Line-based iterative geometric calibration method for a tomosynthesis system.

BACKGROUND: A next generation tomosynthesis (NGT) system, capable of two-dimensional source motion, detector motion in the perpendicular direction, and magnification tomosynthesis, was constructed to investigate different acquisition geometries. Existing position-based geometric calibration methods proved ineffective when applied to the NGT geometries. PURPOSE: A line-based iterative calibration method is developed to perform accurate geometric calibration for the NGT system. METHODS: The proposed method calculates the system geometry through virtual line segments created by pairs of fiducials within a calibration phantom, by minimizing the error between the line equations computed from the true and estimated fiducial projection pairs. It further attempts to correct the 3D fiducial locations based on the initial geometric calibration. The method's performance was assessed via simulation and experimental setups with four distinct NGT geometries: X, T, XZ, and TZ. The X geometry resembles a conventional DBT acquisition along the chest wall. The T geometry forms a "T"-shaped source path in mediolateral (ML) and posteroanterior (PA) directions. A descending detector motion is added to both X and T geometries to form the XZ and TZ geometries, respectively. Simulation studies were conducted to assess the robustness of the method to geometric perturbations and inaccuracies in fiducial locations. Experimental studies were performed to assess the impact of phantom magnification and the performance of the proposed method for various geometries, compared to the traditional position-based method. Star patterns were evaluated for both qualitative and quantitative analyses; the Fourier spectral distortions (FSDs) graphs and the contrast transfer function (CTF) were extracted. The limit of spatial resolution (LSR) was measured at 5% modulation of the CTF. RESULTS: The proposed method presented is highly robust to geometric perturbation and fiducial inaccuracies. After the line-based iterative method, the mean distance between the true and estimated fiducial projections was [X, T, XZ, TZ]: [0.01, 0.01, 0.02, 0.01] mm. The impact of phantom magnification was observed; a contact-mode acquisition of a calibration phantom successfully provided an accurate geometry for 1.85× magnification images of a star pattern, with the X geometry. The FSD graphs for the contact-mode T geometry acquisition presented evidence of super-resolution, with the LSR of [0°-quadrant: 8.57, 90°-quadrant: 8.47] lp/mm. Finally, a contact-mode XZ geometry acquisition and a 1.50× magnification TZ geometry acquisition were reconstructed with three calibration methods-position-based, line-based, and iterative line-based. As more advanced methods are applied, the CTF becomes more isotropic, the FSD graphs demonstrate less spectral leakage as super-resolution is achieved, and the degree of blurring artifacts reduces significantly. CONCLUSIONS: This study introduces a robust calibration method tailored to the unique requirements of advanced tomosynthesis systems. By employing virtual line segments and iterative techniques, we ensure accurate geometric calibration while mitigating the limitations posed by the complex acquisition geometries of the NGT system. Our method's ability to handle various NGT configurations and its tolerance to fiducial misalignment make it a superior choice compared to traditional calibration techniques.

Non-Isocentric Geometry for Next-Generation Tomosynthesis With Super-Resolution.

Our lab at the University of Pennsylvania (UPenn) is investigating novel designs for digital breast tomosynthesis. We built a next-generation tomosynthesis system with a non-isocentric geometry (superior-to-inferior detector motion). This paper examines four metrics of image quality affected by this design. First, aliasing was analyzed in reconstructions prepared with smaller pixelation than the detector. Aliasing was assessed with a theoretical model of r -factor, a metric calculating amplitudes of alias signal relative to input signal in the Fourier transform of the reconstruction of a sinusoidal object. Aliasing was also assessed experimentally with a bar pattern (illustrating spatial variations in aliasing) and 360°-star pattern (illustrating directional anisotropies in aliasing). Second, the point spread function (PSF) was modeled in the direction perpendicular to the detector to assess out-of-plane blurring. Third, power spectra were analyzed in an anthropomorphic phantom developed by UPenn and manufactured by Computerized Imaging Reference Systems (CIRS), Inc. (Norfolk, VA). Finally, calcifications were analyzed in the CIRS Model 020 BR3D Breast Imaging Phantom in terms of signal-to-noise ratio (SNR); i.e., mean calcification signal relative to background-tissue noise. Image quality was generally superior in the non-isocentric geometry: Aliasing artifacts were suppressed in both theoretical and experimental reconstructions prepared with smaller pixelation than the detector. PSF width was also reduced at most positions. Anatomic noise was reduced. Finally, SNR in calcification detection was improved. (A potential trade-off of smaller-pixel reconstructions was reduced SNR; however, SNR was still improved by the detector-motion acquisition.) In conclusion, the non-isocentric geometry improved image quality in several ways.

