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A Case for Wide-Angle Breast Tomosynthesis
Original Investigations
A Case for Wide-Angle Breast Tomosynthesis Ehsan Samei, PhD, John Thompson, MS, Samuel Richard, PhD, James Bowsher, PhD Rationales and Objectives: Conventional mammography is largely limited by superimposed anatomy. Digital breast tomosynthesis (DBT) and computed tomography (CT) alleviate this limitation but with added out-of-plane artifacts or limited chest wall coverage. This article presents a wide-angle breast tomosynthesis (WBT), aimed to provide a practical solution to these limitations, and offers an initial study of its utility in comparison with DBT and CT using a singular evaluation platform. Materials and Methods: Using an anthropomorphic virtual breast phantom, a Monte Carlo code modeled a breast imaging system for three modalities of DBT, WBT, and breast CT (44 , 99 , and 198 total angle range, respectively) at four breast compression levels, all at a constant mean glandular dose level of 1.5 mGy. Reconstructed volumes were generated using iterative reconstruction methods. Lesion detectability was estimated using contrast-to-noise ratio and a channelized Hotelling observer model in terms of the area under the receiver operating characteristic (AUC). Results: Results showed improved detection with increased angular span and compression. The estimated AUCs for WBT were similar to that of CT. Comparative performance averaged over all thicknesses between CT and WBT was 4.3 3.0%, whereas that between WBT and DBT was 5.6 1.0%. At compression levels reflective of the modality (7-, 5-, and 4-cm thickness for CT, WBT, and DBT, respectively), WBT yielded an AUC comparable to CT (performance difference of 1.2%) but superior to DBT (performance difference of 5.5%). Conclusions: The proposed imaging modality showed significant advantages over conventional DBT. WBT exhibited superior imaging performance over DBT at lower compression levels, highlighting further potential for reduced breast compression. Key Words: Anthropomorphic breast phantom; Monte Carlo simulation; iterative reconstruction; wide-angle breast tomosynthesis; Hotelling observer model. ªAUR, 2015
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reast cancer is the leading cause of cancer death in women. It is a global problem and affects countries of all economic levels (1). Earlier detection and treatment could decrease mortality rate by as much as one-third. At present, the main screening program used to identify early breast cancer is mammography (2). Standard twodimensional mammograms have been effective in reducing breast cancer mortality (1), but drawbacks of overlapping structure and limited three-dimensional (3D) information from only cranio-caudal and mediolateral oblique views cause a number of malignant cases to be missed. Clinical studies have shown digital breast tomosynthesis (DBT) to provide significant advantages over mammography by offering better visual information and increased depth perception (3–5). However, the limited acquisition angle range (50 ) makes the 3D data subject to out-of-plane artifacts (6). Breast computed tomog-
Acad Radiol 2015; -:1–10 From the Carl E. Ravin Advanced Imaging Laboratories, Department of Radiology, Duke University, 2424 Erwin Road, Suite 302, Durham, NC 27705 (E.S., J.T., S.R.); and Departments of Biomedical Engineering (E.S.), Physics (E.S.), Medical Physics (E.S.), and Radiation Oncology (J.B.), Duke University, Durham, North Carolina. Received November 7, 2014; accepted February 18, 2015. Address correspondence to: E.S. e-mail: samei@duke. edu ªAUR, 2015 http://dx.doi.org/10.1016/j.acra.2015.02.015
raphy (CT) can provide better depth discrimination, leading to improved tumor detection while eliminating the need for breast compression (7). However, in its current implementation, because of patient positioning in the prone position and geometrical clearance needed for 360 image acquisition, breast CT may suffer from reduced chest wall coverage, especially when imaging women with smaller breasts (7). In this article, we propose a wide-angle breast tomosynthesis (WBT) technique: the technique can alliteratively be recognized as limited angle CT. Compared to conventional breast tomosynthesis systems, WBT increases the acquisition angle range from typical 10 –50 to approximately 100 or more, aiming to reduce out-of-plane artifacts compared to DBT. The projection images are acquired within the maximum angular range possible without obstruction by the patient head and the contralateral breast, anatomic limitations that would reduce the chest wall coverage if the x-ray tube and the detector were to be rotating all around the breast. Figure 1a provides a schematic concept depiction of the hardware. Figure 1b illustrates a superoinferior–oblique geometrical orientation. The acquisition may also be done in the mediolateral–oblique orientation. The exact geometrical set up of the acquisition and the angular range depend on the specific orientation of the breast, the head, the contralateral breast, and how the patient can be positioned by the technologist considering the enhanced angular range. These 1
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Figure 2. The breast phantom and its various components.
METHODS Breast Phantom
Figure 1. Schematic, illustrating front and side view of the prototype wide-angle breast tomosynthesis (a) and one implementation rendition (b). The breast is modestly compressed. The x-ray source rotates along an arc of 100 angular range consecutively with the detector in either superoinferior–oblique or mediolateral–oblique orientation. This proposed geometry should obtain coverage of the breast and the muscle along the chest wall with minimal discomfort to the patient.
issues, although important in the final design of the method, are not the primary objective of this study. Rather, this study aims to investigate the quantitative impact of enhanced angular range on image quality using a consistent simulation platform. In this study, a simulation program was used to create realistic breast phantoms in a vowelized format. A custom Monte Carlo (MC) code based on the Penelope package was developed to model a virtual flat-panel breast tomosynthesis system. DBT, WBT, and CT (44 , 99 , and 198 total angle range, respectively) projections were simulated at four breast compression levels (4, 5, 6, and 7 cm). The glandular dose to the breast was kept at a constant dose level of 1.56 mGy, independent of the breast thickness and acquisition geometry. Iterative reconstruction methods were used to reconstruct the volume. Lesion detectability was estimated from contrast-to-noise ratio (CNR) and Hotelling observer model calculation to examine comparative performance across breast thickness and imaging modalities to assess the potential of WBT. 2
To evaluate the performance of the imaging systems, the study used an anthropomorphic breast phantom designed based on a mathematical model of the breast anatomy. In this phantom (8), the numerical value of each voxel corresponded to an anatomic structure making it compatible with MC–based simulation software. As shown in Figure 2, the phantom model included realistic anatomic details such as skin, ductal network, glandular and adipose tissues, and breast masses and calcifications. A brief description of the breast phantom is provided in this work; a more detailed description can be found in the report by Chen et al. (8). The outer envelope of the breast (ie, skin) was defined as a 0.5-mm layer defined by an elliptical equation whose parameters could be modified to model various level of breast compression. Breast compression was modeled by decreasing the breast thickness while increasing the width, keeping the total volume constant, thus assuming that the breast has incompressible characteristics. A 4.5-mm layer of subcutaneous fat was incorporated underneath the skin layer. The volume beneath the subcutaneous fat contained a combination of adipose and glandular tissues. The percentage of glandular tissue in the breast could be varied to imitate varying densities and the arrangement of the tissue randomized to simulate different ‘‘patients.’’ The ductal network was modeled by a series of branching (dividing) cylinders. The nipple was chosen as the origin for 16 main ducts, possessing certain radii and length, which extended toward the chest wall in different directions. At the end of each cylinder, branching takes place by any of three processes: 1) either the duct continues with a smaller branch, 2) the duct continues with a slight shift in direction but no branching, or 3) the duct gives rise to smaller branches. The radii and lengths of the ‘‘children’’ ducts were scaled by a factor with respect to the ‘‘parent’’ ducts resulting in ducts which are shorter and thinner than the ‘‘parent’’ ducts. The angles of the ‘‘children’’ducts with respect to the ‘‘parent’’ducts were calculated from the old direction and increments in polar and the azimuth angles. The dividing process terminated when the
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ducts reached the envelope of the breast, overlapped other ducts, or reached six levels of branching. The random nature of the ductal network model provided added variability while simulating different ‘‘patients.’’ Breast masses were simulated by an ellipsoid with a dense center and gradually fading edges, using a growth model integrating a randomized stellate pattern (8). Microcalcifications were also incorporated in the model in groups of six particles with a diameter of 0.5 mm each, randomly positioned on a duct within a distance range of 1–4 mm. Figure 3. The geometry of the Monte Carlo simulations.
