**Implementation of a piecewise-linear dynamic attenuator**

P. Shunhavanich, N. R. Bennett, S. S. Hsieh, N. J. Pelc

Journal of Medical Imaging, vol. 6, no. 2, pp. 023502, 2019

**Abstract**

A dynamic prepatient attenuator can modulate flux in a computed tomography (CT) system along both fan and view angles for reduced dose, scatter, and required detector dynamic range. Reducing the dynamic range requirement is crucial for photon counting detectors. One approach, the piecewise-linear attenuator (Hsieh and Pelc, *Med Phys* 2013), has shown promising results both in simulations and an initial prototype. Multiple wedges, each covering a different fan angle range, are moved in the axial direction to change thickness seen in an axial slice. We report on an implementation of a filter with precision components and a control algorithm targeted for a tabletop system. Algorithms for optimizing wedge position and mA modulation and for correcting bowtie-specific beam-hardening are proposed. In experiments, the error between expected and observed bowtie transmission was ∼2 % on average and ∼7 % at maximum for a chest phantom. Within object boundaries, the observed flux dynamic ranges of 42 for a chest and 25 for an abdomen were achieved, corresponding to a reduction factor of 5 and 11 from the object scans without the bowtie. With beam hardening correction, the CT number in soft tissue regions was improved by 79 HU and deviated by 7 HU on average from clinical scanner CT images. The implemented piecewise-linear attenuator is able to dynamically adjust its thickness with high precision to achieve flexible flux control.

View details for DOI 10.1117/1.JMI.6.2.023502

**Noise reduction in photon-counting CT using frequency-dependent optimal weighting**

M. Persson, N. J. Pelc

15th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, vol. 11072, pp. 110721R, 2019

**Abstract**

Spectral computed tomography (CT) allows optimizing image quality by combining the data in several energy channels with optimal weighting factors. In an improvement of this technique, the weighting factors are made dependent on spatial frequency, and previous work has shown that this can improve detectability for a simple detector model. In this work, we investigate the achievable detectability improvement from frequency-dependent weighting for realistic models of photon-counting detectors. We use a Monte-Carlo based simulation model to obtain point-spread functions and autocovariances for two detector models with 0.5 × 0.5 mm^{2} pixels, one CdTe-based with five energy bins and one silicon-based with eight energy bins. We generated noise-only images for two different energy weighting schemes: one where optimal weights were selected individually for each spatial frequency, and one where the weights optimal for zero frequency were applied to all frequencies. The modulation transfer function was set equal in both schemes. Results show that frequency-based weighting can decrease noise variance by 11 % for Si and by 38 % for CdTe, for an edge-enhancing MTF, demonstrating that optimal frequency-dependent weighting has the capability of reducing noise in high-resolution CT images.

View details for DOI 10.1117/12.2534911

**Image-domain insertion of spatially correlated, locally varying noise in CT images**

S. E. Divel, N. J. Pelc

SPIE Medical Imaging 2019: Physics of Medical Imaging , vol. 10948, pp. 1094821, 2019

**Abstract**

Noise simulation methods for computed tomography (CT) scans are powerful tools for assessing image quality at a range of doses without compromising patient care. Current state of the art methods to simulate lower-dose images from standard-dose images insert Poisson or Gaussian noise in the raw projection data; however, these methods are not always feasible. The objective of this work was to develop an efficient tool to insert realistic, spatially correlated, locally varying noise to CT images in the image-domain utilizing information from the image to estimate the local noise power spectrum (NPS) and variance map. In this approach, normally distributed noise is filtered using the inverse Fourier transform of the square root of the estimated NPS to generate noise with the appropriate spatial correlation. The noise is element-wise multiplied by the standard deviation map to produce locally varying noise and is added to the noiseless or high-dose image. Results comparing the insertion of noise in the projection-domain versus the proposed insertion of noise in the image-domain demonstrate excellent agreement. While this image-domain method will never replace projection-domain methods, it shows promise as an alternative for tasks where projection-domain methods are not practical, such as the case for conducting large-scale studies utilizing hundreds of noise realizations or when the raw data is not available.

