Quantitative evaluation of breast density using a dual‐energy technique on a digital breast tomosynthesis system

Abstract Purpose Although breast density is considered a strong risk factor of breast cancer, its quantitative assessment is difficult. To investigate a quantitative method of measuring breast density using dual‐energy mammographic imaging with central digital breast tomosynthesis in physically uniform and nonuniform phantoms. Material and methods The dual‐energy imaging unit used a tungsten anode and silver filter with 30 kVp for high‐energy images and 20 kVp for low‐energy images. Uniform glandular‐equivalent phantoms were used to calibrate a dual‐energy based decomposition algorithm. The first study used uniform breast phantoms which ranged in thicknesses from 20 to 70 mm, in 10‐mm increments, and which provided 30%, 50%, and 70% of breast density. The second study used uniform phantoms ranging from 10% to 90% of breast density. The third study used non‐uniform phantoms (at an average density of 50%) with a thickness which ranged from 20 to 90 mm, in 10‐mm increments. Results The root mean square error of breast density measurements was 2.64–3.34% for the uniform, variable thickness phantoms, 4.17% for the uniform, variable density phantoms, and 4.49% for the nonuniform, variable thickness phantoms. Conclusion The dual‐energy technique could be used to measure breast density with a margin of error of < 10% using digital breast tomosynthesis.

for breast cancer. A recent study has found that the risk of breast cancer is four to five times higher in women whose glandular density is higher than 75% than in those with breast density less than 25%. 2 The possibility of predicting future disease occurrence in individuals could be applicable not only to the design and application of preventive plans but also to interventional trials and clinical decision making. 3 Therefore, it is important to measure clinical breast density accurately and safely. John Wolfe, a pioneer in the field of mammography, put forward a well-cited theory of breast patterns as an index of risk for breast cancer in 1976, that of "breast patterns as an index of risk for developing breast cancer". 4 The current methods used to evaluate breast density include the four-category Breast Imaging Reporting and Data System (BI-RADS) classification system. BI-RADS has demonstrated positive intrareader (k = 0.79-0.86) and interreader (k = 0.65-0.91) agreements, indicating interreader correlation (r) ranging from 0.7 to 0.93, with correlations better for D1 and D4 than for D2 and D3 breast density categories. 5,6 The reproducibility of BI-RADS is generally poor owing to reader subjectivity in breast density assessment, 7 Digital breast tomosynthesis (DBT) is rapidly gaining in popularity worldwide due to its high spatial-resolution tomographic images of the breast and its ability to create reconstructions using multiple low-dose projection images. 15 Early clinical trials show improved sensitivity and specificity of DBT compared with digital mammography (DM). 16,17 Bakic et al 18 determined that breast density may be accurately estimated using central DBT and found substantial inter-and intrareader agreement in breast density estimation between DM and central DBT projection images. Our aim is to investigate the feasibility of the dual-energy technique for quantifying breast density in uniform and nonuniform phantoms using a central DBT system.

2.A | Dual energy decomposition and calibration
It is possible to combine low-and high-energy images to enhance a particular component in a projection image. However, the presence of nonlinear effects precludes the use of linear log subtraction for generating accurate quantitative dual-energy images. According to Kappadath et al, 19 a linear function failed to model both the thickness and glandular ratio. On the contrary, quadratic, cubic, and conic functions could be adequately modeled. For this reason, a cubic model with 13 coefficients should be used for dual-energy calibration. The cubic equation we used [eq. (1)] was: where t (mm) represents the measured glandular thickness, A HE the log-signal functions for high-energy, R the ratio of the log-signal function for low-energy and high-energy (R = A LE /A HE ), and T (mm) the total thickness, using a nonlinear least-squares minimization algorithm (Levenberg-Marquardt). 20 Calibrations were carried out at clinically relevant breast thicknesses using pure adipose and pure glandular phantoms (Computerized Imaging Referencing Systems, Inc. [CIRS], Norfolk, VA, USA).
Eighteen points were selected for dual-energy calibration, which included uniform phantoms with thicknesses of 2-9 cm. The uniform phantoms represented either pure glandular tissue (100% density) or pure adipose tissue (0% density). These measurements were used to build a model and determine the coefficient index (Table 1) for eq. (1). investigated. The first study used three groups of uniform phantoms (30%, 50%, and 70% density) with known thicknesses of 20-70 mm, in 10-mm increments. The second study used uniform phantoms ranging from 10% to 90% density, at 5% intervals, with thickness varying from 15 to 100 mm (we used a 54% phantom rather than a 55% phantom due to material availability) ( Table 2). The third study used nonuniform phantoms with an average density of 50%, ranging in thickness from 20 to 90 mm, in 10-mm increments.