MC Simulation
MC methods were used to simulate the radiographic projections of the breast phantom. A MC code, based on Penelope 2006, was developed to emulate breast imaging systems by simulating the acquisition geometry and the radiographic interactions within the breast phantom. The acquisition geometry is illustrated in Figure 3. A 28kVp tungsten anode x-ray source, 0.3-mm focal spot with 50-mm Rhodium filtration, modeled based on experimentally measured spectra (9), was used to produce an x-ray cone beam using a cone angle of 20.85 typical of breast tomosynthesis. The x-ray source was located 71.32 cm above a flat-panel detector. The center of rotation was situated 12 cm above the detector to allow for detector motions. The base of the breast was kept constant at 4.45 cm below the center of rotation, irrespective of the thickness of the breast. The detector was assumed to be a 250-mm-thick selenium flat-panel detector, with a 28.05 10.63 cm2 dimension and pixel size of 85 mm, generating 3300 1250 pixel projection images. The MC process simulated the Compton and photoelectric interactions of x-rays within the breast model and the detector (9). Radiographic projections of the breast phantom were obtained for DBT, WBT, and breast CT modalities by using acquisition angles of 44 , 99 , and 198 , respectively. The angular increment between sequential projections was kept at 2.75 (10). Three realizations of the breast phantom were generated, by varying the tissue structure and ductal network, to simulate three different ‘‘patients.’’ For each patient, the phantom was also modified to simulate compression at different levels—4, 5, 6, and 7 cm, resulting in a set of 12 phantoms for each of the three modalities. The energy deposited in each voxel was recorded by the MC code. Absorbed dose for each voxel was calculated as the amount of deposited energy per unit mass, Absorbed dose ¼
deposited energy density volume
(1)
The glandular dose to the breast was estimated in pilot MC runs, and the radiation flux per projection was subsequently adjusted in the later runs to achieve a constant total mean glandular dose level of 1.56 mGy, which is equivalent to that of a single mammographic acquisition, independent of the breast thickness and acquisition geometry.
Reconstruction and Processing
Iterative Reconstruction. The projections generated from the MC simulation were used to reconstruct the 3D volume of the breast. Iterative reconstruction techniques are known to be advantageous over analytical reconstruction techniques (11,12) because of their ability to model the physics of various imaging attributes such as scatter and the ability to compensate for undersampled or incomplete data. A drawback has been the computational speed of iterative techniques. Ordered-subset principles have been applied to expectation maximization (EM) algorithms (13), and separable paraboloidal surrogates (SPS) (14) have shown to provide order-of-magnitude acceleration over the stand-alone algorithms. The increased fidelity of the reconstructed images combined with the present available range of high-speed computing processors and parallelization make these methods increasingly viable for clinical use. This study used an iterative code based on ordered-subsets transmission algorithm applied to SPS, shown to converge faster than ordered-subsets EM (14). Nonuniformity Correction. X-ray scatter often creates artifacts in the reconstructed volume resulting in nonuniformity across the breast resulting in reduced contrast and cupping artifacts. A nonuniformity correction was performed by dividing the original volume with a correction volume as Oðx; y; zÞ ¼ Iðx; y; zÞ
hUðx; y; zÞi ; Uðx; y; zÞ
(2)
where, I(x,y,z) is the uncorrected breast volume, O(x,y,z) is the nonuniformity corrected breast volume, U(x,y,z) is the correction volume, and h:i denotes the mean operator. U(x,y,z) was generated from a uniform phantom, of the same size as the breast phantom and material density of 60% glandular–40% adipose tissues resulting in a reconstructed volume with a scatter profile very similar to the original volume. The original volume was further multiplied by the mean of the correction volume to maintain the average pixel value in the corrected volume. Calibration. Reconstructed breast images can provide useful quantitative information for tissue characterization. To 3
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provide accurate and meaningful pixel values, the breast images were calibrated with the reconstruction of a simple phantom with known tissue characteristics. A uniform phantom, consisting of water, was generated that incorporated five spheres of varying density containing a mixture of glandular and adipose tissue fractions of 0%–100%, 25%–75%, 50%– 50%, 75%–25%, and 100%–0%, respectively. ‘‘Calibration’’ volumes were reconstructed, using the same methods as described previously and used to calibrate the values for each reconstruction using Qðx; y; zÞ ¼
Y2 Y1 ½Oðx; y; zÞ Og ðx; y; z; Þ Oa ðx; y; z; Þ Oa ðx; y; z; Þ þ Y1 ;
(3)
where Og(x,y,z) and Oa(x,y,z) denote the mean glandular and adipose values from the calibration phantom, Y1 and Y2 denote the adipose and glandular percentage, and O(x,y,z) and Q(x,y,z) denote the uncalibrated and calibrated breast volumes, respectively.
A linear observer called the Hotelling observer was used in this work, which has been shown to be a good predictor of human observer performance in tasks with simulated lesions embedded in real and simulated anatomic backgrounds (15,16). The Hotelling observer model is the best model in the presence of approximate Gaussian statistics. Channelized versions of this model use linear channels to better model the human observer perception and to reduce dimensionality and computational intensity. In this work, we used the Laguerre–Gauss channels defined as a product of Laguerre polynomials and Gaussians, smooth functions which have been used as channels in estimation of the Hotelling template as (17). wðr; qÞ ¼
n
Ln ðxÞ ¼
n X m¼0
The performance of WBT was compared to that of DBT and CT. Performance evaluation was performed by estimating the detectability of the embedded lesions in the craniocaudal midplane of the breast phantom. This analysis used regions of interest (ROIs) containing lesions and the surrounding backgrounds from the central slices of the reconstructed volumes. Contrast-to-Noise Ratio. CNR provides a simple metric for detectability of larger objects. CNR was computed as follows:
(4)
where mLesion and mBackground denote the mean values of the lesion and the background, respectively, and sBackground denotes the standard deviation of the region surrounding the lesion. The mean lesion value was calculated from the average pixel value of a circular region of diameter 3 mm lying within the lesion (5 mm in diameter). The background was defined as the region lying between two concentric circles: the inner circle had an 8-mm diameter, which excluded any part of the lesion, and the outer circle with a 17-mm diameter, ensured that the mean background value would average any large anatomic variations surrounding the lesion. Hotelling Observer Model. Model human observers provide useful mathematical tools for estimating and predicting human observer performance. Software-based observer models have been used in clinically relevant visual tasks and are used in this work to compare the performance of DBT, WBT, and CT by computing the detectability index for the same task of detecting the embedded masses.
4
anm expðpr 2 =a2 ÞLn ð2pr 2 =a2 Þeimq ;
(5)
m
where the Laguerre polynomial is given as
Performance Evaluation
hQlesion i Qbackground CNR ¼ ; sbackground
XX
ð1Þ
m
n m
xm m!
