An energy- and depth-dependent model for x-ray imaging

A comprehensive model for quantum noise characterization in digital mammography

A version of cascaded systems analysis was developed specifically with the aim of studying quantum noise propagation in x-ray detectors. Signal and quantum noise propagation was then modelled in four types of x-ray detectors used for digital mammography: four flat panel systems, one computed radiography and one slot-scan silicon wafer based photon counting device. As required inputs to the model, the two dimensional (2D) modulation transfer function (MTF), noise power spectra (NPS) and detective quantum efficiency (DQE) were measured for six mammography systems that utilized these different detectors. A new method to reconstruct anisotropic 2D presampling MTF matrices from 1D radial MTFs measured along different angular directions across the detector is described; an image of a sharp, circular disc was used for this purpose. The effective pixel fill factor for the FP systems was determined from the axial 1D presampling MTFs measured with a square sharp edge along the two orthogonal directions of the pixel lattice. Expectation MTFs were then calculated by averaging the radial MTFs over all possible phases and the 2D EMTF formed with the same reconstruction technique used for the 2D presampling MTF. The quantum NPS was then established by noise decomposition from homogenous images acquired as a function of detector air kerma. This was further decomposed into the correlated and uncorrelated quantum components by fitting the radially averaged quantum NPS with the radially averaged EMTF(2). This whole procedure allowed a detailed analysis of the influence of aliasing, signal and noise decorrelation, x-ray capture efficiency and global secondary gain on NPS and detector DQE. The influence of noise statistics, pixel fill factor and additional electronic and fixed pattern noises on the DQE was also studied. The 2D cascaded model and decompositions performed on the acquired images also enlightened the observed quantum NPS and DQE anisotropy.

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.

Validation of columnar CsI x-ray detector responses obtained with hybridMANTIS, a CPU-GPU Monte Carlo code for coupled x-ray, electron, and optical transport

PURPOSE

hybridMANTIS is a Monte Carlo package for modeling indirect x-ray imagers using columnar geometry based on a hybrid concept that maximizes the utilization of available CPU and graphics processing unit processors in a workstation.

METHODS

The authors compare hybridMANTIS x-ray response simulations to previously published MANTIS and experimental data for four cesium iodide scintillator screens. These screens have a variety of reflective and absorptive surfaces with different thicknesses. The authors analyze hybridMANTIS results in terms of modulation transfer function and calculate the root mean square difference and Swank factors from simulated and experimental results.

RESULTS

The comparison suggests that hybridMANTIS better matches the experimental data as compared to MANTIS, especially at high spatial frequencies and for the thicker screens. hybridMANTIS simulations are much faster than MANTIS with speed-ups up to 5260.

CONCLUSIONS

hybridMANTIS is a useful tool for improved description and optimization of image acquisition stages in medical imaging systems and for modeling the forward problem in iterative reconstruction algorithms.

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.

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

PURPOSE

Accurate models of detector blur are crucial for performing meaningful optimizations of three-dimensional (3D) x-ray breast imaging systems as well as for developing reconstruction algorithms that faithfully reproduce the imaged object anatomy. So far, x-ray detector blur has either been ignored or modeled as a shift-invariant symmetric function for these applications. The recent development of a Monte Carlo simulation package called MANTIS has allowed detailed modeling of these detector blur functions and demonstrated the magnitude of the anisotropy for both tomosynthesis and breast CT imaging systems. Despite the detailed results that MANTIS produces, the long simulation times required make inclusion of these results impractical in rigorous optimization and reconstruction algorithms. As a result, there is a need for detector blur models that can be rapidly generated.

METHODS

In this study, the authors have derived an analytical model for deterministic detector blur functions, referred to here as point response functions (PRFs), of columnar CsI phosphor screens. The analytical model is x-ray energy and incidence angle dependent and draws on results from MANTIS to indirectly include complicated interactions that are not explicitly included in the mathematical model. Once the mathematical expression is derived, values of the coefficients are determined by a two-dimensional (2D) fit to MANTIS-generated results based on a figure-of-merit (FOM) that measures the normalized differences between the MANTIS and analytical model results averaged over a region of interest. A smaller FOM indicates a better fit. This analysis was performed for a monochromatic x-ray energy of 25 keV, a CsI scintillator thickness of 150 microm, and four incidence angles (0 degrees, 15 degrees, 30 degrees, and 45 degrees).

