A fast, angle-dependent, analytical model of CsI detector response for optimization of 3D x-ray breast imaging systems

Performance evaluation of digital breast tomosynthesis systems: physical methods and experimental data

Digital breast tomosynthesis (DBT) has become a well-established breast imaging technique, whose performance has been investigated in many clinical studies, including a number of prospective clinical trials. Results from these studies generally point to non-inferiority in terms of microcalcification detection and superior mass-lesion detection for DBT imaging compared to digital mammography (DM). This modality has become an essential tool in the clinic for assessment and ad-hoc screening but is not yet implemented in most breast screening programmes at a state or national level. While evidence on the clinical utility of DBT has been accumulating, there has also been progress in the development of methods for technical performance assessment and quality control of these imaging systems. DBT is a relatively complicated ‘pseudo-3D’ modality whose technical assessment poses a number of difficulties. This paper reviews methods for the technical performance assessment of DBT devices, starting at the component level in part one and leading up to discussion of system evaluation with physical test objects in part two. We provide some historical and basic theoretical perspective, often starting from methods developed for DM imaging. Data from a multi-vendor comparison are also included, acquired under the medical physics quality control protocol developed by EUREF and currently being consolidated by a European Federation of Organisations for Medical Physics working group. These data and associated methods can serve as a reference for the development of reference data and provide some context for clinical studies.

Computational models of direct and indirect X-ray breast imaging detectors for in silico trials

BACKGROUND

To facilitate in silico studies that investigate digital mammography (DM) and breast tomosynthesis (DBT), models replicating the variety in imaging performance of the DM and DBT systems, observed across manufacturers are needed.

PURPOSE

The main purpose of this work is to develop generic physics models for direct and indirect detector technology used in commercially available systems, with the goal of making them available open source to manufacturers to further tweak and develop the exact in silico replicas of their systems.

METHODS

We recently reported on an in silico version of the SIEMENS Mammomat Inspiration DM/DBT system using an open-source GPU-accelerated Monte Carlo x-ray imaging simulation code (MC-GPU). We build on the previous version of the MC-GPU codes to mimic the imaging performances of two other Food and Drug Administration (FDA)-approved DM/DBT systems, such as Hologic Selenia Dimensions (HSD) and the General Electric Senographe Pristina (GSP) systems. In this work, we developed a hybrid technique to model the optical spread and signal crosstalk observed in the GSP and HSD systems. MC simulations are used to track each x-ray photon till its first interaction within the x-ray detector. On the other hand, the signal spread in the x-ray detectors is modeled using previously developed analytical equations. This approach allows us to preserve the modeling accuracy offered by MC methods in the patient body, while speeding up secondary carrier transport (either electron-hole pairs or optical photons) using analytical equations in the detector. The analytical optical spread model for the indirect detector includes the depth-dependent spread and collection of optical photons and relies on a pre-computed set of point response functions that describe the optical spread as a function of depth. To understand the capabilities of the computational x-ray detector models, we compared image quality metrics like modulation transfer function (MTF), normalized noise power spectrum (NNPS), and detective quantum efficiency (DQE), simulated with our models against measured data. Please note that the purpose of these comparisons with measured data would be to gauge if the model developed as part of this work could replicate commercially used direct and indirect technology in general and not to achieve perfect fits with measured data.

RESULTS

We found that the simulated image quality metrics such as MTF, NNPS, and DQE were in reasonable agreement with experimental data. To demonstrate the imaging performance of the three DM/DBT systems, we integrated the detector models with the VICTRE pipeline and simulated DM images of a fatty breast model containing a spiculated mass and a calcium oxalate cluster. In general, we found that the images generated using the indirect model appeared more blurred with a different noise texture and contrast as compared to the systems with direct detectors.

CONCLUSIONS

We have presented computational models of three commercially available FDA-approved DM/DBT systems, which implement both direct and indirect detector technology. The updated versions of the MC-GPU codes that can be used to replicate three systems are available in open source format through GitHub.

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.

Cascaded systems analysis of shift-variant image quality in slit-scanning breast tomosynthesis

PURPOSE

Digital breast tomosynthesis (DBT) is becoming an important part of breast cancer screening and diagnosis. Compared to two-dimensional mammography, tomosynthesis introduces limited three-dimensional (3D) resolution, but maintains high in-plane resolution, low dose, and allows for similar clinical protocols. The scanning motion and oblique projections of tomosynthesis acquisitions introduce shift-variance to the image quality, in addition to effects such as source blurring and geometric magnification. Shift-variant detector response caused by oblique incidence has been extensively studied previously and is most easily mitigated by letting the source and detector move in sync. In addition, conical reconstruction grids, that is, a grid aligned with the central tomosynthesis projection, have been proposed to compensate for magnification effects. This paper introduces a shift-variant cascaded systems model for tomosynthesis and validates it against measurements. As an example, the model was used to investigate the shift-variance of a tomosynthesis system.