Impact of super-resolution and image acquisition on the detection of calcifications in digital breast tomosynthesis.

OBJECTIVES: A virtual clinical trial (VCT) method is proposed to determine the limit of calcification detection in tomosynthesis. METHODS: Breast anatomy, focal findings, image acquisition, and interpretation (n = 14 readers) were simulated using screening data (n = 660 patients). Calcifications (0.2-0.4 mm3) were inserted into virtual breast phantoms. Digital breast tomosynthesis (DBT) acquisitions were simulated assuming various acquisition geometries: source motion (continuous and step-and-shoot), detector element size (140 and 70 µm), and reconstructed voxel size (35-140 µm). VCT results were estimated using multiple-reader multiple-case analyses and d' statistics. Signal-to-noise (SNR) analyses were also performed using BR3D phantoms. RESULTS: Source motion and reconstructed voxel size demonstrated significant changes in the performance of imaging systems. Acquisition geometries that use 70 µm reconstruction voxel size and step-and-shoot motion significantly improved calcification detection. Comparing 70 with 100 µm reconstructed voxel size for step-and-shoot, the ΔAUC was 0.0558 (0.0647) and d' ratio was 1.27 (1.29) for 140 µm (70 µm) detector element size. Comparing step-and-shoot with a continuous motion for a 70 µm reconstructed voxel size, the ΔAUC was 0.0863 (0.0434) and the d' ratio was 1.40 (1.19) for 140 µm (70 µm) detector element. Small detector element sizes (e.g., 70 µm) did not significantly improve detection. The SNR results with the BR3D phantom show that calcification detection is dependent upon reconstructed voxel size and detector element size, supporting VCT results with comparable agreement (ratios: d' = 1.16 ± 0.11, SNR = 1.34 ± 0.13). CONCLUSION: DBT acquisition geometries that use super-resolution (smaller reconstructed voxels than the detector element size) combined with step-and-shoot motion have the potential to improve the detection of calcifications. CLINICAL RELEVANCE: Calcifications may not always be discernable in tomosynthesis because of differences in acquisition and reconstruction methods. VCTs can identify strategies to optimize acquisition and reconstruction parameters for calcification detection in tomosynthesis, most notably through super-resolution in the reconstruction. KEY POINTS: • Super-resolution improves calcification detection and SNR in tomosynthesis; specifically, with the use of smaller reconstruction voxels. • Calcification detection using step-and-shoot motion is superior to that using continuous tube motion. • A detector element size of 70 µm does not provide better detection than 140 µm for small calcifications at the threshold of detectability.

Spatial dependency of multiplanar reconstruction in digital breast tomosynthesis.

