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Dow S, Howansky A, Lubinsky AR, Zhao W. Evaluation of a hybrid direct-indirect active matrix flat-panel imager using Monte Carlo simulation. J Med Imaging (Bellingham) 2020; 7:033501. [PMID: 32411813 DOI: 10.1117/1.jmi.7.3.033501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Accepted: 04/27/2020] [Indexed: 11/14/2022] Open
Abstract
Purpose: Monte Carlo simulations were used to evaluate the imaging properties of a composite direct-indirect active matrix flat-panel imager (AMFPI) with potentially more favorable tradeoffs between x-ray quantum efficiency and spatial resolution than direct or indirect AMFPIs alone. This configuration, referred to as a hybrid AMFPI, comprises a scintillator that is optically coupled to an a-Se direct AMFPI through a transparent electrode and hole blocking layer, such that a-Se acts as both a direct x-ray converter and an optical sensor. Approach: GEANT4 was used to simulate x-ray energy deposition, optical transport, and charge signal generation processes in various hybrid AMPFI configurations under RQA5 and RQA9 x-ray beam conditions. The Fujita-Lubberts-Swank method was used to quantify the impact of irradiation geometry, x-ray converter thicknesses, conversion gain of each layer, and x-ray cross talk between layers on detective quantum efficiency (DQE). Results: Each hybrid configuration had a greater DQE than its direct AMFPI layer alone. The DQE improvement was largest at low spatial frequencies in both front- and back-irradiation (BI) geometries due to increased x-ray quantum efficiency provided by the scintillator. DQE improvements persisted at higher frequencies in BI geometry due to preferential x-ray absorption in a-Se. Matching the x-ray-to-charge conversion gains of a hybrid AMFPI's direct and indirect detection layers affects its Swank factor and, thus, DQE(0). X-ray cross talk has a negligible impact on the DQE ( f ) of hybrid AMFPIs with sufficiently high optical quantum efficiency. Conclusion: An optimized hybrid AMFPI can achieve greater DQE performance than current direct or indirect AMFPIs.
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Affiliation(s)
- Scott Dow
- Stony Brook University, Department of Radiology, Health Sciences Center L4-120, Stony Brook, New York, United States
| | - Adrian Howansky
- Stony Brook University, Department of Radiology, Health Sciences Center L4-120, Stony Brook, New York, United States
| | - Anthony R Lubinsky
- Stony Brook University, Department of Radiology, Health Sciences Center L4-120, Stony Brook, New York, United States
| | - Wei Zhao
- Stony Brook University, Department of Radiology, Health Sciences Center L4-120, Stony Brook, New York, United States
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Acciavatti RJ, Vent TL, Barufaldi B, Wileyto EP, Noël PB, Maidment ADA. Proposing Rapid Source Pulsing for Improved Super-Resolution in Digital Breast Tomosynthesis. PROCEEDINGS OF SPIE--THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING 2020; 11312:113125G. [PMID: 37927528 PMCID: PMC10625487 DOI: 10.1117/12.2542551] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2023]
Abstract
Our previous work showed that digital breast tomosynthesis (DBT) systems are capable of super-resolution, or subpixel resolution relative to the detector. Using a bar pattern phantom, it is possible to demonstrate that there are anisotropies in super-resolution throughout the reconstruction. These anisotropies are lessened in acquisition geometries with narrow spacing between source positions. This paper demonstrates that by re-arranging the source positions in the scan, the anisotropies can be minimized even further. To this end, a theoretical model of the reconstruction of a high-frequency sinusoidal test object was developed from first principles. We modeled the effect of clustering additional source positions around each conventional source position in fine increments (submillimeter). This design can be implemented by rapidly pulsing the source during a continuous sweep of the x-ray tube. It is shown that it is not possible to eliminate the anisotropies in a conventional DBT system with uniformly-spaced source positions, even if the increments of spacing are narrower than those used clinically. However, super-resolution can be achieved everywhere if the source positions are re-arranged in clusters with submillimeter spacing. Our previous work investigated a different approach for optimizing super-resolution through the use of detector motion perpendicular to the breast support. The advantage of introducing rapid source pulsing is that detector motion is no longer required; this mitigates the need for a thick detector housing, which may be cumbersome for patient positioning.
