Spectral information content of Compton scattering events in silicon photon counting detectors.

BACKGROUND: Silicon (Si) is a possible sensor material for photon counting detectors (PCDs). A major drawback of Si is that roughly two-thirds of x-ray interactions in the diagnostic energy range are Compton scattering. Because Compton scattering is an energy-insensitive process, it is commonly assumed that Compton events retain little spectral information. PURPOSE: To quantify how much information can be recovered from Compton scattering events in models of Si PCDs. METHODS: We built a simplified model of Si interactions including two interaction mechanisms: photoelectric effect and Compton scattering. We considered three different binning options that represent strategies for handling Compton events: in Compton censoring, all events under 38 keV (the maximum energy possible from Compton scattering for a 120 keV incident photon) were discarded; in Compton counting, all events between 1 and 38 keV were placed into a single bin; in Compton binning, all events were placed into energy bins of uniform width. These were compared to the ideal detector, which always recorded the correct energy (i.e., 100% photoelectric effect). Every photon was assumed to interact once and only once with Si, and the energy bin width was 5 keV. In the primary analysis, the Si detector was irradiated with a 120 kV spectrum filtered by 30 cm of water, with 99.5% of the arriving spectrum above 38 keV so that there was good separation between photoelectric effect and Compton scattering, and the figures of merit were the Cramér-Rao lower bound (CRLB) of the variance of iodine and water basis material decomposition images, as well as the CRLB of virtual monoenergetic images (i.e., linear combinations of material images) that maximize iodine CNR or water CNR. We also constructed a local linear estimator that attains the CRLB. In secondary analyses, we applied other sources of spectral distortion: (1) a nonzero minimum energy threshold; (2) coarser, 10 keV energy bins; and (3) a model of charge sharing. RESULTS: With our chosen spectrum, 67% of the interactions were Compton scattering. Consistent with this, the material decomposition variance for the Compton censoring model, averaged over both basis materials, was 258% greater than the ideal detector. If Compton events carried no spectral information, the Compton counting model would show similar variance. Instead, its basis material variance was 103% greater than the ideal detector, implying that Compton counts indeed carry significant spectral information. The Compton binning model had a basis material variance 60% greater than the ideal detector. The Compton binning model was not affected by a 5 keV minimum energy threshold, but the variance increased from 60% to 107% when charge sharing was included and to 78% with coarser energy bins. For optimized CNR images, the average variance was 149%, 12%, and 10% higher than the ideal detector for the Compton censoring, counting, and binning models, reinforcing the hypothesis that Compton counts are useful for detection tasks and that precise energy assignments are not necessary. CONCLUSIONS: Substantial spectral information remains after Compton scattering events in silicon PCDs.

Improving model-data mismatch for photon-counting detector model using global and local model parameters.

BACKGROUND: An energy-discriminating capability of a photon counting detector (PCD) can provide many clinical advantages, but several factors, such as charge sharing (CS) and pulse pileup (PP), degrade the capability by distorting the measured x-ray spectrum. To fully exploit the merits of PCDs, it is important to characterize the output of PCDs. Previously proposed PCD output models showed decent agreement with physical PCDs; however, there were still scopes to be improved: a global model-data mismatch and pixel-to-pixel variations. PURPOSES: In this study, we improve a PCD model by using count-rate-dependent model parameters to address the issues and evaluate agreement against physical PCDs. METHODS: The proposed model is based on the cascaded model, and we made model parameters condition-dependent and pixel-specific to deal with the global model-data mismatch and the pixel-to-pixel variation. The parameters are determined by a procedure for model parameter estimation with data acquired from different thicknesses of water or aluminum at different x-ray tube currents. To analyze the effects of having proposed model parameters, we compared three setups of our model: a model with default parameters, a model with global parameters, and a model with global-and-local parameters. For experimental validation, we used CdZnTe-based PCDs, and assessed the performance of the models by calculating the mean absolute percentage errors (MAPEs) between the model outputs and the actual measurements from low count-rates to high count-rates, which have deadtime losses of up to 24%. RESULTS: The outputs of the proposed model visually matched well with the PCD measurements for all test data. For the test data, the MAPEs averaged over all the bins were 49.2-51.1% for a model with default parameters, 8.0-9.8% for a model with the global parameters, and 1.2-2.7% for a model with the global-and-local parameters. CONCLUSION: The proposed model can estimate the outputs of physical PCDs with high accuracy from low to high count-rates. We expect that our model will be actively utilized in applications where the pixel-by-pixel accuracy of a PCD model is important.

Direct energy binning for photon counting detectors: Simulation study.

