Stand-alone cone beam computed tomography (CT) and single-photon emission computed tomography (SPECT) systems capable of complex acquisition trajectories have previously been developed for breast imaging. Fully three-dimensional (3-D) motions of SPECT systems provide views into the chest wall and throughout the entire volume. The polar tilting capability of the CBCT system has shown improvement in sampling close to the chest wall, while eliminating cone beam artifacts. Here, a single hybrid SPECT–CT system, with each individual modality capable of independently traversing complex trajectories around a common pendant breast volume, was developed. We present the practical implementation of this design and preliminary results of the CT system. The fully 3-D SPECT was nested inside the suspended CT gantry and oriented perpendicular to the CT source–detector pair. Both subsystems were positioned on a rotation stage, with the combined polar and azimuthal motions enabling spherical trajectories. Six trajectories were used for initial evaluation of the tilt capable CT system. The developed system can achieve polar tilt angles with a <0.02-deg positioning error and no hysteresis. Initial imaging results demonstrate that additional off-axis projection views of various geometric resolution phantoms facilitate more complete sampling, more consistent attenuation value recovery, and markedly improved reconstructions. This system could have various applications in diagnostic or therapeutic breast imaging.
A novel breast CT system capable of traversing non-traditional 3D trajectories was developed to address cone beam sampling insufficiency for pendant breast imaging. The purpose of this study was to characterize differences in three dimensional x-ray dose distributions in a target volume due to the acquisition trajectory. Three cylindrical phantoms of different diameters and an anthropomorphic breast phantom were scanned in a pendant geometry with two orbits- azimuthal orbit with no polar tilt, and a saddle orbit with ±15° contiguous polar tilts. The phantoms were initially filled with water and then with a 75:25% water: methanol mixture, to simulate different density breast tissues. Fully-3D CT scans were performed using a tungsten anode x-ray source. Ionization chamber calibrated radiochromic film was used to determine average dose delivered to the central sagittal slice of a volume, as well as to visualize the 2D dose distribution across the slice. Results indicated that the mean glandular dose for normal imaging exposures, measured at the central slice across different diameters ranged from 3.93-5.28 mGy, with the lowest average dose measured on the largest diameter cylinder. In all cases, the dose delivered by the saddle was consistently 1-3% lower than the no-tilt scans. These results corroborate previous cylinder Monte Carlo studies which showed a 1% reduction in saddle dose. The average dose measured in the breast phantom filled with 75:25 mixture was slightly higher for saddle. Non-traditional 3D breast CT scans have slightly better dose performance for equal image noise compared with simple, under sampled circular orbits.
KEYWORDS: X-rays, Breast, X-ray computed tomography, 3D acquisition, 3D image processing, Data acquisition, Signal attenuation, 3D metrology, Sensors, Reconstruction algorithms
The 2D scatter-to-primary (SPR) ratios and 3D voxelized difference volumes were characterized for a
cone beam breast CT scanner capable of arbitrary (non-traditional) 3D trajectories. The CT system uses a
30x30cm2 flat panel imager with 197 micron pixellation and a rotating tungsten anode x-ray source with
0.3mm focal spot, with an SID of 70cm. Data were acquired for two cylindrical phantoms (12.5cm and
15cm diameter) filled with three different combinations of water and methanol yielding a range of
uniform densities. Projections were acquired with two acquisition trajectories: 1) simple-circular
azimuthal orbit with fixed tilt; and 2) saddle orbit following a ±15° sinusoidal trajectory around the object.
Projection data were acquired in 2x2 binned mode. Projections were scatter corrected using a beam stop
array method, and the 2D SPR was measured on the projections. The scatter corrected and uncorrected
data were then reconstructed individually using an iterative ordered subsets convex algorithm, and the 3D
difference volumes were calculated as the absolute difference between the two. Results indicate that the
2D SPR is ~7-15% higher on projections with greatest tilt for the saddle orbit, due to the longer x-ray path
length through the volume, compared to the 0° tilt projections. Additionally, the 2D SPR increases with
object diameter as well as density. The 3D voxelized difference volumes are an estimate of the scatter
contribution to the reconstructed attenuation coefficients on a voxel level. They help visualize minor
deficiencies and artifacts in the volumes due to correction methods.
