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

Endorectal digital prostate tomosynthesis (endoDPT): a proof-of-concept study

In this study we present endorectal digital prostate tomosynthesis (endoDPT), a proposed method of high resolution prostate imaging using an endorectal x-ray sensor and an external x-ray source. endoDPT may be useful for visualizing the fine detail of small structures such as low dose rate brachytherapy (LDRBT) seeds that are difficult to visualize with current methods. The resolution of endoDPT was characterized through measurement of the modulation transfer function (MTF) and artifact spread function (ASF) in computational and physical phantoms. The qualitative resolution of endoDPT was assessed relative to computed tomography (CT) through imaging of LDRBT seeds implanted inex vivocanine prostates. The x-ray sensor MTF reached 10% at 11.50 mm^-1, the reconstruction algorithm MTF reached a maximum at 7.08 mm^-1, and the ASF was 2.5 mm (full-width at half-maximum). Fine structures in LDRBT seeds like the 0.05 mm thick shell were visible with endoDPT but not CT. All endoDPT images exhibited an overshoot artifact. The measured MTFs were consistent with other studies using similar x-ray sensors and demonstrated improved resolution compared to digital breast tomosynthesis; this result was due to the smaller endoDPT x-ray sensor detection element size and quantitatively demonstrates the high resolution of endoDPT. The ASF demonstrated worse depth resolution compared to in-plane resolution, due to partial angular sampling; partial angular sampling also caused the observed overshoot artifact in the endoDPT images. However, endoDPT still was able to visualize fine structures such as the LDRBT seed shell to a much higher degree than CT. This high-resolution visualization may be useful for improvements in patient specific LDRBT dosimetry. Overall, these results indicate endoDPT is capable of high in-plane spatial resolution and is thus well poised for optimization and studies assessing clinical utility.

MTF of columnar phosphors with a homogenous part: an analytical approach

A method for the theoretical estimation of the MTF of columnar phosphors with a homogeneous part at the end used in X-ray imaging has been developed. This method considers the light transport inside the scintillator through an analytical modelling, the optical photon beams distribution on the scintillator-optical sensor interface, and uses the definition of the PSF and a Gauss fitted LSF to estimate the MTF of an indirect detector. This method was applied to a columnar CsI:Tl scintillator and validated against experimental results found in literature, and a good agreement was observed. It was found that, by increasing the pixel size of the optical detector and the thickness of the scintillator, the MTF decreased as expected. This method may be used in evaluating the performance of the columnar phosphors used in medical imaging, given their physical and geometrical characteristics.Graphical abstract (a) Side view of a part of the scintillator where five crystal columns with homogeneous ends attached to an optical sensor is shown. (b) Propagation of two random optical photon beams emitted from point K with different angles of emission is shown. All the symbols are explained analytically in the text.

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.

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.

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).

Cascaded systems analysis of photon counting detectors

PURPOSE

Photon counting detectors (PCDs) are an emerging technology with applications in spectral and low-dose radiographic and tomographic imaging. This paper develops an analytical model of PCD imaging performance, including the system gain, modulation transfer function (MTF), noise-power spectrum (NPS), and detective quantum efficiency (DQE).

METHODS

A cascaded systems analysis model describing the propagation of quanta through the imaging chain was developed. The model was validated in comparison to the physical performance of a silicon-strip PCD implemented on an experimental imaging bench. The signal response, MTF, and NPS were measured and compared to theory as a function of exposure conditions (70 kVp, 1-7 mA), detector threshold, and readout mode (i.e., the option for coincidence detection). The model sheds new light on the dependence of spatial resolution, charge sharing, and additive noise effects on threshold selection and was used to investigate the factors governing PCD performance, including the fundamental advantages and limitations of PCDs in comparison to energy-integrating detectors (EIDs) in the linear regime for which pulse pileup can be ignored.

RESULTS

The detector exhibited highly linear mean signal response across the system operating range and agreed well with theoretical prediction, as did the system MTF and NPS. The DQE analyzed as a function of kilovolt (peak), exposure, detector threshold, and readout mode revealed important considerations for system optimization. The model also demonstrated the important implications of false counts from both additive electronic noise and charge sharing and highlighted the system design and operational parameters that most affect detector performance in the presence of such factors: for example, increasing the detector threshold from 0 to 100 (arbitrary units of pulse height threshold roughly equivalent to 0.5 and 6 keV energy threshold, respectively), increased the f50 (spatial-frequency at which the MTF falls to a value of 0.50) by ∼30% with corresponding improvement in DQE. The range in exposure and additive noise for which PCDs yield intrinsically higher DQE was quantified, showing performance advantages under conditions of very low-dose, high additive noise, and high fidelity rejection of coincident photons.