BACKGROUND: Photon counting detectors (PCDs) for x-ray computed tomography (CT) face spectral distortion from pulse pileup and charge sharing. The photon counting scheme used by many PCDs is threshold-subtract (TS) with pulse height analysis (PHA), where each counter counts up-crossing events when pulses exceed an energy threshold. PCD data are not Poisson-distributed due to charge sharing and pulse pileup, but the counting statistics have never been studied yet. PURPOSE: The objectives of this study were (1) to propose a modified photon counting scheme, direct energy binning (DB), that is expected to be robust against pulse pileup; (2) to assess the performance of DB compared to TS; and (3) to evaluate its counting statistics. METHODS: With DB scheme, counter k starts a timer upon an up-crossing event of energy threshold k, and adds a count only if the next higher energy threshold (k+1) was not crossed within a short time window (hence, the pulse peak belongs to the energy bin k). We used Monte Carlo (MC) simulation and assessed count-rate curves and count-rate-dependent spectral imaging task performance for conventional CT imaging as well as water thickness estimation, water-bone material decomposition, and K-edge imaging with tungsten as the K-edge material. We also assessed count-rate-dependent measurement statistics such as expectation, variance, and covariance of total counts as well as energy bin outputs. The agreement with counting statistics models was also evaluated. RESULTS: The DB scheme improved the count-rate curve, that is, mean measured counts as a function of input count-rate, and peaked with 59% higher count-rate capability than the TS scheme (3.5 × 108 counts per second (cps)/mm2 versus 2.3 × 108  cps/mm2 ). The Cramér-Rao lower bounds (CRLB) of the variance of basis line integrals estimation for DB was better than those for TS by 2% for the conventional CT imaging, 30% for water-bone material decomposition, and 32% for K-edge imaging at 1000 mA (at 7.3 × 107  cps/sub-pixel after charge sharing). When count-rates were lower, PCD data statistics were dominated by charge sharing: the variance of total counts and lower energy bins was larger than the mean counts; the covariance of bin data was positive and non-zero. When count-rates were higher, PCD data statistics were dominated by pulse pileup: the variance of data was lower than the mean; the covariance of bin data was negative. The transition between the two regimes occurred smoothly, and pulse pileup dominated the statistics ≥400 mA (when the count-rate after charge sharing was 2.9 × 107  cps/sub-pixel and the probability of count-loss for DB was 37%). Both DB and TS had good agreement with Yu-Fessler's models of total counts; however, DB had a better agreement with Wang's variance and covariance models for energy bin data than TS did. CONCLUSIONS: The proposed DB scheme had several advantages over TS. At low to moderate flux, DB could improve the resilience of PCDs to pulse pileup. Counting statistics deviated from the Poisson distribution due to charge sharing for lower count-rate conditions and pulse pileup for higher count-rate conditions.

Musculoskeletal CT Imaging: State-of-the-Art Advancements and Future Directions.

CT is one of the most widely used modalities for musculoskeletal imaging. Recent advancements in the field include the introduction of four-dimensional CT, which captures a CT image during motion; cone-beam CT, which uses flat-panel detectors to capture the lower extremities in weight-bearing mode; and dual-energy CT, which operates at two different x-ray potentials to improve the contrast resolution to facilitate the assessment of tissue material compositions such as tophaceous gout deposits and bone marrow edema. Most recently, photon-counting CT (PCCT) has been introduced. PCCT is a technique that uses photon-counting detectors to produce an image with higher spatial and contrast resolution than conventional multidetector CT systems. In addition, postprocessing techniques such as three-dimensional printing and cinematic rendering have used CT data to improve the generation of both physical and digital anatomic models. Last, advancements in the application of artificial intelligence to CT imaging have enabled the automatic evaluation of musculoskeletal pathologies. In this review, the authors discuss the current state of the above CT technologies, their respective advantages and disadvantages, and their projected future directions for various musculoskeletal applications.

Inclusion of a GaAs detector model in the Photon Counting Toolkit software for the study of breast imaging systems.

We present an upgraded version of the Photon Counting Toolkit (PcTK), a freely available by request MATLAB tool for the simulation of semiconductor-based photon counting detectors (PCD), which has been extended and validated to account for gallium arsenide (GaAs)-based PCD(s). The modified PcTK version was validated by performing simulations and acquiring experimental data for three different cases. The LAMBDA 60 K module planar detector (X-Spectrum GmbH, Germany) based on the Medipix3 ASIC technology was used in all cases. This detector has a 500-µm thick GaAs sensor and a 256 × 256-pixel array with 55 µm pixel size. The first validation was a comparison between simulated and measured spectra from a 109Cd radionuclide source. In the second validation study, experimental measurements and simulations of mammography spectra were generated to observe the performance of the GaAs version of the PcTK with polychromatic radiation used in conventional x-ray imaging systems. The third validation study used single event analysis to validate the spatio-energetic model of the extended PcTK version. Overall, the software provided a good agreement between simulated and experimental data, validating the accuracy of the GaAs model. The software could be an attractive tool for accurate simulation of breast imaging modalities relying on photon counting detectors and therefore could assist in their characterization and optimization.

Theoretical comparison and optimization of cadmium telluride and gallium arsenide photon-counting detectors for contrast-enhanced spectral mammography.

Purpose: Most photon-counting detectors (PCDs) being developed use cadmium telluride (CdTe), which has nonoptimal characteristic x-ray emission with energies in the range used for breast imaging. New PCD using a gallium arsenide (GaAs) has been developed. Since GaAs has characteristic x-rays lower in energy than those of CdTe, it is hypothesized that this new PCD might be beneficial for spectral x-ray breast imaging. Approach: We performed simulations using realistic mammography x-ray spectra with both CdTe and GaAs PCDs. Five different experiments were conducted, each comparing the performance of CdTe and GaAs: (1) sensitivity of iodine quantification to charge cloud size and electronic noise, (2) effect of photon spectrum on iodine quantification, (3) effect of varying the number of energy bins, (4) a dose analysis to assess any possible dose reduction from using either detector, and (5) spectral performance of ideal CdTe and GaAs PCDs. For each study, 3 sets of 5000 noise realizations were used to calculate the Cramer-Rao lower bound (CRLB) of iodine quantification. Results: For all spectra studied, GaAs gave a lower CRLB for iodine quantification, with 10 of the 12 spectra showing a statistically significant difference ( p ≤ 0.05 ). The photon energy spectrum that optimized iodine detection for both detector materials was the 40 kVp beam with 2-mm Al filtration, which produced CRLBs of 0.282 cm 2 and 0.257 cm 2 for CdTe and GaAs, respectively, when using five energy bins. Conclusion: GaAs is a promising detector material for contrast-enhanced spectral mammography that offers better spectral performance than CdTe.