METHODS

The shift-variant cascaded systems model was validated on a slit-scanning photon-counting DBT system, with synchronous source-detector movement, using simple back-projection in a conical reconstruction volume. The modulation transfer function (MTF), normalized noise-power spectrum (NNPS), and detective quantum efficiency (DQE) were used as figures of merit. Simulations were performed for single points while measurements were done over a finite volume, assuming local shift invariance. To investigate the full extent of shift-variance, 80 locations across the volume were simulated, and the MTF and DQE at 2.5 lp/mm were calculated as a function of position.

RESULTS

The simulated metrics generally agreed well with their corresponding measurements. The frequency at 50% MTF along the scan direction showed a relatively small variation, ranging from 2.1 to 2.4 lp/mm for the different locations. The frequency at 50% MTF along the chest-mammilla direction showed a larger variation, ranging from 2.9 to 3.8 lp/mm. All points exhibited a similarly shaped NNPS but the noise magnitude varied with slice height. The zero-frequency DQE in reconstructed slices was lower than that of the projections, an effect likely caused by noise-aliasing increasing the zero-frequency noise.

CONCLUSIONS

A shift-variant cascaded systems model has been developed for slit-scanning tomosynthesis using simple back-projection. The model was successfully validated against measurements. Even though the study was performed on a slit-scanning system, several parts of the framework can be applied and extended to other tomosynthesis geometries. The conical reconstruction grid has low variation in image quality in the scan direction where the 3D information is acquired, but source and geometric magnification still dominate in the slit direction, causing a larger variation in image quality. We conclude that image quality is close to shift-invariant in the scan direction, but not in the height and chest-mammilla directions, and we recommend that small measurement volumes are used when measuring image quality in these directions to minimize the effects of shift variance.

Analysis of Volume Overestimation Artifacts in the Breast Outline Segmentation in Tomosynthesis

In digital breast tomosynthesis (DBT), the reconstruction is calculated from x-ray projection images acquired over a small range of angles. One step in the reconstruction process is to identify the pixels that fall outside the shadow of the breast, to segment the breast from the background (air). In each projection, rays are back-projected from these pixels to the focal spot. All voxels along these rays are identified as air. By combining these results over all projections, a breast outline can be determined for the reconstruction. This paper quantifies the accuracy of this breast segmentation strategy in DBT. In this study, a physical phantom modeling a breast under compression was analyzed with a prototype next-generation tomosynthesis (NGT) system described in previous work. Multiple wires were wrapped around the phantom. Since the wires are thin and high contrast, their exact location can be determined from the reconstruction. Breast parenchyma was portrayed outside the outline defined by the wires. Specifically, the size of the phantom was overestimated along the posteroanterior (PA) direction; i.e., perpendicular to the plane of conventional source motion. To analyze how the acquisition geometry affects the accuracy of the breast outline segmentation, a computational phantom was also simulated. The simulation identified two ways to improve the segmentation accuracy; either by increasing the angular range of source motion laterally or by increasing the range in the PA direction. The latter approach is a unique feature of the NGT design; the advantage of this approach was validated with our prototype system.

Modelling the transport of optical photons in scintillation detectors for diagnostic and radiotherapy imaging

Computational modelling of radiation transport can enhance the understanding of the relative importance of individual processes involved in imaging systems. Modelling is a powerful tool for improving detector designs in ways that are impractical or impossible to achieve through experimental measurements. Modelling of light transport in scintillation detectors used in radiology and radiotherapy imaging that rely on the detection of visible light plays an increasingly important role in detector design. Historically, researchers have invested heavily in modelling the transport of ionizing radiation while light transport is often ignored or coarsely modelled. Due to the complexity of existing light transport simulation tools and the breadth of custom codes developed by users, light transport studies are seldom fully exploited and have not reached their full potential. This topical review aims at providing an overview of the methods employed in freely available and other described optical Monte Carlo packages and analytical models and discussing their respective advantages and limitations. In particular, applications of optical transport modelling in nuclear medicine, diagnostic and radiotherapy imaging are described. A discussion on the evolution of these modelling tools into future developments and applications is presented.

An analytical approach to the light transport in columnar phosphors. Detector Optical Gain, angular distribution and the CsI:Tl paradigm

PURPOSE

An analytical model has been developed for the light propagation in columnar phosphors, based on the optical photon propagation physical and geometrical principles.

METHODS

This model accounts for the multiple reflections on the sides of the crystal column, as well as for the infinite forward and backward reflections of the propagated optical photon beams created in the crystal bulk. Additionally it considers the lateral propagated optical photon beams after multiple refractions from the neighbor columns and the optical photon attenuation inside the scintillator. The model was used to predict the Detector Optical Gain (DOG), and the angular distribution, of the columnar CsI:Tl scintillators, used in medical imaging.