View details for DOI 10.1117/12.2512453

**Simulation model for evaluating energy-resolving photon-counting CT detectors based on generalized linear-systems framework**

M. Persson, N. J. Pelc

SPIE Medical Imaging 2019: Physics of Medical Imaging , vol. 10948, pp. 10948V, 2019

**Abstract**

Photon counting detectors are interesting candidates for next-generation clinical computed tomography scanners, promising improved contrast-to-noise ratio, spatial resolution and energy information compared to conventional energy-integrating detectors. Most attention is focused on cadmium telluride (CdTe) (or CZT) detectors, but silicon (Si) has been proposed as an alternative. We present detector simulation models fitted to published spectral response data for CdTe and Si, and use linear-systems theory to evaluate the spatial-frequency dependent DQE for lesion quantification and detection. Our fitted spectral response is consistent with Gaussian charge clouds with σ = 20.5 µm independent of energy for CdTe, and σ = 17 µm at 60 keV with an energy dependence of E^{0.54} for Si. For a silicon strip detector with 0.5 × 0.5 mm^{2} pixels separated by a 1D grid of 20 µm tungsten foils, the zero-frequency DQE for iodine detection is 0.43 for 30 mm detector absorption length and 0.46 for 60 mm detector absorption length. For iodine quantification in a water-iodine decomposition, the DQE is 0.26 for 30 mm and 0.27 for 60 mm Si. Compared to this detector, the DQE of a 1.6 mm thick CdTe detector with 0.225 mm pixels and two energy bins is 11-36% higher for water and iodine detection but 28-51% lower for material quantification. The predicted performance of Si is competitive with CdTe, suggesting that further consideration is warranted.

View details for DOI 10.1117/12.2512593

**Fluid‐filled dynamic bowtie filter: Description and comparison with other modulators**

P. Shunhavanich, S. S. Hsieh, N. J. Pelc

Medical physics, vol. 46, no. 1, pp. 127-139, 2019

**Abstract**

*Purpose*: A dynamic bowtie filter can modulate flux along both fan and view angles for reduced patient dose, scatter, and required photon flux, which is especially important for photon counting detectors (PCDs). Among the proposed dynamic bowtie designs, the piecewise‐linear attenuator (Hsieh and Pelc, Med Phys. 2013;40:031910) offers more flexibility than conventional filters, but relies on analog positioning of a limited number of wedges. In this work, we study our previously proposed dynamic attenuator design, the fluid‐filled dynamic bowtie filter (FDBF) that has digital control. Specifically, we use computer simulations to study fluence modulation, reconstructed image noise, and radiation dose and to compare it to other attenuators. FDBF is an array of small channels each of which, if it can be filled with dense fluid or emptied quickly, has a binary effect on the flux. The cumulative attenuation from each channel along the x‐ray path contributes to the FDBF total attenuation.

*Methods*: An algorithm is proposed for selecting which FDBF channels should be filled. Two optimization metrics are considered: minimizing the maximum‐count‐rate for PCDs and minimizing peak‐variance for energy‐integrating detectors (EIDs) at fixed radiation dose (for optimizing dose efficiency). Using simulated chest, abdomen, and shoulder data, the performance is compared with a conventional bowtie and a piecewise‐linear attenuator. For minimizing peak‐variance, a perfect‐attenuator (hypothetical filter capable of adjusting the fluence of each ray individually) and flat‐variance attenuator are also included in the comparison. Two possible fluids, solutions of zinc bromide and gadolinium chloride, were tested.