Model-based pulse pileup and charge sharing compensation for photon counting detectors: A simulation study.

PURPOSE: We aim at developing a model-based algorithm that compensates for the effect of both pulse pileup (PP) and charge sharing (CS) and evaluates the performance using computer simulations. METHODS: The proposed PCP algorithm for PP and CS compensation uses cascaded models for CS and PP we previously developed, maximizes Poisson log-likelihood, and uses an efficient three-step exhaustive search. For comparison, we also developed an LCP algorithm that combines models for a loss of counts (LCs) and CS. Two types of computer simulations, slab- and computed tomography (CT)-based, were performed to assess the performance of both PCP and LCP with 200 and 800 mA, (300 µm)2  × 1.6-mm cadmium telluride detector, and a dead-time of 23 ns. A slab-based assessment used a pair of adipose and iodine with different thicknesses, attenuated X-rays, and assessed the bias and noise of the outputs from one detector pixel; a CT-based assessment simulated a chest/cardiac scan and a head-and-neck scan using 3D phantom and noisy cone-beam projections. RESULTS: With the slab simulation, the PCP had little or no biases when the expected counts were sufficiently large, even though a probability of count loss (PCL) due to dead-time loss or PP was as high as 0.8. In contrast, the LCP had significant biases (>±2 cm of adipose) when the PCL was higher than 0.15. Biases were present with both PCP and LCP when the expected counts were less than 10-120 per datum, which was attributed to the fact that the maximum likelihood did not approach the asymptote. The noise of PCP was within 8% from the Cramér-Rao lower bounds for most cases when no significant bias was present. The two CT studies essentially agreed with the slab simulation study. PCP had little or no biases in the estimated basis line integrals, reconstructed basis density maps, and synthesized monoenergetic CT images. But the LCP had significant biases in basis line integrals when X-ray beams passed through lungs and near the body and neck contours, where the PCLs were above 0.15. As a consequence, basis density maps and monoenergetic CT images obtained by LCP had biases throughout the imaged space. CONCLUSION: We have developed the PCP algorithm that uses the PP-CS model. When the expected counts are more than 10-120 per datum, the PCP algorithm is statistically efficient and successfully compensates for the effect of the spectral distortion due to both PP and CS providing little or no biases in basis line integrals, basis density maps, and monoenergetic CT images regardless of count-rates. In contrast, the LCP algorithm, which models an LC due to pileup, produces severe biases when incident count-rates are high and the PCL is 0.15 or higher.

Assessment of multi-energy inter-pixel coincidence counters for photon-counting detectors at the presence of charge sharing and pulse pileup: A simulation study.

PURPOSE: Spectral distortion due to charge sharing (CS) and pulse pileup (PP) in photon-counting detectors (PCDs) degrades the quality of PCD data. We recently proposed multi-energy inter-pixel coincidence counters (MEICC) that provided spectral cross-talk information related to CS. When PP was absent, the normalized Cramér-Rao lower bounds (nCRLBs) of 225-µm pixel PCDs with MEICC was comparable to those of 450-µm pixel PCD without MEICC. The aim of this study was to assess the performance of PCDs with MEICC in the presence of both CS and PP using computer simulations. METHODS: An in-house Monte Carlo program was modified to incorporate the following four temporal elements: (1) A pulse shape with a pulse duration of 20 ns, (2) delays of up to 10 ns in anode arrival times when photons were incident on pixel boundaries, (3) offsets proportional to a vertical separation between the primary and secondary charge clouds at the rate of ±4 ns per ±100 µm, and (4) a stochastic fluctuation of anode arrival times for all of the charge clouds with a standard deviation of 2 ns. We assessed the performance of five PCDs, (a)-(f), for three spectral tasks, (A)-(C): (a) The conventional PCD, (b) a PCD with MEICC, (c) a PCD with one coincidence counter (1CC), (d) a PCD with a 3 × 3 analog charge summing scheme (ACS), and (e) a PCD with a 3 × 3 digital count summing scheme (DCS); (A) conventional CT imaging with water (i.e., linear attenuation coefficient maps), (B) water-bone material decomposition, and (C) K-edge imaging with tungsten. The tube current was changed from 1 mA to 1000 mA and the nCRLB was assessed. RESULTS: The recorded count rate curves were fitted by the non-paralyzable detection model with the effective deadtime parameter. The best fit was achieved by 25.8 ns for the conventional PCD, 18.6 ns for MEICC and 1CC, 140.5 ns for ACS, and 209.0 ns for DCS. The nCRLBs were strongly dependent on count rates. MEICC provided the best nCRLBs for all of the imaging tasks over the count rate range investigated except for a few conditions such as K-edge imaging at 1 mA. PP decreased the merit of MEICC over the conventional PCD in addressing CS. Nonetheless, MEICC consistently provided better nCRLBs than the conventional PCD did. The nCRLBs of MEICC were in the range of 49-58% of those of the conventional PCD for K-edge imaging, 45-76% for water-bone material decomposition, and 81-88% for the conventional CT imaging (i.e., linear attenuation coefficient maps). ACS provided better nCRLBs than the conventional PCD did only when the effect of PP was minor (e.g., when the counting efficiency of the conventional PCD was higher than 0.95 with the tube current of up to 100 mA). CONCLUSION: Besides a few cases, MEICC provides the best nCRLBs for all of the tasks at all of the count rates. ACS and DCS provide better nCRLBs than the conventional PCD does only when count rates are very low.