RESULTS

The FOMs comparing the analytical model to MANTIS for these parameters were 0.1951 +/- 0.0011, 0.1915 +/- 0.0014, 0.2266 +/- 0.0021, and 0.2416 +/- 0.0074 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. As a comparison, the same FOMs comparing MANTIS to 2D symmetric Gaussian fits to the zero-angle PRF were 0.6234 +/- 0.0020, 0.9058 +/- 0.0029, 1.491 +/- 0.012, and 2.757 +/- 0.039 for the same set of incidence angles. Therefore, the analytical model matches MANTIS results much better than a 2D symmetric Gaussian function. A comparison was also made against experimental data for a 170 microm thick CsI screen and an x-ray energy of 25.6 keV. The corresponding FOMs were 0.3457 +/- 0.0036, 0.3281 +/- 0.0057, 0.3422 +/- 0.0023, and 0.3677 +/- 0.0041 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. In a previous study, FOMs comparing the same experimental data to MANTIS PRFs were found to be 0.2944 +/- 0.0027, 0.2387 +/- 0.0039, 0.2816 +/- 0.0025, and 0.2665 +/- 0.0032 for the same set of incidence angles.

CONCLUSIONS

The two sets of derived FOMs, comparing MANTIS-generated PRFs and experimental data to the analytical model, demonstrate that the analytical model is able to reproduce experimental data with a FOM of less than two times that comparing MANTIs and experimental data. This performance is achieved in less than one millionth the computation time required to generate a comparable PRF with MANTIS. Such small computation times will allow for the inclusion of detailed detector physics in rigorous optimization and reconstruction algorithms for 3D x-ray breast imaging systems.

Singular value description of a digital radiographic detector: theory and measurements

The H operator represents the deterministic performance of any imaging system. For a linear, digital imaging system, this system operator can be written in terms of a matrix, H, that describes the deterministic response of the system to a set of point objects. A singular value decomposition of this matrix results in a set of orthogonal functions (singular vectors) that form the system basis. A linear combination of these vectors completely describes the transfer of objects through the linear system, where the respective singular values associated with each singular vector describe the magnitude with which that contribution to the object is transferred through the system. This paper is focused on the measurement, analysis, and interpretation of the H matrix for digital x-ray detectors. A key ingredient in the measurement of the H matrix is the detector response to a single x ray (or infinitestimal x-ray beam). The authors have developed a method to estimate the 2D detector shift-variant, asymmetric ray response function (RRF) from multiple measured line response functions (LRFs) using a modified edge technique. The RRF measurements cover a range of x-ray incident angles from 0 degree (equivalent location at the detector center) to 30 degrees (equivalent location at the detector edge) for a standard radiographic or cone-beam CT geometric setup. To demonstrate the method, three beam qualities were tested using the inherent, Lu/Er, and Yb beam filtration. The authors show that measures using the LRF, derived from an edge measurement, underestimate the system's performance when compared with the H matrix derived using the RRF. Furthermore, the authors show that edge measurements must be performed at multiple directions in order to capture rotational asymmetries of the RRF. The authors interpret the results of the H matrix SVD and provide correlations with the familiar MTF methodology. Discussion is made about the benefits of the H matrix technique with regards to signal detection theory, and the characterization of shift-variant imaging systems.

Anisotropic imaging performance in breast tomosynthesis

We describe the anisotropy in imaging performance caused by oblique x-ray incidence in indirect detectors for breast tomosynthesis based on columnar scintillator screens. We use MANTIS, a freely available combined x-ray, electron, and optical Monte Carlo transport package which models the indirect detection processes in columnar screens, interaction by interaction. The code has been previously validated against published optical distributions. In this article, initial validation results are provided concerning the blur for particular designs of phosphor screens for which some details with respect to the columnar geometry are available from scanning electron microscopy. The polyenergetic x-ray spectrum utilized comes from a database of experimental data for three different anode/filter/kVp combinations: Mo/Mo at 28 kVp, Rh/Rh at 28 kVp, and W/Al at 42 kVp. The x-ray spectra were then filtered with breast tissue (3, 4, and 6 cm thickness), compression paddle, and support base, according to the oblique paths determined by the incidence angle. The composition of the breast tissue was 50%/50% adipose/glandular tissue mass ratio. Results are reported on the pulse-height statistics of the light output and on spatial blur, expressed as the response of the detector to a pencil beam with a certain incidence angle. Results suggest that the response is nonsymmetrical and that the resolution properties of a tomosynthesis system vary significantly with the angle of x-ray incidence. In contrast, it is found that the noise due to the variability in the number of light photons detected per primary x-ray interaction changes only a few percent. The anisotropy in the response is not less in screens with absorptive backings while the noise introduced by variations in the depth-dependent light output and optical transport is larger. The results suggest that anisotropic imaging performance across the detector area can be incorporated into reconstruction algorithms for improving the image quality of breast tomosynthesis. This study also demonstrates that the assessment of image quality of breast tomosynthesis systems requires a more complete description of the detector response beyond local, center measurements of resolution and noise that assume some degree of symmetry in the detector performance.