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Affiliation(s)
- Raymond J Acciavatti
- University of Pennsylvania, Department of Radiology, 3400 Spruce Street, Philadelphia PA 19104
| | - Trevor L Vent
- University of Pennsylvania, Department of Radiology, 3400 Spruce Street, Philadelphia PA 19104
| | - Bruno Barufaldi
- University of Pennsylvania, Department of Radiology, 3400 Spruce Street, Philadelphia PA 19104
| | - E Paul Wileyto
- University of Pennsylvania, Department of Epidemiology, Biostatistics, & Informatics, 423 Guardian Drive, Philadelphia, PA 19104
| | - Peter B Noël
- University of Pennsylvania, Department of Radiology, 3400 Spruce Street, Philadelphia PA 19104
| | - Andrew D A Maidment
- University of Pennsylvania, Department of Radiology, 3400 Spruce Street, Philadelphia PA 19104
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Huang H, Scaduto DA, Liu C, Yang J, Zhu C, Rinaldi K, Eisenberg J, Liu J, Hoernig M, Wicklein J, Vogt S, Mertelmeier T, Fisher PR, Zhao W. Comparison of contrast-enhanced digital mammography and contrast-enhanced digital breast tomosynthesis for lesion assessment. J Med Imaging (Bellingham) 2019; 6:031407. [PMID: 30766895 DOI: 10.1117/1.jmi.6.3.031407] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2018] [Accepted: 01/10/2019] [Indexed: 01/22/2023] Open
Abstract
Contrast-enhanced digital mammography (CEDM) reveals neovasculature of breast lesions in a two-dimensional contrast enhancement map. Contrast-enhanced digital breast tomosynthesis (CEDBT) provides contrast enhancement in three dimensions, which may improve lesion characterization and localization. We aim to compare CEDM and CEDBT for lesion assessment. Women with breast imaging-reporting and data system 4 or 5 suspicious breast lesion(s) were recruited in our study and were imaged with CEDM and CEDBT in succession under one breast compression. Two radiologists assessed CEDM and CEDBT with both images displayed side-by-side and compared (1) contrast enhancement of lesions and (2) lesion margin using a five-point scale ranging from - 2 (CEDM much better) to + 2 (CEDBT much better). Biopsy identified 19 malignant lesions with contrast enhancement. Our results show that CEDBT provides better lesion margins than CEDM with limited reduction in contrast enhancement. CEDBT delivers less radiation dose compared to CEDM + DBT. Synthetic CEDM can be generated from CEDBT data and provides lesion contrast enhancement comparable to CEDM. CEDBT has potential for clinical applications, such as treatment response monitoring and guidance for biopsy.
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Affiliation(s)
- Hailiang Huang
- Stony Brook Medicine, Department of Radiology, Stony Brook, New York, United States
| | - David A Scaduto
- Stony Brook Medicine, Department of Radiology, Stony Brook, New York, United States
| | - Chunling Liu
- Stony Brook Medicine, Department of Radiology, Stony Brook, New York, United States
| | - Jie Yang
- Stony Brook Medicine, Department of Family, Population and Preventive Medicine, Stony Brook, New York, United States
| | - Chencan Zhu
- Stony Brook University, Department of Applied Mathematics and Statistics, Stony Brook, New York, United States
| | - Kim Rinaldi
- Stony Brook Medicine, Department of Radiology, Stony Brook, New York, United States
| | - Jason Eisenberg
- Stony Brook Medicine, Department of Radiology, Stony Brook, New York, United States
| | - Jingxuan Liu
- Stony Brook Medicine, Department of Pathology, Stony Brook, New York, United States
| | | | | | - Sebastian Vogt
- Siemens Medical Solutions USA Inc., Monument, Colorado, United States
| | | | - Paul R Fisher
- Stony Brook Medicine, Department of Radiology, Stony Brook, New York, United States
| | - Wei Zhao
- Stony Brook Medicine, Department of Radiology, Stony Brook, New York, United States
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Acciavatti RJ, Maidment ADA. Nonstationary model of oblique x-ray incidence in amorphous selenium detectors: II. Transfer functions. Med Phys 2019; 46:505-516. [PMID: 30488455 PMCID: PMC6502710 DOI: 10.1002/mp.13312] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Revised: 10/02/2018] [Accepted: 11/16/2018] [Indexed: 12/23/2022] Open
Abstract
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.