Assessment of Multienergy Interpixel Coincidence Counters (MEICC) for Charge Sharing Correction or Compensation for Photon Counting Detectors With Boxcar Signals.

Recently, multi-energy inter-pixel coincidence counter (MEICC) has been proposed for charge sharing correction and compensation for photon counting detectors (PCDs), which uses energy-dependent coincidence counters to record coincident events between multiple energy windows of a pixel-of-interest and those of neighboring pixels. A Monte Carlo (MC) simulation study was performed to assess the performance of MEICC; however, the performance might have been overestimated in a previous study. The charge sharing increases the number of photons recorded at a PCD pixel at the expense of the spatial resolution, and therefore, when spatially uniform flat-field x-ray signals are used, it gives PCDs with charge sharing more signals than a PCD without charge sharing. In this paper, we propose to use spatially modulated boxcar signals for evaluating the performances for high spatial frequency tasks because they provide consistent signals regardless of the presence of absence of charge sharing. The flat-field signals must be used for low spatial frequency tasks. We assessed the performances of MEICC and other PCDs with both flat-field signals and boxcar signals, with optimal threshold energies, and with two different pixel sizes. As it is expected, normalized Cramér-Rao lower bounds (nCRLBs) measured with the boxcar signals were worse than those with flat-field signals in general. The nCRLBs of MEICC with 225-µm pixel were close to the current 450-µm PCD. We studied a combination of flat-field signals and N×N super-pixels, where the output of N×N pixels were added, using an MC simulation and a simple charge sharing counting model. The study showed that charge sharing had two opposing impacts on the conventional CT imaging-a negative impact with double-counting among N×N pixels and a positive impact with single-counting spill-in and spill-out across the super-pixel boundary-and the positive impact diminished with increasing N. A use of large N×N super-pixels such as N≥25 was suggested to approximate the zero-frequency detection quantum efficiency of PCD with charge sharing.

Three-dimensional regions-of-interest-based intra-operative four-dimensional soft tissue perfusion imaging using a standard x-ray system with no gantry rotation: A simulation study for a proof of concept.

PURPOSE: Many interventional procedures aim at changing soft tissue perfusion or blood flow. One problem at present is that soft tissue perfusion and its changes cannot be assessed in an interventional suite because cone-beam computed tomography is too slow (it takes 4-10 s per volume scan). In order to address the problem, we propose a novel method called IPEN for Intra-operative four-dimensional soft tissue PErfusion using a standard x-ray system with No gantry rotation. METHODS: IPEN uses two input datasets: (a) the contours and locations of three-dimensional regions-of-interest (ROIs) such as arteries and sub-sections of cancerous lesions, and (b) a series of x-ray projection data obtained from an intra-arterial contrast injection to contrast enhancement to wash-out. IPEN then estimates a time-enhancement curve (TEC) for each ROI directly from projections without reconstructing cross-sectional images by maximizing the agreement between synthesized and measured projections with a temporal roughness penalty. When path lengths through ROIs are known for each x-ray beam, the ROI-specific enhancement can be accurately estimated from projections. Computer simulations are performed to assess the performance of the IPEN algorithm. Intra-arterial contrast-enhanced liver scans over 25 s were simulated using XCAT phantom version 2.0 with heterogeneous tissue textures and cancerous lesions. The following four sub-studies were performed: (a) The accuracy of the estimated TECs with overlapped lesions was evaluated at various noise (dose) levels with either homogeneous or heterogeneous lesion enhancement patterns; (b) the accuracy of IPEN with inaccurate ROI contours was assessed; (c) we investigated how overlapping ROIs and noise in projections affected the accuracy of the IPEN algorithm; and (d) the accuracy of the perfusion indices was assessed. RESULTS: The TECs estimated by IPEN were sufficiently accurate at a reference dose level with the root-mean-square deviation (RMSD) of 0.0027 ± 0.0001 cm-1 or 13 ± 1 Hounsfield unit (mean ± standard deviation) for the homogeneous lesion enhancement and 0.0032 ± 0.0005 cm-1 for the heterogeneous enhancement (N = 20 each). The accuracy was degraded with decreasing doses: The RMSD with homogeneous enhancement was 0.0220 ± 0.0003 cm-1 for 20% of the reference dose level. Performing 3 × 3 pixel averaging on projection data improved the RMSDs to 0.0051 ± 0.0002 cm-1 for 20% dose. When the ROI contours were inaccurate, smaller ROI contours resulted in positive biases in TECs, whereas larger ROI contours produced negative biases. The bias remained small, within ± 0.0070 cm-1 , when the Sorenson-Dice coefficients (SDCs) were larger than 0.81. The RMSD of the TEC estimation was strongly associated with the condition of the problem, which can be empirically quantified using the condition number of a matrix A z that maps a vector of ROI enhancement values z to projection data and a weighted variance of projection data: a linear correlation coefficient (R) was 0.794 (P < 0.001). The perfusion index values computed from the estimated TECs agreed well with the true values (R ≥ 0.985, P < 0.0001). CONCLUSION: The IPEN algorithm can estimate ROI-specific TECs with high accuracy especially when 3 × 3 pixel averaging is applied, even when lesion enhancement is heterogeneous, or ROI contours are inaccurate but the SDC is at least 0.81.

Multi-energy inter-pixel coincidence counters for charge sharing correction and compensation in photon counting detectors.