A fully suspended, stand-alone cone beam CT system capable of complex trajectories, in addition to a
simple circular trajectory, has previously been developed and shown to minimize cone beam sampling
insufficiencies and have better sampling close to the chest wall for pendant breast CT imaging. A hybrid
SPECT-CT system with SPECT capable of complex 3D trajectories has already been implemented and is
currently in use. Here, the individual systems are redesigned into one hybrid system where each individual
component is capable of traversing independent, arbitrary trajectories around a pendant breast and anterior
chest wall in a common field of view. The integration also involves key hardware upgrades: a new high
resolution 40x30cm2 flat panel CT imager with an 8mm bezel on two sides for closer chest wall access, a
new x-ray source, and a unique tilting mechanism to enable the spherical trajectories for CT. A novel
method to tilt the CT gantry about a 3D center of rotation is developed and included in the new gantry,
while preserving the fully-3D SPECT system nested within the larger CT gantry. The flexibility of the
integrated system is illustrated.
In current dedicated breast computed tomography (mammotomography) systems, comfortable patient positioning on a
stationary bed restricts the practicable range of source-detector trajectories, thus compromising the system's ability to
adequately image the patient's anterior chest wall. This study examines the effect on detecting small, low-contrast
lesion-like-spheres using limited angle x-ray source-detector trajectories and trajectories that intentionally raise the
tomographic imaging system mid-acquisition. These modified acquisition paths may increase chest wall visualization,
simplify the design of the imaging system and increase patient comfort by allowing the design of an improved patient
bed. Thin walled balloons of various volumes filled with iodine act as surrogate high contrast lesions to initially
investigate the effect of these novel trajectories. Then, stacks of 5mm acrylic spheres regularly spaced in concentric
circles are placed in water to simulate a low contrast environment in a uniform scatter medium. 360° azimuthal scans are
acquired at various bed heights with contiguous projections subsequently removed to create limited angle acquisitions
from 240-360°. Projections from the different bed heights are interwoven to form trajectories that mimic discontinuously
raising the imaging system mid-acquisition. The resulting iteratively reconstructed volumes are evaluated with an
observer study. Initial images suggest that using limited angles and raising the system is possible while increasing the
observer's ability to visualize objects near the chest wall. Based on the results of this study, an improved patient bed to
facilitate chest wall imaging will be designed, and the feasibility of vertical system motion to increase imaged breast
volume explored.
We use a contrast-detail observer study to compare performance of a novel 3D computed mammotomography (CmT)
system with a commercially developed full-field digital mammography (FFDM) system. A contrast-detail phantom
comprised of uniform acrylic spheres of various diameters was developed and placed in a variety of mediums
including uniform water (simulating low contrast lesions within a uniform background), water and acrylic yarn
(simulating low contrast lesions with over/under-lying structure), oil only (simulating higher contrast lesions in a
uniform background), and oil and acrylic yarn (simulating higher contrast lesions with over/under-lying structure).
For CmT, the phantom was placed in a 14.6 cm diameter uncompressed breast phantom and projections acquired using
a simple circular orbit, W-target tube, 60 kVp tube potential, 0.05 cm Ce filtration, 4 mAs per projection, and a CsI(Tl)
digital x-ray detector. Reconstructions used an iterative OSTR algorithm. For FFDM, the phantom was placed in a
5.3-cm-thick compressed breast phantom. Single CC-view mammograms were acquired using a clinical W-target tube
with 50 um Rh filtration, 28 kVp, photo-timed mAs per our clinical mammography operation, and a Selenium-based
flat-panel detector (Mammomat Novation, Siemens). Six observers evaluated the images in terms of the number of
detectable spheres. FFDM performed significantly better for the low contrast lesions in uniform water background
(p<0.05). However, CmT performed significantly better for all other cases (p<0.05). Results indicate that CmT shows
significant advantage in soft tissue detection over FFDM in otherwise low contrast dense breasts.
