Can processed images be used to determine the modulation transfer function and detective quantum efficiency?

Purpose: The modulation transfer function (MTF) and detective quantum efficiency (DQE) of x-ray detectors are key Fourier metrics of performance, valid only for linear and shift-invariant (LSI) systems and generally measured following IEC guidelines requiring the use of raw (unprocessed) image data. However, many detectors incorporate processing in the imaging chain that is difficult or impossible to disable, raising questions about the practical relevance of MTF and DQE testing. We investigate the impact of convolution-based embedded processing on MTF and DQE measurements. Approach: We use an impulse-sampled notation, consistent with a cascaded-systems analysis in spatial and spatial-frequency domains to determine the impact of discrete convolution (DC) on measured MTF and DQE following IEC guidelines. Results: We show that digital systems remain LSI if we acknowledge both image pixel values and convolution kernels represent scaled Dirac δ-functions with an implied sinc convolution of image data. This enables use of the Fourier transform (FT) to determine impact on presampling MTF and DQE measurements. Conclusions: It is concluded that: (i) the MTF of DC is always an unbounded cosine series; (ii) the slanted-edge method yields the true presampling MTF, even when using processed images, with processing appearing as an analytic filter with cosine-series MTF applied to raw presampling image data; (iii) the DQE is unaffected by discrete-convolution-based processing with a possible exception near zero-points in the presampling MTF; and (iv) the FT of the impulse-sampled notation is equivalent to the Z transform of image data.

Monte-Carlo study of contrast-enhanced spectral mammography with cadmium telluride photon-counting x-ray detectors.

BACKGROUND: Contrast-enhanced spectral mammography (CESM) with photon-counting x-ray detectors (PCDs) can be used to improve the classification of breast cancers as benign or malignant. Commercially-available PCD-based mammography systems use silicon-based PCDs. Cadmium-telluride (CdTe) PCDs may provide a practical advantage over silicon-based PCDs because they can be implemented as large-area detectors that are more easily adaptable to existing mammography systems. PURPOSE: The purpose of this work is to optimize CESM implemented with CdTe PCDs and to investigate the influence of the number of energy bins, electronic noise level, pixel size, and anode material on image quality. METHODS: We developed a Monte Carlo model of the energy-bin-dependent modulation transfer functions (MTFs) and noise power spectra, including spatioenergetic noise correlations. We validated model predictions using a CdTe PCD with analog charge summing for charge-sharing suppression. Using the ideal-observer detectability, we optimized CESM for the task of detecting a 7-mm-diameter iodine nodule embedded in a breast with 50% glandularity. We optimized the tube voltage, beam filtration, and the location of energy thresholds for 50 and 100- µ $\mu$ m pixels, tungsten and molybdenum anodes, and two electronic noise levels. One of the electronic noise levels was that of the experimental system; the other was half that of the experimental system. Optimization was performed for CdTe PCDs with two or three energy bins. We also estimated the impact of anatomic noise due to background parenchymal enhancement and computed the minimum detectable iodine area density in the presence of quantum and anatomic noise. RESULTS: Model predictions of the MTFs and noise power spectra agreed well with experiment. For optimized systems, adding a third energy bin increased quantum noise levels and reduced detectability by ∼55% compared to two-bin approaches that simply suppress contrast between fibroglandular and adipose tissue. Decreasing the electronic noise standard deviation from 3.4 to 1.7 keV increased iodine detectability by ∼5% and ∼30% for two-bin imaging and three-bin imaging, respectively. After optimizing for tube voltage, beam filtration, and the location of energy thresholds, there was ∼a 3% difference in iodine detectability between molybdenum and tungsten anodes for two-bin imaging, but for three-bin imaging, molybdenum anodes provided up to 14% increase in detectability relative to tungsten anodes. Anatomic noise decreased iodine detectability by 15% to 40%, with greater impact for lower electronic noise settings and larger pixel sizes. CONCLUSIONS: For CESM implemented with CdTe PCDs, (1) quantitatively-accurate three-material decompositions using three energy bins are associated with substantial increases in quantum noise relative to two-energy-bin approaches that simply suppress contrast between fibroglandular and adipose tissues; (2) tungsten and molybdenum anodes can provide nearly equal iodine detectability for two-bin imaging, but molybdenum provides a modest detectability advantage for three-bin imaging provided that all other technique parameters are optimized; (3) reducing pixel sizes from 100 to 50  µ $\mu$ m can reduce detectability by up to 20% due to charge sharing; (4) anatomic noise due to background parenchymal enhancement is estimated to have a substantial impact on lesion visibility, reducing detectability by approximately 30%.

Signal-difference-to-noise comparison of temporal subtraction, kV-switching dual-energy and photon-counting dual-energy x-ray angiography.