*Results*: To obtain the same SNR as routine clinical protocols, the proposed FDBF reduces the maximum‐count‐rate (across projection data, averaged over the test objects) of PCDs to 1.2 Mcps/mm^{2}, which is 55.8 and 3.3 times lower than the max‐count‐rate of the conventional bowtie and the piecewise‐linear bowtie, respectively. (Averaged across objects for FDBF, the max‐count‐rate without object and FDBF is 2063.5 Mcps/mm^{2}, and the max‐count‐rate with object without FDBF is 749.8 Mcps/mm^{2}.) Moreover, for the peak‐variance analysis, the FDBF can reduce entrance‐energy‐fluence (sum of energy incident on objects, used as a surrogate for dose) to 34% of the entrance‐energy‐fluence from the conventional filter on average while achieving the same peak noise level. Its entrance‐energy‐fluence reduction performance is only 7% worse than the perfect‐attenuator on average and is 13% better than the piecewise‐linear filter for chest and shoulder. Furthermore, the noise‐map in reconstructed image domain from the FDBF is more uniform than the piecewise‐linear filter, with 3 times less variation across the object. For the dose reduction task, the zinc bromide solution performed slightly poorer than stainless steel but was better than the gadolinium chloride solution.

*Conclusions*: The FDBF allows finer control over flux distribution compared to piecewise‐linear and conventional bowtie filters. It can reduce the required maximum‐count‐rate for PCDs to a level achievable by current detector designs and offers a high dose reduction factor.

View details for DOI 10.1002/mp.13272

**A framework for performance characterization of energy‐resolving photon‐counting detectors**

M. Persson, P. L. Rajbhandary, N. J. Pelc

Medical Physics , vol. 45, no. 11, pp. 4897-4915, 2018

**Abstract**

*Purpose*: Photon‐counting, energy‐resolving detectors are subject to intense research interest, and there is a need for a general framework for performance assessment of these detectors. The commonly used linear‐systems theory framework, which measures detector performance in terms of noise‐equivalent quanta (NEQ) and detective quantum efficiency (DQE) is widely used for characterizing conventional x‐ray detectors but does not take energy‐resolving capabilities into account. The purpose of this work is to extend this framework to encompass energy‐resolving photon‐counting detectors and elucidate how the imperfect energy response and other imperfections in real‐world detectors affect imaging performance, both for feature detection and for material quantification tasks.

*Method*: We generalize NEQ and DQE to matrix‐valued quantities as functions of spatial frequency, and show how these matrices can be calculated from simple Monte Carlo simulations. To demonstrate how the new metrics can be interpreted, we compute them for simplified models of fluorescence and Compton scatter in a photon‐counting detector and for a Monte Carlo model of a CdTe detector with 0.5 x 0.5 mm^{2} pixels.

*Results*: Our results show that the ideal‐linear‐observer performance for any detection or material quantification task can be calculated from the proposed generalized NEQ and DQE metrics. We also demonstrate that the proposed NEQ metric is closely related to a generalized version of the Cramér‐Rao lower bound commonly used for assessing material quantification performance. Off‐diagonal elements in the NEQ and DQE matrices are shown to be related to loss of energy information due to imperfect energy resolution. The Monte Carlo model of the CdTe detector predicts a zero‐frequency dose efficiency relative to an ideal detector of 0.86 and 0.65 for detecting water and bone, respectively. When the task instead is to quantify these materials, the corresponding values are 0.34 for water and 0.26 for bone.

*Conclusions*: We have developed a framework for assessing the performance of photon‐counting energy‐resolving detectors and shown that the matrix‐valued NEQ and DQE metrics contain sufficient information for calculating the dose efficiency for both detection and quantification tasks, the task having any spatial and energy dependence. This framework will be beneficial for the development and optimization of photon‐counting x‐ray detectors.

View details for DOI 10.1002/mp.13172

**Photon-counting CT: technical principles and clinical prospects**

M. J. Willemink, M. Persson, A. Pourmorteza, N. J. Pelc, D. Fleischmann

Radiology, vol. 289, no. 2, pp. 293-312, 2018

**Abstract**

Photon-counting CT is an emerging technology with the potential to dramatically change clinical CT. Photon-counting CT uses new energy-resolving x-ray detectors, with mechanisms that differ substantially from those of conventional energy-integrating detectors. Photon-counting CT detectors count the number of incoming photons and measure photon energy. This technique results in higher contrast-to-noise ratio, improved spatial resolution, and optimized spectral imaging. Photon-counting CT can reduce radiation exposure, reconstruct images at a higher resolution, correct beam-hardening artifacts, optimize the use of contrast agents, and create opportunities for quantitative imaging relative to current CT technology. In this review, the authors will explain the technical principles of photon-counting CT in nonmathematical terms for radiologists and clinicians. Following a general overview of the current status of photon-counting CT, they will explain potential clinical applications of this technology.