Tomosynthesis acquires projections over a limited angular range, resulting in anisotropic sampling in the Fourier domain. The volume of the sampled space is therefore spatially dependent; different Fourier components are sampled for the same object, depending upon where the object is located relative to the system origin. A next-generation tomosynthesis (NGT) system was developed at the University of Pennsylvania to increase the spatial isotropy in DBT, by incorporating additional system motions. In this work, we investigate the spatial dependency of image quality in tomosynthesis and compare conventional and NGT tomosynthesis in terms of multiplanar reconstruction (MPR). Two test objects, a high-frequency star pattern and a low-frequency octagon phantom, were placed throughout the detector field of view at various obliquities to analyze the anisotropic nature of tomosynthesis. Reconstructions of the star pattern were analyzed both qualitatively and quantitatively using the Fourier distortion metric (FSD). Reconstructions of the octagon phantom were analyzed qualitatively. In a separate experiment, a container filled with water and acrylic beads of various diameters were imaged at various locations to simulate low-contrast objects mimicking breast tissue. We show that the spatial dependency of MPR is unique to the tilt angle, orientation, and frequency of the input. The NGT geometry benefitted the visualization of objects by reducing the out-of-plane artifacts in MPR.

Impact of Tomosynthesis Acquisition on 3D Segmentations of Breast Outline and Adipose/Dense Tissue with AI: A Simulation-Based Study.

Digital breast tomosynthesis (DBT) reconstructions introduce out-of-plane artifacts and false-tissue boundaries impacting the dense/adipose and breast outline (convex hull) segmentations. A virtual clinical trial method was proposed to segment both the breast tissues and the breast outline in DBT reconstructions. The DBT images of a representative population were simulated using three acquisition geometries: a left-right scan (conventional, I), a two-directional scan in the shape of a "T" (II), and an extra-wide range (XWR, III) left-right scan at a six-times higher dose than I. The nnU-Net was modified including two losses for segmentation: (1) tissues and (2) breast outline. The impact of loss (1) and the combination of loss (1) and (2) was evaluated using models trained with data simulating geometry I. The impact of the geometry was evaluated using the combined loss (1&2). The loss (1&2) improved the convex hull estimates, resolving 22.2% of the false classification of air voxels. Geometry II was superior to I and III, resolving 99.1% and 96.8% of the false classification of air voxels. Geometry III (Dice = (0.98, 0.94)) was superior to I (0.92, 0.78) and II (0.93, 0.74) for the tissue segmentation (adipose, dense, respectively). Thus, the loss (1&2) provided better segmentation, and geometries T and XWR improved the dense/adipose and breast outline segmentations relative to the conventional scan.

Multiclass Segmentation of Breast Tissue and Suspicious Findings: A Simulation-Based Study for the Development of Self-Steering Tomosynthesis.

In breast tomosynthesis, multiple low-dose projections are acquired in a single scanning direction over a limited angular range to produce cross-sectional planes through the breast for three-dimensional imaging interpretation. We built a next-generation tomosynthesis system capable of multidirectional source motion with the intent to customize scanning motions around "suspicious findings". Customized acquisitions can improve the image quality in areas that require increased scrutiny, such as breast cancers, architectural distortions, and dense clusters. In this paper, virtual clinical trial techniques were used to analyze whether a finding or area at high risk of masking cancers can be detected in a single low-dose projection and thus be used for motion planning. This represents a step towards customizing the subsequent low-dose projection acquisitions autonomously, guided by the first low-dose projection; we call this technique "self-steering tomosynthesis." A U-Net was used to classify the low-dose projections into "risk classes" in simulated breasts with soft-tissue lesions; class probabilities were modified using post hoc Dirichlet calibration (DC). DC improved the multiclass segmentation (Dice = 0.43 vs. 0.28 before DC) and significantly reduced false positives (FPs) from the class of the highest risk of masking (sensitivity = 81.3% at 2 FPs per image vs. 76.0%). This simulation-based study demonstrated the feasibility of identifying suspicious areas using a single low-dose projection for self-steering tomosynthesis.

Beyond Breast Density: Risk Measures for Breast Cancer in Multiple Imaging Modalities.