(6)
The first few Laguerre polynomials are L0 ðxÞ ¼ 1; L1 ðxÞ ¼ x þ 1; L2 ðxÞ ¼
1 2 ðx 4x þ 2Þ: 2!
The variance of the Gaussian is defined by a distance scale related to the signal radius. This study had a value of 8 to maximize the area under the receiver operating characteristic (AUC) for our lesions. Test statistics were computed from the correlation between the image and a template derived from the signal and signalabsent image. Variance in the image is described by the covariance matrix (18). T K ¼ ½g hgi ½g hgi ;
(7)
where hgi is the expectation value of the image matrix g and T denotes the transpose operator. The template derived from the channelized Hotelling observer models can be written as (18) w ¼ Kv1
hD
E D Ei gv=s gv=n ;
(8)
where Kv = VTKV, and V is the matrix containing the spatial weights of each channel profile, gv=s and gv=n denote the signal-present and signal-absent vectors processed by the channel weights. ROI from seven central slices within the lesion in the reconstructed data provided a signal-present image for estimating the signal-present data vector, gv=s . The signal-absent data vector, gv=n , was estimated from slices lying above and below the lesions. A phantom was created by embedding the lesions, described in Breast Phantom section, along the craniocaudal
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midplane of a uniform breast containing water. ROI from seven central slices within the lesion in the reconstructed data provided a ‘‘signal-only’’ image for estimating the template w for the six lesions. Detectability Index. Model responses were calculated as the dot product of the template with the signal-present and signal-absent vectors, li ¼ w t gi ;
(9)
where gi denotes the signal or signal absent at the ith location and w is the template at the corresponding lesion location. Signal-present and signal-absent responses were computed for the six lesions for each patient (3), modality (3), and breast thickness (4). Receiver operating characteristic (ROC) curves were generated for each of the lesions for each individual case from the signal-present and signal-absent model responses in line with the signal-known-exactly-but-variable paradigm, where each set of images contained a different but known lesion. The probability density functions of the signalpresent and signal-absent responses were calculated and then thresholded to obtain an ROC curve for each lesion (19). The ROCs for each of the six lesions were averaged along the true-positive fractions to obtain an ROC for a specific breast. ROCs for the three patients under the same thickness and modality were averaged. The trapezoidal rule was used to calculate the AUC, and the inverse of the error function of the AUC was used to determine the detectability index (d’) as (19,20). 0
d ¼ 2 ðerf 1 ð2 AUC 1ÞÞ;
(10)
where erf denotes the error function. AUC can be estimated from the reverse of this equation (20,21).
RESULTS Projections and Reconstruction
Figure 4 shows the fluence per projection as a function of phantom thickness for DBT, WBT, and CT and a comparison to the corresponding fluence per projection for mammography. X-ray fluence per projection was set to ensure a fixed mean glandular dose of 1.56 mGy. Dose was computed using MC methods. This adjustment was performed to maintain a fixed glandular dose irrespective of acquisition angular range or breast compression level. Figure 5 shows the phantom at four compression levels resulting in breast thicknesses of 4, 5, 6, and 7 cm. The corresponding projections from the MC simulations (Fig 5b) demonstrate the realistic nature of the phantom. Brighter pixels correspond to glandular tissue indicating the higher density relative to the slightly darker adipose tissue. Short sections of the ductal network with microcalcifications can be observed, which appear to be harder to visualize with
Figure 4. Plot of fluence per projection versus phantom thickness for mammography, DBT, WBT, and CT acquisition techniques with corresponding total angle range of 0 , 44 , 99 , and 198 and with 1, 17, 37, and 73 projections, respectively. Fluence per projection was modified to maintain a fixed mean glandular dose at 1.56 mGy. CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wide-angle breast tomosynthesis.
increasing breast thickness. The embedded lesions are not easily visible in the projection images. Furthermore, variation in the breast width can be observed with various breast compression levels. Figure 6a shows midplane slices with the embedded lesions from reconstructed volumes for DBT, WBT, and CT of the 4-cm thick breast phantom. Slices from the reconstructed volumes (Fig 6a) show the scatter cupping artifact as nonuniform brightness radiating outward from the center. The uniform phantom used for scatter correction is shown in Figure 6b. The calibration phantom, shown in Figure 6c, provides attenuation values for adipose and glandular tissues at various percentages. The postprocessed images are shown in Figure 6d, where the images show minimal artifacts and exhibit pixel values reflecting tissue attenuation values. Variation in image quality with increasing number of iterations can be observed in Figure 7, illustrating CT images at four breast thicknesses reconstructed with two, four, six, and eight iterations. In the first iterations, the images are blurry, but the images become progressively sharper as the iteration number increases. Reconstructing the images with more than five or six iterations was found to be detrimental because of increased noise in the images. Figure 8 displays images for the 5-cm breast reconstructed using the three imaging modalities with two, four, six, and eight iterations, similar tradeoffs between resolution and noise as a function of number of iterations can be appreciated. Qualitatively, lesion detectability seems much reduced in the case of DBT compared to CTand WBT. DBT contains increased overlying anatomic noise, which makes the lesions less conspicuous. In general, it took 10 minutes to reconstruct the DBT images and approximately 45 minutes to reconstruct the CT volume. 5
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Figure 5. Variation in breast compression provides four breasts of increasing thickness (a). (b) The central projection from the Monte Carlo simulation of the breast phantom for each of the breast thicknesses.
Figure 6. Central slices containing lesions taken from the reconstructed volumes are shown (a). The nonuniformity scatter can be seen from the bright edges and needs to be removed using a correction phantom (b) which contains the same artifact. The reconstructed images are 32bit volumes which were calibrated to a 16-bit range using a calibration phantom which contained spheres of varying densities of glandular and adipose tissue (c). The slices after correction and calibration (d).
Performance Evaluation
Plots of CNR as a function of iteration are shown in Figure 9a–d. In all cases, a peak is reached at the optimal number of iterations after which the CNR decreases. In the case of the 4-cm breast, two or three iterations were sufficient to ensure maximum performance, whereas in the cases with reduced compression, maximum performance was found at higher number of iterations. Figure 9e shows the relative performance of modalities at optimum number of iterations. Averaging across all breast thicknesses, the performance of CT was better than WBT by 13.4 5.3%. The difference of performance between WBT and DBT was 15.1 7.0%. The analysis can also be presented in terms of AUC using the reverse of Equation (10), (Fig 10). By taking an average of the AUC parameters across all breast thicknesses, the performance of CT was better than WBT by 2.4 1.1%, whereas the difference of performance between WBT and DBT was 3.4% 1.2%. In terms of the analysis using the Hotelling observer model, Figure 11 shows the ROCs using Laguerre–Gauss channels. 6
CT has a nearly ideal ROC performance, and WBT performs better than DBT in all cases. Increasing thickness affects the performance of each imaging modality. Performance of WBT over DBT was found to be 5.6 1.0% greater at the same thickness. Comparatively, CT had 4.3 3.0% improvement over WBT. However, analyses of individual cases, reflected in the error bars of Figure 11, reveal that there is a certain amount of variability in the lesion detectability in breasts of different thicknesses, but in all cases, we see the benefits of a wider angle of acquisition. As shown, WBT exhibits lesser variance and better performance over DBT. Comparison at levels of compression that better reflect the imaging modality was also performed. For instance, CT requires little or no compression, whereas DBT uses a higher degree of compression. Therefore, comparing DBT at highest compression, CT at least compression, and WBT at moderate compression (4-, 7-, and 5-cm breast thickness, respectively), it was seen that WBT performed comparably to CT (1.2% performance difference) and better than DBT (5.5% performance difference) using the observer model analyses.
