Spectral diffusion: an algorithm for robust material decomposition of spectral CT data

Virtual computed-tomography system for deep-learning-based material decomposition

Objective. Material decomposition (MD) evaluates the elemental composition of human tissues and organs via computed tomography (CT) and is indispensable in correlating anatomical images with functional ones. A major issue in MD is inaccurate elemental information about the real human body. To overcome this problem, we developed a virtual CT system model, by which various reconstructed images can be generated based on ICRP110 human phantoms with information about six major elements (H, C, N, O, P, and Ca). Approach. We generated CT datasets labelled with accurate elemental information using the proposed generative CT model and trained a deep learning (DL)-based model to estimate the material distribution with the ICRP110 based human phantom as well as the digital Shepp–Logan phantom. The accuracy in quad-, dual-, and single-energy CT cases was investigated. The influence of beam-hardening artefacts, noise, and spectrum variations were analysed with testing datasets including elemental density and anatomical shape variations. Main results. The results indicated that this DL approach can realise precise MD, even with single-energy CT images. Moreover, noise, beam-hardening artefacts, and spectrum variations were shown to have minimal impact on the MD. Significance. Present results suggest that the difficulty to prepare a large CT database can be solved by introducing the virtual CT system and the proposed technique can be applied to clinical radiodiagnosis and radiotherapy.

Spectral Photon Counting CT: Imaging Algorithms and Performance Assessment

Photon counting x-ray detectors (PCDs) with spectral capabilities have the potential to revolutionize computed tomography (CT) for medical imaging. The ideal PCD provides accurate energy information for each incident x-ray, and at high spatial resolution. This information enables material-specific imaging, enhanced radiation dose efficiency, and improved spatial resolution in CT images. In practice, PCDs are affected by non-idealities, including limited energy resolution, pulse pileup, and cross talk due to charge sharing, K-fluorescence, and Compton scattering. In order to maximize their performance, PCDs must be carefully designed to reduce these effects and then later account for them during correction and post-acquisition steps. This review article examines algorithms for using PCDs in spectral CT applications, including how non-idealities impact image quality. Performance assessment metrics that account for spatial resolution and noise such as the detective quantum efficiency (DQE) can be used to compare different PCD designs, as well as compare PCDs with conventional energy integrating detectors (EIDs). These methods play an important role in enhancing spectral CT images and assessing the overall performance of PCDs.

Image-domain Material Decomposition for Spectral CT using a Generalized Dictionary Learning

The spectral computed tomography (CT) has huge advantages by providing accurate material information. Unfortunately, due to the instability or overdetermination of material decomposition model, the accuracy of material decomposition can be compromised in practice. Very recently, the dictionary learning based image-domain material decomposition (DLIMD) can obtain high accuracy for material decompositions from reconstructed spectral CT images. This method can explore the correlation of material components to some extent by training a unified dictionary from all material images. In addition, the dictionary learning based prior as a penalty is applied on material components independently, and many parameters would be carefully elaborated in practice. Because the concentration of contrast agent in clinical applications is low, it can result in data inconsistency for dictionary based representation during the iteration process. To avoid the aforementioned limitations and further improve the accuracy of materials, we first construct a generalized dictionary learning based image-domain material decomposition (GDLIMD) model. Then, the material tensor image is unfolded along the mode-1 to enhance the correlation of different materials. Finally, to avoid the data inconsistency of low iodine contrast, a normalization strategy is employed. Both physical phantom and tissue-synthetic phantom experiments demonstrate the proposed GDLIMD method outperforms the DLIMD and direct inversion (DI) methods.

Deep-learning-based direct inversion for material decomposition

PURPOSE

To develop a convolutional neural network (CNN) that can directly estimate material density distribution from multi-energy computed tomography (CT) images without performing conventional material decomposition.