Modeling granular phosphor screens by Monte Carlo methods

The intrinsic phosphor properties are of significant importance for the performance of phosphor screens used in medical imaging systems. In previous analytical-theoretical and Monte Carlo studies on granular phosphor materials, values of optical properties, and light interaction cross sections were found by fitting to experimental data. These values were then employed for the assessment of phosphor screen imaging performance. However, it was found that, depending on the experimental technique and fitting methodology, the optical parameters of a specific phosphor material varied within a wide range of values, i.e., variations of light scattering with respect to light absorption coefficients were often observed for the same phosphor material. In this study, x-ray and light transport within granular phosphor materials was studied by developing a computational model using Monte Carlo methods. The model was based on the intrinsic physical characteristics of the phosphor. Input values required to feed the model can be easily obtained from tabulated data. The complex refractive index was introduced and microscopic probabilities for light interactions were produced, using Mie scattering theory. Model validation was carried out by comparing model results on x-ray and light parameters (x-ray absorption, statistical fluctuations in the x-ray to light conversion process, number of emitted light photons, output light spatial distribution) with previous published experimental data on Gd2O2S: Tb phosphor material (Kodak Min-R screen). Results showed the dependence of the modulation transfer function (MTF) on phosphor grain size and material packing density. It was predicted that granular Gd2O2S: Tb screens of high packing density and small grain size may exhibit considerably better resolution and light emission properties than the conventional Gd2O2S: Tb screens, under similar conditions (x-ray incident energy, screen thickness).

Anisotropic imaging performance in indirect x-ray imaging detectors

We report on the variability in imaging system performance due to oblique x-ray incidence, and the associated transport of quanta (both x rays and optical photons) through the phosphor, in columnar indirect digital detectors. The analysis uses MANTIS, a combined x-ray, electron, and optical Monte Carlo transport code freely available. We describe the main features of the simulation method and provide some validation of the phosphor screen models considered in this work. We report x-ray and electron three-dimensional energy deposition distributions and point-response functions (PRFs), including optical spread in columnar phosphor screens of thickness 100 and 500 microm, for 19, 39, 59, and 79 keV monoenergetic x-ray beams incident at 0 degrees, 10 degrees, and 15 degrees. In addition, we present pulse-height spectra for the same phosphor thickness, x-ray energies, and angles of incidence. Our results suggest that the PRF due to the phosphor blur is highly nonsymmetrical, and that the resolution properties of a columnar screen in a tomographic, or tomosynthetic imaging system varies significantly with the angle of x-ray incidence. Moreover, we find that the noise due to the variability in the number of light photons detected per primary x-ray interaction, summarized in the information or Swank factor, is somewhat independent of thickness and incidence angle of the x-ray beam. Our results also suggest that the anisotropy in the PRF is not less in screens with absorptive backings, while the noise introduced by variations in the gain and optical transport is larger. Predictions from MANTIS, after additional validation, can provide the needed understanding of the extent of such variations, and eventually, lead to the incorporation of the changes in imaging performance with incidence angle into the reconstruction algorithms for volumetric x-ray imaging systems.

MANTIS: combined x-ray, electron and optical Monte Carlo simulations of indirect radiation imaging systems

We describe MANTIS (Monte carlo x-rAy electroN opTical Imaging Simulation), a tool for simulating imaging systems that tracks x-rays, electrons and optical photons in arbitrary materials and complex geometries. The x-ray and electron transport and involved physics models are from the PENELOPE package, and the optical transport and corresponding physics models are from DETECT-II and include Fresnel refraction and reflection at material boundaries, bulk absorption and scattering. Complex geometries can be handled with the aid of the geometry routines included in PENELOPE. When x-rays or electrons interact and deposit energy in the scintillator, the code generates a number of optical quanta according to a user-selected model for the conversion process. The optical photons are then tracked until they reach an absorption event, which in some cases contributes to the output signal, or escape from the geometry. We demonstrate the capabilities of this new tool with respect to the statistics of the optical signal detected and to the three-dimensional point-response functions corresponding to columnar phosphor screens.