A hybrid SPECT-CT system for dedicated 3D breast imaging (mammotomography) is currently under development. Each imaging system will be placed on top of a single rotation stage and moved in unison azimuthally, with the SPECT system additionally capable of polar and radial motions. In this initial prototype, the CT system will initially be positioned at a fixed polar tilt. Using a phantom with three tungsten wires, the MTF of the CT system was measured in 3D for different CT system tilts. A phantom with uniformly arranged 0.5cm diameter acrylic spheres was suspended in air in the CT field of view, and also placed at multiple locations and orientations inside an oil-filled breast phantom to evaluate the effect of CT system tilt on lesion visibility and distortion. Projection images were collected using various simple circular orbits with fixed polar tilts ranging between ±15°, and complex 3D saddle trajectories including combined polar and azimuthal motions at maximum polar tilt angles. Reconstructions were performed using an iterative reconstruction algorithm on 4x4 binned projection images with 0.508mm3 voxels. There was minor variation in the MTF in the imaged volume for the CT system at all trajectories, potentially due to the use of an iterative reconstruction algorithm. Results from the spherical cross phantoms indicated that there was more reconstruction inaccuracy and geometric distortion in the reconstructed slices with simple circular orbits with fixed tilt in contrast to complex 3D trajectories. Line profiles further showed a cupping artifact in planes farther away from the flat plane of the x-ray cone beam placed at different tilts. However, this cupping artifact was not seen for images acquired with complex 3D trajectories. This indicated that cupping artifacts can also be caused by undersampled cone beam data. These findings generally indicate that despite insufficient sampling with the cone beam imaging geometry, it is possible to place the CT system at a stationary polar tilt with the CT tube positioned upward such that a patient can be comfortably placed above the system and allow complete sampling near the top of the pendant, uncompressed breast and chest wall. However, a complex 3D trajectory allows for more complete sampling of the entire image volume.
A hybrid SPECT-CT system for dedicated 3D breast cancer imaging (mammotomography) is in development. Using
complex 3D imaging acquisition trajectories, the versatile integrated system will be capable of contouring and imaging
an uncompressed breast suspended in a 3D volume located below a radio-opaque patient bed, providing co-registered
volumetric anatomical and functional information. This study examines tradeoffs involved in the design of the patient
bed to satisfy concomitant and competing technical and ergonomic requirements specific to this imaging paradigm. The
complementary source-detector arrangement of the CT system is geometrically more restrictive than that of the single
detector SPECT system. Additionally, the compact dimensions and size of the CT system components (primarily the x-ray
tube) are key constraints on the bed design and so the focus is concentrated there. Using computer-aided design
software, several design geometry options are examined to simultaneously consider and optimize the following
parameters: image magnification, imaged breast volume, azimuthal imaging span, and patient comfort. Several CT
system source to image distances are examined (55-80cm), as well as axial patient tilt up to 35°. An optimal patient bed
design for a completely under-bed hybrid imaging system was determined. A 60cm SID, magnification factor of ~1.5,
and patient bed angled at ~15° provided the optimal dimensions. Additional bed dimensions allow the CT projection
beam to nearly entirely image the chest wall, however at the cost of reduced angular sampling for CT. Acquired x-ray
mammotomographic image data is used to assess the feasibility of this reduced angle acquisition approach.
A novel phantom has been developed to measure the modulation transfer function (MTF) in 3D for x-ray computed tomography. The phantom consists of three tungsten wires, positioned nearly orthogonal to each other. Simultaneous measurements of the MTF are taken at various locations along the three orthogonal reconstructed planes. Our computed mammotomography (CmT) system uses a Varian Paxscan 2520 digital x-ray detector which can be positioned anywhere in ~2pi steradian band and can have arbitrary trajectories. With a half-cone beam geometry and with the phantom positioned near the center of rotation, projection images are acquired over 360 degrees. Various 3D orbits are evaluated including vertical axis of rotation and saddle. Reconstructions were performed using an iterative ordered-subsets transmission algorithm on rebinned projection images, using various numbers of iterations. Rotation of reconstructed slices isolated each wire into its own plane. At various locations along the length of each wire, corresponding MTFs were calculated from 1D line spread functions. Through measurement, accuracy of wire method was verified by comparison of the projection MTFs computed from a wire and a standard edge device. Results indicated minor variations in MTF among the three orthogonal planes, which imply a high degree of uniform sampling in the imaged volume. Findings indicate that the phantom can be used to assess the intrinsic image resolution in 3D as well as potential degradative effects of measurements in various media.
A dual modality SPECT/CT computed mammotomography (CmT) system for dedicated functional/structural breast
imaging is under development. In simultaneous, dual-modality imaging, contamination of the transmission (x-ray) image
by emission photons from the uncompressed, pendant breast and torso is an important consideration in the design of
hybrid imaging hardware. The lack of a collimator on the transmission image detector implies increased geometric
efficiency of primary and scattered emission photons from the breast and neighboring torso region that potentially
increase transmission image noise. This study investigates the nature and extent of this cross contamination. Projection
and tomographic x-ray images are obtained with and without emission activity in a realistic anthropomorphic torso and
various breast phantoms, and also with and without lead shielding on the torso for a variety of x-ray exposure times.