RESULTS

The model was validated against CsI:Tl optical photon transmission published results and good agreement was observed. It was, also, found that the DOG is affected by the length of the columns, as well as the incident X-ray energy spectrum. The results of the angular distribution are in accordance with the theory that the longer crystal columns have more directional light distribution.

CONCLUSIONS

The results of DOG are in accordance with the use of short crystal columns for lower energies (mammography) and the use of long crystal columns for higher energies (general radiology). Angular distribution was found more directive for long crystal columns.

Deriving depth-dependent light escape efficiency and optical Swank factor from measured pulse height spectra of scintillators

PURPOSE

Pulse height spectroscopy has been used by investigators to deduce the imaging properties of scintillators. Pulse height spectra (PHS) are used to compute the Swank factor, which describes the variation in scintillator light output per x-ray interaction. The spread in PHS measured below the K-edge is related to the optical component of the Swank factor, i.e., variations in light escape efficiency from different depths of x-ray interaction in the scintillator, denoted ε¯(z). Optimizing scintillators for medical imaging applications requires understanding of these optical properties, as they determine tradeoffs between parameters such as x-ray absorption, light yield, and spatial resolution. This work develops a model for PHS acquisition such that the effect of measurement uncertainty can be removed. This method allows ε¯(z) to be quantified on an absolute scale and permits more accurate estimation of the optical Swank factor of scintillators.

METHODS

The pulse height spectroscopy acquisition chain was modeled as a linear system of stochastic gain stages. Analytical expressions were derived for signal and noise propagation through the PHS chain, accounting for deterministic and stochastic aspects of x-ray absorption, scintillation, and light detection with a photomultiplier tube. The derived expressions were used to calculate PHS of thallium-doped cesium iodide (CsI) scintillators using parameters that were measured, calculated, or known from literature. PHS were measured at 25 and 32 keV of CsI samples designed with an optically reflective or absorptive backing, with or without a fiber-optic faceplate (FOP), and with thicknesses ranging from 150-1000 μm. Measured PHS were compared with calculated PHS, then light escape model parameters were varied until measured and modeled results reached agreement. Resulting estimates of ε¯(z) were used to calculate each scintillator's optical Swank factor.

RESULTS

For scintillators of the same optical design, only minor differences in light escape efficiency were observed between samples with different thickness. As thickness increased, escape efficiency decreased by up to 20% for interactions furthest away from light collection. Optical design (i.e., backing and FOP) predominantly affected the magnitude and relative variation in ε¯(z). Depending on interaction depth and scintillator thickness, samples with an absorptive backing and FOP were estimated to yield 4.1-13.4 photons/keV. Samples with a reflective backing and FOP yielded 10.4-18.4 keV^-1 , while those with a reflective backing and no FOP yielded 29.5-52.0 keV^-1 . Optical Swank factors were approximately 0.9 and near-unity in samples featuring an absorptive or reflective backing, respectively.

CONCLUSIONS

This work uses a modeling approach to remove the noise introduced by the measurement apparatus from measured PHS. This method allows absolute quantification of ε¯(z) and more accurate estimation of the optical Swank factor of scintillators. The method was applied to CsI scintillators with different thickness and optical design, and determined that optical design more strongly affects ε¯(z) and Swank factor than differences in CsI thickness. Despite large variations in ε¯(z) between optical designs, the Swank factor of all evaluated samples is above 0.9. Information provided by this methodology can help validate Monte Carlo simulations of structured CsI and optimize scintillator design for x-ray imaging applications.

Digital Breast Tomosynthesis: State of the Art

This topical review on digital breast tomosynthesis (DBT) is provided with the intent of describing the state of the art in terms of technology, results from recent clinical studies, advanced applications, and ongoing efforts to develop multimodality imaging systems that include DBT. Particular emphasis is placed on clinical studies. The observations of increase in cancer detection rates, particularly for invasive cancers, and the reduction in false-positive rates with DBT in prospective trials indicate its benefit for breast cancer screening. Retrospective multireader multicase studies show either noninferiority or superiority of DBT compared with mammography. Methods to curtail radiation dose are of importance. (©) RSNA, 2015.

Theoretical and Monte Carlo optimization of a stacked three-layer flat-panel x-ray imager for applications in multi-spectral medical imaging

We propose a new design of a stacked three-layer flat-panel x-ray detector for dual-energy (DE) imaging. Each layer consists of its own scintillator of individual thickness and an underlying thin-film-transistor-based flat-panel. Three images are obtained simultaneously in the detector during the same x-ray exposure, thereby eliminating any motion artifacts. The detector operation is two-fold: a conventional radiography image can be obtained by combining all three layers' images, while a DE subtraction image can be obtained from the front and back layers' images, where the middle layer acts as a mid-filter that helps achieve spectral separation. We proceed to optimize the detector parameters for two sample imaging tasks that could particularly benefit from this new detector by obtaining the best possible signal to noise ratio per root entrance exposure using well-established theoretical models adapted to fit our new design. These results are compared to a conventional DE temporal subtraction detector and a single-shot DE subtraction detector with a copper mid-filter, both of which underwent the same theoretical optimization. The findings are then validated using advanced Monte Carlo simulations for all optimized detector setups. Given the performance expected from initial results and the recent decrease in price for digital x-ray detectors, the simplicity of the three-layer stacked imager approach appears promising to usher in a new generation of multi-spectral digital x-ray diagnostics.