METHODS

The proposed CNN (denoted as Incept-net) followed the general framework of encoder-decoder network, with an assumption that local image information was sufficient for modeling the nonlinear physical process of multi-energy CT. Incept-net was implemented with a customized loss function, including an in-house-designed image-gradient-correlation (IGC) regularizer to improve edge preservation. The network consisted of two types of customized multibranch modules exploiting multiscale feature representation to improve the robustness over local image noise and artifacts. Inserts with various densities of different materials [hydroxyapatite (HA), iodine, a blood-iodine mixture, and fat] were scanned using a research photon-counting detector (PCD) CT with two energy thresholds and multiple radiation dose levels. The network was trained using phantom image patches only, and tested with different-configurations of full field-of-view phantom and in vivo porcine images. Furthermore, the nominal mass densities of insert materials were used as the labels in CNN training, which potentially provided an implicit mass conservation constraint. The Incept-net performance was evaluated in terms of image noise, detail preservation, and quantitative accuracy. Its performance was also compared to common material decomposition algorithms including least-square-based material decomposition (LS-MD), total-variation regularized material decomposition (TV-MD), and U-net-based method.

RESULTS

Incept-net improved accuracy of the predicted mass density of basis materials compared with the U-net, TV-MD, and LS-MD: the mean absolute error (MAE) of iodine was 0.66, 1.0, 1.33, and 1.57 mgI/cc for Incept-net, U-net, TV-MD, and LS-MD, respectively, across all iodine-present inserts (2.0-24.0 mgI/cc). With the LS-MD as the baseline, Incept-net and U-net achieved comparable noise reduction (both around 95%), both higher than TV-MD (85%). The proposed IGC regularizer effectively helped both Incept-net and U-net to reduce image artifact. Incept-net closely conserved the total mass densities (i.e., mass conservation constraint) in porcine images, which heuristically validated the quantitative accuracy of its outputs in anatomical background. In general, Incept-net performance was less dependent on radiation dose levels than the two conventional methods; with approximately 40% less parameters, the Incept-net achieved relatively improved performance than the comparator U-net, indicating that performance gain by Incept-net was not achieved by simply increasing network learning capacity.

CONCLUSION

Incept-net demonstrated superior qualitative image appearance, quantitative accuracy, and lower noise than the conventional methods and less sensitive to dose change. Incept-net generalized and performed well with unseen image structures and different material mass densities. This study provided preliminary evidence that the proposed CNN may be used to improve the material decomposition quality in multi-energy CT.

Nanoparticle contrast agents for X-ray imaging applications

X-ray imaging is the most widely used diagnostic imaging method in modern medicine and several advanced forms of this technology have recently emerged. Iodinated molecules and barium sulfate suspensions are clinically approved X-ray contrast agents and are widely used. However, these existing contrast agents provide limited information, are suboptimal for new X-ray imaging techniques and are developing safety concerns. Thus, over the past 15 years, there has been a rapid growth in the development of nanoparticles as X-ray contrast agents. Nanoparticles have several desirable features such as high contrast payloads, the potential for long circulation times, and tunable physicochemical properties. Nanoparticles have also been used in a range of biomedical applications such as disease treatment, targeted imaging, and cell tracking. In this review, we discuss the principles behind X-ray contrast generation and introduce new types of X-ray imaging modalities, as well as potential elements and chemical compositions that are suitable for novel contrast agent development. We focus on the progress in nanoparticle X-ray contrast agents developed to be renally clearable, long circulating, theranostic, targeted, or for cell tracking. We feature agents that are used in conjunction with the newly developed multi-energy computed tomography and mammographic imaging technologies. Finally, we offer perspectives on current limitations and emerging research topics as well as expectations for the future development of the field. This article is categorized under: Diagnostic Tools > in vivo Nanodiagnostics and Imaging Nanotechnology Approaches to Biology > Nanoscale Systems in Biology.

The Experimental Study on Geometric Calibration and Material Discrimination for In Vivo Dual-Energy CT Imaging

Photon-counting detector (PCD) can identify absorption features in the multiple ranges of photon energies, which has a great potential in material discrimination. In this paper, we focused on in vivo dual-energy CT imaging to characterize different biomedical compositions. The precision of material decomposition in post-reconstruction space depends on the quality of reconstructed CT images; we used the locally linear embedding (LLE) based online geometric calibration method and GPU-based reconstruction toolbox to reconstruct high-quality CT images. Then, we performed the real experiment and studied materials decomposition with basis material model to discriminate soft tissue and cortical bone of small animal. Finally, the experimental results demonstrated that the proposed method could reconstruct small animal CT images with more slim structures and details, and improve the precision of materials decomposition in dual-energy CT imaging.