Results for emission-source contamination of transmission images are quantified in terms of a mean and standard
deviation of regions of interest. There was an observed trend of increased contamination with increasing emission
radioactivity in the projection images when the x-ray detector was located immediately beneath the torso phantom, but
no discernible effect when the detector was lateral to (and beneath) the torso. Torso shielding mitigated this
contamination somewhat. Indeed, in reconstructed CmT data, there was both a decrease in SNR and concomitant
decrease in mean attenuation coefficient with increasing emission radioactivity contamination. These results are
consistent with the expected increased noise due to a uniform emission irradiation of the detector and hence the resulting
apparent increase in detected x-ray transmission events (which yield a lower reconstructed attenuation coefficient value).
Despite the emission contamination in both projection and reconstructed images, the contamination is uncorrelated, and
indeed no reconstruction artifacts were observed under the various measured conditions. This indicates that a simple
contamination correction may be possible to the projection data prior to reconstruction.
We use a previously reported, optimized quasi-monochromatic beam technique together with unique complex
acquisition trajectories made possible with a novel, dedicated
cone-beam transmission computed mammotomography
(CmT) system to investigate effects of low dose imaging of pendant, uncompressed breasts. Investigators have used a
guideline of dose for CmT type applications as that used for
dual-view mammography (4-6 mGy for average breast
size). This dose is somewhat arbitrary, and it may be possible to reduce this significantly without sacrificing image
quality using our quasi-monochromatic x-ray beam, 3D complex acquisition orbits, and iterative reconstruction
techniques. A low-scatter acrylic resolution phantom in various media, a breast phantom with sponge and oil-filled
lesions, and a cadaver breast are used to evaluate the effect of lowered dose on resolution and image artifacts.
Complex saddle acquisition trajectories (necessary to overcome
cone-beam distortion) are carried out for total
exposures of 96, 300, and 600 mAs over 240 projections. These exposures relate approximately to 1/10th, 1/3rd, and
2/3rd of the standard dual view mammography dose for an average sized 50% adipose/glandular breast. Iterative
reconstruction uses an OSTR algorithm with 0.125 mm3 voxels. Image artifacts increased as dose was reduced but did
not appear to greatly degrade image quality except at the lowest contrast tested (1% absolute contrast). As expected,
noise increased as dose was reduced. However, this did not appear to affect resolution for rods in air (high contrast),
nor rods in oil (20% absolute contrast). Resolution was reduced for rods in water (1% absolute contrast) due to
increased prevalence of image artifacts as well as increased noise. Breast phantom imaging of soft lesions in a highly
glandular breast (6% absolute contrast) clearly yielded the 60uL and all larger volume lesions. Preliminary biological
breast tissue results illustrate excellent subjective image quality at all dose levels tested. Results indicate that our
quasi-monochromatic beam together with complex orbit capability and iterative reconstruction has the potential to
provide sufficient image quality for practical 3D mammotomography of uncompressed breasts at significantly lower
dose than dual view mammography. This is nominally a 2-fold improvement over other approaches using circular
orbits and broader spectral x-ray beams. While simple image filtering (post-reconstruction smoothing) could improve
noise quality, improvements in image artifact correction and scatter correction are required to more accurately
determine the lower limits on dose. A contrast-detail study is also warranted with a greater variety of lesion sizes and
contrasts.
A compact, dual modality computed mammotomography (CmT) and single photon emission computed tomography
(SPECT) system for dedicated 3D breast imaging is in development. The CmT component utilizes novel, heavy K-edge
filtration to practicably narrow the energy spectrum of the cone-shaped x-ray beam incident on the patient's pendant,
uncompressed breast. This quasi-monochromatic beam in CmT is expected to improve discrimination of tissue with
very similar attenuation coefficients while restraining dose levels to below that of existing dual view mammography.