PURPOSE: Smaller pixel sizes of x-ray photon counting detectors (PCDs) are advantageous for count rate capabilities but disadvantageous for charge sharing. With charge sharing, the energy of an x-ray photon may be split and one photon may produce two or more counts at adjacent pixels, both at lower energies than the incident energy. This "double-counting" increases noise variance and degrades the spectral response. Overall, it has a significantly negative impact on the performance of PCD-based computed tomography (CT). Charge sharing is induced by the detection physics and occurs regardless of count rates; thus, it is impossible to avoid. We propose in this paper a method that has a potential to address both noise and bias added by charge sharing. METHODS: We propose applying a multi-energy inter-pixel coincidence counter (MEICC) technique, which uses energy-dependent coincidence counters, keeps the book of charge sharing events during data acquisition, and provides the exact number of charge sharing occurrences, which can be used to either correct or compensate for them after the acquisition is completed. MEICC does not interfere with the primary counting process; therefore, PCDs with MEICC will remain as fast as those without MEICC. MEICC can be implemented using current electronics technology because its inter-pixel coincidence counters used to handle digital data are rather simple. We evaluated Cramér-Rao lower bound (CRLB) of PCDs with and without MEICC using a Monte Carlo simulation. RESULTS: When the number of energy windows was four or larger and eight neighboring pixels were used, the CRLBs of 225-µm PCD with MEICC normalized by those of the current PCD with the same number of windows were 0.361-0.383 for water density images of two basis functions, which was only 5.7-16.4% worse than those of a PCD without charge sharing (which were at 0.329-0.358). In contrast, the normalized CRLBs of the PCD with one coincidence counter were 0.466-0.499, which were 37.3-45.6% worse than the PCD without charge sharing. The use of eight neighboring pixels provided ~10% better CRLB values than four neighboring pixels for MEICC. With four energy windows, decreasing the number of coincidence counters from 16 to 9 only slightly increased the CRLB from 0.255 to 0.269 (which corresponded to as little as a 5.5% change). The normalized CRLBs of MEICC for K-edge imaging (gold) were 0.295-0.426, while those of the one coincidence counter were 0.926-0.959 and the ideal PCDs were 0.126-0.146. CONCLUSIONS: The proposed MEICC provides spectral information that can be used to address charge sharing problems in PCDs and is expected to satisfy the requirements for clinical x-ray CT. MEICC is very effective, especially for K-edge imaging, which requires accurate spectral information.

Spatio-energetic cross-talk in photon counting detectors: N × N binning and sub-pixel masking.

PURPOSE: Smaller pixel sizes of x-ray photon counting detectors (PCDs) benefit count rate capabilities but increase cross-talk and "double-counting" between neighboring PCD pixels. When an x-ray photon produces multiple (n) counts at neighboring (sub-)pixels and they are added during post-acquisition N × N binning process, the variance of the final PCD output-pixel will be larger than its mean. In the meantime, anti-scatter grids are placed at the pixel boundaries in most of x-ray CT systems and will decrease cross-talk between sub-pixels because the grids mask sub-pixels underneath them, block the primary x-rays, and increase the separation distance between active sub-pixels. The aim of this paper was, first, to study the PCD statistics with various N × N binning schemes and three different masking methods in the presence of cross-talks, and second, to assess one of the most fundamental performances of x-ray CT: soft tissue contrast visibility. METHODS: We used a PCD cross-talk model (Photon counting toolkit, PcTK) and produced cross-talk data between 3 × 3 neighboring sub-pixels and calculated the mean, variance, and covariance of output-pixels with each of N × N binning scheme [4 × 4 binning, 2 × 2 binning, and 1 × 1 binning (i.e., no binning)] and three different sub-pixel masking methods (no mask, 1-D mask, and 2-D mask). We then set up simulation to evaluate the soft tissue contrast visibility. X-rays of 120 kVp were attenuated by 10-40 cm-thick water, with the right side of PCDs having 0.5 cm thicker water than the left side. A pair of output-pixels across the left-right boundary were used to assess the sensitivity index (SI or d'), which typically ranges 0-1 and is a generalized signal-to-noise ratio and a statistics used in signal detection theory. RESULTS: Binning a larger number of sub-pixels resulted in larger mean counts and larger variance-to-mean ratio when the lower threshold of the energy window was lower than the half of the incident energy. Mean counts are in the order of no mask (the largest), 1-D mask, and 2-D mask but the difference in variance-to-mean ratio was small. For a given sub-pixel size and masking method, binning more sub-pixels degraded the normalized SI values but the difference between 4 × 4 binning and 1 × 1 binning was typically less than 0.06. 1-D mask provided better normalized SI values than no mask and 2-D mask for side-by-side case and the improvements were larger with fewer binnings, although the difference was less than 0.10. 2-D mask was the best for embedded case. The normalized SI values of combined binning, sub-pixel size, and masking were in the order of 1 × 1 (900 µm)2 binning, 2 × 2 (450 µm)2 binning, and 4 × 4 (225 µm)2 binning for a given masking method but the difference between each of them were typically 0.02-0.05. CONCLUSION: We have evaluated the effect of double-counting between PCD sub-pixels with various binning and masking methods. SI values were better with fewer number of binning and larger sub-pixels. The difference among various binning and masking methods, however, was typically less than 0.06, which might result in a dose penalty of 13% if the CT system were linear.

Image quality characteristics for virtual monoenergetic images using dual-layer spectral detector CT: Comparison with conventional tube-voltage images.