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Figure 7. Computed tomography images of increasing thickness varying with respect to increasing number of iterations of the reconstruction. As the number of iterations increases, the images become sharper and noisier. The thicker breasts show reduced lesion conspicuity.
Figure 8. Images of CT, WBT, and DBT for the 5-cm breast at various iterations. The lesions in both CT and WBT can be easily discerned, whereas DBT shows low lesion conspicuity. CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wide-angle breast tomosynthesis.
DISCUSSION DBT has advantages over mammography but is limited by artifacts because of its limited acquisition angle range (22). Performance of breast CT in terms of image quality and resolution is superior to that of DBT, but difficulties in imaging breasts of small sizes and poor chest wall coverage make it unsuitable as a diagnostic tool for all patients. Our proposed breast imaging modality has a geometry which would provide adequate chest wall coverage. We have shown that increasing the acquisition angle from 50 to only even 100 provides a significant improvement in terms of contrast and lesion detectability. Performance of WBT was closer to CT than DBT in both evaluation techniques. However, considering that the current implementation of CT involves no compression, our data indicate that WBT (with modest compression) can provide a performance comparable to CT. In this study, we developed a system that can be used to evaluate and compare various volumetric breast imaging
modalities. The developed breast phantom provided a versatile anthropomorphic model. Its ability to represent a wide variety of patients; to imitate various breast-related diseases; and to incorporate easily in simulation programs makes this phantom a unique and useful model. Combined with MC simulation, the phantom provides a powerful framework for performance assessment of various imaging systems including systems with stationary detectors (eg, conventional tomosynthesis) and moving detectors (eg, CT). The iterative reconstruction was found to provide highperformance reconstructions of volumes in the presence of limited angular coverage. Though iterative methods require increased computation resources, future work will investigate the benefits of parallel processing and high-speed computation processors on our iterative reconstruction code. In that light, WBT provides similar imaging performance to DBT at lower compression levels. In Figures 9 and 11, we can see that performance of WBT at breast thickness of
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Figure 9. Contrast-to-noise ratio as a function of the number of iterations for each of the breast thicknesses (a–d). (e) The relative performance at the optimal number of iterations for each modality and thickness. CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wideangle breast tomosynthesis.
6 cm is slightly better than DBTat 4 cm. Pain during screening mammography examinations due to breast compression has been cited as a reason for women to avoid regular screenings and hence reduce its effectiveness (9). Reduction of breast compression would alleviate patient discomfort during the clinical examinations and thereby increase the number of women likely to undergo regular breast examinations. Because the intended geometry for WBT is to be based on that of the present implementation of standard DBT, the chest wall coverage was assumed to be as much as that of standard 8
DBT. A physical implementation will need to be constructed and clinical trials performed to actually assess the actual chest wall coverage while increasing the acquisition angle range. Unlike some radiographic imaging implementations wherein the x-ray tube current is varied depending on the thickness of tissue the x-ray beam needs to pass through, this study did not modulate the x-ray tube current while imaging compressed breasts. This issue would have a bearing on the required noise performance of the detector at low exposure levels per projection as well. Only quantum noise was present in projections.
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Figure 10. Relative contrast-to-noise ratio performance in terms of AUC at the optimal number of iterations for each modality and thickness. AUC, area under the receiver operating characteristic; CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wide-angle breast tomosynthesis.
Figure 11. Receiver operating characteristics of CT, WBT, and DBT modalities (a–d) obtained using the Hotelling observer model with Laguerre–Gauss channels and corresponding detectability index (d’) calculated in terms of the AUC at the optimal iteration (e). The error bars reflect the variability of performance across patients. AUC, area under the receiver operating characteristic; CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wideangle breast tomosynthesis.
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No nonquantum noise attributes of the detector were modeled in this investigation. As such, the results of this study are reflective of the comparative image quality of these modalities, provided that the instrumentation noise from the detector can be considered negligible. (Photon counting detector technology offers a notable advantage in that regard.) This issue, however, is a performance requirement for WBT and CT and, along with the exact geometrical arrangement and implementation of WBT and its optimization for differentsized breasts, remains a topic of future studies. Notwithstanding the conclusions of the study, certain limitations should be acknowledged. First, the breast phantom model that we used has been shown to be a reasonable but not precise representation of actual breast anatomy. The voxelised nature might further introduce artifacts into the simulation process that needs to be assessed (8). Second, the statistical significance is likely to be limited by the fact that the study was implemented with a small number of phantoms. Third, because of computational limitations, we modeled the three modalities under a single technique condition, which might not be optimal for a given modality (23). For example, the technique used by current prototype CT systems is based on a higher energy x-ray beam. The assessment of system performance as a function of technique and dose remain topics of future investigations. CONCLUSIONS The proposed imaging modality, called WBT, showed significant advantages over standard DBT based on analyses using CNR and channelized Hotelling observer models. WBT was closer to CT in terms of imaging performance and exhibited improved performance over DBT at lower compression levels, highlighting further potential of reduced breast compression. Our study further used a unique breast phantom model and MC-based simulation program that can be used to model various breast imaging systems. REFERENCES 1. Boyle P, Levin B, eds. World Caner Report 2008. Lyon, France: World Health Organization Press, 2008. 2. Elmore JG, Armstrong K, Lehman CD, et al. Screening for breast cancer. JAMA 2005; 293(10):1245–1256.