BACKGROUND: Dual-energy (DE) x-ray angiography with photon-counting detectors (PCDs) may enable single-exposure DE imaging of coronary vasculature. PURPOSE: To compare the iodine signal-difference-to-noise ratio (SDNR) of single-exposure DE angiography with digital subtraction angiography (DSA) and kV-switching DE angiography for matched patient x-ray exposure. METHODS: In a phantom study, we determined the technique parameters that maximized the iodine SDNR per root entrance air kerma for DSA, kV-switching DE angiography and single-exposure DE angiography. We measured SDNR from images of a phantom consisting of an iodine step-wedge immersed in a water tank of either 20  or 30 cm in thickness. We also imaged a phantom with simulated vessels embedded in background clutter and measured vessel SDNR. For this second phantom, we also applied anti-correlated noise reduction (ACNR) and calculated the resulting iodine SDNR. All images were acquired using a cadmium telluride PCD with two energy bins and analog charge summing for charge sharing suppression. The energy-discrimination capabilities were only used for the single-exposure DE approach. Optimized techniques were compared in terms of SDNR per root air kerma for two levels of x-ray scatter. RESULTS: For the same patient x-ray exposure, the SDNR of single-exposure DE imaging without ACNR was 75% to 85% of that of kV-switching DE imaging (also without ACNR) and DSA, the latter two of which had nearly equal SDNR. The single-exposure DE approach required ∼50% of the tube load of the kV-switching approach to achieve the same SDNR. For matched patient air kermas, the single exposure approach required only ∼25% of the tube load of the kV-switching approach. ACNR increased SDNR by 2.4 and 3.0 for kV-switching and single-exposure DE imaging, respectively. CONCLUSIONS: Photon-counting, single-exposure DE angiography can suppress soft tissues and provide iodine SDNR levels comparable to DSA and kV-switching DE angiography for matched patient radiation exposures. When ACNR is used to reduce DE image noise, the SDNR of single-exposure DE imaging and kV-switching DE imaging exceed that of DSA by more than a factor of two. Compared to kV-switching DE imaging, single-exposure DE imaging requires substantially lower tube loading to achieve the same SDNR.

An experimental framework for assessing the detective quantum efficiency of spectroscopic x-ray detectors.

BACKGROUND: Assessing the performance of spectroscopic x-ray detectors (SXDs) requires measurement of the frequency-dependent detective quantum efficiency (DQE). Analytical expressions of the task-based DQE and task-independent DQE of SXDs have been presented in the literature, but standardizable experimental methods for measuring them have not. The task-based DQE quantifies the efficiency with which an SXD uses the x-ray quanta incident upon it to either quantify or detect a basis material (e.g., soft tissue or bone) of interest. The task-independent DQE is akin to the conventional DQE in that it is independent of the basis material to be detected or quantified. PURPOSE: The purpose of this paper is to develop an experimental framework to present a method for experimental analysis of the DQE of SXDs, including the task-based DQE and task-independent DQE. METHODS: We develop methods to measure the frequency-dependent DQE for task of quantifying or detecting a perturbation in a known basis material. We also develop methods for measuring a task-independent DQE. We show that the task-based DQEs and the task-independent DQE can be measured using a modest extension of the methods prescribed by International Electrotechnical Commission (IEC). Specifically, measuring the task-independent DQE requires measuring the modulation transfer function (MTF) and noise power spectrum (NPS) of each energy-bin image, in addition to the cross NPS between energy-bin images. Measuring the task-based DQEs requires an additional measurement of the transmission fraction through a thin basis-material absorber. We implemented the developed methods using standardized IEC x-ray spectra, aluminum (Al) and polymethyl methacrylyte (PMMA) basis materials, and a cadmium telluride (CdTe) SXD equipped with two energy bins and analog charge summing (ACS) for charge-sharing suppression. We also performed a regression analysis to determine whether or not the task-independent DQE is predictive of the task-based DQEs. RESULTS: Experimental results of the task-based DQEs were consistent with simulation results presented in the literature. In general, and as expected, ACS increased the task-based DQEs and task-independent DQE. This effect was most pronounced for quantification tasks, in some instances yielding a five-fold increase in the DQE. For both spectra, with and without ACS for charge sharing correction, the task-based DQEs were linearly related to the task-independent DQE, as demonstrated by R2 -values ranging from 0.89 to 1.00. CONCLUSIONS: We have extended experimental DQE analysis to SXDs that count photons in multiple energy bins in a single x-ray exposure. The developed framework is an extension of existing IEC methods, and provides a standardized approach to assessing the performance of SXDs.

Xenon-enhanced dual-energy tomosynthesis for functional imaging of respiratory disease-Concept and phantom study.

