Model-based Material Decomposition Research Articles

Quantitative Dual-Energy Imaging of Bone Marrow Edema Using Multisource Cone-Beam CT with Model-Based Decomposition.

We investigated the feasibility of dual-energy (DE) detection of bone marrow edema (BME) using a dedicated extremity cone-beam CT (CBCT) with a unique three-source x-ray unit. The sources can be operated at different energies to enable single-scan DE acquisitions. However, they are arranged parallel to the axis of rotation, resulting in incomplete sampling and precluding the application of DE projection-domain decompositions (PDD) for beam-hardening reduction. Therefore, we propose a novel combination of a model-based "one-step" DE two-material decomposition followed by a constrained image-domain change-of-basis to obtain virtual non-calcium (VNCa) images for BME detection. DE projections were obtained using an "alternating-kV" protocol by operating the peripheral two sources of the CBCT system at low-energy (60 kV, 0.105 mAs/frame) and the central source at high-energy (100 kV, 0.028 mAs/frame), for a total of 600 frames over 216° of gantry rotation. Projections were processed with detector lag, glare and fast Monte Carlo (MC)-based iterative scatter corrections. Model-based material decomposition (MBMD) was then implemented to obtain aluminum (Al) and polyethylene (PE) volume fraction images with minimal beam-hardening. Statistical ray weights in MBMD were modified to account for regions with highly oblique sampling by the peripheral sources. To generate the VNCa maps, image-domain decomposition (IDD) constrained by the volume conservation principle (VCP) was performed to convert the Al and PE MBMD images into volume fractions of water, fat and cortical bone. Accuracy of BME detection was evaluated using physical phantom data acquired on the multi-source extremity CBCT scanner. The proposed framework estimated the volume of BME with ~10% error. The MC-based scatter corrections and the modified MBMD ray weights were essential to achieve such performance - the error without MC scatter corrections was >30%, whereas the uniformity of estimated VNCa images was 3x improved using the modified weights compared to the conventional weights. The proposed DE decomposition framework was able to overcome challenges of high scatter and incomplete sampling to achieve BME detection on a CBCT system with axially-distributed x-ray sources.

Tunable Neural Networks for Multi-Material Image Formation from Spectral CT Measurements.

Quantitative estimation of multi-material density images is an important goal for Spectral CT imaging. However, material decomposition is a poorly-conditioned nonlinear inverse problem. Maximum-likelihood model-based material decomposition results in very noisy material density image estimates. One increasingly popular strategy for noise reduction is to apply deep neural networks for multi-material image formation. The most common loss function is mean squared error with respect to supervised target images such as ground truth or higher-dose cases. However, we believe that the mean-squared error loss function has several issues for multi-material image formation. In this work, we present a new loss function which includes multiple noise realizations with separate weights on covariance and bias for joint denoising of all material bases. By modulating these weights, it is possible to tune the image quality of neural network output images. To demonstrate our proposed approach, we conducted a simulation of a water/calcium/gadolinium spectral CT imaging scenario using a deep neural network for multi-material image denoising. Our results show that by changing the weights of our proposed loss function, it is possible to control the tradeoff between variance and bias for individual materials as well as the control over the bias coupling between materials.

Design Optimization of Spatial-Spectral Filters for Cone-Beam CT Material Decomposition.

Spectral CT has shown promise for high-sensitivity quantitative imaging and material decomposition. This work presents a new device called a spatial-spectral filter (SSF) which consists of a tiled array of filter materials positioned near the x-ray source that is used to modulate the spectral shape of the x-ray beam. The filter is moved to obtain projection data that is sparse in each spectral channel. To process this sparse data, we employ a one-step direct model-based material decomposition (MBMD) to reconstruct basis material density images directly from the SSF CT data. To evaluate different possible SSF designs, we define a new Fisher-information-based predictive image quality metric called separability index which characterizes the ability of a spectral CT system to distinguish between the signals from two or more materials. This spectral CT performance metric can be used to optimize spectral CT system design. We conducted simulation-based design optimization study to find optimized combinations of filter materials, filter thicknesses, filter widths, and source settings. Finally, we present MBMD results using simulated SSF CT measurements from the optimized designs to demonstrate the ability to reconstruct basis material density images and to show the benefits of the optimized designs. Our results indicate that optimizing SSF CT for separability leads to high-performance at material discrimination tasks.

Model-based three-material decomposition in dual-energy CT using the volume conservation constraint

Objective. We develop a model-based optimization algorithm for ‘one-step’ dual-energy (DE) CT decomposition of three materials directly from projection measurements. Approach. Since the three-material problem is inherently undetermined, we incorporate the volume conservation principle (VCP) as a pair of equality and nonnegativity constraints into the objective function of the recently reported model-based material decomposition (MBMD). An optimization algorithm (constrained MBMD, CMBMD) is derived that utilizes voxel-wise separability to partition the volume into a VCP-constrained region solved using interior-point iterations, and an unconstrained region (air surrounding the object, where VCP is violated) solved with conventional two-material MBMD. Constrained MBMD (CMBMD) is validated in simulations and experiments in application to bone composition measurements in the presence of metal hardware using DE cone-beam CT (CBCT). A kV-switching protocol with non-coinciding low- and high-energy (LE and HE) projections was assumed. CMBMD with decomposed base materials of cortical bone, fat, and metal (titanium, Ti) is compared to MBMD with (i) fat-bone and (ii) fat-Ti bases. Main results. Three-material CMBMD exhibits a substantial reduction in metal artifacts relative to the two-material MBMD implementations. The accuracies of cortical bone volume fraction estimates are markedly improved using CMBMD, with ∼5–10× lower normalized root mean squared error in simulations with anthropomorphic knee phantoms (depending on the complexity of the metal component) and ∼2–2.5× lower in an experimental test-bench study. Significance. In conclusion, we demonstrated one-step three-material decomposition of DE CT using volume conservation as an optimization constraint. The proposed method might be applicable to DE applications such as bone marrow edema imaging (fat-bone-water decomposition) or multi-contrast imaging, especially on CT/CBCT systems that do not provide coinciding LE and HE ray paths required for conventional projection-domain DE decomposition.