Digital breast tomosynthesis: studies of the effects of acquisition geometry on contrast-to-noise ratio and observer preference of low-contrast objects in breast phantom images

The effect of acquisition geometry in digital breast tomosynthesis was evaluated with studies of contrast-to-noise ratios (CNRs) and observer preference. Contrast-detail (CD) test objects in 5 cm thick phantoms with breast-like backgrounds were imaged. Twelve different angular acquisitions (average glandular dose for each ~1.1 mGy) were performed ranging from narrow angle 16° with 17 projection views (16d17p) to wide angle 64d17p. Focal slices of SART-reconstructed images of the CD arrays were selected for CNR computations and the reader preference study. For the latter, pairs of images obtained with different acquisition geometries were randomized and scored by 7 trained readers. The total scores for all images and readings for each acquisition geometry were compared as were the CNRs. In general, readers preferred images acquired with wide angle as opposed to narrow angle geometries. The mean percent preferred was highly correlated with tomosynthesis angle (R = 0.91). The highest scoring geometries were 60d21p (95%), 64d17p (80%), and 48d17p (72%); the lowest scoring were 16d17p (4%), 24d9p (17%) and 24d13p (33%). The measured CNRs for the various acquisitions showed much overlap but were overall highest for wide-angle acquisitions. Finally, the mean reader scores were well correlated with the mean CNRs (R = 0.83).

Digital breast tomosynthesis: observer performance of clustered microcalcification detection on breast phantom images acquired with an experimental system using variable scan angles, angular increments, and number of projection views

PURPOSE

To investigate the dependence of microcalcification cluster detectability on tomographic scan angle, angular increment, and number of projection views acquired at digital breast tomosynthesis ( DBT digital breast tomosynthesis ).

MATERIALS AND METHODS

A prototype DBT digital breast tomosynthesis system operated in step-and-shoot mode was used to image breast phantoms. Four 5-cm-thick phantoms embedded with 81 simulated microcalcification clusters of three speck sizes (subtle, medium, and obvious) were imaged by using a rhodium target and rhodium filter with 29 kV, 50 mAs, and seven acquisition protocols. Fixed angular increments were used in four protocols (denoted as scan angle, angular increment, and number of projection views, respectively: 16°, 1°, and 17; 24°, 3°, and nine; 30°, 3°, and 11; and 60°, 3°, and 21), and variable increments were used in three (40°, variable, and 13; 40°, variable, and 15; and 60°, variable, and 21). The reconstructed DBT digital breast tomosynthesis images were interpreted by six radiologists who located the microcalcification clusters and rated their conspicuity.

RESULTS

The mean sensitivity for detection of subtle clusters ranged from 80% (22.5 of 28) to 96% (26.8 of 28) for the seven DBT digital breast tomosynthesis protocols; the highest sensitivity was achieved with the 16°, 1°, and 17 protocol (96%), but the difference was significant only for the 60°, 3°, and 21 protocol (80%, P < .002) and did not reach significance for the other five protocols (P = .01-.15). The mean sensitivity for detection of medium and obvious clusters ranged from 97% (28.2 of 29) to 100% (24 of 24), but the differences fell short of significance (P = .08 to >.99). The conspicuity of subtle and medium clusters with the 16°, 1°, and 17 protocol was rated higher than those with other protocols; the differences were significant for subtle clusters with the 24°, 3°, and nine protocol and for medium clusters with 24°, 3°, and nine; 30°, 3°, and 11; 60°, 3° and 21; and 60°, variable, and 21 protocols (P < .002).

CONCLUSION

With imaging that did not include x-ray source motion or patient motion during acquisition of the projection views, narrow-angle DBT digital breast tomosynthesis provided higher sensitivity and conspicuity than wide-angle DBT digital breast tomosynthesis for subtle microcalcification clusters.

Investigation of statistical iterative reconstruction for dedicated breast CT

PURPOSE

Dedicated breast CT has great potential for improving the detection and diagnosis of breast cancer. Statistical iterative reconstruction (SIR) in dedicated breast CT is a promising alternative to traditional filtered backprojection (FBP). One of the difficulties in using SIR is the presence of free parameters in the algorithm that control the appearance of the resulting image. These parameters require tuning in order to achieve high quality reconstructions. In this study, the authors investigated the penalized maximum likelihood (PML) method with two commonly used types of roughness penalty functions: hyperbolic potential and anisotropic total variation (TV) norm. Reconstructed images were compared with images obtained using standard FBP. Optimal parameters for PML with the hyperbolic prior are reported for the task of detecting microcalcifications embedded in breast tissue.