BACKGROUND: Xenon-enhanced dual-energy (DE) computed tomography (CT) and hyperpolarized noble-gas magnetic resonance imaging (MRI) provide maps of lung ventilation that can be used to detect chronic obstructive pulmonary disease (COPD) early in its development and predict respiratory exacerbations. However, xenon-enhanced DE-CT requires high radiation doses and hyper-polarized noble-gas MRI is expensive and only available at a handful of institutions globally. PURPOSE: To present xenon-enhanced dual-energy tomosynthesis (XeDET) for low-dose, low-cost functional imaging of respiratory disease in an experimental phantom study. METHODS: We propose using digital tomosynthesis to produce Xe-enhanced low-energy (LE) and high-energy (HE) coronal images. DE subtraction of the LE and HE images is used to suppress soft tissues. We used an imaging phantom to investigate image quality in terms of the area under the reciever operating characteristic curve (AUC) for the Non-PreWhitening model observer with an Eye filter and internal noise (NPWEi). The phantom simulated anatomic clutter due to lung parenchyma and attenuation due to soft tissue and lung tissue. Aluminum slats were used to simulate rib structures. A stepwedge consisting of an acrylic casing with sealed cylindrical air-filled cavities was used to simulate ventilation defects with step thicknesses of 0.5, 1, and 2 cm and cylindrical radii of 0.5, 0.75, and 1 cm. The phantom was ventilated with Xe and projection data were acquired using a flat-panel detector, a tube-voltage combination of 60/140 kV with 1.2  mm of copper filtration on the HE spectrum and an angular range of ± 15 ∘ $\pm 15^{\circ}$ in 1° increments. The AUC of a NPWEi observer that has access only to a single coronal slice was calculated from measurements of the three-dimensional noise power spectrum and signal template. The AUC was calculated as a function of ventilation defect thickness and radius for total patient entrance air kermas ranging from 1.42 to 2.84 mGy with and without rib-simulating Al slats. For the AUC analysis, the observer internal noise level was obtained from an ad hoc calibration to a high-dose data set. RESULTS: XeDET was able to suppress parenchyma-simulating clutter in coronal images enabling visualization of the simulated ventilation defects, but the limited angle acquisition resulted in residual clutter due to out-of-plane bone-mimmicking structures. The signal power of the defects increased linearly with defect radius and showed a ten-fold to fifteen-fold increase in signal power when the defect thickness increased from 0.5 to 2 cm. These trends agreed with theoretical predictions. Along the depth dimension, the power of the defects decreased exponentially with distance from the center of the defects with full-width half maxima that varied from 1.85 to 2.85 cm depending on the defect thickness and radius. The AUCs of the 1-cm-radius defect that was 2 cm in thickness ranged from good (0.8-0.9) to excellent (0.9-1.0) over the range of air kermas considered. CONCLUSIONS: Xenon-enhanced DE tomosynthesis has the potential to enable functional imaging of respiratory disease and should be further investigated as a low-cost alternative to MRI-based approaches and a low-dose alternative to CT-based approaches.

Experimental optimization of single-exposure dual-energy angiography with photon-counting x-ray detectors.

BACKGROUND: Photon-counting x-ray detectors may enable single-exposure dual-energy (DE) x-ray angiography. PURPOSE: The purpose of this paper is to experimentally optimize the energy thresholds and tube voltage for single-exposure DE x-ray angiography. METHODS: We optimized single-exposure DE x-ray angiography using the iodine signal-difference-to-noise ratio (SDNR) per root patient air kerma (κ) as a figure of merit. We measured the iodine SDNR by imaging an iodine stepwedge immersed in a water tank with a depth of 30 cm in the direction of x-ray propagation. The stepwedge was imaged using tube voltages ranging from 90 to 150 kV and a cadmium telluride (CdTe) x-ray detector with two energy bins and analog charge summing for charge sharing suppression. The energy threshold that separates the two energy bins was varied from approximately 35 keV to approximately 75% of the maximum energy of the x-ray beam. Curve fitting was used to determine the threshold that maximized SDNR / κ $\mathrm{SDNR}/\sqrt {\kappa }$ . The effect of scatter was determined from measurements of the scatter-to-primary ratios (SPRs) of the low-energy and high-energy images and a semi-empirical model of the relationship between SDNR and SPR. Using the optimal parameters, we imaged a phantom with vessel-simulating structures and background clutter. RESULTS: The optimal energy thresholds increased monotonically from ∼50 to ∼85 keV over the range of tube voltages considered. For tube voltages greater than 90 kV, the optimal energy thresholds consistently allocated approximately two thirds of all detected primary photons to the low energy bin; this ratio was preserved without scatter. Consistent with prior modeling studies, SDNR / κ $\mathrm{SDNR}/\sqrt {\kappa }$ increased monotonically with tube voltage from 90 to 150 kV; SDNR / κ $\mathrm{SDNR}/\sqrt {\kappa }$ at 150 kV was approximately 38% higher than that at 90 kV for an iodine area density of ∼50 mg/cm2 . Scatter reduced SDNR by approximately 25% for SPRs of ∼1 and 0.4 in low-energy and high-energy images, respectively. CONCLUSIONS: Achieving optimal image quality in single-exposure DE angiography with photon-counting x-ray detectors will require high tube voltages (i.e., >130 kV) and, for thick patients, energy thresholds that allocate approximately two thirds of all primary photons to the low-energy image. Future work will compare the image quality of singe-exposure photon-counting and kV-switching approaches to DE x-ray angiography.

Experimental feasibility of xenon-enhanced dual-energy radiography for imaging of lung function.