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.

Joint Statistical Iterative Material Image Reconstruction for Spectral Computed Tomography Using a Semi-Empirical Forward Model

By acquiring tomographic measurements with several distinct photon energy spectra, spectral computed tomography (spectral CT) is able to provide additional material-specific information compared with conventional CT. This information enables the generation of material selective images, which have found various applications in medical imaging. However, material decomposition typically leads to noise amplification and a degradation of the signal-to-noise ratio. This is still a fundamental problem of spectral CT, especially for low-dose medical applications. Inspired by the success for low-dose conventional CT, several statistical iterative reconstruction algorithms for spectral CT have been developed. These algorithms typically rely on detailed knowledge about the spectrum and the detector response. Obtaining this knowledge is often difficult in practice, especially if photon counting detectors are used to acquire the energy specific information. In this paper, a new algorithm for joint statistical iterative material image reconstruction is presented. It relies on a semi-empirical forward model which is tuned by calibration measurements. This strategy allows to model spatially varying properties of the imaging system without requiring detailed prior knowledge of the system parameters. We employ an efficient optimization algorithm based on separable surrogate functions to accelerate convergence and reduce the reconstruction time. Numerical as well as real experiments show that our new algorithm leads to reduced statistical bias and improved image quality compared with projection-based material decomposition followed by analytical or iterative image reconstruction.

Evaluation of spectral photon counting computed tomography K-edge imaging for determination of gold nanoparticle biodistribution in vivo

Spectral photon counting computed tomography (SPCCT) is an emerging medical imaging technology. SPCCT scanners record the energy of incident photons, which allows specific detection of contrast agents due to measurement of their characteristic X-ray attenuation profiles. This approach is known as K-edge imaging. Nanoparticles formed from elements such as gold, bismuth or ytterbium have been reported as potential contrast agents for SPCCT imaging. Furthermore, gold nanoparticles have many applications in medicine, such as adjuvants for radiotherapy and photothermal ablation. In particular, longitudinal imaging of the biodistribution of nanoparticles would be highly attractive for their clinical translation. We therefore studied the capabilities of a novel SPCCT scanner to quantify the biodistribution of gold nanoparticles in vivo. PEGylated gold nanoparticles were used. Phantom imaging showed that concentrations measured on gold images correlated well with known concentrations (slope = 0.94, intercept = 0.18, RMSE = 0.18, R² = 0.99). The SPCCT system allowed repetitive and quick acquisitions in vivo, and follow-up of changes in the AuNP biodistribution over time. Measurements performed on gold images correlated with the inductively coupled plasma-optical emission spectrometry (ICP-OES) measurements in the organs of interest (slope = 0.77, intercept = 0.47, RMSE = 0.72, R² = 0.93). TEM results were in agreement with the imaging and ICP-OES in that much higher concentrations of AuNPs were observed in the liver, spleen, bone marrow and lymph nodes (mainly in macrophages). In conclusion, we found that SPCCT can be used for repetitive and non-invasive determination of the biodistribution of gold nanoparticles in vivo.

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.

Iterative reconstruction for dual energy CT with an average image-induced nonlocal means regularization

Reducing radiation dose in dual energy computed tomography (DECT) is highly desirable but it may lead to excessive noise in the filtered backprojection (FBP) reconstructed DECT images, which can inevitably increase the diagnostic uncertainty. To obtain clinically acceptable DECT images from low-mAs acquisitions, in this work we develop a novel scheme based on measurement of DECT data. In this scheme, inspired by the success of edge-preserving non-local means (NLM) filtering in CT imaging and the intrinsic characteristics underlying DECT images, i.e. global correlation and non-local similarity, an averaged image induced NLM-based (aviNLM) regularization is incorporated into the penalized weighted least-squares (PWLS) framework. Specifically, the presented NLM-based regularization is designed by averaging the acquired DECT images, which takes the image similarity within the two energies into consideration. In addition, the weighted least-squares term takes into account DECT data-dependent variance. For simplicity, the presented scheme was termed as 'PWLS-aviNLM'. The performance of the presented PWLS-aviNLM algorithm was validated and evaluated on digital phantom, physical phantom and patient data. The extensive experiments validated that the presented PWLS-aviNLM algorithm outperforms the FBP, PWLS-TV and PWLS-NLM algorithms quantitatively. More importantly, it delivers the best qualitative results with the finest details and the fewest noise-induced artifacts, due to the aviNLM regularization learned from DECT images. This study demonstrated the feasibility and efficacy of the presented PWLS-aviNLM algorithm to improve the DECT reconstruction and resulting material decomposition.