METHODS

Computer simulations were used to acquire projections in a half-cone beam geometry. The modeled setup describes a realistic breast CT benchtop system, with an x-ray spectra produced by a point source and an a-Si, CsI:Tl flat-panel detector. A voxelized anthropomorphic breast phantom with 280 μm microcalcification spheres embedded in it was used to model attenuation properties of the uncompressed woman's breast in a pendant position. The reconstruction of 3D images was performed using the separable paraboloidal surrogates algorithm with ordered subsets. Task performance was assessed with the ideal observer detectability index to determine optimal PML parameters.

RESULTS

The authors' findings suggest that there is a preferred range of values of the roughness penalty weight and the edge preservation threshold in the penalized objective function with the hyperbolic potential, which resulted in low noise images with high contrast microcalcifications preserved. In terms of numerical observer detectability index, the PML method with optimal parameters yielded substantially improved performance (by a factor of greater than 10) compared to FBP. The hyperbolic prior was also observed to be superior to the TV norm. A few of the best-performing parameter pairs for the PML method also demonstrated superior performance for various radiation doses. In fact, using PML with certain parameter values results in better images, acquired using 2 mGy dose, than FBP-reconstructed images acquired using 6 mGy dose.

CONCLUSIONS

A range of optimal free parameters for the PML algorithm with hyperbolic and TV norm-based potentials is presented for the microcalcification detection task, in dedicated breast CT. The reported values can be used as starting values of the free parameters, when SIR techniques are used for image reconstruction. Significant improvement in image quality can be achieved by using PML with optimal combination of parameters, as compared to FBP. Importantly, these results suggest improved detection of microcalcifications can be obtained by using PML with lower radiation dose to the patient, than using FBP with higher dose.

Oblique reconstructions in tomosynthesis. II. Super-resolution

PURPOSE

In tomosynthesis, super-resolution has been demonstrated using reconstruction planes parallel to the detector. Super-resolution allows for subpixel resolution relative to the detector. The purpose of this work is to develop an analytical model that generalizes super-resolution to oblique reconstruction planes.

METHODS

In a digital tomosynthesis system, a sinusoidal test object is modeled along oblique angles (i.e., "pitches") relative to the plane of the detector in a 3D divergent-beam acquisition geometry. To investigate the potential for super-resolution, the input frequency is specified to be greater than the alias frequency of the detector. Reconstructions are evaluated in an oblique plane along the extent of the object using simple backprojection (SBP) and filtered backprojection (FBP). By comparing the amplitude of the reconstruction against the attenuation coefficient of the object at various frequencies, the modulation transfer function (MTF) is calculated to determine whether modulation is within detectable limits for super-resolution. For experimental validation of super-resolution, a goniometry stand was used to orient a bar pattern phantom along various pitches relative to the breast support in a commercial digital breast tomosynthesis system.

RESULTS

Using theoretical modeling, it is shown that a single projection image cannot resolve a sine input whose frequency exceeds the detector alias frequency. The high frequency input is correctly visualized in SBP or FBP reconstruction using a slice along the pitch of the object. The Fourier transform of this reconstructed slice is maximized at the input frequency as proof that the object is resolved. Consistent with the theoretical results, experimental images of a bar pattern phantom showed super-resolution in oblique reconstructions. At various pitches, the highest frequency with detectable modulation was determined by visual inspection of the bar patterns. The dependency of the highest detectable frequency on pitch followed the same trend as the analytical model. It was demonstrated that super-resolution is not achievable if the pitch of the object approaches 90°, corresponding to the case in which the test frequency is perpendicular to the breast support. Only low frequency objects are detectable at pitches close to 90°.

CONCLUSIONS

This work provides a platform for investigating super-resolution in oblique reconstructions for tomosynthesis. In breast imaging, this study should have applications in visualizing microcalcifications and other subtle signs of cancer.

A virtual trial framework for quantifying the detectability of masses in breast tomosynthesis projection data

PURPOSE

Digital breast tomosynthesis (DBT) is a promising breast cancer screening tool that has already begun making inroads into clinical practice. However, there is ongoing debate over how to quantitatively evaluate and optimize these systems, because different definitions of image quality can lead to different optimal design strategies. Powerful and accurate tools are desired to extend our understanding of DBT system optimization and validate published design principles.