Our previous extensive simulation studies showed the optimal energy range that provides maximum dose efficiency for
a 50/50 adipose/glandular breast is in the 35-40keV range. This current study aims to experimentally validate previous
simulation results. Here, experimental pre-breast and post-breast collimated x-ray beam spectral measurements are
made under tube operating voltages between 40-100kVp using filter materials from Z=13-74, with K-edge values
spanning that of Ce (K=40.4keV), and using different attenuating thicknesses of filter material, approximately
equivalent to the 200th and 500th attenuating value layer (VL) thickness. Ce-filtered post breast spectra for 8cm to 18cm
breasts are measured for a range of breast adipose/glandular compositions. Evaluated figures of merit include mean
beam energy, spectral full-width at tenth-maximum, beam hardening and dose for the range of breast sizes.
Measurements are shown to corroborate the simulations, and both indicate that for a given dose a 200th VL of Ce
filtration may have the most optimal performance in the dedicated mammotomography paradigm.
KEYWORDS: Breast, Distortion, Chest, Imaging systems, Computing systems, 3D image reconstruction, 3D acquisition, 3D image processing, Breast imaging, Sensors
We investigate cone-beam acquisitions implemented on a novel dedicated cone-beam transmission computed mammotomography (CmT) system with unique arbitrary orbit capability for pendant, uncompressed breasts. We use a previously reported optimized quasi-monochromatic beam technique together with orbits made possible with a novel CmT gantry system, to evaluate Vertical-Axis-Of-Rotation (VAOR), Circle-Plus-Two-Arcs (CP2A), and Saddle trajectories. Aquisition parameters include: W target, 60 kVp tube potential, 100th VL Nd filtration, 1.25 mAs, 55 cm SID, CsI(Tl) digital flat panel x-ray detector, and 7.7cm diameter uniform disc (Defrise) and resolution phantoms. Complex orbits were also performed for a realistic breast phantom. Reconstructions used an iterative ordered subsets transmission (OSTR) algorithm with 4x4 binned projections, 8 subsets, and 10 iterations, with 0.125 mm3 voxels. We evaluate the results for image artifacts, distortion, and resolution. Reconstructed images of the disc coronal and sagittal slices show significant distortion of the discs and phantom interfaces away from the central plane of the cone-beam for VAOR, less distortion for CP2A, and minimal distortion for the complex 3D Saddle orbit. Resolution phantoms indicate no loss of resolution with the Saddle orbit, with the smallest 1.1mm diameter rods clearly resolved. Other image artifacts such as streaking were also significantly reduced in the Saddle orbit case. Results indicate that arbitrary orbits of pendant uncompressed breasts using cone-beam acquisitions and OSTR iterative reconstructions can be successfully implemented for dedicated CmT to improve angular sampling with significant reduction in distortion and other image artifacts. This capability has the potential to improve the performance of dedicated CmT by adequately sampling the breast and anterior chest volumes of prone patients with pendant, uncompressed breasts.
Our effort to implement a volumetric x-ray computed mammotomography (CmT) system dedicated to imaging breast disease comprises: demonstrated development of a quasi-monochromatic x-ray beam providing minimal dose and other optimal imaging figures of merit; new development of a compact, variable field-of-view, fully-3D acquisition gantry with a digital flat-panel detector facilitating more nearly complete sampling of frequency space and the physical breast volume; incorporation of iterative ordered-subsets transmission (OSTR) image reconstruction allowing modeling of the system matrix. Here, we describe the prototype 3D gantry and demonstrate initial system performance. Data collected on the prototype gantry demonstrate the feasibility of using OSTR with realistic reconstruction times. The gantry consists of a rotating W-anode x-ray tube using ultra-thick K-edge filtration, and an ~20x25cm2 digital flat-panel detector located at <60cm SID. This source/detector combination can be shifted laterally changing the location of the central ray relative to the system center-of-rotation, hence changing the effective imaging field-of-view, and is mounted on a goniometric cradle allowing <50° polar tilt, then on a 360° azimuthal rotation stage. Combined, these stages provide for positioning flexibility in a banded region about a sphere, facilitating simple circle-plus-arc-like trajectories, as well as considerably more complex 3D trajectories. Complex orbits are necessary to avoid physical hindrances from the patient while acquiring the largest imaging volume of the breast. The system capabilities are demonstrated with fully-3D reconstructed images of geometric sampling and resolution phantoms, a fabricated breast phantom containing internal features of interest, and a cadaveric breast specimen. This compact prototype provides flexibility in dedicated, fully-3D CmT imaging of healthy and diseased breasts.