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3. Niklason LT, Christian BT, Niklason LE, et al. Digital tomosynthesis in breast imaging. Radiology 1997; 205:399–406. 4. Suryanarayanan S, Karellas A, Vedantham S, et al. Comparison of tomosynthesis methods used with digital mammography. Academic Radiology 2000; 7:1085–1097. 5. Dobbins JT, Godfrey DJ. Digital x-ray tomosynthesis: current state of the art and clinical potential. Physics in Medicine and Biology 2003; 48:R65–R106. 6. Hu YH, Zhao W, Mertelmeier T, et al. ‘‘Image artifact in digital breast tomosynthesis and its dependence of system and reconstruction parameters’’, IWDM 2008. LNCS 2008; 5116:628–634. 7. Lindfors KK, Boone JM, Nelson TR, et al. Dedicated breast CT: initial clinical experience. Radiology 2008; 246(3):725–733. 8. Chen B, Shorey J, Nolte L, et al. An anthropomorphic breast model for breast imaging simulation and optimization. Academic Radiology 2011; 18(5):536–546. 9. Saunders RS, Samei E, Lo JY, et al. Can compression be reduced for breast tomosynthesis? Monte Carlo study on mass and micro-calcification conspicuity in tomosynthesis. Radiology 2009; 251(3):673–682. 10. Chawla AS, Lo JY, Baker JA, et al. Optimized image acquisition for breast tomosynthesis in projection and reconstruction space. Med. Phys 2009; 36(11):4859–4869. 11. Zbijewski W, Beekman FJ. Comparison of methods for suppressing edge and aliasing artifacts in iterative x-ray CT reconstruction. Phys. Med. Biol 2006; 51:1877–1889. 12. Lasio GM, Whiting BR, Williamson JF. Statistical reconstruction for x-ray computed tomography using energy-integrating detectors. Phys. Med. Biol 2007; 52:2247–2266. 13. Lange K, Fessler JA. Globally convergent algorithms for maximum a posteriori transmission tomography. IEEE Trans. Image Processing 1995; 4(10):1430–1438. 14. Erdogan H, Fessler JA. Ordered subsets algorithms for transmission tomography. Phys. Med. Biol 1999; 44:2835–2851. 15. Burgess AE, Jacobson FL, Judy PF. Human observer detection experiments with mammograms and power-law noise. Med. Phys 2001; 28: 419–437. 16. Eckstein MP, Abbey CK, Whiting JS. Human vs. model observers in anatomic backgrounds. Proc. SPIE 1998; 3340:16–26. 17. Barrett HH, Abbey CK, Gallas B, et al. Stabilized estimates of Hotellingobserver detections performance in patient-structured noise. Proc. SPIE 1998; 3340:27–43. 18. Eckstein M, Abbey CK, Bochud FO. A practical guide to model observers for visual detection in synthetic and natural noisy images SPIE. In: Handbook of Medical Imaging. Cambridge, UK: Cambridge University Press, 2010; 593–628. 19. Chawla AS, Samei E, Saunders R, et al. Effect of dose reduction on the detection of mammographic lesions: a mathematical observer model analysis. Med. Phys 2007; 34(8):3385–3398. 20. ICRU Report 54. Medical imaging—the assessment of image quality. Bethesda, MD: International Commission on Radiation Units and Measurements, 1996. 21. Barrett HH, Myers KJ. Foundations of image science. In: Saleh BE, ed. Wiley Interscience, 2004. 22. Chawla AS, Samei E, Lo JY, et al. A mathematical model platform for optimizing a multi-projection breast imaging system. Med. Phys 2008; 35(4): 1337–1345. 23. Samei E, Saunders RS, Baker JA, et al. Digital mammography: impact of reduced dose on diagnostic performance. Radiology 2007; 243:396–404.
A Case for Wide-Angle Breast Tomosynthesis Ehsan Samei, PhD, John Thompson, MS, Samuel Richard, PhD, James Bowsher, PhD Rationales and Objectives: Conventional mammography is largely limited by superimposed anatomy. Digital breast tomosynthesis (DBT) and computed tomography (CT) alleviate this limitation but with added out-of-plane artifacts or limited chest wall coverage. This article presents a wide-angle breast tomosynthesis (WBT), aimed to provide a practical solution to these limitations, and offers an initial study of its utility in comparison with DBT and CT using a singular evaluation platform. Materials and Methods: Using an anthropomorphic virtual breast phantom, a Monte Carlo code modeled a breast imaging system for three modalities of DBT, WBT, and breast CT (44 , 99 , and 198 total angle range, respectively) at four breast compression levels, all at a constant mean glandular dose level of 1.5 mGy. Reconstructed volumes were generated using iterative reconstruction methods. Lesion detectability was estimated using contrast-to-noise ratio and a channelized Hotelling observer model in terms of the area under the receiver operating characteristic (AUC). Results: Results showed improved detection with increased angular span and compression. The estimated AUCs for WBT were similar to that of CT. Comparative performance averaged over all thicknesses between CT and WBT was 4.3 3.0%, whereas that between WBT and DBT was 5.6 1.0%. At compression levels reflective of the modality (7-, 5-, and 4-cm thickness for CT, WBT, and DBT, respectively), WBT yielded an AUC comparable to CT (performance difference of 1.2%) but superior to DBT (performance difference of 5.5%). Conclusions: The proposed imaging modality showed significant advantages over conventional DBT. WBT exhibited superior imaging performance over DBT at lower compression levels, highlighting further potential for reduced breast compression. Key Words: Anthropomorphic breast phantom; Monte Carlo simulation; iterative reconstruction; wide-angle breast tomosynthesis; Hotelling observer model. ªAUR, 2015
B
reast cancer is the leading cause of cancer death in women. It is a global problem and affects countries of all economic levels (1). Earlier detection and treatment could decrease mortality rate by as much as one-third. At present, the main screening program used to identify early breast cancer is mammography (2). Standard twodimensional mammograms have been effective in reducing breast cancer mortality (1), but drawbacks of overlapping structure and limited three-dimensional (3D) information from only cranio-caudal and mediolateral oblique views cause a number of malignant cases to be missed. Clinical studies have shown digital breast tomosynthesis (DBT) to provide significant advantages over mammography by offering better visual information and increased depth perception (3–5). However, the limited acquisition angle range (50 ) makes the 3D data subject to out-of-plane artifacts (6). Breast computed tomog-
Acad Radiol 2015; -:1–10 From the Carl E. Ravin Advanced Imaging Laboratories, Department of Radiology, Duke University, 2424 Erwin Road, Suite 302, Durham, NC 27705 (E.S., J.T., S.R.); and Departments of Biomedical Engineering (E.S.), Physics (E.S.), Medical Physics (E.S.), and Radiation Oncology (J.B.), Duke University, Durham, North Carolina. Received November 7, 2014; accepted February 18, 2015. Address correspondence to: E.S. e-mail: samei@duke. edu ªAUR, 2015 http://dx.doi.org/10.1016/j.acra.2015.02.015
raphy (CT) can provide better depth discrimination, leading to improved tumor detection while eliminating the need for breast compression (7). However, in its current implementation, because of patient positioning in the prone position and geometrical clearance needed for 360 image acquisition, breast CT may suffer from reduced chest wall coverage, especially when imaging women with smaller breasts (7). In this article, we propose a wide-angle breast tomosynthesis (WBT) technique: the technique can alliteratively be recognized as limited angle CT. Compared to conventional breast tomosynthesis systems, WBT increases the acquisition angle range from typical 10 –50 to approximately 100 or more, aiming to reduce out-of-plane artifacts compared to DBT. The projection images are acquired within the maximum angular range possible without obstruction by the patient head and the contralateral breast, anatomic limitations that would reduce the chest wall coverage if the x-ray tube and the detector were to be rotating all around the breast. Figure 1a provides a schematic concept depiction of the hardware. Figure 1b illustrates a superoinferior–oblique geometrical orientation. The acquisition may also be done in the mediolateral–oblique orientation. The exact geometrical set up of the acquisition and the angular range depend on the specific orientation of the breast, the head, the contralateral breast, and how the patient can be positioned by the technologist considering the enhanced angular range. These 1
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Figure 2. The breast phantom and its various components.