Chronic obstructive pulmonary disease (COPD) is a leading cause of death worldwide. We experimentally investigated the feasibility of two-dimensional xenon-enhanced dual-energy (XeDE) radiography for imaging of lung function. We optimized image quality under quantum-noise-limited conditions using a chest phantom consisting of a rectangular chamber representing the thoracic volume and PMMA slabs simulating x-ray attenuation by soft tissue. A sealed, air-filled cavity with thin PMMA walls was positioned inside the chamber to simulate a 2 cm thick ventilation defect. The chamber was ventilated with xenon and dual-energy imaging was performed using a diagnostic x-ray tube and a flat-panel detector. The contrast-to-noise ratio of ventilation defects normalized by patient x-ray exposure maximized at a kV-pair of approximately 60/140-kV and when approximately one third of the total exposure was allocated to the HE image. We used the optimized technique to image a second phantom that contained lung-parenchyma-mimicking PMMA clutter, rib-mimicking aluminum slats and an insert that simulated ventilation defects with thicknesses ranging from 0.5 cm to 2 cm and diameters ranging from 1 cm to 2 cm. From the resulting images we computed the area under the receiver operating characteristic curve (AUC) of the non-prewhitening model observer with an eye filter and internal noise. For a xenon concentration of 75%, good AUCs (i.e. 0.8-0.9) to excellent AUCs (i.e. >0.9) were obtained when the defect diameter is greater than 1.3 cm and defect thickness is 1 cm. When the xenon concentration was reduced to 50%, the AUC was ∼0.9 for defects 1.2 cm in diameter and ∼1.5 cm in thickness. Two-dimensional XeDE radiography may therefore enable detection of functional abnormalities associated with early-stage COPD, for which xenon ventilation defects can occupy up to 20% of the lung volume, and should be further developed as a low-cost alternative to MRI-based approaches and a low-dose alternative to CT-based approaches.

Theoretical comparison of energy-resolved and digital-subtraction angiography.

BACKGROUND: X-ray coronary angiography is a sub-optimal vascular imaging technique because it cannot suppress un-enhanced anatomy that may obscure the visualization of coronary artery disease. PURPOSE: The purpose of this paper is to evaluate the theoretical image quality of energy-resolved x-ray angiography (ERA) implemented with spectroscopic x-ray detectors (SXDs), which may overcome limitations of x-ray coronary angiography. METHODS: We modeled the large-area signal-difference-to-noise (SDNR) of contrast-enhanced vasculature in ERA images and compared with that of digital-subtraction angiography (DSA), which served as a gold standard vascular imaging technique. To this end, we used calibrated numerical models of the response of cadmium telluride SXDs including the effects of charge sharing, electronic noise, and energy thresholding. Our models assumed zero scatter, no pulse pile up and small signals such that image contrast is approximately linear in the area density of contrast agents. For DSA, we similarly modeled x-ray detection by cesium iodide energy-integrating detectors using validated numerical models. For ERA, we investigated iodine and gadolinium (Gd) contrast agents, two-material and three-material decompositions, analog charge summing for charge sharing correction, and optimized image quality with respect to the tube voltage and energy thresholds assuming cadmium telluride SXDs with three energy bins. RESULTS: Our analysis reveals that a three-material decomposition using iodine contrast agents will require x-ray exposures that are approximately 400 times those of DSA to achieve the same SDNR as DSA in coronary applications, and is therefore not feasible in a clinical setting. However, three-material decompositions with Gd contrast agents have the potential to provide SDNR that is ∼45% of that of DSA for matched patient air kerma. For two-material decompositions that suppress soft-tissue, ERA has the potential to produce images with SDNR that is 50%-75% of that of DSA for matched patient air kermas but lower levels of tube loading. Achieving these SDNR levels will require the use of analog charge summing for charge sharing correction, which increased SDNR by up to a factor of 1.7 depending on the contrast agent and whether or not a two-material or three-material decomposition was assumed. CONCLUSIONS: We conclude that three-material ERA implemented with Gd contrast agents and two-material ERA implemented with either iodine or Gd contrast agents, should be investigated as alternatives to DSA in situations where motion artifacts preclude the use of DSA, such as in coronary imaging.

The detective quantum efficiency of cadmium telluride photon-counting x-ray detectors in breast imaging applications.

PURPOSE: In breast imaging applications, cadmium telluride (CdTe) photon counting x-ray detectors (PCDs) may reduce radiation dose and enable single-shot multi-energy x-ray imaging. The purpose of this work is to determine the upper limits of the detective quantum efficiency (DQE) of CdTe PCDs for x-ray mammography and to compare them with the published DQEs of energy-integrating detectors (EIDs) and other PCDs. METHODS: We calibrated and validated a Monte Carlo (MC) model of the DQE of CdTe PCDs using an XCounter CdTe PCD. Our model accounted for charge sharing, electronic noise, and charge summation logic. We used a 28 kVp Mo/Mo spectrum hardened by 3.9 cm of Lucite to optimize the detector thickness and energy threshold for pixel sizes of 50, 85, and 100 µ ${{\mu}}$ m with and without inter-pixel charge summation logic. The figure of merit used for optimization was the integral of the DQE, which is equivalent to the detectability index for a delta function task function, which represents a high-frequency task. RESULTS: For an electronic noise level equal to that of the XCounter, the optimal DQE(0) without charge summing was 0.74. Charge summing for charge-sharing correction reduced DQE(0) by 14% due to an increase in electronic noise. Reducing the electronic noise to ∼0.5 keV per pixel in combination with charge summing resulted in DQE(0) ≈ $ \approx $ 0.78 for 85  µ ${{\mu}}$ m pixels, which is approximately equal to that of a-Se and slot-scanning silicon-strip PCDs. At higher spatial frequencies, and for matched pixel sizes, the DQE was inferior to that of a-Se EIDs and superior to that of slot-scanning silicon-strip PCDs in the scan direction but inferior in the slit direction. CONCLUSIONS: (1) CdTe PCDs have the potential to provide a zero-frequency DQE equal to that of a-Se EIDs and slot-scanning silicon-strip PCDs, but this will require electronic noise levels ∼0.5 keV per pixel. (2) At mid-to-high spatial frequencies the DQE of CdTe PCDs may be (a) inferior to that of a-Se EIDs and slot-scanning silicon-strip PCDs in the slit direction, and (b) superior to slot-scanning silicon-strip PCDs in the scan direction.