With the development of several classes of dedicated emission and transmission imaging technologies utilizing ionizing radiation for improved breast cancer detection and in vivo characterization, it is extremely useful to have available anthropomorphic breast phantoms in a variety of shapes, sizes and malleability prior to clinical imaging.
These anthropomorphic phantoms can be used to evaluate the implemented imaging approaches given a known quantity, the phantom, and to evaluate the variability of the measurement due to the imaging system chain. Thus, we have developed a set of fillable and incompressible breast phantoms ranging in volume from 240 to 1730mL with nipple-to-chest distances from 3.8 to 12cm. These phantoms are mountable and exchangeable on either a uniform chest plate or anthropomorphic torso phantom containing tissue equivalent bones and surface tissue. Another fillable ~700mL breast phantom with solid anterior chest plate is intentionally compressible, and can be used for direct comparisons between standard planar imaging approaches using mild-to-severe compression, partially compressed tomosynthesis, and uncompressed computed mammotomography applications. These phantoms can be filled with various fluids (water and oil based liquids) to vary the fatty tissue background composition. Shaped cellulose sponges with two cell densities are fabricated and can be added to the breasts to simulate connective tissue. Additionally,
microcalcifications can be simulated by peppering slits in the sponges with oyster shell fragments. These phantoms have a utility in helping to evaluate clinical imaging paradigms with known input object parameters using basic imaging characterization, in an effort to further evaluate contemporary and next generation imaging tools. They may additionally provide a means to collect known data samples for task based optimization studies.
Simulation results from previous studies indicate that a quasi-monochromatic x-ray beam can be produced using a newly developed beam filtration technique. This technique utilizes heavy filtration with novel high Z filter materials having k-edges just above those of CsI, producing a near monochromatic beam with mean energy optimized for detection. The value of a near monochromatic x-ray source for a fully 3D tomography application is the expected improved ability to separate tissues with very small differences in attenuation coefficients for a range of uncompressed breast sizes while maintaining dose levels at or below existing dual view mammography. In this study, we experimentally investigate a set of filter materials (Al, Cu, Ag, Ce, W, and Pb), filter thicknesses (10th, 100th, and 200th VL), and tube potentials (40-80 kVp) using a newly constructed test apparatus. Initial experimental results corroborate simulations and indicate that this approach can improve image quality (SNR) at constant dose. Al, Cu, W, and Pb provide optimal exposure efficiency results at 60 kVp and above. Decreasing relative improvements are observed above 100th VL filter thickness at 78 cm SID. Results are obtained without significant tube heating (except at 40 kVp). In addition, simulations indicate significant reductions in beam hardening. This optimized beam will be incorporated into a novel cone-beam x-ray computed mammotomography sub-system together with an emission tomograph in a dual modality CT/SPECT application specific emission and transmission tomography system for fully 3D uncompressed breast imaging.
The purpose of this study was to determine the optimum beam quality in terms of kVp and filtration for a tungsten-target x-ray source for a newly developed cone beam computed mammotomography application. The optimized beam is expected to yield enhanced image quality along with a low dose, equal to or less than that of dual view x-ray mammography. X-ray spectra were computer generated for a range of tube potentials, filter materials, and filter and breast thicknesses. The uncompressed breast was modeled from 8, 12, and 16 cm thick tissue, and breast lesions were modeled as a 0.5 cm thick striated muscle mass and a 0.02 cm thick microcalcification. The detector was modeled as a digital flat-panel detector with a 0.06 cm thick CsI x-ray absorption layer. Figures of merit computed included the ratio of the mean beam energy post-breast to pre-breast as an index of beam hardening, ratio of lesion contrasts with and without filtering, and SNR/exposure. Tube potentials between 50 and 70 kVp provided continuous spectra that, when filtered with Z-filters between 56 and 62 yielded quasi-monochromatic x-ray spectra with optimal SNR/exposure and contrast while providing minimum beam hardening. Figures of merit improve with increasing filter thickness, but diminishing returns are seen beyond the 500th value attenuation layer. While uncompressed breast thickness affected absolute values of the measurement criteria, they had little effect on beam hardening and contrast ratio and did not alter the optimal operating range. Filter thickness near the 500th value layer is expected to be well within the operating range for an intended commercial x-ray tube, indicating that these highly attenuating filters can provide superior performance for mammotomography.
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