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

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.

Experimental validation of Fastcat kV and MV cone beam CT (CBCT) simulator

PURPOSE

To experimentally validate the Fastcat cone beam computed tomography (CBCT) simulator against kV and MV CBCT images acquired with a Varian Truebeam linac.

METHODS

kV and MV CBCT images of a Catphan 504 phantom were acquired using a 100 kVp beam with the on-board imager (OBI) and a 6 MV treatment beam with the electronic portal imaging device (EPID), respectively. The kV Fastcat simulation was performed using detailed models of the x-ray source, bowtie filter, a high resolution voxelized virtual Catphan phantom, anti-scatter grid, and the CsI scintillating detector. Likewise, an MV Fastcat CBCT was simulated with detailed models for the beam energy spectrum, flattening filter, a high-resolution voxelized virtual Catphan phantom, and the gadolinium oxysulfide (GOS) scintillating detector. Experimental and simulated CBCT images of the phantom were compared with respect to HU values, contrast to noise ratio (CNR), and dose linearity. Detector modulation transfer function (MTF) for the two detectors were also experimentally validated. Fastcat's dose calculations were compared to Monte Carlo (MC) dose calculations performed with Topas.

RESULTS

For the kV and MV simulations, respectively: Contrast agreed within 14 and 9 HUs and detector MTF agreed within 4.2% and 2.5%. Likewise, CNR had a root mean squared error (RMSE) of 2.6% and 1.4%. Dose agreed within 2.4% and 1.6% of MC values. The kV and MV CBCT images took 71 and 72 s to simulate in Fastcat with 887 and 493 projections, respectively.

CONCLUSIONS

We present a multienergy experimental validation of a fast and accurate CBCT simulator against a commercial linac. The simulator is open source and all models found in this work can be downloaded from https://github.com/jerichooconnell/fastcat.git.

fastCAT: Fast cone beam CT (CBCT) simulation

PURPOSE

To develop fastCAT, a fast cone-beam computed tomography (CBCT) simulator. fastCAT uses pre-calculated Monte Carlo (MC) CBCT phantom-specific scatter and detector response functions to reduce simulation time for megavoltage (MV) and kilovoltage (kV) CBCT imaging.

METHODS

Pre-calculated x-ray beam energy spectra, detector optical spread functions and energy deposition, and phantom scatter kernels are combined with GPU raytracing to produce CBCT volumes. MV x-ray beam spectra are simulated with EGSnrc for 2.5- and 6 MeV electron beams incident on a variety of target materials and kV x-ray beam spectra are calculated analytically for an x-ray tube with a tungsten anode. Detectors were modeled in Geant4 extended by Topas and included optical transport in the scintillators. Two MV detectors were modeled-a standard Varian AS1200 GOS detector and a novel CWO high detective quantum efficiency detector. A kV CsI detector was also modeled. Energy-dependent scatter kernels were created in Topas for two 16 cm diameter phantoms: A Catphan 515 contrast phantom and an anthropomorphic head phantom. The Catphan phantom contained inserts of 1-5 mm in diameter of six different tissue types: brain, deflated lung, compact and cortical bone, adipose, and B-100.

RESULTS

fastCAT simulations retain high fidelity to measurements and MC simulations: MTF curves were within 3.5% and 1.2% of measured values for the CWO and GOS detectors, respectively. HU values and CNR in a fastCAT Catphan 515 simulation were seen to be within 95% confidence intervals of an equivalent MC simulation for all of the tissues with root mean squared errors less than 16 HU and 1.6 in HU values and CNR comparisons, respectively. The anthropomorphic head phantom CWO detector CBCT image resulted in much higher tissue contrast and lower noise compared to the GOS detector CBCT image. A fastCAT simulation of the Catphan 515 module with an image size of 1024  ×  1024  ×  10 voxels took 61 s on a GPU while the equivalent Topas MC was estimated to take more than 0.3 CPU years.

CONCLUSIONS

We present an open source fast CBCT simulation with high fidelity to MC simulations. The fastCAT python package can be found at https://github.com/jerichooconnell/fastCAT.git.

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.

