital focusing on women's health care, scored the breast tissue
composition displayed in each image. Reviewers were instructed to evaluate the
tissue composition using the BI-RADS standard
[11]. This standard divides
the composition of breast tissue into the four categories: category 1, almost
entirely fat; category 2, scattered fibroglandular densities; category 3,
heterogeneously dense tissue, and category 4, extremely dense tissue.
Reviewers recorded their ratings on a continuous scale by entering the data
into a computerized scoring form with a slider control, which enabled them to
assign ratings that fell between the integral categories specified by the
BI-RADS standard. For each patient, the scores of the three radiologists were
averaged to produce the value that we used as a gold standard.
Thickness Correction
The nonlinearity of film's characteristic curve and the lack of uniform
tissue thickness during projection mammography are two of the factors that
combine to obfuscate any direct association between mammographic density and
tissue composition. The primary intent of this study was to determine whether
adjusting for tissue thickness provided any demonstrable benefit to the
accuracy of the estimation procedure. Our method of estimating tissue
thickness assumes that pixel densities are linearly related to exposure, so we
must first adjust pixel values for nonlinearities in the combined
characteristic curves of the film and digitizer. We did not correct for other
important factors such as the heel effect and scatter.
D-log10-E curve linearization.—Because tissue
thickness measurement and pixel value correction are both based on pixel
densitometric readings, the nonlinearity of the exposure—density curve
of the film can reduce the accuracy of any calculations that rely on
quantitative measures of tissue X-ray attenuation. Pixel values were corrected
for these nonlinearities by combining the characteristic curve of the film
(obtained from manufacturer's literature) with the characteristic curve of the
digitizer, which in this case was calibrated to be linear to the film density.
The inverse of the combined function was approximated by splining so that the
digitized density values could be converted to values that were linearly
proportional to tissue attenuation. A typical example of such a curve is
depicted in Figure 2. All pixel
values in the breast tissue area of the mammograms were adjusted using this
method.
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Fig. 2. —Sigmoid curve in graph is combined characteristic function
curve of film and film digitizer. Dashed line illustrates relationship of
energy exposure and radiographic intensity after linearization of function
curve.
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Distance mapping and tissue-thickness correction.—The skin
line and, in the case of mediolateral oblique views, pectoral muscle edge were
automatically detected. Each breast-tissue pixel in the digitized mammogram
was labeled with its minimum euclidean distance to the skin line, as
determined by an exhaustive search of skin-line pixels. For each specific
distance r (measured in pixels), we calculated a value in optical
density (D) units, D(r), as the mean, plus one SD, of all
pixel values at a distance r. The resultant value is an approximation
that biases the mean density values in the direction of pure fat tissue
because it is based on the assumption that some pixels at each distance
represent fat but others represent a mixture of tissues. The value
D(r) was considered to be a rough approximation of the exposure
resulting from pure adipose tissue, as measured at a distance r from
the skin line.
To smooth the empiric estimates, we performed a least-squares fit of
D(r) with the function
where Dmin and Dmax are the minimal
and maximal estimates of pixel values associated with pure fat tissue and
k controls the shape of the function being fitted to the data. Values
of k, Dmin, and Dmax were estimated
for each individual image. This particular function was chosen because of the
ease in performing the numeric calculations it offered and because the form of
the graph seemed to accurately reflect the actual data. In any event, use of a
theoretic model based on assumptions about the elastic deformation of a breast
was not feasible because such a model would also have to account for factors
such as the heel effect and scatter, both of which are difficult to predict in
individual patients. A typical example of such a fit is depicted in
Figure 3.
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Fig. 3. —Function curve in graph shows thickness index, represented by
normalized pixel value, as function of distance from skin line. Solid line
represents estimated mean change in optical density for pure fat pixels, with
respect to distance from skin line. Optical density values increase toward
skin line as thickness of breast tissue decreases. Corresponding fitted
function is represented by dashed line.
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For each distance r within an image, a thickness correction
coefficient, C(r), was calculated from the function above with the
equation
Each linearized pixel in the breast tissue area is corrected by multiplying
its value by C(r), with r as the distance of the particular
pixel from the skin line. After images had been adjusted, they were visually
examined on a cathode-ray-tube display for quality assurance.