METHODS

The authors developed a virtual trial framework for task-specific DBT assessment that uses digital phantoms, open-source x-ray transport codes, and a projection-space, spatial-domain observer model for quantitative system evaluation. The authors considered evaluation of reconstruction algorithms as a separate problem and focused on the information content in the raw, unfiltered projection images. Specifically, the authors investigated the effects of scan angle and number of angular projections on detectability of a small (3 mm diameter) signal embedded in randomly-varying anatomical backgrounds. Detectability was measured by the area under the receiver-operating characteristic curve (AUC). Experiments were repeated for three test cases where the detectability-limiting factor was anatomical variability, quantum noise, or electronic noise. The authors also juxtaposed the virtual trial framework with other published studies to illustrate its advantages and disadvantages.

RESULTS

The large number of variables in a virtual DBT study make it difficult to directly compare different authors' results, so each result must be interpreted within the context of the specific virtual trial framework. The following results apply to 25% density phantoms with 5.15 cm compressed thickness and 500 μm(3) voxels (larger 500 μm(2) detector pixels were used to avoid voxel-edge artifacts): 1. For raw, unfiltered projection images in the anatomical-variability-limited regime, AUC appeared to remain constant or increase slightly with scan angle. 2. In the same regime, when the authors fixed the scan angle, AUC increased asymptotically with the number of projections. The threshold number of projections for asymptotic AUC performance depended on the scan angle. In the quantum- and electronic-noise dominant regimes, AUC behaviors as a function of scan angle and number of projections sometimes differed from the anatomy-limited regime. For example, with a fixed scan angle, AUC generally decreased with the number of projections in the electronic-noise dominant regime. These results are intended to demonstrate the capabilities of the virtual trial framework, not to be used as optimization rules for DBT.

CONCLUSIONS

The authors have demonstrated a novel simulation framework and tools for evaluating DBT systems in an objective, task-specific manner. This framework facilitates further investigation of image quality tradeoffs in DBT.

Observation of super-resolution in digital breast tomosynthesis

PURPOSE

Digital breast tomosynthesis (DBT) is a 3D x-ray imaging modality in which tomographic sections of the breast are generated from a limited range of tube angles. Because oblique x-ray incidence shifts the image of an object in subpixel detector element increments with each increasing projection angle, it is demonstrated that DBT is capable of super-resolution (i.e., subpixel resolution).

METHODS

By convention, DBT reconstructions are performed on planes parallel to the breast support at various depths of the breast volume. In order for resolution in each reconstructed slice to be comparable to the detector, the pixel size should match that of the detector elements; hence, the highest frequency that can be resolved in the plane of reconstruction is the alias frequency of the detector. This study considers reconstruction grids with much smaller pixelation to visualize higher frequencies. For analytical proof of super-resolution, a theoretical framework is developed in which the reconstruction of a high frequency sinusoidal input is calculated using both simple backprojection (SBP) and filtered backprojection. To study the frequency spectrum of the reconstruction, its Fourier transform is also determined. The experimental feasibility of super-resolution was investigated by acquiring images of a bar pattern phantom with frequencies higher than the detector alias frequency.

RESULTS

Using analytical modeling, it is shown that the central projection cannot resolve frequencies exceeding the detector alias frequency. The Fourier transform of the central projection is maximized at a lower frequency than the input as evidence of aliasing. By contrast, SBP reconstruction can resolve the input, and its Fourier transform is correctly maximized at the input frequency. Incorporating filters into the reconstruction smoothens pixelation artifacts in the spatial domain and reduces spectral leakage in the Fourier domain. It is also demonstrated that the existence of super-resolution is dependent on position in the reconstruction and on the directionality of the input frequency. Consistent with the analytical results, experimental reconstructions of bar patterns showed visibility of frequencies greater than the detector alias frequency. Super-resolution was present at positions predicted from analytical modeling.

CONCLUSIONS

This work demonstrates the existence of super-resolution in DBT. Super-resolution has the potential to impact the visualization of fine structural details in the breast, such as microcalcifications and other subtle signs of cancer.

Proposing a New Velocity Profile for Continuous X-Ray Tube Motion in Digital Breast Tomosynthesis

In digital breast tomosynthesis (DBT), a 3D image of the breast is generated from x-ray projections at various angles. There are two mechanisms for acquiring projection images in DBT, step-and-shoot motion and continuous tube motion. The benefit of continuous tube motion is shorter scan time and hence less patient motion; the trade-off is focal spot blurring. To minimize focal spot blurring in a system with continuous tube motion, this study proposes a new velocity profile for the x-ray tube during the scan. Unlike existing systems for which the x-ray tube has constant angular velocity, we investigate a smoothly-varying tube velocity that approaches zero during each projection and is larger between projections. With this unique design, the filtered backprojection reconstruction of a sinusoidal test object was calculated, and modulation was determined at various frequencies. It is shown that the newly proposed tube velocity yields increased modulation in the reconstruction relative to a conventional system with continuous tube motion. The modulation in the re-designed system differs minimally from an analogous step-and-shoot system operated with the same scan time. This improvement in image quality was validated with reconstructions of microcalcifications in computer breast phantoms. It is known that continuous tube motion reduces the contrast of microcalcifications relative to step- and-shoot systems; we show that the newly proposed tube motion increases the contrast of microcalcifications compared to conventional continuous tube motion. In conclusion, this work proposes a strategy for optimizing the velocity of tube motion in DBT.