Modeling and evaluation of a high-resolution CMOS detector for cone-beam CT of the extremities

PURPOSE

Quantitative assessment of trabecular bone microarchitecture in extremity cone-beam CT (CBCT) would benefit from the high spatial resolution, low electronic noise, and fast scan time provided by complementary metal-oxide semiconductor (CMOS) x-ray detectors. We investigate the performance of CMOS sensors in extremity CBCT, in particular with respect to potential advantages of thin (<0.7 mm) scintillators offering higher spatial resolution.

METHODS

A cascaded systems model of a CMOS x-ray detector incorporating the effects of CsI:Tl scintillator thickness was developed. Simulation studies were performed using nominal extremity CBCT acquisition protocols (90 kVp, 0.126 mAs/projection). A range of scintillator thickness (0.35-0.75 mm), pixel size (0.05-0.4 mm), focal spot size (0.05-0.7 mm), magnification (1.1-2.1), and dose (15-40 mGy) was considered. The detectability index was evaluated for both CMOS and a-Si:H flat-panel detector (FPD) configurations for a range of imaging tasks emphasizing spatial frequencies associated with feature size aobj. Experimental validation was performed on a CBCT test bench in the geometry of a compact orthopedic CBCT system (SAD = 43.1 cm, SDD = 56.0 cm, matching that of the Carestream OnSight 3D system). The test-bench studies involved a 0.3 mm focal spot x-ray source and two CMOS detectors (Dalsa Xineos-3030HR, 0.099 mm pixel pitch) - one with the standard CsI:Tl thickness of 0.7 mm (C700) and one with a custom 0.4 mm thick scintillator (C400). Measurements of modulation transfer function (MTF), detective quantum efficiency (DQE), and CBCT scans of a cadaveric knee (15 mGy) were obtained for each detector.

RESULTS

Optimal detectability for high-frequency tasks (feature size of ~0.06 mm, consistent with the size of trabeculae) was ~4× for the C700 CMOS detector compared to the a-Si:H FPD at nominal system geometry of extremity CBCT. This is due to ~5× lower electronic noise of a CMOS sensor, which enables input quantum-limited imaging at smaller pixel size. Optimal pixel size for high-frequency tasks was <0.1 mm for a CMOS, compared to ~0.14 mm for an a-Si:H FPD. For this fine pixel pitch, detectability of fine features could be improved by using a thinner scintillator to reduce light spread blur. A 22% increase in detectability of 0.06 mm features was found for the C400 configuration compared to C700. An improvement in the frequency at 50% modulation (f₅₀ ) of MTF was measured, increasing from 1.8 lp/mm for C700 to 2.5 lp/mm for C400. The C400 configuration also achieved equivalent or better DQE as C700 for frequencies above ~2 mm^-1 . Images of cadaver specimens confirmed improved visualization of trabeculae with the C400 sensor.

CONCLUSIONS

The small pixel size of CMOS detectors yields improved performance in high-resolution extremity CBCT compared to a-Si:H FPDs, particularly when coupled with a custom 0.4 mm thick scintillator. The results indicate that adoption of a CMOS detector in extremity CBCT can benefit applications in quantitative imaging of trabecular microstructure in humans.

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.

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.

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.

hybridMANTIS: a CPU-GPU Monte Carlo method for modeling indirect x-ray detectors with columnar scintillators

The computational modeling of medical imaging systems often requires obtaining a large number of simulated images with low statistical uncertainty which translates into prohibitive computing times. We describe a novel hybrid approach for Monte Carlo simulations that maximizes utilization of CPUs and GPUs in modern workstations. We apply the method to the modeling of indirect x-ray detectors using a new and improved version of the code MANTIS, an open source software tool used for the Monte Carlo simulations of indirect x-ray imagers. We first describe a GPU implementation of the physics and geometry models in fastDETECT2 (the optical transport model) and a serial CPU version of the same code. We discuss its new features like on-the-fly column geometry and columnar crosstalk in relation to the MANTIS code, and point out areas where our model provides more flexibility for the modeling of realistic columnar structures in large area detectors. Second, we modify PENELOPE (the open source software package that handles the x-ray and electron transport in MANTIS) to allow direct output of location and energy deposited during x-ray and electron interactions occurring within the scintillator. This information is then handled by optical transport routines in fastDETECT2. A load balancer dynamically allocates optical transport showers to the GPU and CPU computing cores. Our hybridMANTIS approach achieves a significant speed-up factor of 627 when compared to MANTIS and of 35 when compared to the same code running only in a CPU instead of a GPU. Using hybridMANTIS, we successfully hide hours of optical transport time by running it in parallel with the x-ray and electron transport, thus shifting the computational bottleneck from optical tox-ray transport. The new code requires much less memory than MANTIS and, asa result, allows us to efficiently simulate large area detectors.

Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI

PURPOSE

To develop a dynamic lesion phantom that is capable of producing physiological kinetic curves representative of those seen in human dynamic contrast-enhanced MRI (DCE-MRI) data. The objective of this phantom is to provide a platform for the quantitative comparison of DCE-MRI protocols to aid in the standardization and optimization of breast DCE-MRI.

METHODS

The dynamic lesion consists of a hollow, plastic mold with inlet and outlet tubes to allow flow of a contrast agent solution through the lesion over time. Border shape of the lesion can be controlled using the lesion mold production method. The configuration of the inlet and outlet tubes was determined using fluid transfer simulations. The total fluid flow rate was determined using x-ray images of the lesion for four different flow rates (0.25, 0.5, 1.0, and 1.5 ml/s) to evaluate the resultant kinetic curve shape and homogeneity of the contrast agent distribution in the dynamic lesion. High spatial and temporal resolution x-ray measurements were used to estimate the true kinetic curve behavior in the dynamic lesion for benign and malignant example curves. DCE-MRI example data were acquired of the dynamic phantom using a clinical protocol.

RESULTS

The optimal inlet and outlet tube configuration for the lesion molds was two inlet molds separated by 30° and a single outlet tube directly between the two inlet tubes. X-ray measurements indicated that 1.0 ml/s was an appropriate total fluid flow rate and provided truth for comparison with MRI data of kinetic curves representative of benign and malignant lesions. DCE-MRI data demonstrated the ability of the phantom to produce realistic kinetic curves.

CONCLUSIONS

The authors have constructed a dynamic lesion phantom, demonstrated its ability to produce physiological kinetic curves, and provided estimations of its true kinetic curve behavior. This lesion phantom provides a tool for the quantitative evaluation of DCE-MRI protocols, which may lead to improved discrimination of breast cancer lesions.

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.

X-ray properties of an anthropomorphic breast phantom for MRI and x-ray imaging

The purpose of this study is to characterize the x-ray properties of a dual-modality, anthropomorphic breast phantom whose MRI properties have been previously evaluated. The goal of this phantom is to provide a platform for optimization and standardization of two- and three-dimensional x-ray and MRI breast imaging modalities for the purpose of lesion detection and discrimination. The phantom is constructed using a mixture of lard and egg whites, resulting in a variable, tissue-mimicking structure with separate adipose- and glandular-mimicking components. The phantom can be produced with either a compressed or uncompressed shape. Mass attenuation coefficients of the phantom materials were estimated using elemental compositions from the USDA National Nutrient Database for Standard Reference and the atomic interaction models from the Monte Carlo code PENELOPE and compared with human values from the literature. The image structure was examined quantitatively by calculating and comparing spatial covariance matrices of the phantom and patient mammography images. Finally, a computerized version of the phantom was created by segmenting a computed tomography scan and used to simulate x-ray scatter of the phantom in a mammography geometry. Mass attenuation coefficients of the phantom materials were within 20% and 15% of the values for adipose and glandular tissues, respectively, which is within the estimation error of these values. Matching was improved at higher energies (>20 keV). Tissue structures in the phantom have a size similar to those in the patient data, but are slightly larger on average. Correlations in the patient data appear to be longer than those in the phantom data in the anterior-posterior direction; however, they are within the error bars of the measurement. Simulated scatter-to-primary ratio values of the phantom images were as high as 85% in some areas and were strongly affected by the heterogeneous nature of the phantom. Key physical x-ray properties of the phantom have been quantitatively evaluated and shown to be comparable to those of breast tissue. Since the MRI properties of the phantom have been previously evaluated, we believe it is a useful tool for quantitative evaluation of two- and three-dimensional x-ray and MRI breast imaging modalities for the purpose of lesion detection and characterization.