Breast Tissue Composition Classification
Feature extraction.—The features used for classifying breast
tissue composition were derived from the histogram of values obtained from
tissue over the breast area. For thickness-corrected images, adjusted pixel
values were counted for the histogram according to the fractional thickness
the pixels represented. Pixels in uncorrected images were all counted as if
they represented the same tissue thickness or volume. Features derived from
the histogram included the lowest intensity value of the image, the ratio
between the lowest intensity value and the highest intensity value, the ratio
of the distance between the initial and the peak values to the total range of
the distance, and the ratio of the number of pixels falling between the peak
and the highest intensity values to the total number of pixels. These features
(normalized before being used in the neural network) were chosen to describe
the general characteristics of the histographic distribution.
Neural network classifier.—A backpropagation neural network
was established to classify tissue composition with the features derived from
histograms of either corrected or uncorrected pixel values
(Fig. 4). Our neural network
consisted of an input layer with four inputs (the histographic features
described previously), a hidden layer with three nodes, and one output node.
The reviewers' scores were used to train the neural network.
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Fig. 4. —Diagram illustrates structure of neural network classifier
used in study: an input layer with four inputs (histographic features
identified in text), a hidden layer with three nodes, and one output node.
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Verification.—We adopted a 10-fold cross-validation scheme
to train and test the neural network. To have approximately equal numbers of
cases in each composition category in the 10 data sets, we initially sorted
the cases into four groups. Group 1 was composed of images with scores of
0.0-0.9 (BI-RADS category 1), group 2 was composed of images with scores of
1.0-1.9 (BI-RADS category 2), group 3 was composed of images with scores of
2.0-2.9 (BI-RADS category 3), and group 4 was composed of images with scores
of 3.0-4.0 (BI-RADS category 4). Each group was then randomly divided into 10
subsets, and each data set used in the cross-validation was constructed from
one subset from each of the four groups. The size of a data set was either 19
or 20 images drawn from a database of 195 cases. Evaluation of the neural
network involved 10 cycles during which one data set in turn was identified as
the testing set, and the remaining nine data sets were used to train the
neural network. The data collected from 10 trials were averaged to produce the
final results.
Results
Figure
5A,5B,5C,5D
shows a comparison between corrected images and the uncorrected digitized
image data. Subjective examination of the thickness-corrected images revealed
an enhanced image presentation with structural information remaining unaltered
by the correction algorithms. The correction methods can be applied to images
regardless of their tissue composition classification, as shown in the
examples presented in Fig.
6A,6B,6C,6D,6E,6F,6G,6H.
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Fig. 6A. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Thickness-corrected image of breast of 72-year-old woman shows
tissue that is almost entirely fat. Compare with corresponding mammogram
(E).
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Fig. 6B. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Thickness-corrected image of breast of 56-year-old woman reveals
tissue with scattered fibroglandular densities. Compare with corresponding
mammogram (F).
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Fig. 6C. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Thickness-corrected image of breast of 49-year-old woman shows
heterogeneously dense tissue. Compare with corresponding mammogram
(G).
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Fig. 6D. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Thickness-corrected image of breast of 42-year-old woman reveals
extremely dense tissue. Compare with corresponding mammogram (H).
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Fig. 6E. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Original mammograms corresponding to A—D.
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Fig. 6F. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Original mammograms corresponding to A—D.
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Fig. 6G. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Original mammograms corresponding to A—D.
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Fig. 6H. —Thickness-corrected images paired with original mammograms
illustrate applicability of tissue-thickness-correction algorithms in various
tissue types. Original mammograms corresponding to A—D.
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The correct score for each image was assumed to be the average of the three
reviewers' scores. We compared differences among the scores given by the
radiologists for each image. As shown in
Table 1, the difference between
the scores of pairs of the reviewers were in some cases more than one BI-RADS
category. The absolute differences from the mean scores of all three
reviewers' scores were also calculated for the radiologists' interpretations.
The SD of these differences was 0.26 ± 0.19. Using the variance between
reviewers, we defined a criterion for judging whether the neural network
correctly classified a case—a classification was considered correct if
it fell within a range of 0.5 units on either side of the truth-value (actual
tissue ratio derived from corresponding MR images).