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Affiliation(s)
- Raymond J. Acciavatti
- Department of RadiologyPerelman School of Medicine at the University of PennsylvaniaPhiladelphiaPA19104‐4206USA
| | - Andrew D. A. Maidment
- Department of RadiologyPerelman School of Medicine at the University of PennsylvaniaPhiladelphiaPA19104‐4206USA
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Hu YH, Fueglistaller R, Myronakis M, Rottmann J, Wang A, Shedlock D, Morf D, Baturin P, Huber P, Star-Lack J, Berbeco R. Physics considerations in MV-CBCT multi-layer imager design. Phys Med Biol 2018; 63:125016. [PMID: 29846180 DOI: 10.1088/1361-6560/aac8c6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Megavoltage (MV) cone-beam computed tomography (CBCT) using an electronic portal imaging (EPID) offers advantageous features, including 3D mapping, treatment beam registration, high-z artifact suppression, and direct radiation dose calculation. Adoption has been slowed by image quality limitations and concerns about imaging dose. Developments in imager design, including pixelated scintillators, structured phosphors, inexpensive scintillation materials, and multi-layer imager (MLI) architecture have been explored to improve EPID image quality and reduce imaging dose. The present study employs a hybrid Monte Carlo and linear systems model to determine the effect of detector design elements, such as multi-layer architecture and scintillation materials. We follow metrics of image quality including modulation transfer function (MTF) and noise power spectrum (NPS) from projection images to 3D reconstructions to in-plane slices and apply a task based figure-of-merit, the ideal observer signal-to-noise ratio (d') to determine the effect of detector design on object detectability. Generally, detectability was limited by detector noise performance. Deploying an MLI imager with a single scintillation material for all layers yields improvement in noise performance and d' linear with the number of layers. In general, improving x-ray absorption using thicker scintillators results in improved DQE(0). However, if light yield is low, performance will be affected by electronic noise at relatively high doses, resulting in rapid image quality degradation. Maximizing image quality in a heterogenous MLI detector (i.e. multiple different scintillation materials) is most affected by limiting total noise. However, while a second-order effect, maximizing total spatial resolution of the MLI detector is a balance between the intensity contribution of each layer against its individual MTF. So, while a thinner scintillator may yield a maximal individual-layer MTF, its quantum efficiency will be relatively low in comparison to a thicker scintillator and thus, intensity contribution may be insufficient to noticeably improve the total detector MTF.
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Affiliation(s)
- Yue-Houng Hu
- Department of Radiation Oncology, Division of Medical Physics and Biophysics, Brigham and Women's Hospital, Dana-Farber Cancer Institute and Harvard Medical School, Boston, MA 02115, United States of America
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Hu YH, Myronakis M, Rottmann J, Wang A, Morf D, Shedlock D, Baturin P, Star-Lack J, Berbeco R. A novel method for quantification of beam's-eye-view tumor tracking performance. Med Phys 2017; 44:5650-5659. [PMID: 28887836 DOI: 10.1002/mp.12572] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Revised: 08/21/2017] [Accepted: 08/31/2017] [Indexed: 12/12/2022] Open
Abstract
PURPOSE In-treatment imaging using an electronic portal imaging device (EPID) can be used to confirm patient and tumor positioning. Real-time tumor tracking performance using current digital megavolt (MV) imagers is hindered by poor image quality. Novel EPID designs may help to improve quantum noise response, while also preserving the high spatial resolution of the current clinical detector. Recently investigated EPID design improvements include but are not limited to multi-layer imager (MLI) architecture, thick crystalline and amorphous scintillators, and phosphor pixilation and focusing. The goal of the present study was to provide a method of quantitating improvement in tracking performance as well as to reveal the physical underpinnings of detector design that impact tracking quality. The study employs a generalizable ideal observer methodology for the quantification of tumor tracking performance. The analysis is applied to study both the effect of increasing scintillator thickness on a standard, single-layer imager (SLI) design as well as the effect of MLI architecture on tracking performance. METHODS The present study uses