Breast density is an independent risk factor for breast cancer. In digital mammography and digital breast tomosynthesis, breast density is assessed visually using the four-category scale developed by the American College of Radiology Breast Imaging Reporting and Data System (5th edition as of November 2022). Epidemiologically based risk models, such as the Tyrer-Cuzick model (version 8), demonstrate superior modeling performance when mammographic density is incorporated. Beyond just density, a separate mammographic measure of breast cancer risk is parenchymal textural complexity. With advancements in radiomics and deep learning, mammographic textural patterns can be assessed quantitatively and incorporated into risk models. Other supplemental screening modalities, such as breast US and MRI, offer independent risk measures complementary to those derived from mammography. Breast US allows the two components of fibroglandular tissue (stromal and glandular) to be visualized separately in a manner that is not possible with mammography. A higher glandular component at screening breast US is associated with higher risk. With MRI, a higher background parenchymal enhancement of the fibroglandular tissue has also emerged as an imaging marker for risk assessment. Imaging markers observed at mammography, US, and MRI are powerful tools in refining breast cancer risk prediction, beyond mammographic density alone.

MaasPenn Radiomics Reproducibility Score: A Novel Quantitative Measure for Evaluating the Reproducibility of CT-Based Handcrafted Radiomic Features.

The reproducibility of handcrafted radiomic features (HRFs) has been reported to be affected by variations in imaging parameters, which significantly affect the generalizability of developed signatures and translation to clinical practice. However, the collective effect of the variations in imaging parameters on the reproducibility of HRFs remains unclear, with no objective measure to assess it in the absence of reproducibility analysis. We assessed these effects of variations in a large number of scenarios and developed the first quantitative score to assess the reproducibility of CT-based HRFs without the need for phantom or reproducibility studies. We further assessed the potential of image resampling and ComBat harmonization for removing these effects. Our findings suggest a need for radiomics-specific harmonization methods. Our developed score should be considered as a first attempt to introduce comprehensive metrics to quantify the reproducibility of CT-based handcrafted radiomic features. More research is warranted to demonstrate its validity in clinical contexts and to further improve it, possibly by the incorporation of more realistic situations, which better reflect real patients' situations.

Achieving Isotropic Super-Resolution with a Non-Isocentric Acquisition Geometry in a Next-Generation Tomosynthesis System.

We have constructed a prototype next-generation tomosynthesis (NGT) system that supports a non-isocentric acquisition geometry for digital breast tomosynthesis (DBT). In this geometry, the detector gradually descends in the superior-to-inferior direction. The aim of this work is to demonstrate that this geometry offers isotropic super-resolution (SR), unlike clinical DBT systems which are characterized by anisotropies in SR. To this end, a theoretical model of a sinusoidal test object was developed with frequency exceeding the alias frequency of the detector. We simulated two geometries: (1) a conventional geometry with a stationary detector, and (2) a non-isocentric geometry. The input frequency was varied over the full 360° range of angles in the plane of the object. To investigate whether SR was achieved, we calculated the Fourier transform of the reconstruction. The amplitude of the tallest peak below the alias frequency was measured relative to the peak at the input frequency. This ratio (termed the r-factor) should approach zero to achieve high-quality SR. In the conventional geometry, the r-factor was minimized (approaching zero) if the orientation of the frequency was parallel with the source motion, yet exceeded unity (prohibiting SR) in the orientation perpendicular to the source motion. However, in the non-isocentric geometry, the r-factor was minimized (approaching zero) for all orientations of the frequency, meaning SR was achieved isotropically. In summary, isotropic SR in DBT can be achieved using the non-isocentric acquisition geometry supported by the NGT system.

Incorporating Robustness to Imaging Physics into Radiomic Feature Selection for Breast Cancer Risk Estimation.