PURPOSE: To investigate the image quality characteristics for virtual monoenergetic images compared with conventional tube-voltage image with dual-layer spectral CT (DLCT). METHODS: Helical scans were performed using a first-generation DLCT scanner, two different sizes of acrylic cylindrical phantoms, and a Catphan phantom. Three different iodine concentrations were inserted into the phantom center. The single-tube voltage for obtaining virtual monoenergetic images was set to 120 or 140 kVp. Conventional 120- and 140-kVp images and virtual monoenergetic images (40-200-keV images) were reconstructed from slice thicknesses of 1.0 mm. The CT number and image noise were measured for each iodine concentration and water on the 120-kVp images and virtual monoenergetic images. The noise power spectrum (NPS) was also calculated. RESULTS: The iodine CT numbers for the iodinated enhancing materials were similar regardless of phantom size and acquisition method. Compared with the iodine CT numbers of the conventional 120-kVp images, those for the monoenergetic 40-, 50-, and 60-keV images increased by approximately 3.0-, 1.9-, and 1.3-fold, respectively. The image noise values for each virtual monoenergetic image were similar (for example, 24.6 HU at 40 keV and 23.3 HU at 200 keV obtained at 120 kVp and 30-cm phantom size). The NPS curves of the 70-keV and 120-kVp images for a 1.0-mm slice thickness over the entire frequency range were similar. CONCLUSION: Virtual monoenergetic images represent stable image noise over the entire energy spectrum and improved the contrast-to-noise ratio than conventional tube voltage using the dual-layer spectral detector CT.

Spatio-energetic cross-talk in photon counting detectors: Numerical detector model (PcTK) and workflow for CT image quality assessment.

PURPOSE: The interpixel cross-talk of energy-sensitive photon counting x-ray detectors (PCDs) has been studied and an analytical model (version 2.1) has been developed for double-counting between neighboring pixels due to charge sharing and K-shell fluorescence x-ray emission followed by its reabsorption (Taguchi K, et al., Medical Physics 2016;43(12):6386-6404). While the model version 2.1 simulated the spectral degradation well, it had the following problems that has been found to be significant recently: (1) The spectrum is inaccurate with smaller pixel sizes; (2) the charge cloud size must be smaller than the pixel size; (3) the model underestimates the spectrum/counts for 10-40 keV; and (4) the model version 2.1 cannot handlen-tuple-counting withn > 2 (i.e., triple-counting or higher). These problems are inherent to the design of the model version 2.1; therefore, we developed a new model and addressed these problems in this study. METHODS: We propose a new PCD cross-talk model (version 3.2; Pc TK for "photon counting toolkit") that is based on a completely different design concept from the previous version. It uses a numerical approach and starts with a 2-D model of charge sharing (as opposed to an analytical approach and a 1-D model with version 2.1) and addresses all of the four problems. The model takes the following factors into account: (1) shift-variant electron density of the charge cloud (Gaussian-distributed), (2) detection efficiency, (3) interactions between photons and PCDs via photoelectric effect, and (4) electronic noise. Correlated noisy PCD data can be generated using either a multivariate normal random number generator or a Poisson random number generator. The effect of the two parameters, the effective charge cloud diameter (d0 ) and pixel size (dpix ), was studied and results were compared with Monte Carlo simulations and the previous model version 2.1. Finally, a script for the workflow for CT image quality assessment has been developed, which started with a few material density images, generated material-specific sinogram (line integrals) data, noisy PCD data with spectral distortion using the model version 3.2, and reconstructed PCD- CT images for four energy windows. RESULTS: The model version 3.2 addressed all of the four problems listed above. The spectra withdpix  = 56-113 µm agreed with that of Medipix3 detector withdpix  = 55-110 µm without charge summing mode qualitatively. The counts for 10-40 keV were larger than the previous model (version 2.1) and agreed with MC simulations very well (root-mean-square difference values with model version 3.2 were decreased to 16%-67% of the values with version 2.1). There were many non-zero off-diagonal elements withn-tuple-counting withn > 2 in the normalized covariance matrix of 3 × 3 neighboring pixels. Reconstructed images showed biases and artifacts attributed to the spectral distortion due to the charge sharing and fluorescence x rays. CONCLUSION: We have developed a new PCD model for spatio-energetic cross-talk and correlation between PCD pixels. The workflow demonstrated the utility of the model for general or task-specific image quality assessments for the PCD- CT.Note: The program (Pc TK) and the workflow scripts have been made available to academic researchers. Interested readers should visit the website (pctk.jhu.edu) or contact the corresponding author.

"X-Map 2.0" for Edema Signal Enhancement for Acute Ischemic Stroke Using Non-Contrast-Enhanced Dual-Energy Computed Tomography.