Generalized DQE analysis of radiographic and dual-energy imaging using flat-panel detectors

Analysis of detective quantum efficiency (DQE) is an important component of the investigation of imaging performance for flat-panel detectors (FPDs). Conventional descriptions of DQE are limited, however, in that they take no account of anatomical noise (i.e., image fluctuations caused by overlying anatomy), even though such noise can be the most significant limitation to detectability, often outweighing quantum or electronic noise. We incorporate anatomical noise in experimental and theoretical descriptions of the "generalized DQE" by including a spatial-frequency-dependent noise-power term, S(B), corresponding to background anatomical fluctuations. Cascaded systems analysis (CSA) of the generalized DQE reveals tradeoffs between anatomical noise and the factors that govern quantum noise. We extend such analysis to dual-energy (DE) imaging, in which the overlying anatomical structure is selectively removed in image reconstructions by combining projections acquired at low and high kVp. The effectiveness of DE imaging in removing anatomical noise is quantified by measurement of S(B) in an anthropomorphic phantom. Combining the generalized DQE with an idealized task function to yield the detectability index, we show that anatomical noise dramatically influences task-based performance, system design, and optimization. For the case of radiography, the analysis resolves a fundamental and illustrative quandary: The effect of kVp on imaging performance, which is poorly described by conventional DQE analysis but is clarified by consideration of the generalized DQE. For the case of DE imaging, extension of a generalized CSA methodology reveals a potentially powerful guide to system optimization through the optimal selection of the tissue cancellation parameter. Generalized task-based analysis for DE imaging shows an improvement in the detectability index by more than a factor of 2 compared to conventional radiography for idealized detection tasks.

Extension of x-ray imaging linear systems analysis to detectors with energy discrimination capability

A figure of merit, the broad-spectrum generalized detective quantum efficiency, which describes the performance of digital detectors designed for broad-spectrum x-ray imaging is derived from linear response theory. This measure of the imaging efficacy of an x-ray sensor is obtained when detector contrast modulation in the domain of x-ray energy is introduced in the Fourier-based analysis of digital systems. A method is proposed to scale existing figures of merit according to the energy-dependent response of the detector and the spectral shape of the x-ray beam. The new figure of merit obtained with this method provides an extended description of system performance when comparing energy-integrating, single-photon counting, and future energy-sensitive x-ray imaging sensors. The applicability of this linear system analysis is restricted to the tasks of low-contrast object detection in radiography. The method for scaling the figure of merit to take into consideration broad-spectrum conditions is applied to mammography for future energy-dependent detectors. An approximation valid in the typical mammographic x-ray energy range is used to calculate the broad-spectrum generalized detective quantum efficiency at zero spatial frequency, for several mammographic x-ray spectra. X-ray energy weighting in mammography is investigated in the context of simulated tumors and microcalcifications detection by comparing this figure of merit, calculated for different detector technologies, under ideal imaging conditions, at zero spatial frequency.

Lubberts effect in columnar phosphors

Noise transfer in granular x-ray imaging phosphor screens is not proportional to the square of the magnitude of the signal transfer when the transfer properties are considered for the entire screen thickness, unless appropriately weighted at each depth of interaction. This property, known as the Lubberts effect, has not yet been studied in columnar structured screens because of a lack of a generalized description of the depth-dependent light transport. In this paper, we investigate the signal and noise transfer characteristics of columnar phosphors used in digital mammography detectors using DETECT-II, an optical Monte Carlo light transport simulation code. We first validate our choice of optical parameters for the description of granular and columnar screens using published normalized modulation transfer (MTF) experimental data. Our calculations of MTF match empirically measured MTFs for a granular film/screen analog system, and for an indirect x-ray digital imaging system with CsI:Tl screen representative of digital mammography systems. Using the depth-dependent spread functions and collection efficiencies, we calculate the signal and noise transfer functions and the Lubberts fraction, which is the ratio of the signal transfer function to the noise transfer function, for different screen thicknesses of granular and columnar phosphors. We find that the Lubberts fraction of a 85 microm granular screen model corresponding to a Gd2O2S:Tb screen is similar to the fraction for a 100 microm columnar CsI:Tl screen.