Digital mammography has seen an explosion in the number of radiomic features used for risk-assessment modeling. However, having more features is not necessarily beneficial, as some features may be overly sensitive to imaging physics (contrast, noise, and image sharpness). To measure the effects of imaging physics, we analyzed the feature variation across imaging acquisition settings (kV, mAs) using an anthropomorphic phantom. We also analyzed the intra-woman variation (IWV), a measure of how much a feature varies between breasts with similar parenchymal patterns-a woman's left and right breasts. From 341 features, we identified "robust" features that minimized the effects of imaging physics and IWV. We also investigated whether robust features offered better case-control classification in an independent data set of 575 images, all with an overall BI-RADS® assessment of 1 (negative) or 2 (benign); 115 images (cases) were of women who developed cancer at least one year after that screening image, matched to 460 controls. We modeled cancer occurrence via logistic regression, using cross-validated area under the receiver-operating-characteristic curve (AUC) to measure model performance. Models using features from the most-robust quartile of features yielded an AUC = 0.59, versus 0.54 for the least-robust, with p < 0.005 for the difference among the quartiles.

Reply to Orlhac, F.; Buvat, I. Comment on "Ibrahim et al. The Effects of In-Plane Spatial Resolution on CT-Based Radiomic Features' Stability with and without ComBat Harmonization. Cancers 2021, 13, 1848".

We would like to thank Orlhac and Buvat [...].

Computational Breast Anatomy Simulation Using Multi-Scale Perlin Noise.

Virtual clinical trials (VCTs) of medical imaging require realistic models of human anatomy. For VCTs in breast imaging, a multi-scale Perlin noise method is proposed to simulate anatomical structures of breast tissue in the context of an ongoing breast phantom development effort. Four Perlin noise distributions were used to replace voxels representing the tissue compartments and Cooper's ligaments in the breast phantoms. Digital mammography and tomosynthesis projections were simulated using a clinical DBT system configuration. Power-spectrum analyses and higher-order statistics properties using Laplacian fractional entropy (LFE) of the parenchymal texture are presented. These objective measures were calculated in phantom and patient images using a sample of 140 clinical mammograms and 500 phantom images. Power-law exponents were calculated using the slope of the curve fitted in the low frequency [0.1, 1.0] mm-1 region of the power spectrum. The results show that the images simulated with our prior and proposed Perlin method have similar power-law spectra when compared with clinical mammograms. The power-law exponents calculated are -3.10, -3.55, and -3.46, for the log-power spectra of patient, prior phantom and proposed phantom images, respectively. The results also indicate an improved agreement between the mean LFE estimates of Perlin-noise based phantoms and patients than our prior phantoms and patients. Thus, the proposed method improved the simulation of anatomic noise substantially compared to our prior method, showing close agreement with breast parenchyma measures.

The Effects of In-Plane Spatial Resolution on CT-Based Radiomic Features' Stability with and without ComBat Harmonization.

While handcrafted radiomic features (HRFs) have shown promise in the field of personalized medicine, many hurdles hinder its incorporation into clinical practice, including but not limited to their sensitivity to differences in acquisition and reconstruction parameters. In this study, we evaluated the effects of differences in in-plane spatial resolution (IPR) on HRFs, using a phantom dataset (n = 14) acquired on two scanner models. Furthermore, we assessed the effects of interpolation methods (IMs), the choice of a new unified in-plane resolution (NUIR), and ComBat harmonization on the reproducibility of HRFs. The reproducibility of HRFs was significantly affected by variations in IPR, with pairwise concordant HRFs, as measured by the concordance correlation coefficient (CCC), ranging from 42% to 95%. The number of concordant HRFs (CCC > 0.9) after resampling varied depending on (i) the scanner model, (ii) the IM, and (iii) the NUIR. The number of concordant HRFs after ComBat harmonization depended on the variations between the batches harmonized. The majority of IMs resulted in a higher number of concordant HRFs compared to ComBat harmonization, and the combination of IMs and ComBat harmonization did not yield a significant benefit. Our developed framework can be used to assess the reproducibility and harmonizability of RFs.

Development of Magnification Tomosynthesis for Superior Resolution in Diagnostic Mammography.