Hybrid spectral CT reconstruction

Current photon counting x-ray detector (PCD) technology faces limitations associated with spectral fidelity and photon starvation. One strategy for addressing these limitations is to supplement PCD data with high-resolution, low-noise data acquired with an energy-integrating detector (EID). In this work, we propose an iterative, hybrid reconstruction technique which combines the spectral properties of PCD data with the resolution and signal-to-noise characteristics of EID data. Our hybrid reconstruction technique is based on an algebraic model of data fidelity which substitutes the EID data into the data fidelity term associated with the PCD reconstruction, resulting in a joint reconstruction problem. Within the split Bregman framework, these data fidelity constraints are minimized subject to additional constraints on spectral rank and on joint intensity-gradient sparsity measured between the reconstructions of the EID and PCD data. Following a derivation of the proposed technique, we apply it to the reconstruction of a digital phantom which contains realistic concentrations of iodine, barium, and calcium encountered in small-animal micro-CT. The results of this experiment suggest reliable separation and detection of iodine at concentrations ≥ 5 mg/ml and barium at concentrations ≥ 10 mg/ml in 2-mm features for EID and PCD data reconstructed with inherent spatial resolutions of 176 μm and 254 μm, respectively (point spread function, FWHM). Furthermore, hybrid reconstruction is demonstrated to enhance spatial resolution within material decomposition results and to improve low-contrast detectability by as much as 2.6 times relative to reconstruction with PCD data only. The parameters of the simulation experiment are based on an in vivo micro-CT experiment conducted in a mouse model of soft-tissue sarcoma. Material decomposition results produced from this in vivo data demonstrate the feasibility of distinguishing two K-edge contrast agents with a spectral separation on the order of the energy resolution of the PCD hardware.

An effective noise reduction method for multi-energy CT images that exploit spatio-spectral features

PURPOSE

To develop and evaluate an image-domain noise reduction method for multi-energy CT (MECT) data.

METHODS

Multi-Energy Non-Local Means (MENLM) is a technique that uses the redundant information in MECT images to achieve noise reduction. In this method, spatio-spectral features are used to determine the similarity between pixels, making the similarity evaluation more robust to image noise. The performance of this MENLM filter was tested on images acquired on a whole-body research photon counting CT system. The impact of filtering on image quality was quantitatively evaluated in phantom studies in terms of image noise level (standard deviation of pixel values), noise power spectrum (NPS), in-plane and cross-plane spatial resolution, CT number accuracy, material decomposition performance, and subjective low-contrast spatial resolution using the American College of Radiology (ACR) CT accreditation phantom. Clinical feasibility was assessed by performing MENLM on contrast-enhanced swine images and unenhanced cadaver head images using clinically relevant doses and dose rates.

RESULTS

The phantom studies demonstrated that the MENLM filter reduced noise substantially and still preserved the shape and peak frequency of the NPS. With 80% noise reduction, MENLM filtering caused no degradation of high-contrast spatial resolution, as illustrated by the modulation transfer function (MTF) and slice sensitivity profile (SSP). CT number accuracy was also maintained for all energy channels, demonstrating that energy resolution was not affected by filtering. Material decomposition performance was improved with MENLM filtering. The subjective evaluation using the ACR phantom demonstrated an improvement in low-contrast performance. MENLM achieved effective noise reduction in both contrast-enhanced swine images and unenhanced cadaver head images, resulting in improved detection of subtle vascular structures and the differentiation of white/gray matter.