CONCLUSIONS

The model for PCD signal and noise performance agreed with measurements of detector signal, MTF, and NPS and provided a useful basis for understanding complex dependencies in PCD imaging performance and the potential advantages (and disadvantages) in comparison to EIDs as well as an important guide to task-based optimization in developing new PCD imaging systems.

Task-based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

PURPOSE

Nonstationarity is an important aspect of imaging performance in CT and cone-beam CT (CBCT), especially for systems employing iterative reconstruction. This work presents a theoretical framework for both filtered-backprojection (FBP) and penalized-likelihood (PL) reconstruction that includes explicit descriptions of nonstationary noise, spatial resolution, and task-based detectability index. Potential utility of the model was demonstrated in the optimal selection of regularization parameters in PL reconstruction.

METHODS

Analytical models for local modulation transfer function (MTF) and noise-power spectrum (NPS) were investigated for both FBP and PL reconstruction, including explicit dependence on the object and spatial location. For FBP, a cascaded systems analysis framework was adapted to account for nonstationarity by separately calculating fluence and system gains for each ray passing through any given voxel. For PL, the point-spread function and covariance were derived using the implicit function theorem and first-order Taylor expansion according to Fessler ["Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Trans. Image Process. 5(3), 493-506 (1996)]. Detectability index was calculated for a variety of simple tasks. The model for PL was used in selecting the regularization strength parameter to optimize task-based performance, with both a constant and a spatially varying regularization map.

RESULTS

Theoretical models of FBP and PL were validated in 2D simulated fan-beam data and found to yield accurate predictions of local MTF and NPS as a function of the object and the spatial location. The NPS for both FBP and PL exhibit similar anisotropic nature depending on the pathlength (and therefore, the object and spatial location within the object) traversed by each ray, with the PL NPS experiencing greater smoothing along directions with higher noise. The MTF of FBP is isotropic and independent of location to a first order approximation, whereas the MTF of PL is anisotropic in a manner complementary to the NPS. Task-based detectability demonstrates dependence on the task, object, spatial location, and smoothing parameters. A spatially varying regularization "map" designed from locally optimal regularization can improve overall detectability beyond that achievable with the commonly used constant regularization parameter.

CONCLUSIONS

Analytical models for task-based FBP and PL reconstruction are predictive of nonstationary noise and resolution characteristics, providing a valuable framework for understanding and optimizing system performance in CT and CBCT.

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.

Optical photon transport in powdered-phosphor scintillators. Part 1. Multiple-scattering and validity of the Boltzmann transport equation

PURPOSE

In Part 1 of this two-part work, predictions for light transport in powdered-phosphor screens are made, based on three distinct approaches. Predictions of geometrical optics-based ray tracing through an explicit microscopic model (EMM) for screen structure are compared to a Monte Carlo program based on the Boltzmann transport equation (BTE) and Swank's diffusion equation solution. The purpose is to: (I) highlight the additional assumptions of the BTE Monte Carlo method and Swank's model (both previously used in the literature) with respect to the EMM approach; (II) demonstrate the equivalences of the approaches under well-defined conditions and; (III) identify the onset and severity of any discrepancies between the models. A package of computer code (called phsphr) is supplied which can be used to reproduce the BTE Monte Carlo results presented in this work.

METHODS

The EMM geometrical optics ray-tracing model is implemented for hypothesized microstructures of phosphor grains in a binder. The BTE model is implemented as a Monte Carlo program with transport parameters, derived from geometrical optics, as inputs. The analytical solution of Swank to the diffusion equation is compared to the EMM and BTE predictions. Absorbed fractions and MTFs are calculated for a range of binder-to-phosphor relative refractive indices (n = 1.1-5.0), screen thicknesses (t = 50-200 μm), and packing fill factors (pf = 0.04-0.54).

RESULTS

Disagreement between the BTE and EMM approaches increased with n and pf. For the largest relative refractive index (n = 5) and highest packing fill (pf = 0.5), the BTE model underestimated the absorbed fraction and MTF50, by up to 40% and 20%, respectively. However, for relative refractive indices typical of real phosphor screens (n ≤ 2), such as Gd2O2S:Tb, the BTE and EMM predictions agreed well at all simulated packing densities. In addition, Swank's model agreed closely with the BTE predictions when the screen was thick enough to be considered turbid.

CONCLUSIONS

Although some assumptions of the BTE are violated in realistic powdered-phosphor screens, these appear to lead to negligible effects in the modeling of optical transport for typical phosphor and binder refractive indices. Therefore it is reasonable to use Monte Carlo codes based on the BTE to treat this problem. Furthermore, Swank's diffusion equation solution is an adequate approximation if a turbidity condition, presented here, is satisfied.

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.