METHODS Breast Phantom
Figure 1. Schematic, illustrating front and side view of the prototype wide-angle breast tomosynthesis (a) and one implementation rendition (b). The breast is modestly compressed. The x-ray source rotates along an arc of 100 angular range consecutively with the detector in either superoinferior–oblique or mediolateral–oblique orientation. This proposed geometry should obtain coverage of the breast and the muscle along the chest wall with minimal discomfort to the patient.
issues, although important in the final design of the method, are not the primary objective of this study. Rather, this study aims to investigate the quantitative impact of enhanced angular range on image quality using a consistent simulation platform. In this study, a simulation program was used to create realistic breast phantoms in a vowelized format. A custom Monte Carlo (MC) code based on the Penelope package was developed to model a virtual flat-panel breast tomosynthesis system. DBT, WBT, and CT (44 , 99 , and 198 total angle range, respectively) projections were simulated at four breast compression levels (4, 5, 6, and 7 cm). The glandular dose to the breast was kept at a constant dose level of 1.56 mGy, independent of the breast thickness and acquisition geometry. Iterative reconstruction methods were used to reconstruct the volume. Lesion detectability was estimated from contrast-to-noise ratio (CNR) and Hotelling observer model calculation to examine comparative performance across breast thickness and imaging modalities to assess the potential of WBT. 2
To evaluate the performance of the imaging systems, the study used an anthropomorphic breast phantom designed based on a mathematical model of the breast anatomy. In this phantom (8), the numerical value of each voxel corresponded to an anatomic structure making it compatible with MC–based simulation software. As shown in Figure 2, the phantom model included realistic anatomic details such as skin, ductal network, glandular and adipose tissues, and breast masses and calcifications. A brief description of the breast phantom is provided in this work; a more detailed description can be found in the report by Chen et al. (8). The outer envelope of the breast (ie, skin) was defined as a 0.5-mm layer defined by an elliptical equation whose parameters could be modified to model various level of breast compression. Breast compression was modeled by decreasing the breast thickness while increasing the width, keeping the total volume constant, thus assuming that the breast has incompressible characteristics. A 4.5-mm layer of subcutaneous fat was incorporated underneath the skin layer. The volume beneath the subcutaneous fat contained a combination of adipose and glandular tissues. The percentage of glandular tissue in the breast could be varied to imitate varying densities and the arrangement of the tissue randomized to simulate different ‘‘patients.’’ The ductal network was modeled by a series of branching (dividing) cylinders. The nipple was chosen as the origin for 16 main ducts, possessing certain radii and length, which extended toward the chest wall in different directions. At the end of each cylinder, branching takes place by any of three processes: 1) either the duct continues with a smaller branch, 2) the duct continues with a slight shift in direction but no branching, or 3) the duct gives rise to smaller branches. The radii and lengths of the ‘‘children’’ ducts were scaled by a factor with respect to the ‘‘parent’’ ducts resulting in ducts which are shorter and thinner than the ‘‘parent’’ ducts. The angles of the ‘‘children’’ducts with respect to the ‘‘parent’’ducts were calculated from the old direction and increments in polar and the azimuth angles. The dividing process terminated when the
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ducts reached the envelope of the breast, overlapped other ducts, or reached six levels of branching. The random nature of the ductal network model provided added variability while simulating different ‘‘patients.’’ Breast masses were simulated by an ellipsoid with a dense center and gradually fading edges, using a growth model integrating a randomized stellate pattern (8). Microcalcifications were also incorporated in the model in groups of six particles with a diameter of 0.5 mm each, randomly positioned on a duct within a distance range of 1–4 mm. Figure 3. The geometry of the Monte Carlo simulations.
MC Simulation
MC methods were used to simulate the radiographic projections of the breast phantom. A MC code, based on Penelope 2006, was developed to emulate breast imaging systems by simulating the acquisition geometry and the radiographic interactions within the breast phantom. The acquisition geometry is illustrated in Figure 3. A 28kVp tungsten anode x-ray source, 0.3-mm focal spot with 50-mm Rhodium filtration, modeled based on experimentally measured spectra (9), was used to produce an x-ray cone beam using a cone angle of 20.85 typical of breast tomosynthesis. The x-ray source was located 71.32 cm above a flat-panel detector. The center of rotation was situated 12 cm above the detector to allow for detector motions. The base of the breast was kept constant at 4.45 cm below the center of rotation, irrespective of the thickness of the breast. The detector was assumed to be a 250-mm-thick selenium flat-panel detector, with a 28.05 10.63 cm2 dimension and pixel size of 85 mm, generating 3300 1250 pixel projection images. The MC process simulated the Compton and photoelectric interactions of x-rays within the breast model and the detector (9). Radiographic projections of the breast phantom were obtained for DBT, WBT, and breast CT modalities by using acquisition angles of 44 , 99 , and 198 , respectively. The angular increment between sequential projections was kept at 2.75 (10). Three realizations of the breast phantom were generated, by varying the tissue structure and ductal network, to simulate three different ‘‘patients.’’ For each patient, the phantom was also modified to simulate compression at different levels—4, 5, 6, and 7 cm, resulting in a set of 12 phantoms for each of the three modalities. The energy deposited in each voxel was recorded by the MC code. Absorbed dose for each voxel was calculated as the amount of deposited energy per unit mass, Absorbed dose ¼
deposited energy density volume
(1)
The glandular dose to the breast was estimated in pilot MC runs, and the radiation flux per projection was subsequently adjusted in the later runs to achieve a constant total mean glandular dose level of 1.56 mGy, which is equivalent to that of a single mammographic acquisition, independent of the breast thickness and acquisition geometry.
Reconstruction and Processing
Iterative Reconstruction. The projections generated from the MC simulation were used to reconstruct the 3D volume of the breast. Iterative reconstruction techniques are known to be advantageous over analytical reconstruction techniques (11,12) because of their ability to model the physics of various imaging attributes such as scatter and the ability to compensate for undersampled or incomplete data. A drawback has been the computational speed of iterative techniques. Ordered-subset principles have been applied to expectation maximization (EM) algorithms (13), and separable paraboloidal surrogates (SPS) (14) have shown to provide order-of-magnitude acceleration over the stand-alone algorithms. The increased fidelity of the reconstructed images combined with the present available range of high-speed computing processors and parallelization make these methods increasingly viable for clinical use. This study used an iterative code based on ordered-subsets transmission algorithm applied to SPS, shown to converge faster than ordered-subsets EM (14). Nonuniformity Correction. X-ray scatter often creates artifacts in the reconstructed volume resulting in nonuniformity across the breast resulting in reduced contrast and cupping artifacts. A nonuniformity correction was performed by dividing the original volume with a correction volume as Oðx; y; zÞ ¼ Iðx; y; zÞ
hUðx; y; zÞi ; Uðx; y; zÞ
(2)
where, I(x,y,z) is the uncorrected breast volume, O(x,y,z) is the nonuniformity corrected breast volume, U(x,y,z) is the correction volume, and h:i denotes the mean operator. U(x,y,z) was generated from a uniform phantom, of the same size as the breast phantom and material density of 60% glandular–40% adipose tissues resulting in a reconstructed volume with a scatter profile very similar to the original volume. The original volume was further multiplied by the mean of the correction volume to maintain the average pixel value in the corrected volume. Calibration. Reconstructed breast images can provide useful quantitative information for tissue characterization. To 3
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provide accurate and meaningful pixel values, the breast images were calibrated with the reconstruction of a simple phantom with known tissue characteristics. A uniform phantom, consisting of water, was generated that incorporated five spheres of varying density containing a mixture of glandular and adipose tissue fractions of 0%–100%, 25%–75%, 50%– 50%, 75%–25%, and 100%–0%, respectively. ‘‘Calibration’’ volumes were reconstructed, using the same methods as described previously and used to calibrate the values for each reconstruction using Qðx; y; zÞ ¼
Y2 Y1 ½Oðx; y; zÞ Og ðx; y; z; Þ Oa ðx; y; z; Þ Oa ðx; y; z; Þ þ Y1 ;
(3)
where Og(x,y,z) and Oa(x,y,z) denote the mean glandular and adipose values from the calibration phantom, Y1 and Y2 denote the adipose and glandular percentage, and O(x,y,z) and Q(x,y,z) denote the uncalibrated and calibrated breast volumes, respectively.