CONCLUSION

In MECT, MENLM achieved around 80% noise reduction and greatly improved material decomposition performance and the detection of subtle anatomical/low-contrast features while maintaining spatial and energy resolution. MENLM filtering may improve diagnostic or functional analysis accuracy and facilitate radiation dose and contrast media reduction for MECT.

TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT

This work develops a material reconstruction method for spectral CT, namely Total Image Constrained Material Reconstruction (TICMR), to maximize the utility of projection data in terms of both spectral information and high signal-to-noise ratio (SNR). This is motivated by the following fact: when viewed as a spectrally-integrated measurement, the projection data can be used to reconstruct a total image without spectral information, which however has a relatively high SNR; when viewed as a spectrally-resolved measurement, the projection data can be utilized to reconstruct the material composition, which however has a relatively low SNR. The material reconstruction synergizes material decomposition and image reconstruction, i.e., the direct reconstruction of material compositions instead of a two-step procedure that first reconstructs images and then decomposes images. For material reconstruction with high SNR, we propose TICMR with nonlocal total variation (NLTV) regularization. That is, first we reconstruct a total image using spectrally-integrated measurement without spectral binning, and build the NLTV weights from this image that characterize nonlocal image features; then the NLTV weights are incorporated into a NLTV-based iterative material reconstruction scheme using spectrally-binned projection data, so that these weights serve as a high-SNR reference to regularize material reconstruction. Note that the nonlocal property of NLTV is essential for material reconstruction, since material compositions may have significant local intensity variations although their structural information is often similar. In terms of solution algorithm, TICMR is formulated as an iterative reconstruction method with the NLTV regularization, in which the nonlocal divergence is utilized based on the adjoint relationship. The alternating direction method of multipliers is developed to solve this sparsity optimization problem. The proposed TICMR method was validated using both simulated and experimental data. In comparison with FBP and total-variation-based iterative method, TICMR had improved image quality, e.g., contrast-to-noise ratio and spatial resolution.

Spectrotemporal CT data acquisition and reconstruction at low dose

PURPOSE

X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D+dual energy+time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols.

METHODS

The authors approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer.

RESULTS

Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol.

CONCLUSIONS

Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time.

Technical Note: spektr 3.0-A computational tool for x-ray spectrum modeling and analysis

PURPOSE

A computational toolkit (spektr 3.0) has been developed to calculate x-ray spectra based on the tungsten anode spectral model using interpolating cubic splines (TASMICS) algorithm, updating previous work based on the tungsten anode spectral model using interpolating polynomials (TASMIP) spectral model. The toolkit includes a matlab (The Mathworks, Natick, MA) function library and improved user interface (UI) along with an optimization algorithm to match calculated beam quality with measurements.

METHODS

The spektr code generates x-ray spectra (photons/mm(2)/mAs at 100 cm from the source) using TASMICS as default (with TASMIP as an option) in 1 keV energy bins over beam energies 20-150 kV, extensible to 640 kV using the TASMICS spectra. An optimization tool was implemented to compute the added filtration (Al and W) that provides a best match between calculated and measured x-ray tube output (mGy/mAs or mR/mAs) for individual x-ray tubes that may differ from that assumed in TASMICS or TASMIP and to account for factors such as anode angle.

RESULTS

The median percent difference in photon counts for a TASMICS and TASMIP spectrum was 4.15% for tube potentials in the range 30-140 kV with the largest percentage difference arising in the low and high energy bins due to measurement errors in the empirically based TASMIP model and inaccurate polynomial fitting. The optimization tool reported a close agreement between measured and calculated spectra with a Pearson coefficient of 0.98.

CONCLUSIONS

The computational toolkit, spektr, has been updated to version 3.0, validated against measurements and existing models, and made available as open source code. Video tutorials for the spektr function library, UI, and optimization tool are available.