The neural network's performance was calculated as the percentage of
correct classifications for images with and without correction (Fig.
7A,7B).
Using this measure of performance, the neural network based on corrected
images had a better performance than that based on uncorrected images.
Although we incorporated only parameters derived from the pixel-value
histogram, we achieved an accuracy of 71% using corrected images compared with
67% accuracy using uncorrected images. The McNemar test (one tail) for one
sample indicated that this improvement is statistically significant
(significance level = 0.05; p = 0.038).
We also investigated the classification performance in each tissue
composition category in the corrected images. In both category 2 (score range,
1.0-1.9) and category 3 (score range, 2.0-2.9), an accuracy rate of 76% was
achieved. In category 1 (score range, 0-0.9) and category 4 (score range,
3.0-4.0), accuracy rates of 61% and 47%, respectively, were achieved, as shown
in Table 2.
Discussion
We have shown that adjusting certain pixel values from digitized mammograms
before using the data to train and test a neural network for classification of
tissue composition improves the ultimate performance of the network. This
finding is not surprising because the parameters used for classifying tissue
are based on features derived from histograms of the pixel values. The
nonlinearity of the characteristic curve for film and the potential
nonlinearity of the digitizer combined with the lack of uniformity of
breast-tissue thickness during compression conspire to reduce the accuracy of
the apparent relationship between digitized film densities and the X-ray
attenuation of breast tissue. Once digitized pixel values have been adjusted
for these factors, the histogram of pixel values is a much more accurate
representation of the actual attenuation of the breast tissue. The benefits of
these corrections would likely provide similar benefits to any analysis that
relies predominately on a quantitative assessment of breast tissue attenuation
as reflected in mammograms.
The overall accuracy of the neural network using corrected image data was
71% (p < 0.05). However, as shown in
Table 2, the accuracy for both
tissue category 1 and category 4 images was significantly lower than for
category 2 and category 3 images. Images at both extremes of composition,
being much less common in our screening environment, were underrepresented in
our data set. As we increase the number of cases used in training the neural
network, we expect the magnitudes of the differences in accuracy among
categories to diminish.
For the purposes of our study, the truth for each image was defined to be
the mean classification scores of the three radiologists participating in the
study. Because human reviewers have substantial inter- and intrareviewer
variability and because the criterion used to make their assessments is not
designed to maximize quantitative accuracy, the performance of the neural
network may be impaired to some extent by the inconsistent performance of the
radiologists. To eliminate problems related to the subjectivity of human
reviewers, we must adopt more objective standards, such as volumetric data
from breast MR imaging.
The criterion for breast tissue composition adopted for this study was the
BI-RADS standard, by which the tissue in breasts is classified as belonging to
one of four categories. The limited resolution of such a scheme likely
contributes to the difficulty in clarifying any association between
composition estimates and risk of breast cancer. The neural network provides
results on a continuous scale. If the scale can be calibrated to an objective
and quantitatively accurate standard, these kinds of correlations may be
possible.
Our goal is, therefore, to develop more accurate methods for estimating
tissue composition from mammograms. Ultimately, such methods would have to be
calibrated and tested against a gold standard. The standard we are proposing
for this purpose is based on volumetric measures from breast MR images.
Specifically, the proposed paradigm would involve analyzing cases of patients
for whom both MR images and mammograms were acquired. A neural network would
be trained to classify parameters derived from the mammograms using the actual
tissue ratio derived from corresponding MR images as truth-values. For
physics-based reasons, we believe that most of the information about tissue
composition can be recovered from a mammogram, despite ambiguities introduced
by the projection process.
For the neural network classifier in our study, we chose features for
tissue classification that were all derived from histograms of tissue pixel
values. Other kinds of features, such as measures of image texture, may
provide additional information about composition, which are independent of
measures derived from histograms and will likely provide important additional
benefits to such classification. Although many issues remain to be addressed,
we believe that the development of an objective and accurate automated
classifier has great potential as a tool for understanding and investigating
the relationship between breast tissue composition and the risk of breast
cancer.
Acknowledgments
We thank the staff of Magee-Womens Hospital for their extensive assistance
in developing the data set used in this study.
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Top
Abstract
Introduction
= thickness-corrected images; 
= original images. Graphs
illustrate results from training (A) and testing (B) sets.