the ideal observer signal-to-noise ratio (d') as a surrogate for tracking performance. We employ functions which model clinically relevant tasks and generalized frequency-domain imaging metrics to connect image quality with tumor tracking. A detection task for relevant Cartesian shapes (i.e., spheres and cylinders) was used to quantitate trackability of cases employing fiducial markers. Automated lung tumor tracking algorithms often leverage the differences in benign and malignant lung tissue textures. These types of algorithms (e.g., soft-tissue localization - STiL) were simulated by designing a discrimination task, which quantifies the differentiation of tissue textures, measured experimentally and fit as a power-law in trend (with exponent β) using a cohort of MV images of patient lungs. The modeled MTF and NPS were used to investigate the effect of scintillator thickness and MLI architecture on tumor tracking performance. RESULTS Quantification of MV images of lung tissue as an inverse power-law with respect to frequency yields exponent values of β = 3.11 and 3.29 for benign and malignant tissues, respectively. Tracking performance with and without fiducials was found to be generally limited by quantum noise, a factor dominated by quantum detective efficiency (QDE). For generic SLI construction, increasing the scintillator thickness (gadolinium oxysulfide - GOS) from a standard 290 μm to 1720 μm reduces noise to about 10%. However, 81% of this reduction is appreciated between 290 and 1000 μm. In comparing MLI and SLI detectors of equivalent individual GOS layer thickness, the improvement in noise is equal to the number of layers in the detector (i.e., 4) with almost no difference in MTF. Further, improvement in tracking performance was slightly less than the square-root of the reduction in noise, approximately 84-90%. In comparing an MLI detector with an SLI with a GOS scintillator of equivalent total thickness, improvement in object detectability is approximately 34-39%. CONCLUSIONS We have presented a novel method for quantification of tumor tracking quality and have applied this model to evaluate the performance of SLI and MLI EPID designs. We showed that improved tracking quality is primarily limited by improvements in NPS. When compared to very thick scintillator SLI, employing MLI architecture exhibits the same gains in QDE, but by mitigating the effect of optical Swank noise, results in more dramatic improvements in tracking performance.
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Affiliation(s)
- Yue-Houng Hu
- Department of Radiation Oncology, Division of Medical Physics and Biophysics, Brigham and Women's Hospital, Dana-Farber Cancer Institute and Harvard Medical School, 75 Francis St, ASB1 L2, Boston, MA, 02115, USA
| | - Marios Myronakis
- Department of Radiation Oncology, Division of Medical Physics and Biophysics, Brigham and Women's Hospital, Dana-Farber Cancer Institute and Harvard Medical School, 75 Francis St, ASB1 L2, Boston, MA, 02115, USA
| | - Joerg Rottmann
- Department of Radiation Oncology, Division of Medical Physics and Biophysics, Brigham and Women's Hospital, Dana-Farber Cancer Institute and Harvard Medical School, 75 Francis St, ASB1 L2, Boston, MA, 02115, USA
| | - Adam Wang
- Varian Medical Systems, 3100 Hansen Way, Palo Alto, CA, 94304, USA
| | - Daniel Morf
- Varian Medical Systems, Taefernstrasse 5, Baden-Daettwil, 5405, Switzerland
| | - Daniel Shedlock
- Varian Medical Systems, 3100 Hansen Way, Palo Alto, CA, 94304, USA
| | - Paul Baturin
- Varian Medical Systems, 3100 Hansen Way, Palo Alto, CA, 94304, USA
| | - Josh Star-Lack
- Varian Medical Systems, 3100 Hansen Way, Palo Alto, CA, 94304, USA
| | - Ross Berbeco
- Department of Radiation Oncology, Division of Medical Physics and Biophysics, Brigham and Women's Hospital, Dana-Farber Cancer Institute and Harvard Medical School, 75 Francis St, ASB1 L2, Boston, MA, 02115, USA
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Zhao C, Kanicki J. Task-Based Modeling of a 5k Ultra-High-Resolution Medical Imaging System for Digital Breast Tomosynthesis. IEEE TRANSACTIONS ON MEDICAL IMAGING 2017; 36:1820-1831. [PMID: 28436856 DOI: 10.1109/tmi.2017.2695982] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