A detective quantum efficiency for spectroscopic X-ray imaging detectors.

PURPOSE: Spectroscopic X-ray detectors (SXDs) are under development for X-ray imaging applications. Recent efforts to extend the detective quantum efficiency (DQE) to SXDs impose a barrier to experimentation and/or do not provide a task-independent measure of detector performance. The purpose of this article is to define a task-independent DQE for SXDs that can be measured using a modest extension of established DQE-metrology methods. METHODS: We defined a task-independent spectroscopic DQE and performed a simulation study to determine the relationship between the zero-frequency DQE and the ideal-observer signal-to-noise ratio (SNR) of low-frequency soft-tissue, bone, iodine, and gadolinium signals. In our simulations, we used calibrated models of the spatioenergetic response of cadmium telluride (CdTe) and cadmium-zinc-telluride (CdZnTe) SXDs. We also measured the zero-frequency DQE of a CdTe detector with two energy bins and of a CdZnTe detector with up to six energy bins for an RQA9 spectrum and compared with model predictions. RESULTS: The spectroscopic DQE accounts for spectral distortions, energy-bin-dependent spatial resolution, interbin spatial noise correlations, and intrabin spatial noise correlations; it is mathematically equivalent to the squared SNR per unit fluence of the generalized least-squares estimate of the height of an X-ray impulse in a uniform noisy background. The zero-frequency DQE has a strong linear relationship with the ideal-observer SNR of low-frequency soft-tissue, bone, iodine, and gadolinium signals, and can be expressed in terms of the product of the quantum efficiency and a Swank noise factor that accounts for DQE degradation due to, for example, charge sharing (CS) and electronic noise. The spectroscopic Swank noise factor of the CdTe detector was measured to be 0.81 ± 0.04 and 0.83 ± 0.04 with and without anticoincidence logic for CS suppression, respectively. The spectroscopic Swank noise factor of the CdZnTe detector operated with four energy bins was measured to be 0.82 ± 0.02 which is within 5% of the theoretical value. CONCLUSIONS: The spectroscopic DQE defined here is (1) task-independent, (2) can be measured using a modest extension of existing DQE-metrology methods, and (3) is predictive of the ideal-observer SNR of soft-tissue, bone, iodine, and gadolinium signals. For CT applications, the combination of CS and electronic noise in CdZnTe spectroscopic detectors will degrade the zero-frequency DQE by 10 %-20 % depending on the electronic noise level and pixel size.

Theoretical feasibility of dual-energy radiography for structural and functional imaging of chronic obstructive pulmonary disease.

PURPOSE: Chronic obstructive pulmonary disease (COPD) affects ∼200 million people worldwide. We propose two-dimensional (2D) dual-energy (DE) x-ray imaging of lung structure and function for the assessment of COPD, and investigate the resulting image quality theoretically. METHODS: We investigated xenon-enhanced DE (XeDE) radiography for functional imaging of COPD and unenhanced DE radiography for structural imaging of COPD. We modeled the ability of human observers to detect ventilation defects in XeDE images and emphysema in (unenhanced) DE images using the detectability index ( d ' ) as a figure of merit. We accounted for the extent of emphysematous destruction and functional impairment as a function of disease severity, defect/lesion contrast, spatial resolution, x-ray scatter, quantum noise, anatomic noise, and the efficiency of human observers. Whether or not disease was detectable was determined based on a detectability threshold of two. For (unenhanced) DE imaging of emphysema, we compared detectability with that of single-energy (SE) imaging. Models of signal and noise were compared to published data. RESULTS: Models of signal and noise agreed well with published data, and model predictions of the detectability of emphysema by SE radiography were consistent with poor sensitivity (i.e., d ' < 1 ) to mild to moderate COPD but moderate sensitivity (i.e., d ' > 1.5 ) to severe COPD. The detectability of emphysema by DE radiography was greater than that of SE radiography, but did not cross the threshold of detectability for mild to moderate COPD. The detectability index for XeDE imaging exceeded the detectability threshold for mild, moderate, and severe COPD. CONCLUSIONS: Dual-energy radiography may offer modest improvements in the detection of emphysema relative to SE imaging, but will unlikely enable detecting mild and moderate COPD. However, XeDE radiography may enable detection of functional abnormalities associated with mild, moderate and severe COPD at x-ray exposures typical of those used in conventional chest radiography, thus warranting further investigation as a low-dose, low-cost alternative to CT- and MRI-based approaches for functional imaging of COPD.

Frequency-dependent signal and noise in spectroscopic x-ray imaging.