A review of breast tomosynthesis. Part I. The image acquisition process

Mammography is a very well-established imaging modality for the early detection and diagnosis of breast cancer. However, since the introduction of digital imaging to the realm of radiology, more advanced, and especially tomographic imaging methods have been made possible. One of these methods, breast tomosynthesis, has finally been introduced to the clinic for routine everyday use, with potential to in the future replace mammography for screening for breast cancer. In this two part paper, the extensive research performed during the development of breast tomosynthesis is reviewed, with a focus on the research addressing the medical physics aspects of this imaging modality. This first paper will review the research performed on the issues relevant to the image acquisition process, including system design, optimization of geometry and technique, x-ray scatter, and radiation dose. The companion to this paper will review all other aspects of breast tomosynthesis imaging, including the reconstruction process.

Optimization of phosphor-based detector design for oblique x-ray incidence in digital breast tomosynthesis

PURPOSE

In digital breast tomosynthesis (DBT), a volumetric reconstruction of the breast is generated from a limited range of x-ray projections. One trade-off of DBT is resolution loss in the projections due to non-normal (i.e., oblique) x-ray incidence. Although degradation in image quality due to oblique incidence has been studied using empirical data and Monte Carlo simulations, a theoretical treatment has been lacking. The purpose of this work is to extend Swank's calculations of the transfer functions of turbid granular phosphors to oblique incidence. The model is ultimately used as a tool for optimizing the design of DBT detectors.

METHODS

A quantum-limited system and 20 keV x-rays are considered. Under these assumptions, the modulation transfer function (MTF) and noise power spectra (NPS) are derived using the diffusion approximation to the Boltzmann equation to model optical scatter within the phosphor. This approach is applicable to a nonstructured scintillator such as gadolinium oxysulfide doped with terbium (Gd(2)O(2)S:Tb), which is commonly used in breast imaging and which can reasonably approximate other detector materials. The detective quantum efficiency (DQE) is then determined from the Nishikawa formulation, where it is written as the product of the x-ray quantum detection efficiency, the Swank factor, and the Lubberts fraction. Transfer functions are calculated for both front- and back-screen configurations, which differ by positioning the photocathode at the exit or entrance point of the x-ray beam, respectively.

RESULTS

In the front-screen configuration, MTF and DQE are found to have considerable angular dependence, while NPS is shown to vary minimally with projection angle. As expected, the high frequency MTF and DQE are degraded substantially at large angles. By contrast, all transfer functions for the back-screen configuration have the advantage of significantly less angular dependence. Using these models, we investigated the possibility for optimizing the design of DBT detectors. As an example optimization strategy, the phosphor thickness which maximizes the DQE at a fixed frequency is analyzed. This work demonstrates that the optimal phosphor thickness for the front-screen is angularly dependent, shifting to lower thickness at higher angles. Conversely, the back-screen is not optimized by a single thickness but instead attains reasonably high DQE values over a large range of thicknesses. Although the back-screen configuration is not suited for current detectors using a glass substrate, it may prove to be preferred in future detectors using newly proposed plastic thin-film transistor (TFT) substrates.

CONCLUSIONS

Using the diffusion approximation to the Boltzmann equation to model the spread of light in a scintillator, this paper develops an analytical model of MTF, NPS, and DQE for a phosphor irradiated obliquely. The model is set apart from other studies on oblique incidence in being derived from first principles. This work has applications in the optimization of DBT detector design.

Oblique incidence effects in direct x-ray detectors: a first-order approximation using a physics-based analytical model

PURPOSE

The authors describe the modifications to a previously developed analytical model of indirect CsI:Tl-based detector response required for studying oblique x-ray incidence effects in direct semiconductor-based detectors. This first-order approximation analysis allows the authors to describe the associated degradation in resolution in direct detectors and compare the predictions to the published data for indirect detectors.

METHODS

The proposed model is based on a physics-based analytical description developed by Freed et al. ["A fast, angle-dependent, analytical model of CsI detector response for optimization of 3D x-ray breast imaging systems," Med. Phys. 37(6), 2593-2605 (2010)] that describes detector response functions for indirect detectors and oblique incident x rays. The model, modified in this work to address direct detector response, describes the dependence of the response with x-ray energy, thickness of the transducer layer, and the depth-dependent blur and collection efficiency.