OBJECTIVES: A novel imaging technique ("X-map") has been developed to identify acute ischemic lesions for stroke patients using non-contrast-enhanced dual-energy computed tomography (NE-DE-CT). Using the 3-material decomposition technique, the original X-map ("X-map 1.0") eliminates fat and bone from the images, suppresses the gray matter (GM)-white matter (WM) tissue contrast, and makes signals of edema induced by severe ischemia easier to detect. The aim of this study was to address the following 2 problems with the X-map 1.0: (1) biases in CT numbers (or artifacts) near the skull of NE-DE-CT images and (2) large intrapatient and interpatient variations in X-map 1.0 values. MATERIALS AND METHODS: We improved both an iterative beam-hardening correction (iBHC) method and the X-map algorithm. The new iBHC (iBHC2) modeled x-ray physics more accurately. The new X-map ("X-map 2.0") estimated regional GM values-thus, maximizing the ability to suppress the GM-WM contrast, make edema signals quantitative, and enhance the edema signals that denote an increased water density for each pixel. We performed a retrospective study of 11 patients (3 men, 8 women; mean age, 76.3 years; range, 68-90 years) who presented to the emergency department with symptoms of acute stroke. Images were reconstructed with the old iBHC (iBHC1) and the iBHC2, and biases in CT numbers near the skull were measured. Both X-map 2.0 maps and X-map 1.0 maps were computed from iBHC2 images, both with and without a material decomposition-based edema signal enhancement (ESE) process. X-map values were measured at 5 to 9 locations on GM without infarct per patient; the mean value was calculated for each patient (we call it the patient-mean X-map value) and subtracted from the measured X-map values to generate zero-mean X-map values. The standard deviation of the patient-mean X-map values over multiple patients denotes the interpatient variation; the standard deviation over multiple zero-mean X-map values denotes the intrapatient variation. The Levene F test was performed to assess the difference in the standard deviations with different algorithms. Using 5 patient data who had diffusion weighted imaging (DWI) within 2 hours of NE-DE-CT, mean values at and near ischemic lesions were measured at 7 to 14 locations per patient with X-map images, CT images (low kV and high kV), and DWI images. The Pearson correlation coefficient was calculated between a normalized increase in DWI signals and either X-map or CT. RESULTS: The bias in CT numbers was lower with iBHC2 than with iBHC1 in both high- and low-kV images (2.5 ± 2.0 HU [95% confidence interval (CI), 1.3-3.8 HU] for iBHC2 vs 6.9 ± 2.3 HU [95% CI, 5.4-8.3 HU] for iBHC1 with high-kV images, P < 0.01; 1.5 ± 3.6 HU [95% CI, -0.8 to 3.7 HU] vs 12.8 ± 3.3 HU [95% CI, 10.7-14.8 HU] with low-kV images, P < 0.01). The interpatient variation was smaller with X-map 2.0 than with X-map 1.0, both with and without ESE (4.3 [95% CI, 3.0-7.6] for X-map 2.0 vs 19.0 [95% CI, 13.3-22.4] for X-map 1.0, both with ESE, P < 0.01; 3.0 [95% CI, 2.1-5.3] vs 12.0 [95% CI, 8.4-21.0] without ESE, P < 0.01). The intrapatient variation was also smaller with X-map 2.0 than with X-map 1.0 (6.2 [95% CI, 5.3-7.3] vs 8.5 [95% CI, 7.3-10.1] with ESE, P = 0.0122; 4.1 [95% CI, 3.6-4.9] vs 6.3 [95% CI, 5.5-7.6] without ESE, P < 0.01). The best 3 correlation coefficients (R) with DWI signals were -0.733 (95% CI, -0.845 to -0.560, P < 0.001) for X-map 2.0 with ESE, -0.642 (95% CI, -0.787 to -0.429, P < 0.001) for high-kV CT, and -0.609 (95% CI, -0.766 to -0.384, P < 0.001) for X-map 1.0 with ESE. CONCLUSION: Both of the 2 problems outlined in the objectives have been addressed by improving both iBHC and X-map algorithm. The iBHC2 improved the bias in CT numbers and the visibility of GM-WM contrast throughout the brain space. The combination of iBHC2 and X-map 2.0 with ESE decreased both intrapatient and interpatient variations of edema signals significantly and had a strong correlation with DWI signals in terms of the strength of edema signals.

Updated recommendation on molecular-targeted therapy for metastatic renal cell cancer.

Molecular-targeted therapy was recommended for the systemic therapy of renal cell cancer (RCC) in the RCC guidelines, but these guidelines do not address the order of administration of the multiple presently available agents. There are several aspects that remain unknown regarding the optimal administration order and combination of molecular-targeted drugs. Until the optimal treatment sequence is determined by clinical trials, treatment individualization is required for each patient based on patient and disease characteristics. We herein investigate 12 cases of RCC patients who received axitinib. Axitinib was used as the first-line drug in 4 cases, second-line in 5 cases, third-line in 1 case and as a fourth-line drug in 2 cases. Partial response (PR) was observed in 4 cases (30%) and stable disease in 4 cases (30%) during axitinib treatment, with an overall response rate of 60%. The duration of PR ranged from 6 to 19 months. Based on our cases, axitinib exhibited reasonable therapeutic efficacy as first- as well as second-line treatment. However, more cases are required to draw firm conclusions.

Vectors through a cross-sectional image (VCI): A visualization method for four-dimensional motion analysis for cardiac computed tomography.

BACKGROUND: Cardiac computed tomography (CT) has the potential for fully four-dimensional (4D for 3D plus time) motion analysis of the heart. We aimed at developing a method for assessment and presentation of the 4D motion for multi-phase, contrast-enhanced cardiac CT data sets and demonstrating its clinical applicability. METHODS: Four patients with normal cardiac function, old myocardial infarction (OMI), takotsubo cardiomyopathy, and hypertrophic cardiomyopathy (HCM) underwent contrast-enhanced cardiac CT for one heartbeat using a 320-row CT scanner with no tube current modulation. CT images for 10 cardiac phases (with a 10%-increment of the R-R interval) were reconstructed with the isotropic effective resolution of (0.5 mm)3 An image-based motion-estimation (iME) algorithm, developed previously, has been used to estimate a time series of 3D cardiac motion, from the end-systole to the other nine phases. The iME uses down-sampled images with a resolution of (1.0 mm)3 deforms the end-systole images non-rigidly to match images at other phases. Once the agreement is maximized, iME outputs a 3D motion vector defined for each voxel for each phase, that smoothly changes over voxels and phases. The proposed visualization method, which is called "vectors through a cross-sectional image (VCI)," presents 3D vectors from the end-diastole to the end-systole as arrows with an end-diastole CT slice. We performed visual assessment of the VCI with calculated the mean vector lengths to evaluate regional left ventricular (LV) contraction. RESULTS: The VCI images showed the magnitude and direction of systolic 3D vectors, including the through-plane motion, and successfully visualized the relations of LV wall segments and abnormal regional wall motion. Decreased regional motion and asymmetric motion due to hypokinetic infarct segment, takotsubo cardiomyopathy, and hyper trophic cardiomyopathy was clearly observed. It was easy to appreciate the relation of the abnormal regional wall motion to the affected LV wall segments. The mean vector lengths of the affected segments with pathologies were clearly smaller than the other unaffected segments (1.2-1.7 mm versus 2.5-4.7 mm). CONCLUSIONS: VCI images could capture the magnitude and direction of through-plane motion and show the relations of LV wall segments and abnormal wall motion.