A linear observer called the Hotelling observer was used in this work, which has been shown to be a good predictor of human observer performance in tasks with simulated lesions embedded in real and simulated anatomic backgrounds (15,16). The Hotelling observer model is the best model in the presence of approximate Gaussian statistics. Channelized versions of this model use linear channels to better model the human observer perception and to reduce dimensionality and computational intensity. In this work, we used the Laguerre–Gauss channels defined as a product of Laguerre polynomials and Gaussians, smooth functions which have been used as channels in estimation of the Hotelling template as (17). wðr; qÞ ¼
n
Ln ðxÞ ¼
n X m¼0
The performance of WBT was compared to that of DBT and CT. Performance evaluation was performed by estimating the detectability of the embedded lesions in the craniocaudal midplane of the breast phantom. This analysis used regions of interest (ROIs) containing lesions and the surrounding backgrounds from the central slices of the reconstructed volumes. Contrast-to-Noise Ratio. CNR provides a simple metric for detectability of larger objects. CNR was computed as follows:
(4)
where mLesion and mBackground denote the mean values of the lesion and the background, respectively, and sBackground denotes the standard deviation of the region surrounding the lesion. The mean lesion value was calculated from the average pixel value of a circular region of diameter 3 mm lying within the lesion (5 mm in diameter). The background was defined as the region lying between two concentric circles: the inner circle had an 8-mm diameter, which excluded any part of the lesion, and the outer circle with a 17-mm diameter, ensured that the mean background value would average any large anatomic variations surrounding the lesion. Hotelling Observer Model. Model human observers provide useful mathematical tools for estimating and predicting human observer performance. Software-based observer models have been used in clinically relevant visual tasks and are used in this work to compare the performance of DBT, WBT, and CT by computing the detectability index for the same task of detecting the embedded masses.
4
anm expðpr 2 =a2 ÞLn ð2pr 2 =a2 Þeimq ;
(5)
m
where the Laguerre polynomial is given as
Performance Evaluation
hQlesion i Qbackground CNR ¼ ; sbackground
XX
ð1Þ
m
n m
xm m!
(6)
The first few Laguerre polynomials are L0 ðxÞ ¼ 1; L1 ðxÞ ¼ x þ 1; L2 ðxÞ ¼
1 2 ðx 4x þ 2Þ: 2!
The variance of the Gaussian is defined by a distance scale related to the signal radius. This study had a value of 8 to maximize the area under the receiver operating characteristic (AUC) for our lesions. Test statistics were computed from the correlation between the image and a template derived from the signal and signalabsent image. Variance in the image is described by the covariance matrix (18). T K ¼ ½g hgi ½g hgi ;
(7)
where hgi is the expectation value of the image matrix g and T denotes the transpose operator. The template derived from the channelized Hotelling observer models can be written as (18) w ¼ Kv1
hD
E D Ei gv=s gv=n ;
(8)
where Kv = VTKV, and V is the matrix containing the spatial weights of each channel profile, gv=s and gv=n denote the signal-present and signal-absent vectors processed by the channel weights. ROI from seven central slices within the lesion in the reconstructed data provided a signal-present image for estimating the signal-present data vector, gv=s . The signal-absent data vector, gv=n , was estimated from slices lying above and below the lesions. A phantom was created by embedding the lesions, described in Breast Phantom section, along the craniocaudal
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midplane of a uniform breast containing water. ROI from seven central slices within the lesion in the reconstructed data provided a ‘‘signal-only’’ image for estimating the template w for the six lesions. Detectability Index. Model responses were calculated as the dot product of the template with the signal-present and signal-absent vectors, li ¼ w t gi ;
(9)
where gi denotes the signal or signal absent at the ith location and w is the template at the corresponding lesion location. Signal-present and signal-absent responses were computed for the six lesions for each patient (3), modality (3), and breast thickness (4). Receiver operating characteristic (ROC) curves were generated for each of the lesions for each individual case from the signal-present and signal-absent model responses in line with the signal-known-exactly-but-variable paradigm, where each set of images contained a different but known lesion. The probability density functions of the signalpresent and signal-absent responses were calculated and then thresholded to obtain an ROC curve for each lesion (19). The ROCs for each of the six lesions were averaged along the true-positive fractions to obtain an ROC for a specific breast. ROCs for the three patients under the same thickness and modality were averaged. The trapezoidal rule was used to calculate the AUC, and the inverse of the error function of the AUC was used to determine the detectability index (d’) as (19,20). 0
d ¼ 2 ðerf 1 ð2 AUC 1ÞÞ;
(10)
where erf denotes the error function. AUC can be estimated from the reverse of this equation (20,21).
RESULTS Projections and Reconstruction
Figure 4 shows the fluence per projection as a function of phantom thickness for DBT, WBT, and CT and a comparison to the corresponding fluence per projection for mammography. X-ray fluence per projection was set to ensure a fixed mean glandular dose of 1.56 mGy. Dose was computed using MC methods. This adjustment was performed to maintain a fixed glandular dose irrespective of acquisition angular range or breast compression level. Figure 5 shows the phantom at four compression levels resulting in breast thicknesses of 4, 5, 6, and 7 cm. The corresponding projections from the MC simulations (Fig 5b) demonstrate the realistic nature of the phantom. Brighter pixels correspond to glandular tissue indicating the higher density relative to the slightly darker adipose tissue. Short sections of the ductal network with microcalcifications can be observed, which appear to be harder to visualize with
Figure 4. Plot of fluence per projection versus phantom thickness for mammography, DBT, WBT, and CT acquisition techniques with corresponding total angle range of 0 , 44 , 99 , and 198 and with 1, 17, 37, and 73 projections, respectively. Fluence per projection was modified to maintain a fixed mean glandular dose at 1.56 mGy. CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wide-angle breast tomosynthesis.
increasing breast thickness. The embedded lesions are not easily visible in the projection images. Furthermore, variation in the breast width can be observed with various breast compression levels. Figure 6a shows midplane slices with the embedded lesions from reconstructed volumes for DBT, WBT, and CT of the 4-cm thick breast phantom. Slices from the reconstructed volumes (Fig 6a) show the scatter cupping artifact as nonuniform brightness radiating outward from the center. The uniform phantom used for scatter correction is shown in Figure 6b. The calibration phantom, shown in Figure 6c, provides attenuation values for adipose and glandular tissues at various percentages. The postprocessed images are shown in Figure 6d, where the images show minimal artifacts and exhibit pixel values reflecting tissue attenuation values. Variation in image quality with increasing number of iterations can be observed in Figure 7, illustrating CT images at four breast thicknesses reconstructed with two, four, six, and eight iterations. In the first iterations, the images are blurry, but the images become progressively sharper as the iteration number increases. Reconstructing the images with more than five or six iterations was found to be detrimental because of increased noise in the images. Figure 8 displays images for the 5-cm breast reconstructed using the three imaging modalities with two, four, six, and eight iterations, similar tradeoffs between resolution and noise as a function of number of iterations can be appreciated. Qualitatively, lesion detectability seems much reduced in the case of DBT compared to CTand WBT. DBT contains increased overlying anatomic noise, which makes the lesions less conspicuous. In general, it took 10 minutes to reconstruct the DBT images and approximately 45 minutes to reconstruct the CT volume. 5
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Figure 5. Variation in breast compression provides four breasts of increasing thickness (a). (b) The central projection from the Monte Carlo simulation of the breast phantom for each of the breast thicknesses.
Figure 6. Central slices containing lesions taken from the reconstructed volumes are shown (a). The nonuniformity scatter can be seen from the bright edges and needs to be removed using a correction phantom (b) which contains the same artifact. The reconstructed images are 32bit volumes which were calibrated to a 16-bit range using a calibration phantom which contained spheres of varying densities of glandular and adipose tissue (c). The slices after correction and calibration (d).