RESULTS

The authors report the detector response functions for indirect and direct detector models for typical thicknesses utilized in clinical systems for full-field digital mammography (150 microm for indirect CsI:Tl and 200 microm for a-Se direct detectors). The results suggest that the oblique incidence effect in a semiconductor detector differs from that in indirect detectors in two ways: The direct detector model produces a sharper overall PRF compared to the response corresponding to the indirect detector model for normal x-ray incidence and a larger relative increase in blur along the x-ray incidence direction compared to that found in indirect detectors with respect to the response at normal incidence angles.

CONCLUSIONS

Compared to the effect seen in indirect detectors, the direct detector model exhibits a sharper response at normal x-ray incidence and a larger relative increase in blur along the x-ray incidence direction with respect to the blur in the orthogonal direction. The results suggest that the oblique incidence effect in direct detectors can be considered to be caused mostly by the geometry of the path where the x-ray beam and its secondary particles deposit energy in the semiconductor layer.

A statistical, task-based evaluation method for three-dimensional x-ray breast imaging systems using variable-background phantoms

PURPOSE

For the last few years, development and optimization of three-dimensional (3D) x-ray breast imaging systems, such as digital breast tomosynthesis (DBT) and computed tomography, have drawn much attention from the medical imaging community, either academia or industry. However, there is still much room for understanding how to best optimize and evaluate the devices over a large space of many different system parameters and geometries. Current evaluation methods, which work well for 2D systems, do not incorporate the depth information from the 3D imaging systems. Therefore, it is critical to develop a statistically sound evaluation method to investigate the usefulness of inclusion of depth and background-variability information into the assessment and optimization of the 3D systems.

METHODS

In this paper, we present a mathematical framework for a statistical assessment of planar and 3D x-ray breast imaging systems. Our method is based on statistical decision theory, in particular, making use of the ideal linear observer called the Hotelling observer. We also present a physical phantom that consists of spheres of different sizes and materials for producing an ensemble of randomly varying backgrounds to be imaged for a given patient class. Lastly, we demonstrate our evaluation method in comparing laboratory mammography and three-angle DBT systems for signal detection tasks using the phantom's projection data. We compare the variable phantom case to that of a phantom of the same dimensions filled with water, which we call the uniform phantom, based on the performance of the Hotelling observer as a function of signal size and intensity.

RESULTS

Detectability trends calculated using the variable and uniform phantom methods are different from each other for both mammography and DBT systems.

CONCLUSIONS

Our results indicate that measuring the system's detection performance with consideration of background variability may lead to differences in system performance estimates and comparisons. For the assessment of 3D systems, to accurately determine trade offs between image quality and radiation dose, it is critical to incorporate randomness arising from the imaging chain including background variability into system performance calculations.

Experimental validation of Monte Carlo (MANTIS) simulated x-ray response of columnar CsI scintillator screens

PURPOSE

MANTIS is a Monte Carlo code developed for the detailed simulation of columnar CsI scintillator screens in x-ray imaging systems. Validation of this code is needed to provide a reliable and valuable tool for system optimization and accurate reconstructions for a variety of x-ray applications. Whereas previous validation efforts have focused on matching of summary statistics, in this work the authors examine the complete point response function (PRF) of the detector system in addition to relative light output values.

METHODS

Relative light output values and high-resolution PRFs have been experimentally measured with a custom setup. A corresponding set of simulated light output values and PRFs have also been produced, where detailed knowledge of the experimental setup and CsI:Tl screen structures are accounted for in the simulations. Four different screens were investigated with different thicknesses, column tilt angles, and substrate types. A quantitative comparison between the experimental and simulated PRFs was performed for four different incidence angles (0 degrees, 15 degrees, 30 degrees, and 45 degrees) and two different x-ray spectra (40 and 70 kVp). The figure of merit (FOM) used measures the normalized differences between the simulated and experimental data averaged over a region of interest.

RESULTS

Experimental relative light output values ranged from 1.456 to 1.650 and were in approximate agreement for aluminum substrates, but poor agreement for graphite substrates. The FOMs for all screen types, incidence angles, and energies ranged from 0.1929 to 0.4775. To put these FOMs in context, the same FOM was computed for 2D symmetric Gaussians fit to the same experimental data. These FOMs ranged from 0.2068 to 0.8029. Our analysis demonstrates that MANTIS reproduces experimental PRFs with higher accuracy than a symmetric 2D Gaussian fit to the experimental data in the majority of cases. Examination of the spatial distribution of differences between the PRFs shows that the main reason for errors between MANTIS and the experimental data is that MANTIS-generated PRFs are sharper than the experimental PRFs.

CONCLUSIONS

The experimental validation of MANTIS performed in this study demonstrates that MANTIS is able to reliably predict experimental PRFs, especially for thinner screens, and can reproduce the highly asymmetric shape seen in the experimental data. As a result, optimizations and reconstructions carried out using MANTIS should yield results indicative of actual detector performance. Better characterization of screen properties is necessary to reconcile the simulated light output values with experimental data.