2.C | Image acquisition and processing
A commercial DBT unit (Selenia TM Dimensions TM System; Hologic, Bedford, MA, USA) was used for image acquisition. The device was equipped with a tungsten (W) anode x-ray tube and x-ray filters of rhodium (Rh), silver (Ag), and aluminum (Al). Different filters produce optimal x-ray spectra on the basis of breast thickness, breast composition, and the desired imaging mode. In this study, an Ag filter was selected to increase spectral separation for the high-energy beam in a dual-energy composition. 12 Central DBT imaging was acquired at 0-degree projection with a spatial resolution of 70 μm per pixel using a detector with a 24 × 29-cm 2 field of view, corresponding to a 3328 × 4096 matrix. As in Feng and Sechopoulos, 21 high-energy images were set at 30 kVp and 100 mAs, a clinical protocol for an "average" breast. The low-energy images were acquired at 20 kVp and 25 mAs, the lowest available setting on the DBT system. 22 For central DBT, the breast phantoms were positioned for the craniocaudal view and were compressed using a standard force of 11 daN.
We repeated this study three times during three months, acquiring a total of 129 measurements.
Mean glandular dose (MGD), the average value of absorbed dose in the breast with glandular tissue, was also used for an estimation of radiation-induced breast cancer risk from mammography. It can be calculated from the eq. (2): where ESE, i.e., entrance skin exposure, is expressed in roentgens (R), and D gN is the normalized dose conversion factor in mGy/R resulting from an incident exposure in air of 1R, being a function of breast density, breast thickness, X-ray beam quality (i.e., tube potential and half-value layer), and anode/filter combination.
All image processing was performed using MATLAB software, version 7.10.0.499 (MathWorks, Natick, MA, USA). All uniform and nonuniform materials were measured for both thickness and density, providing an accurate estimation.

2.D | Density measurement
As images were acquired and dual-energy decomposition was performed, each pair of low-and high-energy images was used to translate glandular and adipose material from pixels into thickness. A region of interest (ROI) was established for each image, and the mean glandular thickness (T g ) was measured. The mean measured density (D m ) was calculated by dividing the mean glandular thickness by the total thickness. This value was multiplied by 100 to convert the fractional density to a percentage [eq. (3)]: For the uniform-thickness phantoms, the mean of each phantom image was sampled with a circular ROI (radius of 200 pixels) at the center-of-mass; the standard deviation (SD) was also measured. For the nonuniform phantom study, a user-determined threshold (aimed at attempting to involve the entire phantom) was used when considering the heterogeneous features (Fig. 1). The process of selecting the ROIs was carried out on the high-energy images, and this set of ROIs was used on both low-and high-energy images without modification.

2.E | Error analysis
The root mean square error (RMSE) for density estimation was calculated using eq. (4): where D k represented the known density.

| RESULTS
Results for the three phantom studies are tabulated in Tables 3-5.
The measured glandular thickness and density are shown as the

| DISCUSSION
Breast density is one of the strongest predictors of breast cancer risk. The extent of breast density can be modified by several factors.
Increasing age and menopause 23 are independent contributors to a decrease in breast density. 24 Elevated body mass index has been associated with low breast density, whereas increased age at first childbirth has been associated with high breast density. 25 Pregnancy at an early age decreases breast density, and this beneficial effect appears to be permanent. 26 Postmenopausal hormonal therapies that include both estrogen and progesterone are associated with an increase in breast density that decreases upon discontinuation of therapy. 27  (compared with 4.17% in uniform phantoms), even though this was the first used of a commercial DBT unit for breast density evaluation (Table 5).
At present, the classical Wolfe four-grade (BI-  Fig. 3 The dual-energy DBT used in our study results in a dose comparable to that of routine DM. There are some limitations in this study; the first, regression coefficients in Table 1 such as A HE or R value might be changed depending on detector type (Y6-or Y8), software version and calibration. So, other coefficients could be taken into consideration for modification breast density accuracy in the future.
Another limitation is the absence of an x-ray scatter correction, which is the predominant source of error in breast density measurement using dual energy mammography. In addition, we used a newly proposed algorithm for which more study is needed to verify efficacy. Future clinical implementation of this technique is expected using a clinical protocol in which automatic exposure control, as high-energy imaging, is combined with low-dose 3D projection, as low-energy imaging. Previously, some 2D interactive computer programs have also been used to generate a percentage mammographic density. 5,38,39 These methods, as well as other similar interactive computer and qualitative estimates, assess a 3D organ using 2D techniques, so are likely to be limited. Therefore, DBT potentially has sufficient superiority, which provides 2D and 3D imaging for diagnosis while offering quantification of breast density as a risk factor for breast cancer.

CONF LICT OF I NTEREST
The authors declare no competing financial interests.