Estimation of Basis Line-Integrals in a Spectral Distortion-Modeled Photon Counting Detector Using Low-Rank Approximation-Based X-Ray Transmittance Modeling: K-Edge Imaging Application.

Photon counting detectors (PCDs) provide multiple energy-dependent measurements for estimating basis line-integrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, and so on. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth X-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model X-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the X-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: estimating the x-ray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.

Motion estimation for cardiac functional analysis using two x-ray computed tomography scans.

PURPOSE: This work concerns computed tomography (CT)-based cardiac functional analysis (CFA) with a reduced radiation dose. As CT-CFA requires images over the entire heartbeat, the scans are often performed at 10-20% of the tube current settings that are typically used for coronary CT angiography. A large image noise then degrades the accuracy of motion estimation. Moreover, even if the scan was performed during the sinus rhythm, the cardiac motion observed in CT images may not be cyclic with patients with atrial fibrillation. In this study, we propose to use two CT scan data, one for CT angiography at a quiescent phase at a standard dose and the other for CFA over the entire heart beat at a lower dose. METHODS: We have made the following four modifications to an image-based cardiac motion estimation method we have previously developed for a full-dose retrospectively gated coronary CT angiography: (a) a full-dose prospectively gated coronary CT angiography image acquired at the least motion phase was used as the reference image; (b) a three-dimensional median filter was applied to lower-dose retrospectively gated cardiac images acquired at 20 phases over one heartbeat in order to reduce image noise; (c) the strength of the temporal regularization term was made adaptive; and (d) a one-dimensional temporal filter was applied to the estimated motion vector field in order to decrease jaggy motion patterns. We describe the conventional method iME1 and the proposed method iME2 in this article. Five observers assessed the accuracy of the estimated motion vector field of iME2 and iME1 using a 4-point scale. The observers repeated the assessment with data presented in a new random order 1 week after the first assessment session. RESULTS: The study confirmed that the proposed iME2 was robust against the mismatch of noise levels, contrast enhancement levels, and shapes of the chambers. There was a statistically significant difference between iME2 and iME1 (accuracy score, 2.08 ± 0.81 versus 2.77 ± 0.98, P < 0.01) and the improvement by the score of + 0.69 seemed clinically relevant. Inter-observer concordance was good: The inter-class correlation coefficient was 0.63 and Kendall's rank correlation coefficients were in the range of 0.41-0.67 (P < 0.01), respectively. Intra-observer reproducibility between sessions was good with the inter-class correlation coefficient of 0.76. CONCLUSION: We have proposed iME2 method for CT-CFA with two CT scans. The observer study verified the robustness and accuracy of iME2 method and its improved performance over iME1 method.

Improved Estimation of Coronary Plaque and Luminal Attenuation Using a Vendor-specific Model-based Iterative Reconstruction Algorithm in Contrast-enhanced CT Coronary Angiography.

RATIONALE AND OBJECTIVES: To investigate the stabilities of plaque attenuation and coronary lumen for different plaque types, stenotic degrees, lumen densities, and reconstruction methods using coronary vessel phantoms and the visualization of coronary plaques in clinical patients through coronary computed tomography (CT) angiography. MATERIALS AND METHODS: We performed 320-detector volume scanning of vessel tubes with stenosis and a tube without stenosis using three types of plaque CT numbers. The stenotic degrees were 50% and 75%. Images were reconstructed with filtered back projection (FBP) and two types of iterative reconstructions (AIDR3D and FIRST [forward-projected model-based iterative reconstruction solution]), with stenotic CT number of approximately 40, 80, and 150 HU (Hounsfield unit), respectively. In each case, the tubing of the coronary vessel was filled with diluted contrast material and distilled water to reach the target lumen CT numbers of approximately 350 HU and 450 HU, and 0 HU, respectively. Peak lumen and plaque CT numbers were measured to calculate the lumen-plaque contrast. In addition, we retrospectively evaluated the image quality with regard to coronary arterial lumen and the plaque in 10 clinical patients on a 4-point scale. RESULTS: At 50% stenosis, the plaque CT number with contrast enhancement increased for FBP and AIDR3D, and the difference in the plaque CT number with and without contrast enhancement was 15-44 HU for FBP and 10-31 HU for AIDR3D. However, the plaque CT number for FIRST had a smaller variation and the difference with and without contrast enhancement was -12 to 8 HU. The visual evaluation score for the vessel lumen was 2.8 ± 0.6, 3.5 ± 0.5, and 3.7 ± 0.5 for FBP, AIDR3D, and FIRST, respectively. CONCLUSIONS: The FIRST method controls the increase in plaque density and the lumen-plaque contrast. Consequently, it improves the visualization of coronary plaques in coronary CT angiography.