High-resolution, low-noise X-ray detectors based on CMOS active pixel sensor (APS) technology have demonstrated superior imaging performance for digital breast tomosynthesis (DBT). This paper presents a task-based model for a high-resolution medical imaging system to evaluate its ability to detect simulated microcalcifications and masses as lesions for breast cancer. A 3-D cascaded system analysis for a 50- [Formula: see text] pixel pitch CMOS APS X-ray detector was integrated with an object task function, a medical imaging display model, and the human eye contrast sensitivity function to calculate the detectability index and area under the ROC curve (AUC). It was demonstrated that the display pixel pitch and zoom factor should be optimized to improve the AUC for detecting small microcalcifications. In addition, detector electronic noise of smaller than 300 e- and a high display maximum luminance (>1000 cd/cm 2) are desirable to distinguish microcalcifications of [Formula: see text] in size. For low contrast mass detection, a medical imaging display with a minimum of 12-bit gray levels is recommended to realize accurate luminance levels. A wide projection angle range of greater than ±30° in combination with the image gray level magnification could improve the mass detectability especially when the anatomical background noise is high. On the other hand, a narrower projection angle range below ±20° can improve the small, high contrast object detection. Due to the low mass contrast and luminance, the ambient luminance should be controlled below 5 cd/ [Formula: see text]. Task-based modeling provides important firsthand imaging performance of the high-resolution CMOS-based medical imaging system that is still at early stage development for DBT. The modeling results could guide the prototype design and clinical studies in the future.
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Scaduto DA, Tousignant O, Zhao W. Experimental characterization of a direct conversion amorphous selenium detector with thicker conversion layer for dual‐energy contrast‐enhanced breast imaging. Med Phys 2017; 44:3965-3977. [PMID: 28543761 DOI: 10.1002/mp.12358] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Revised: 03/29/2017] [Accepted: 05/09/2017] [Indexed: 12/17/2022] Open
Affiliation(s)
- David A. Scaduto
- Department of Radiology Stony Brook Medicine Stony Brook NY 11794‐8460 USA
| | | | - Wei Zhao
- Department of Radiology Stony Brook Medicine Stony Brook NY 11794‐8460 USA
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Zhao C, Vassiljev N, Konstantinidis AC, Speller RD, Kanicki J. Three-dimensional cascaded system analysis of a 50µm pixel pitch wafer-scale CMOS active pixel sensor x-ray detector for digital breast tomosynthesis. Phys Med Biol 2017; 62:1994-2017. [DOI: 10.1088/1361-6560/aa586c] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Contillo A, Di Domenico G, Cardarelli P, Gambaccini M, Taibi A. A novel approach to background subtraction in contrast-enhanced dual-energy digital mammography with commercially available mammography devices: Polychromaticity correction. Med Phys 2016; 42:6641-50. [PMID: 26520754 DOI: 10.1118/1.4933199] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
PURPOSE Contrast-enhanced digital mammography is an image subtraction technique that is able to improve the detectability of lesions in dense breasts. One of the main sources of error, when the technique is performed by means of commercial mammography devices, is represented by the intrinsic polychromaticity of the x-ray beams. The aim of the work is to propose an iterative procedure, which only assumes the knowledge of a small set of universal quantities, to take into account the polychromaticity and correct the subtraction results accordingly. METHODS In order to verify the procedure, it has been applied to an analytical simulation of a target containing a contrast medium and to actual radiographs of a breast phantom containing cavities filled with a solution of the same medium. RESULTS The reconstructed densities of contrast medium were compared, showing very good agreement between the theoretical predictions and the experimental results already after the first iteration. Furthermore, the convergence of the iterative procedure was studied, showing that only a small number of iterations is necessary to reach limiting values. CONCLUSIONS The proposed procedure represents an efficient solution to the polychromaticity issue, qualifying therefore as a viable alternative to inverse-map functions.
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Affiliation(s)
- Adriano Contillo
- Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, Ferrara I-44122, Italy
| | - Giovanni Di Domenico
- Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, Ferrara I-44122, Italy
| | - Paolo Cardarelli
- Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, Ferrara I-44122, Italy
| | - Mauro Gambaccini
- Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, Ferrara I-44122, Italy
| | - Angelo Taibi
- Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, Ferrara I-44122, Italy
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