PURPOSE: We present a new framework for theoretical analysis of the noise power spectrum (NPS) of photon-counting x-ray detectors, including simple photon-counting detectors (SPCDs) and spectroscopic x-ray detectors (SXDs), the latter of which use multiple energy thresholds to discriminate photon energies. METHODS: We show that the NPS of SPCDs and SXDs, including spatio-energetic noise correlations, is determined by the joint probability density function (PDF) of deposited photon energies, which describes the probability of recording two photons of two different energies in two different elements following a single-photon interaction. We present an analytic expression for this joint PDF and calculate the presampling and digital NPS of CdTe SPCDs and SXDs. We calibrate our charge sharing model using the energy response of a cadmium zinc telluride (CZT) spectroscopic x-ray detector and compare theoretical results with Monte Carlo simulations. RESULTS: Our analysis shows that charge sharing increases pixel signal-to-noise ratio (SNR), but degrades the zero-frequency signal-to-noise performance of SPCDs and SXDs. In all cases considered, this degradation was greater than 10%. Comparing the presampling NPS with the sampled NPS showed that degradation in zero-frequency performance is due to zero-frequency noise aliasing induced by charge sharing. CONCLUSIONS: Noise performance, including spatial and energy correlations between elements and energy bins, are described by the joint PDF of deposited energies which provides a method of determining the photon-counting NPS, including noise-aliasing effects and spatio-energetic effects in spectral imaging. Our approach enables separating noise due to x-ray interactions from that associated with sampling, consistent with cascaded systems analysis of energy-integrating systems. Our methods can be incorporated into task-based assessment of image quality for the design and optimization of spectroscopic x-ray detectors.

Cascaded systems analysis of anatomic noise in digital mammography and dual-energy digital mammography.

In x-ray based imaging of the breast, contrast between fibroglandular (Fg) tissue and adipose (Ad) tissue is a source of anatomic noise. The goal of this work was to validate by simulation and experiment a mathematical framework for modelling the Fg component of anatomic noise in digital mammograpy (DM) and dual-energy (DE) DM. Our mathematical framework unifies and generalizes existing approaches. We compared mathematical predictions directly with empirical measurements of the anatomic noise power spectrum of the CIRS BR3D structured breast phantom using two clinical mammography systems and four beam qualities. Our simulation and experimental results showed agreement with mathematical predictions. As a demonstration of utility, we used our mathematical framework in a theoretical spectral optimization of DM for the task of detecting breast masses. Our theoretical optimization showed that the optimal tube voltage for DM may be higher than that based on predictions that do not account for anatomic noise, in agreement with recent theoretical findings. Additionally, our theoretical optimization predicts that filtering tungsten-anode x-ray spectra with rhodium has little influence on lesion detectability, in contrast with previous findings. The mathematical methods validated in this work can be incorporated easily into cascaded systems analysis of breast imaging systems and will be useful when optimizating novel techniques for x-ray-based imaging of the breast.

Cascaded systems analysis of charge sharing in cadmium telluride photon-counting x-ray detectors.

PURPOSE: Single-photon-counting (SPC) and spectroscopic x-ray detectors are under development in academic and industry laboratories for medical imaging applications. The spatial resolution of SPC and spectroscopic x-ray detectors is an important design criterion. The purpose of this article was to extend the cascaded systems approach to include a description of the spatial resolution of SPC and spectroscopic x-ray imaging detectors. METHODS: A cascaded systems approach was used to model reabsorption of characteristic x rays, Coulomb repulsion, and diffusion in SPC and spectroscopic x-ray detectors. In addition to reabsorption, diffusion, and Coulomb repulsion, the model accounted for x-ray conversion to electron-hole (e-h) pairs, integration of e-h pairs in detector elements, electronic noise, and energy thresholding. The probability density function (PDF) describing the number of e-h pairs was propagated through each stage of the model and was used to derive new theoretical expressions for the large-area gain and modulation transfer function (MTF) of CdTe SPC x-ray detectors, and the energy bin sensitivity functions and MTFs of CdTe spectroscopic detectors. Theoretical predictions were compared with the results of MATLAB-based Monte Carlo (MC) simulations and published data. Comparisons were also made with the MTF of energy-integrating systems. RESULTS: Under general radiographic conditions, reabsorption, diffusion, and Coulomb repulsion together artificially inflate count rates by 20% to 50%. For thicker converters (e.g. 1000 µm) and larger detector elements (e.g. 500 µm pixel pitch) these processes result in modest inflation (i.e. ∼10%) in apparent count rates. Our theoretical and MC analyses predict that SPC MTFs will be degraded relative to those of energy-integrating systems for fluoroscopic, general radiographic, and CT imaging conditions. In most cases, this degradation is modest (i.e., ∼10% at the Nyquist frequency). However, for thicker converters, the SPC MTF can be degraded by up to 25% at the Nyquist frequency relative to EI systems. Additionally, unlike EI systems, the MTF of spectroscopic systems is strongly dependent on photon energy, which results in energy-bin-dependent spatial resolution in spectroscopic systems. CONCLUSIONS: The PDF-transfer approach to modeling signal transfer through SPC and spectroscopic x-ray imaging systems provides a framework for understanding system performance. Application of this approach demonstrated that charge sharing artificially inflates the SPC image signal and degrades the MTF of SPC and spectroscopic systems relative to energy-integrating systems. These results further motivate the need for anticharge-sharing circuits to mitigate the effects of charge sharing on SPC and spectroscopic x-ray image quality.

Deadtime effects in quantification of 177Lu activity for radionuclide therapy.