A comparative analysis of OTF, NPS, and DQE in energy integrating and photon counting digital x-ray detectors

PURPOSE

One of the benefits of photon counting (PC) detectors over energy integrating (EI) detectors is the absence of many additive noise sources, such as electronic noise and secondary quantum noise. The purpose of this work is to demonstrate that thresholding voltage gains to detect individual x rays actually generates an unexpected source of white noise in photon counters.

METHODS

To distinguish the two detector types, their point spread function (PSF) is interpreted differently. The PSF of the energy integrating detector is treated as a weighting function for counting x rays, while the PSF of the photon counting detector is interpreted as a probability. Although this model ignores some subtleties of real imaging systems, such as scatter and the energy-dependent amplification of secondary quanta in indirect-converting detectors, it is useful for demonstrating fundamental differences between the two detector types. From first principles, the optical transfer function (OTF) is calculated as the continuous Fourier transform of the PSF, the noise power spectra (NPS) is determined by the discrete space Fourier transform (DSFT) of the autocovariance of signal intensity, and the detective quantum efficiency (DQE) is found from combined knowledge of the OTF and NPS. To illustrate the calculation of the transfer functions, the PSF is modeled as the convolution of a Gaussian with the product of rect functions. The Gaussian reflects the blurring of the x-ray converter, while the rect functions model the sampling of the detector.

RESULTS

The transfer functions are first calculated assuming outside noise sources such as electronic noise and secondary quantum noise are negligible. It is demonstrated that while OTF is the same for two detector types possessing an equivalent PSF, a frequency-independent (i.e., "white") difference in their NPS exists such that NPS(PC) > or = NPS(EI) and hence DQE(PC) < or = DQE(EI). The necessary and sufficient condition for equality is that the PSF is a binary function given as zero or unity everywhere. In analyzing the model detector with Gaussian blurring, the difference in NPS and DQE between the two detector types is found to increase with the blurring of the x-ray converter. Ultimately, the expression for the additive white noise of the photon counter is compared against the expression for electronic noise and secondary quantum noise in an energy integrator. Thus, a method is provided to determine the average secondary quanta that the energy integrator must produce for each x ray to have superior DQE to a photon counter with the same PSF.

CONCLUSIONS

This article develops analytical models of OTF, NPS, and DQE for energy integrating and photon counting digital x-ray detectors. While many subtleties of real imaging systems have not been modeled, this work is illustrative in demonstrating an additive source of white noise in photon counting detectors which has not yet been described in the literature. One benefit of this analysis is a framework for determining the average secondary quanta that an energy integrating detector must produce for each x ray to have superior DQE to competing photon counting technology.

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.

Effect of oblique X-ray incidence in flat-panel computed tomography of the breast

We quantify the variation in resolution due to anisotropy caused by oblique X-ray incidence in indirect flat-panel detectors for computed tomography breast imaging systems. We consider a geometry and detector type utilized in breast computed tomography (CT) systems currently being developed. Our methods rely on mantis, a combined X-ray, electron, and optical Monte Carlo transport open source code. The physics models are the most accurate available in general-purpose Monte Carlo packages in the diagnostic energy range. We consider maximum-obliquity angles of 10 ( degrees ) and 13 ( degrees ) at the centers of the 30 and 40 cm detector edges, respectively, and 16 ( degrees ) at the corner of the detector. Our results indicate that blur is asymmetric and that the resolution properties vary significantly with the angle (or location) of incidence. Our results suggest that the asymmetry can be as high as a factor of 2.6 between orthogonal directions. Anisotropy maps predicted by mantis provide an understanding of the effect that such variations have on the imaging system and allow more accurate modeling and optimization of breast CT systems. These maps of anisotropy across the detector could lead to improved reconstruction and help motivate physics-based strategies for computer detection of breast lesions.