Our previous work showed that digital breast tomosynthesis (DBT) supports super-resolution (SR). Clinical systems are not yet designed to optimize SR; this can be demonstrated with a high-frequency line-resolution pattern. SR is achieved if frequencies are oriented laterally, but not if frequencies are oriented in the perpendicular direction; i.e., the posteroanterior (PA) direction. We are developing a next-generation tomosynthesis (NGT) prototype with new trajectories for the x-ray source. This system is being designed to optimize SR not just for screening, but also for diagnostic mammography; specifically, for magnification DBT (M-DBT). SR is not achieved clinically in magnification mammography, since the acquisition is 2D. The aim of this study is to investigate SR in M-DBT, and analyze how anisotropies differ from screening DBT (S-DBT). We have a theoretical model of a high-frequency sinusoidal test object. First, a conventional scanning motion (directed laterally) was simulated. In the PA direction, SR was not achieved in either S-DBT or M-DBT. Next, the scanning motion was angled relative to the lateral direction. This motion introduces submillimeter offsets in source positions in the PA direction. Theoretical modeling demonstrated that SR was achieved in M-DBT, but not in S-DBT, in the PA direction. This work shows that, with the use of magnification, anisotropies in SR are more sensitive to small offsets in the source motion, leading to insights into how to design M-DBT systems.

Calculation of Radiomic Features to Validate the Textural Realism of Physical Anthropomorphic Phantoms for Digital Mammography.

In this paper, radiomic features are used to validate the textural realism of two anthropomorphic phantoms for digital mammography. One phantom was based off a computational breast model; it was 3D printed by CIRS (Computerized Imaging Reference Systems, Inc., Norfolk, VA) under license from the University of Pennsylvania. We investigate how the textural realism of this phantom compares against a phantom derived from an actual patient's mammogram ("Rachel", Gammex 169, Madison, WI). Images of each phantom were acquired at three kV in 1 kV increments using auto-time technique settings. Acquisitions at each technique setting were repeated twice, resulting in six images per phantom. In the raw ("FOR PROCESSING") images, 341 features were calculated; i.e., gray-level histogram, co-occurrence, run length, fractal dimension, Gabor Wavelet, local binary pattern, Laws, and co-occurrence Laws features. Features were also calculated in a negative screening population. For each feature, the middle 95% of the clinical distribution was used to evaluate the textural realism of each phantom. A feature was considered realistic if all six measurements in the phantom were within the middle 95% of the clinical distribution. Otherwise, a feature was considered unrealistic. More features were actually found to be realistic by this definition in the CIRS phantom (305 out of 341 features or 89.44%) than in the phantom derived from a specific patient's mammogram (261 out of 341 features or 76.54%). We conclude that the texture is realistic overall in both phantoms.

Super-Resolution in Digital Breast Tomosynthesis: Limitations of the Conventional System Design and Strategies for Optimization.

Our previous work explored the use of super-resolution as a way to improve the visibility of calcifications in digital breast tomosynthesis. This paper demonstrates that there are anisotropies in super-resolution throughout the reconstruction, and investigates new motion paths for the x-ray tube to suppress these anisotropies. We used a theoretical model of a sinusoidal test object to demonstrate the existence of the anisotropies. In addition, high-frequency test objects were simulated with virtual clinical trial (VCT) software developed for breast imaging. The simulated objects include a lead bar pattern phantom as well as punctate calcifications in a breast-like background. In a conventional acquisition geometry in which the source motion is directed laterally, we found that super-resolution is not achievable if the frequency is oriented in the perpendicular direction (posteroanteriorly). Also, there are positions, corresponding to various slices above the breast support, at which super-resolution is inherently not achievable. The existence of these anisotropies was validated with VCT simulations. At locations predicted by theoretical modeling, the bar pattern phantom showed aliasing, and the spacing between individual calcifications was not properly resolved. To show that super-resolution can be optimized by re-designing the acquisition geometry, we applied our theoretical model to the analysis of new motion paths for the x-ray tube; specifically, motions with more degrees of freedom and with more rapid pulsing (submillimeter spacing) between source positions. These two strategies can be used in combination to suppress the anisotropies in super-resolution.