View details for DOI 10.1148/radiol.2018172656

**Modeling charge transport in photon-counting detectors**

Y. Fang, C. Xu, Y. Yao, N. J. Pelc, M. Danielsson, A. Badano

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 899, pp. 115-121, 2018

**Abstract**

The purpose of this study is to review and compare simulation methods for describing the transport of charge clouds in silicon based semiconductor detectors and investigate the effects on energy spectrum for silicon based photon-counting strip detectors. Charge clouds and detailed carrier transport are simulated and compared using two different approaches including analytical and Monte Carlo schema. The results of the simulations are evaluated using pulse-height spectra (PHS) for a silicon strip detector with edge on geometry at two energies (25 and 75 keV) at various X-ray absorption locations relative to the pixel boundary and detector depth. The findings confirm carrier diffusion plays a large role in the charge sharing effect in photon counting detectors, in particular when the photon is absorbed near the pixel boundary far away from the pixel electrode. The results are further compared in terms of the double-counting probability for X-ray photons absorbed near the pixel boundary as a function of the threshold energy. Monte Carlo and analytical models show reasonable agreement (2% relative error in swank factor) for charge sharing effects for a silicon strip detector with edge-on geometry. For 25 keV mono-energetic photons absorbed at 5 µm from the pixel boundary, the theoretical threshold energy at 10% double-counting probability based on charge sharing is 5.5, 8.5 and 9.2 keV for absorption depths of 50, 250 and 450 µm from the electrode, respectively. The transport of charge clouds affects the spectral characteristics of photon counting detectors and the double-counting probability results show the theoretical threshold energy to avoid double-counting as a function of X-ray energy and X-ray interaction locations for silicon and can be considered for future studies of charge sharing effects.

View details for DOI 10.1016/j.nima.2018.05.027

**Effect of Spectral Degradation and Spatio-Energy Correlation in X-Ray PCD for Imaging**

P. L. Rajbhandary, S. S. Hsieh, N. J. Pelc

IEEE Transactions on Medical Imaging, vol. 37, no. 8, pp. 1910-1919, 2018

**Abstract**

Charge sharing, scatter, and fluorescence events in a photon counting detector can result in counting of a single incident photon in multiple neighboring pixels, each at a fraction of the true energy. This causes energy distortion and correlation of data across energy bins in neighboring pixels (spatio-energy correlation), with the severity depending on the detector pixel size and detector material. If a “macro-pixel” is formed by combining the counts from multiple adjacent small pixels, it will exhibit correlations across its energy bins. Understanding these effects can be crucial for detector design and for model-based imaging applications. This paper investigates the impact of these effects in basis material and effective monoenergetic estimates using the Cramér-Rao Lower Bound. To do so, we derive a correlation model for the multicounting events. CdTe detectors with grids of pixels with side length of 250 μm, 500 μm, and 1 mm were compared, with binning of 4 × 4, 2 × 2, and 1 × 1 pixels, respectively, to keep the same net 1 mm^{2} aperture constant. The same flux was applied to each. The mean and covariance matrix of measured photon counts were derived analytically using spatio-energy response functions precomputed from Monte Carlo simulations. Our results show that a 1 mm 2 macropixel with 250 × 250 μm^{2} sub-pixels shows 35% higher standard deviation than a single 1 mm^{2} pixel for material-specific imaging, while the penalty for effective monoenergetic imaging is <10% compared with a single 1 mm^{2} pixel. Potential benefits of sub-pixels (higher spatial resolution and lower pulse pile-up effects) are important but were not investigated here.

