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

Nanomedicine for Diagnosis and Treatment of Atherosclerosis

With the changing disease spectrum, atherosclerosis has become increasingly prevalent worldwide and the associated diseases have emerged as the leading cause of death. Due to their fascinating physical, chemical, and biological characteristics, nanomaterials are regarded as a promising tool to tackle enormous challenges in medicine. The emerging discipline of nanomedicine has filled a huge application gap in the atherosclerotic field, ushering a new generation of diagnosis and treatment strategies. Herein, based on the essential pathogenic contributors of atherogenesis, as well as the distinct composition/structural characteristics, synthesis strategies, and surface design of nanoplatforms, the three major application branches (nanodiagnosis, nanotherapy, and nanotheranostic) of nanomedicine in atherosclerosis are elaborated. Then, state-of-art studies containing a sequence of representative and significant achievements are summarized in detail with an emphasis on the intrinsic interaction/relationship between nanomedicines and atherosclerosis. Particularly, attention is paid to the biosafety of nanomedicines, which aims to pave the way for future clinical translation of this burgeoning field. Finally, this comprehensive review is concluded by proposing unresolved key scientific issues and sharing the vision and expectation for the future, fully elucidating the closed loop from atherogenesis to the application paradigm of nanomedicines for advancing the early achievement of clinical applications.

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.

A data-driven maximum likelihood classification for nanoparticle agent identification in photon-counting CT

The nanoparticle agent, combined with a targeting factor reacting with lesions, enables specific CT imaging. Thus, the identification of the nanoparticle agents has the potential to improve clinical diagnosis. Thanks to the energy sensitivity of the photon-counting detector (PCD), it can exploit the K-edge of the nanoparticle agents in the clinical x-ray energy range to identify the agents. In this paper, we propose a novel data-driven approach for nanoparticle agent identification using the PCD. We generate two sets of training data consisting of PCD measurements from calibration phantoms, one in the presence of nanoparticle agent and the other in the absence of the agent. For a given sinogram of PCD counts, the proposed method calculates the normalized log-likelihood sinogram for each class (class 1: with the agent, class 2: without the agent) using theKnearest neighbors (KNN) estimator, backproject the sinograms, and compare the backprojection images to identify the agent. We also proved that the proposed algorithm is equivalent to the maximum likelihood-based classification. We studied the robustness of dose reduction with gold nanoparticles as the K-edge contrast media and demonstrated that the proposed method identifies targets with different concentrations of the agents without background noise.

Technical Note: The nearest neighborhood-based approach for estimating basis line-integrals using photon-counting detector

PURPOSE

This study aims to develop a calibration-based estimator for the photon-counting detector (PCD)-based x-ray computed tomography.

METHODS

We propose the nearest neighborhood (NN)-based estimator, which searches for the nearest calibration data for a given PCD output and sets the associated basis line-integrals as the estimate. Searching for the nearest neighbors can be accelerated using the pre-calculated k-d tree for the data.

RESULTS

The proposed method is compared to the model-based maximum likelihood (ML) estimator. For slab phantom study, both ML and NN-based methods achieve the Cramér-Rao lower bound and are unbiased for various combinations of three basis materials (water, bone, and gold). The proposed method is also validated for K-edge imaging and presents almost unbiased Au concentrations in the region of interest.

CONCLUSIONS

The proposed NN-based method is demonstrated to be as accurate as the model-based ML estimator, but it is computationally efficient and requires only calibration measurements.

Photon-counting x-ray detectors for CT

The introduction of photon-counting detectors is expected to be the next major breakthrough in clinical x-ray computed tomography (CT). During the last decade, there has been considerable research activity in the field of photon-counting CT, in terms of both hardware development and theoretical understanding of the factors affecting image quality. In this article, we review the recent progress in this field with the intent of highlighting the relationship between detector design considerations and the resulting image quality. We discuss detector design choices such as converter material, pixel size, and readout electronics design, and then elucidate their impact on detector performance in terms of dose efficiency, spatial resolution, and energy resolution. Furthermore, we give an overview of data processing, reconstruction methods and metrics of imaging performance; outline clinical applications; and discuss potential future developments.