Proposing Rapid Source Pulsing for Improved Super-Resolution in Digital Breast Tomosynthesis.

Our previous work showed that digital breast tomosynthesis (DBT) systems are capable of super-resolution, or subpixel resolution relative to the detector. Using a bar pattern phantom, it is possible to demonstrate that there are anisotropies in super-resolution throughout the reconstruction. These anisotropies are lessened in acquisition geometries with narrow spacing between source positions. This paper demonstrates that by re-arranging the source positions in the scan, the anisotropies can be minimized even further. To this end, a theoretical model of the reconstruction of a high-frequency sinusoidal test object was developed from first principles. We modeled the effect of clustering additional source positions around each conventional source position in fine increments (submillimeter). This design can be implemented by rapidly pulsing the source during a continuous sweep of the x-ray tube. It is shown that it is not possible to eliminate the anisotropies in a conventional DBT system with uniformly-spaced source positions, even if the increments of spacing are narrower than those used clinically. However, super-resolution can be achieved everywhere if the source positions are re-arranged in clusters with submillimeter spacing. Our previous work investigated a different approach for optimizing super-resolution through the use of detector motion perpendicular to the breast support. The advantage of introducing rapid source pulsing is that detector motion is no longer required; this mitigates the need for a thick detector housing, which may be cumbersome for patient positioning.

Robust Radiomic Feature Selection in Digital Mammography: Understanding the Effect of Imaging Acquisition Physics Using Phantom and Clinical Data Analysis.

Studies have shown that combining calculations of radiomic features with estimates of mammographic density results in an even better assessment of breast cancer risk than density alone. However, to ensure that risk assessment calculations are consistent across different imaging acquisition settings, it is important to identify features that are not overly sensitive to changes in these settings. In this study, digital mammography (DM) images of an anthropomorphic phantom ("Rachel", Gammex 169, Madison, WI) were acquired at various technique settings. We varied kV and mAs, which control contrast and noise, respectively. DM images in women with negative screening exams were also analyzed. Radiomic features were calculated in the raw ("FOR PROCESSING") DM images; i.e., grey-level histogram, co-occurrence, run length, fractal dimension, Gabor Wavelet, local binary pattern, Laws, and co-occurrence Laws features. For each feature, the range of variation across technique settings in phantom images was calculated. This range was scaled against the range of variation in the clinical distribution (specifically, the range corresponding to the middle 90% of the distribution). In order for a radiomic feature to be considered robust, this metric of imaging acquisition variation (IAV) should be as small as possible (approaching zero). An IAV threshold of 0.25 was proposed for the purpose of this study. Out of 341 features, 284 features (83%) met the threshold IAV ≤ 0.25. In conclusion, we have developed a method to identify robust radiomic features in DM.

Non-stationary model of oblique x-ray incidence in amorphous selenium detectors: I. Point spread function.