BACKGROUND: The aim of this study was to investigate the deadtime (DT) effects that are present in 177Lu images acquired after radionuclide therapy injection, assess differences in DT based on the full spectrum and the photopeak-only measurements, and design a method to correct for the deadtime losses. A Siemens SymbiaT SPECT/CT camera with a medium energy collimator was used. A 295-mL bottle was placed off-center inside a large cylinder filled with water, and 177Lu activity was sequentially added up to a maximum of 9.12 GBq. The true count rates vs. observed count rates were plotted and fitted to the DT paralyzable model. This analysis was performed using counts recorded in the full spectrum and in other energy windows. The DT correction factors were calculated using the percentage difference between the true and the observed count rates. RESULTS: The DT values of 5.99 ± 0.02 µs, 4.60 ± 0.052 µs, and 0.19 ± 0.18 µs were obtained for the primary photons (PP) recorded in the 113- and 208-keV photopeaks and for the full spectrum, respectively. For the investigated range of count rates, the DT correction factors of up to 23% were observed for PP corresponding to the 113-keV photopeak, while for the 208-keV photopeak values of up to 20% were obtained. These values were almost three times higher than the deadtime correction factors derived from the full spectrum. CONCLUSIONS: The paralyzable model showed to be appropriate for the investigated range of counts, which were five to six times higher than those observed in the patient post-therapy imaging. Our results suggest that the deadtime corrections should be based on count losses in the scatter-corrected photopeak window and not on the deadtime determined from the full spectrum. Finally, a general procedure that can be followed to correct patient images for deadtime is presented.

Accuracy of 177Lu activity quantification in SPECT imaging: a phantom study.

BACKGROUND: The aim of the study is to assess accuracy of activity quantification of 177Lu studies performed according to recommendations provided by the committee on Medical Internal Radiation Dose (MIRD) pamphlets 23 and 26. The performances of two scatter correction and three segmentation methods were compared. Additionally, the accuracy of tomographic and planar methods for determination of the camera normalization factor (CNF) was evaluated. Eight phantoms containing inserts of different sizes and shapes placed in air, water, and radioactive background were scanned using a Siemens SymbiaT SPECT/CT camera. Planar and tomographic scans with 177Lu sources were used to measure CNF. Images were reconstructed with our SPEQToR software using resolution recovery, attenuation, and two scatter correction methods (analytical photon distribution interpolated (APDI) and triple energy window (TEW)). Segmentation was performed using a fixed threshold method for both air and cold water scans. For hot water experiments three segmentation methods were compared as folows: a 40% fixed threshold, segmentation based on CT images, and our iterative adaptive dual thresholding (IADT). Quantification error, defined as the percent difference between experimental and true activities, was evaluated. RESULTS: Quantification error for scans in air was better for TEW scatter correction (<6%) than for APDI (<11%). This trend was reversed for scans in water (<10% for APDI and <14% for TEW). For hot water, the best results (<18% for small objects and <5% for objects >100 ml) were obtained when APDI and IADT were used for scatter correction and segmentation, respectively. Additionally, we showed that planar acquisitions with scatter correction and tomographic scans provide similar CNF values. This is an important finding because planar acquisitions are easier to perform than tomographic scans. TEW and APDI resulted in similar quantification errors with APDI showing a small advantage for objects placed in medium with non-uniform density. CONCLUSIONS: Following the MIRD recommendations for data acquisition and reconstruction resulted in accurate activity quantification (errors <5% for large objects). However, techniques for better organ/tumor segmentation must still be developed.

Accuracy, reproducibility, and uncertainty analysis of thyroid-probe-based activity measurements for determination of dose calibrator settings.

PURPOSE: In the nuclear medicine department, the activity of radiopharmaceuticals is measured using dose calibrators (DCs) prior to patient injection. The DC consists of an ionization chamber that measures current generated by ionizing radiation (emitted from the radiotracer). In order to obtain an activity reading, the current is converted into units of activity by applying an appropriate calibration factor (also referred to as DC dial setting). Accurate determination of DC dial settings is crucial to ensure that patients receive the appropriate dose in diagnostic scans or radionuclide therapies. The goals of this study were (1) to describe a practical method to experimentally determine dose calibrator settings using a thyroid-probe (TP) and (2) to investigate the accuracy, reproducibility, and uncertainties of the method. As an illustration, the TP method was applied to determine 188Re dial settings for two dose calibrator models: Atomlab 100plus and Capintec CRC-55tR. METHODS: Using the TP to determine dose calibrator settings involved three measurements. First, the energy-dependent efficiency of the TP was determined from energy spectra measurements of two calibration sources (152Eu and 22Na). Second, the gamma emissions from the investigated isotope (188Re) were measured using the TP and its activity was determined using γ-ray spectroscopy methods. Ambient background, scatter, and source-geometry corrections were applied during the efficiency and activity determination steps. Third, the TP-based 188Re activity was used to determine the dose calibrator settings following the calibration curve method [B. E. Zimmerman et al., J. Nucl. Med. 40, 1508-1516 (1999)]. The interobserver reproducibility of TP measurements was determined by the coefficient of variation (COV) and uncertainties associated to each step of the measuring process were estimated. The accuracy of activity measurements using the proposed method was evaluated by comparing the TP activity estimates of 99mTc, 188Re, 131I, and 57Co samples to high purity Ge (HPGe) γ-ray spectroscopy measurements. RESULTS: The experimental 188Re dial settings determined with the TP were 76.5 ± 4.8 and 646 ± 43 for Atomlab 100plus and Capintec CRC-55tR, respectively. In the case of Atomlab 100plus, the TP-based dial settings improved the accuracy of 188Re activity measurements (confirmed by HPGe measurements) as compared to manufacturer-recommended settings. For Capintec CRC-55tR, the TP-based settings were in agreement with previous results [B. E. Zimmerman et al., J. Nucl. Med. 40, 1508-1516 (1999)] which demonstrated that manufacturer-recommended settings overestimate 188Re activity by more than 20%. The largest source of uncertainty in the experimentally determined dial settings was due to the application of a geometry correction factor, followed by the uncertainty of the scatter-corrected photopeak counts and the uncertainty of the TP efficiency calibration experiment. When using the most intense photopeak of the sample's emissions, the TP method yielded accurate (within 5% errors) and reproducible (COV = 2%) measurements of sample's activity. The relative uncertainties associated with such measurements ranged from 6% to 8% (expanded uncertainty at 95% confidence interval, k = 2). CONCLUSIONS: Accurate determination/verification of dose calibrator dial settings can be performed using a thyroid-probe in the nuclear medicine department.