Experimental study of photon-counting CT neural network material decomposition under conditions of pulse pileup

Purpose: We investigated the performance of a neural network (NN) material decomposition method under varying pileup conditions. Approach: Experiments were performed at tube current settings that provided count rates incident on the detector through air equal to 9%, 14%, 27%, 40%, and 54% of the maximum detector count rate. An NN was trained for each count-rate level using transmission measurements through known thicknesses of basis materials (PMMA and aluminum). The NN trained for each count-rate level was applied to x-ray transmission measurements through test materials and to CT data of a rod phantom. Material decomposition error was evaluated as the distance in basis material space between the estimated thicknesses and ground truth. Results: There was no clear trend between count-rate level and material decomposition error for all test materials except neoprene. As an example result, Teflon error was 0.33 cm at the 9% count-rate level and 0.12 cm at the 54% count-rate level for the x-ray transmission experiments. Decomposition error increased with count-rate level for the neoprene test case, with 0.65-cm error at 9% count-rate level and 1.14-cm error at the 54% count-rate level. In the CT study, material decomposition error decreased with increasing incident count rate. For example, the material decomposition error for Teflon was 0.089, 0.066, 0.054 at count-rate levels of 14%, 27%, and 40%, respectively. Conclusions: Results demonstrate over a range of incident count-rate levels that an NN trained at a specific count-rate level can learn the relationship between photon-counting spectral measurements and basis material thicknesses.

Generating anthropomorphic phantoms using fully unsupervised deformable image registration with convolutional neural networks

PURPOSE

Computerized phantoms have been widely used in nuclear medicine imaging for imaging system optimization and validation. Although the existing computerized phantoms can model anatomical variations through organ and phantom scaling, they do not provide a way to fully reproduce the anatomical variations and details seen in humans. In this work, we present a novel registration-based method for creating highly anatomically detailed computerized phantoms. We experimentally show substantially improved image similarity of the generated phantom to a patient image.

METHODS

We propose a deep-learning-based unsupervised registration method to generate a highly anatomically detailed computerized phantom by warping an XCAT phantom to a patient computed tomography (CT) scan. We implemented and evaluated the proposed method using the NURBS-based XCAT phantom and a publicly available low-dose CT dataset from TCIA. A rigorous tradeoff analysis between image similarity and deformation regularization was conducted to select the loss function and regularization term for the proposed method. A novel SSIM-based unsupervised objective function was proposed. Finally, ablation studies were conducted to evaluate the performance of the proposed method (using the optimal regularization and loss function) and the current state-of-the-art unsupervised registration methods.

RESULTS

The proposed method outperformed the state-of-the-art registration methods, such as SyN and VoxelMorph, by more than 8%, measured by the SSIM and less than 30%, by the MSE. The phantom generated by the proposed method was highly detailed and was almost identical in appearance to a patient image.

CONCLUSIONS

A deep-learning-based unsupervised registration method was developed to create anthropomorphic phantoms with anatomies labels that can be used as the basis for modeling organ properties. Experimental results demonstrate the effectiveness of the proposed method. The resulting anthropomorphic phantom is highly realistic. Combined with realistic simulations of the image formation process, the generated phantoms could serve in many applications of medical imaging research.

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.

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.

Spectral Angiography Material Decomposition Using an Empirical Forward Model and a Dictionary-Based Regularization

By resolving the energy of the incident X-ray photons, spectral X-ray imaging with photon counting detectors offers additional material-specific information compared to conventional X-ray imaging. This additional information can be used to improve clinical diagnosis for various applications. However, spectral imaging still faces several challenges. Amplified noise and a reduced signal-to-noise ratio on the decomposed basis material images remain a major problem, especially for low-dose applications. Furthermore, it is challenging to construct an accurate model of the spectral measurement acquisition process. In this paper, we present a novel algorithm for projection-based material decomposition. It uses an empirical polynomial model that is tuned by calibration measurements. We combine this method with a statistical model of the measured photon counts and a dictionary-based joint regularization approach. We focused on spectral coronary angiography as a potential clinical application of projection-based material decomposition with photon counting detectors. Numerical and real experiments show that spectral angiography with realistic dose levels and gadolinium contrast agent concentrations are feasible using the proposed decomposition algorithm and currently available photon-counting detector technology.

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.

Increased separability of K-edge nanoparticles by photon-counting detectors for spectral micro-CT

BACKGROUND

X-ray CT/micro-CT methods with photon-counting detectors (PCDs) and high Z materials are a hot research topic. One method using PCDs allows for spectral imaging in 5 energy windows while conventional X-ray detectors only collect energy-integrating data.

OBJECTIVE

To demonstrate the enhanced separation of contrast materials by using PCDs, multivariate analysis, and linear discriminant methods.

METHODS

Phantoms containing iodine and aqueous nanomaterials were scanned on a MARS spectral micro-CT. Image volumes were segmented into separate material-specific populations. Contrast comparisons were made by calculating T2 test statistics in the univariate, pseudo-conventional and multivariate, spectral CT data sets. Separability after Fisher discriminant analysis (FDA) was also assessed.

RESULTS

The T2 values calculated for material comparisons increased as a result of the spectral expansion. The majority of the tested contrast agents showed increased T2 values by a factor of ∼2 -3. The total significant T2 statistics in the pure and mixed lanthanide image sets increased in the spectral data set.

CONCLUSION

This work consolidates the groundwork for photon-counting-based material decomposition with micro-CT, facilitating future development of novel nanomaterials and their preclinical applications.