View details for DOI 10.1109/TMI.2018.2834369

**Measurements of the relationship between CT Hounsfield units and acoustic velocity and how it changes with photon energy and reconstruction method**

T. D. Webb, S. A. Leung, J. Rosenberg, P. Ghanouni, J. J. Dahl, N. J. Pelc, K. Butts Pauly

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 65, no. 7, pp. 1111-1124, 2018

**Abstract**

Transcranial magnetic resonance-guided focused ultrasound continues to gain traction as a noninvasive treatment option for a variety of pathologies. Focusing ultrasound through the skull can be accomplished by adding a phase correction to each element of a hemispherical transducer array. The phase corrections are determined with acoustic simulations that rely on speed of sound estimates derived from CT scans. While several studies have investigated the relationship between acoustic velocity and CT Hounsfield units (HUs), these studies have largely ignored the impact of X-ray energy, reconstruction method, and reconstruction kernel on the measured HU, and therefore the estimated velocity, and none have measured the relationship directly. In this paper, 91 ex vivo human skull fragments from two skulls are imaged by 80 CT scans with a variety of energies and reconstruction methods. The average HU from each fragment is found for each scan and correlated with the speed of sound measured using a through transmission technique in that fragment. As measured by the R-squared value, the results show that CT is able to account for 23%-53% of the variation in velocity in the human skull. Both the X-ray energy and the reconstruction technique significantly alter the R-squared value and the linear relationship between HU and speed of sound in bone. Accounting for these variations will lead to more accurate phase corrections and more efficient transmission of acoustic energy through the skull.

View details for DOI 10.1109/TUFFC.2018.2827899

**Spectral resolution and high‐flux capability tradeoffs in CdTe detectors for clinical CT**

S. S. Hsieh, P. L. Rajbhandary, N. J. Pelc

Medical Physics, vol. 45, no. 4, pp. 1433-1443, 2018

**Abstract**

*Purpose*: Photon‐counting detectors using CdTe or CZT substrates are promising candidates for future CT systems but suffer from a number of nonidealities, including charge sharing and pulse pileup. By increasing the pixel size of the detector, the system can improve charge sharing characteristics at the expense of increasing pileup. The purpose of this work is to describe these considerations in the optimization of the detector pixel pitch.

*Methods*: The transport of x-rays through the CdTe substrate was simulated in a Monte Carlo fashion using GEANT4. Deposited energy was converted into charges distributed as a Gaussian function with size dependent on interaction depth to capture spreading from diffusion and Coulomb repulsion. The charges were then collected in a pixelated fashion. Pulse pileup was incorporated separately with Monte Carlo simulation. The Cramér–Rao lower bound (CRLB) of the measurement variance was numerically estimated for the basis material projections. Noise in these estimates was propagated into CT images. We simulated pixel pitches of 250, 350, and 450 microns and compared the results to a photon counting detector with pileup but otherwise ideal energy response and an ideal dual‐energy system (80/140 kVp with tin filtration). The modeled CdTe thickness was 2 mm, the incident spectrum was 140 kVp and 500 mA, and the effective dead time was 67 ns. Charge summing circuitry was not modeled. We restricted our simulations to objects of uniform thickness and did not consider the potential advantage of smaller pixels at high spatial frequencies.

*Results*: At very high x‐ray flux, pulse pileup dominates and small pixel sizes perform best. At low flux or for thick objects, charge sharing dominates and large pixel sizes perform best. At low flux and depending on the beam hardness, the CRLB of variance in basis material projections tasks can be 32%–55% higher with a 250 micron pixel pitch compared to a 450 micron pixel pitch. However, both are about four times worse in variance than the ideal photon counting detector. The optimal pixel size depends on a number of factors such as x‐ray technique and object size. At high technique (140 kVp/500 mA), the ratio of variance for a 450 micron pixel compared to a 250 micron pixel size is 2126%, 200%, 97%, and 78% when imaging 10, 15, 20, and 25 cm of water, respectively. If 300 mg/cm^{2} of iodine is also added to the object, the variance ratio is 117%, 91%, 74%, and 72%, respectively. Nonspectral tasks, such as equivalent monoenergetic imaging, are less sensitive to spectral distortion.

*Conclusions*: The detector pixel size is an important design consideration in CdTe detectors. Smaller pixels allow for improved capabilities at high flux but increase charge sharing, which in turn compromises spectral performance. The optimal pixel size will depend on the specific task and on the charge shaping time.

View details for DOI 10.1002/mp.12799