Detective quantum efficiency of photon-counting x-ray detectors.

PURPOSE: Single-photon-counting (SPC) x-ray imaging has the potential to improve image quality and enable novel energy-dependent imaging methods. Similar to conventional detectors, optimizing image SPC quality will require systems that produce the highest possible detective quantum efficiency (DQE). This paper builds on the cascaded-systems analysis (CSA) framework to develop a comprehensive description of the DQE of SPC detectors that implement adaptive binning. METHODS: The DQE of SPC systems can be described using the CSA approach by propagating the probability density function (PDF) of the number of image-forming quanta through simple quantum processes. New relationships are developed to describe PDF transfer through serial and parallel cascades to accommodate scatter reabsorption. Results are applied to hypothetical silicon and selenium-based flat-panel SPC detectors including the effects of reabsorption of characteristic/scatter photons from photoelectric and Compton interactions, stochastic conversion of x-ray energy to secondary quanta, depth-dependent charge collection, and electronic noise. Results are compared with a Monte Carlo study. RESULTS: Depth-dependent collection efficiency can result in substantial broadening of photopeaks that in turn may result in reduced DQE at lower x-ray energies (20-45 keV). Double-counting interaction events caused by reabsorption of characteristic/scatter photons may result in falsely inflated image signal-to-noise ratio and potential overestimation of the DQE. CONCLUSIONS: The CSA approach is extended to describe signal and noise propagation through photoelectric and Compton interactions in SPC detectors, including the effects of escape and reabsorption of emission/scatter photons. High-performance SPC systems can be achieved but only for certain combinations of secondary conversion gain, depth-dependent collection efficiency, electronic noise, and reabsorption characteristics.

Analytic model of energy-absorption response functions in compound X-ray detector materials.

The absorbed energy distribution (AED) in X-ray imaging detectors is an important factor that affects both energy resolution and image quality through the Swank factor and detective quantum efficiency. In the diagnostic energy range (20-140 keV), escape of characteristic photons following photoelectric absorption and Compton scatter photons are primary sources of absorbed-energy dispersion in X-ray detectors. In this paper, we describe the development of an analytic model of the AED in compound X-ray detector materials, based on the cascaded-systems approach, that includes the effects of escape and reabsorption of characteristic and Compton-scatter photons. We derive analytic expressions for both semi-infinite slab and pixel geometries and validate our approach by Monte Carlo simulations. The analytic model provides the energy-dependent X-ray response function of arbitrary compound materials without time-consuming Monte Carlo simulations. We believe this model will be useful for correcting spectral distortion artifacts commonly observed in photon-counting applications and optimal design and development of novel X-ray detectors.

The detective quantum efficiency of photon-counting x-ray detectors using cascaded-systems analyses.

PURPOSE: Single-photon counting (SPC) x-ray imaging has the potential to improve image quality and enable new advanced energy-dependent methods. The purpose of this study is to extend cascaded-systems analyses (CSA) to the description of image quality and the detective quantum efficiency (DQE) of SPC systems. METHODS: Point-process theory is used to develop a method of propagating the mean signal and Wiener noise-power spectrum through a thresholding stage (required to identify x-ray interaction events). The new transfer relationships are used to describe the zero-frequency DQE of a hypothetical SPC detector including the effects of stochastic conversion of incident photons to secondary quanta, secondary quantum sinks, additive noise, and threshold level. Theoretical results are compared with Monte Carlo calculations assuming the same detector model. RESULTS: Under certain conditions, the CSA approach can be applied to SPC systems with the additional requirement of propagating the probability density function describing the total number of image-forming quanta through each stage of a cascaded model. Theoretical results including DQE show excellent agreement with Monte Carlo calculations under all conditions considered. CONCLUSIONS: Application of the CSA method shows that false counts due to additive electronic noise results in both a nonlinear image signal and increased image noise. There is a window of allowable threshold values to achieve a high DQE that depends on conversion gain, secondary quantum sinks, and additive noise.