Performance Evaluation
Plots of CNR as a function of iteration are shown in Figure 9a–d. In all cases, a peak is reached at the optimal number of iterations after which the CNR decreases. In the case of the 4-cm breast, two or three iterations were sufficient to ensure maximum performance, whereas in the cases with reduced compression, maximum performance was found at higher number of iterations. Figure 9e shows the relative performance of modalities at optimum number of iterations. Averaging across all breast thicknesses, the performance of CT was better than WBT by 13.4 5.3%. The difference of performance between WBT and DBT was 15.1 7.0%. The analysis can also be presented in terms of AUC using the reverse of Equation (10), (Fig 10). By taking an average of the AUC parameters across all breast thicknesses, the performance of CT was better than WBT by 2.4 1.1%, whereas the difference of performance between WBT and DBT was 3.4% 1.2%. In terms of the analysis using the Hotelling observer model, Figure 11 shows the ROCs using Laguerre–Gauss channels. 6
CT has a nearly ideal ROC performance, and WBT performs better than DBT in all cases. Increasing thickness affects the performance of each imaging modality. Performance of WBT over DBT was found to be 5.6 1.0% greater at the same thickness. Comparatively, CT had 4.3 3.0% improvement over WBT. However, analyses of individual cases, reflected in the error bars of Figure 11, reveal that there is a certain amount of variability in the lesion detectability in breasts of different thicknesses, but in all cases, we see the benefits of a wider angle of acquisition. As shown, WBT exhibits lesser variance and better performance over DBT. Comparison at levels of compression that better reflect the imaging modality was also performed. For instance, CT requires little or no compression, whereas DBT uses a higher degree of compression. Therefore, comparing DBT at highest compression, CT at least compression, and WBT at moderate compression (4-, 7-, and 5-cm breast thickness, respectively), it was seen that WBT performed comparably to CT (1.2% performance difference) and better than DBT (5.5% performance difference) using the observer model analyses.
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Figure 7. Computed tomography images of increasing thickness varying with respect to increasing number of iterations of the reconstruction. As the number of iterations increases, the images become sharper and noisier. The thicker breasts show reduced lesion conspicuity.
Figure 8. Images of CT, WBT, and DBT for the 5-cm breast at various iterations. The lesions in both CT and WBT can be easily discerned, whereas DBT shows low lesion conspicuity. CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wide-angle breast tomosynthesis.
DISCUSSION DBT has advantages over mammography but is limited by artifacts because of its limited acquisition angle range (22). Performance of breast CT in terms of image quality and resolution is superior to that of DBT, but difficulties in imaging breasts of small sizes and poor chest wall coverage make it unsuitable as a diagnostic tool for all patients. Our proposed breast imaging modality has a geometry which would provide adequate chest wall coverage. We have shown that increasing the acquisition angle from 50 to only even 100 provides a significant improvement in terms of contrast and lesion detectability. Performance of WBT was closer to CT than DBT in both evaluation techniques. However, considering that the current implementation of CT involves no compression, our data indicate that WBT (with modest compression) can provide a performance comparable to CT. In this study, we developed a system that can be used to evaluate and compare various volumetric breast imaging
modalities. The developed breast phantom provided a versatile anthropomorphic model. Its ability to represent a wide variety of patients; to imitate various breast-related diseases; and to incorporate easily in simulation programs makes this phantom a unique and useful model. Combined with MC simulation, the phantom provides a powerful framework for performance assessment of various imaging systems including systems with stationary detectors (eg, conventional tomosynthesis) and moving detectors (eg, CT). The iterative reconstruction was found to provide highperformance reconstructions of volumes in the presence of limited angular coverage. Though iterative methods require increased computation resources, future work will investigate the benefits of parallel processing and high-speed computation processors on our iterative reconstruction code. In that light, WBT provides similar imaging performance to DBT at lower compression levels. In Figures 9 and 11, we can see that performance of WBT at breast thickness of
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Figure 9. Contrast-to-noise ratio as a function of the number of iterations for each of the breast thicknesses (a–d). (e) The relative performance at the optimal number of iterations for each modality and thickness. CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wideangle breast tomosynthesis.
6 cm is slightly better than DBTat 4 cm. Pain during screening mammography examinations due to breast compression has been cited as a reason for women to avoid regular screenings and hence reduce its effectiveness (9). Reduction of breast compression would alleviate patient discomfort during the clinical examinations and thereby increase the number of women likely to undergo regular breast examinations. Because the intended geometry for WBT is to be based on that of the present implementation of standard DBT, the chest wall coverage was assumed to be as much as that of standard 8
DBT. A physical implementation will need to be constructed and clinical trials performed to actually assess the actual chest wall coverage while increasing the acquisition angle range. Unlike some radiographic imaging implementations wherein the x-ray tube current is varied depending on the thickness of tissue the x-ray beam needs to pass through, this study did not modulate the x-ray tube current while imaging compressed breasts. This issue would have a bearing on the required noise performance of the detector at low exposure levels per projection as well. Only quantum noise was present in projections.
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Figure 10. Relative contrast-to-noise ratio performance in terms of AUC at the optimal number of iterations for each modality and thickness. AUC, area under the receiver operating characteristic; CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wide-angle breast tomosynthesis.
Figure 11. Receiver operating characteristics of CT, WBT, and DBT modalities (a–d) obtained using the Hotelling observer model with Laguerre–Gauss channels and corresponding detectability index (d’) calculated in terms of the AUC at the optimal iteration (e). The error bars reflect the variability of performance across patients. AUC, area under the receiver operating characteristic; CT, computed tomography; DBT, digital breast tomosynthesis; WBT, wideangle breast tomosynthesis.
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No nonquantum noise attributes of the detector were modeled in this investigation. As such, the results of this study are reflective of the comparative image quality of these modalities, provided that the instrumentation noise from the detector can be considered negligible. (Photon counting detector technology offers a notable advantage in that regard.) This issue, however, is a performance requirement for WBT and CT and, along with the exact geometrical arrangement and implementation of WBT and its optimization for differentsized breasts, remains a topic of future studies. Notwithstanding the conclusions of the study, certain limitations should be acknowledged. First, the breast phantom model that we used has been shown to be a reasonable but not precise representation of actual breast anatomy. The voxelised nature might further introduce artifacts into the simulation process that needs to be assessed (8). Second, the statistical significance is likely to be limited by the fact that the study was implemented with a small number of phantoms. Third, because of computational limitations, we modeled the three modalities under a single technique condition, which might not be optimal for a given modality (23). For example, the technique used by current prototype CT systems is based on a higher energy x-ray beam. The assessment of system performance as a function of technique and dose remain topics of future investigations. CONCLUSIONS The proposed imaging modality, called WBT, showed significant advantages over standard DBT based on analyses using CNR and channelized Hotelling observer models. WBT was closer to CT in terms of imaging performance and exhibited improved performance over DBT at lower compression levels, highlighting further potential of reduced breast compression. Our study further used a unique breast phantom model and MC-based simulation program that can be used to model various breast imaging systems. REFERENCES 1. Boyle P, Levin B, eds. World Caner Report 2008. Lyon, France: World Health Organization Press, 2008. 2. Elmore JG, Armstrong K, Lehman CD, et al. Screening for breast cancer. JAMA 2005; 293(10):1245–1256.
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