A neural network-based method for spectral distortion correction in photon counting x-ray CT

Spectral CT using a photon counting x-ray detector (PCXD) shows great potential for measuring material composition based on energy dependent x-ray attenuation. Spectral CT is especially suited for imaging with K-edge contrast agents to address the otherwise limited contrast in soft tissues. We have developed a micro-CT system based on a PCXD. This system enables both 4 energy bins acquisition, as well as full-spectrum mode in which the energy thresholds of the PCXD are swept to sample the full energy spectrum for each detector element and projection angle. Measurements provided by the PCXD, however, are distorted due to undesirable physical effects in the detector and can be very noisy due to photon starvation in narrow energy bins. To address spectral distortions, we propose and demonstrate a novel artificial neural network (ANN)-based spectral distortion correction mechanism, which learns to undo the distortion in spectral CT, resulting in improved material decomposition accuracy. To address noise, post-reconstruction denoising based on bilateral filtration, which jointly enforces intensity gradient sparsity between spectral samples, is used to further improve the robustness of ANN training and material decomposition accuracy. Our ANN-based distortion correction method is calibrated using 3D-printed phantoms and a model of our spectral CT system. To enable realistic simulations and validation of our method, we first modeled the spectral distortions using experimental data acquired from (109)Cd and (133)Ba radioactive sources measured with our PCXD. Next, we trained an ANN to learn the relationship between the distorted spectral CT projections and the ideal, distortion-free projections in a calibration step. This required knowledge of the ground truth, distortion-free spectral CT projections, which were obtained by simulating a spectral CT scan of the digital version of a 3D-printed phantom. Once the training was completed, the trained ANN was used to perform distortion correction on any subsequent scans of the same system with the same parameters. We used joint bilateral filtration to perform noise reduction by jointly enforcing intensity gradient sparsity between the reconstructed images for each energy bin. Following reconstruction and denoising, the CT data was spectrally decomposed using the photoelectric effect, Compton scattering, and a K-edge material (i.e. iodine). The ANN-based distortion correction approach was tested using both simulations and experimental data acquired in phantoms and a mouse with our PCXD-based micro-CT system for 4 bins and full-spectrum acquisition modes. The iodine detectability and decomposition accuracy were assessed using the contrast-to-noise ratio and relative error in iodine concentration estimation metrics in images with and without distortion correction. In simulation, the material decomposition accuracy in the reconstructed data was vastly improved following distortion correction and denoising, with 50% and 20% reductions in material concentration measurement error in full-spectrum and 4 energy bins cases, respectively. Overall, experimental data confirms that full-spectrum mode provides superior results to 4-energy mode when the distortion corrections are applied. The material decomposition accuracy in the reconstructed data was vastly improved following distortion correction and denoising, with as much as a 41% reduction in material concentration measurement error for full-spectrum mode, while also bringing the iodine detectability to 4-6 mg ml(-1). Distortion correction also improved the 4 bins mode data, but to a lesser extent. The results demonstrate the experimental feasibility and potential advantages of ANN-based distortion correction and joint bilateral filtration-based denoising for accurate K-edge imaging with a PCXD. Given the computational efficiency with which the ANN can be applied to projection data, the proposed scheme can be readily integrated into existing CT reconstruction pipelines.

In vivo small animal micro-CT using nanoparticle contrast agents

Computed tomography (CT) is one of the most valuable modalities for in vivo imaging because it is fast, high-resolution, cost-effective, and non-invasive. Moreover, CT is heavily used not only in the clinic (for both diagnostics and treatment planning) but also in preclinical research as micro-CT. Although CT is inherently effective for lung and bone imaging, soft tissue imaging requires the use of contrast agents. For small animal micro-CT, nanoparticle contrast agents are used in order to avoid rapid renal clearance. A variety of nanoparticles have been used for micro-CT imaging, but the majority of research has focused on the use of iodine-containing nanoparticles and gold nanoparticles. Both nanoparticle types can act as highly effective blood pool contrast agents or can be targeted using a wide variety of targeting mechanisms. CT imaging can be further enhanced by adding spectral capabilities to separate multiple co-injected nanoparticles in vivo. Spectral CT, using both energy-integrating and energy-resolving detectors, has been used with multiple contrast agents to enable functional and molecular imaging. This review focuses on new developments for in vivo small animal micro-CT using novel nanoparticle probes applied in preclinical research.