PURPOSE: In previous work, a theoretical model of the point spread function (PSF) for oblique x-ray incidence in amorphous selenium (a-Se) detectors was proposed. The purpose of this paper is to develop a complementary model that includes two additional features. First, the incidence angle and the directionality of ray incidence are calculated at each position, assuming a divergent x-ray beam geometry. This approach allows the non-stationarity of the PSF to be modeled. Second, this paper develops a framework that is applicable to a digital system, unlike previous work which did not model the presence of a thin-film transistor (TFT) array. METHODS: At each point on the detector, the incidence angle and the ray incidence direction are determined using ray tracing. Based on these calculations, an existing model for the PSF of the x-ray converter (Med Phys. 1995;22:365-374) is generalized to a non-stationary model. The PSF is convolved with the product of two rectangle functions, which model the sampling of the TFT array. The rectangle functions match the detector element (del) size in two dimensions. RESULTS: It is shown that the PSF can be calculated in closed form. This solution is used to simulate a digital mammography (DM) system at two x-ray energies (20 and 40 keV). Based on the divergence of the x-ray beam, the direction of ray incidence varies with position. Along this direction, the PSF is broader than the reference rect function matching the del size. The broadening is more pronounced with increasing obliquity. At high energy, the PSF deviates more strongly from the reference rect function, indicating that there is more blurring. In addition, the PSF is calculated along the polar angle perpendicular to the ray incidence direction. For this polar angle, the shape of the PSF is dependent upon whether the ray incidence direction is parallel with the sides of the detector. If the ray incidence direction is parallel with either dimension, the PSF is a perfect rectangle function, matching the del size. However, if the ray incidence direction is at an oblique angle relative to the sides of the detector, the PSF is not rectangular. These results illustrate the non-stationarity of the PSF. CONCLUSIONS: This paper demonstrates that an existing model of the PSF of a-Se detectors can be generalized to include the effects of non-stationarity and digitization. The PSF is determined in closed form. This solution offers the advantage of shorter computation time relative to approaches that use numerical methods. This model is a tool for simulating a-Se detectors in future work, such as in virtual clinical trials with computational phantoms.

Nonstationary model of oblique x-ray incidence in amorphous selenium detectors: II. Transfer functions.

PURPOSE: One limitation of experimental techniques for quantifying resolution and noise in detectors is that the measurement is made in a region-of-interest (ROI). With theoretical modeling, these properties can be measured at a point, allowing for quantification of spatial anisotropy. This paper calculates nonstationary transfer functions for amorphous selenium (a-Se) detectors in breast imaging. We use this model to demonstrate the performance advantage of a "next-generation" tomosynthesis (NGT) system, which is capable of x-ray source motion with more degrees of freedom than a clinical tomosynthesis system. METHODS: Using Swank's formulation, the optical transfer function (OTF) and presampled noise power spectra (NPS) are determined based on the point spread function derived in Part 1. The modulation transfer function (MTF) is found from the normalized modulus of the OTF. To take into account the presence of digitization, the presampled NPS is convolved with a two-dimensional comb function, for which the period along each direction is the reciprocal of the detector element size. The detective quantum efficiency (DQE) is then determined from combined knowledge of the OTF and NPS. RESULTS: First, the model is used to demonstrate the loss of image quality due to oblique x-ray incidence. The MTF is calculated along various polar angles, corresponding to different orientations of the input frequency. The MTF is independent of the incidence angle if the polar angle is perpendicular to the ray incidence direction. However, along other polar angles, oblique incidence results in MTF degradation at high frequencies. The MTF degradation is most substantial along the ray incidence direction. Unlike the MTF, the normalized NPS (NNPS) is independent of the incidence angle. To measure the relative signal-to-noise, the DQE is also calculated. Oblique incidence yields high-frequency DQE degradation, which is more pronounced than the MTF degradation. This arises because the DQE is proportionate with the square of the MTF. Ultimately, this model is used to evaluate how the image quality varies over the detector area. For various projection images, we calculate the variation in the incidence angle over this area. With the NGT system, the source can be positioned in such a way that this variation is minimized, and hence the DQE exhibits less anisotropy. To achieve this improvement in the image quality, the source needs to have a component of motion in the posteroanterior (PA) direction, which is perpendicular to the conventional direction of source motion in tomosynthesis. CONCLUSIONS: In a-Se detectors, the DQE at high frequencies is degraded due to oblique incidence. The DQE degradation is more pronounced than the MTF degradation. This model is used to quantify the spatial variation in DQE over the detector area. The use of PA source motion is a strategy for minimizing this variation and thus improving the image quality.