High-resolution model-based material decomposition in dual-layer flat-panel CBCT.

Spectral CT uses energy-dependent measurements that enable material discrimination in addition to reconstruction of structural information. Flat-panel detectors (FPDs) have been widely used in dedicated and interventional systems to deliver high spatial resolution, volumetric cone-beam CT (CBCT) in compact and OR-friendly designs. In this work, we derive a model-based method that facilitates high-resolution material decomposition in a spectral CBCT system equipped with a prototype dual-layer FPD. Through high-fidelity modeling of multilayer detector, we seek to avoid resolution loss that is present in more traditional processing and decomposition approaches. A physical model for spectral measurements in dual-layer flat-panel CBCT is developed including layer-dependent differences in system geometry, spectral sensitivities, and detector blur (e.g., due to varied scintillator thicknesses). This forward model is integrated into a model-based material decomposition (MBMD) method based on minimization of a penalized weighted least-squared (PWLS) objective function. The noise and resolution performance of this approach was compared with traditional projection-domain decomposition (PDD) and image-domain decomposition (IDD) approaches as well as one-step MBMD with lower-fidelity models that use approximated geometry, projection interpolation, or an idealized system geometry without system blur model. Physical studies using high-resolution three-dimensional (3D)-printed water-iodine phantoms were conducted to demonstrate the high-resolution imaging performance of the compared decomposition methods in iodine basis images and synthetic monoenergetic images. Physical experiments demonstrate that the MBMD methods incorporating an accurate geometry model can yield higher spatial resolution iodine basis images and synthetic monoenergetic images than PDD and IDD results at the same noise level. MBMD with blur modeling can further improve the spatial-resolution compared with the decomposition results obtained with IDD, PDD, and MBMD methods with lower-fidelity models. Using the MBMD without or with blur model can increase the absolute modulation at 1.75 lp/mm by 10% and 22% compared with IDD at the same noise level. The proposed model-based material decomposition method for a dual-layer flat-panel CBCT system has demonstrated an ability to extend high-resolution performance through sophisticated detector modeling including the layer-dependent blur. The proposed work has the potential to not only facilitate high-resolution spectral CT in interventional and dedicated CBCT systems, but may also provide the opportunity to evaluate different flat-panel design trade-offs including multilayer FPDs with mismatched geometries, scintillator thicknesses, and spectral sensitivities.

A prototype spatial-spectral CT system for material decomposition with energy-integrating detectors.

Spectral CT has great potential for a variety of clinical applications due to improved tissue and material discrimination over conventional single-energy CT. Many clinical and preclinical spectral CT systems have two spectral channels enabling dual-energy CT. Strategies include split filtration, dual-layer detectors, photon-counting detectors, and kVp switching. The motivation for this work is the development of an x-ray source spectral modulation device with three or more spectral channels to enable high-sensitivity multi-material decomposition with energy-integrating detectors. We present spatial-spectral filters which are a new x-ray source modulation technology with the potential for additional channel diversity. The filtering device consists of an array of K-edge materials which divide the x-ray beam into spectrally varied beamlets. This design allows for an arbitrary number of spectral channels-trading off spatial and spectral information. We use a one-step model-based material decomposition (MBMD) algorithm to iteratively estimate material density images directly from the spatial-spectral CT data. In this work, we present a prototype spatial-spectral filter integrated with an x-ray CT test bench. The filter is composed of an array of tin, erbium, tantalum, and lead filter tiles which spatially modulate the system spectral sensitivity pattern. In a simulation study, we investigate the particular problem of mis-calibration between the data acquisition and the reconstruction model. With an understanding of the required model accuracy, we present a spectral calibration method to estimate the critical model parameters. To demonstrate feasibility of the spatial-spectral filter with a calibrated beamlet model, we collected a spatial-spectral CT scan of a multicontrast-enhanced phantom containing water, iodine, and gadolinium solutions. With simulations, we show that material decomposition is possible with spatial-spectral-filtered CT data, and we demonstrate the importance of a well-calibrated physical model. We find a 50% increase in error for focal spot model mismatch of 0.27mm and gap width model mismatch of 16mμ. With physical results, we demonstrate that the calibrated system model is in close agreement with the measured data, and that the reconstructed material density images match the ground truth concentrations for the multicontrast phantom. Empirical results indicate gadolinium density estimation had an error of 17-58% mostly due to a systematic constant bias of 0.30-0.60mg/ml. Water density estimates are within 1% and iodine estimates are within 10% of ground truth. These preliminary results demonstrate the potential of spatial-spectral filters to enable multicontrast imaging. Moreover, this device is compatible with energy-integrating detectors and so provides a feasible modification to enable spectral CT imaging with existing single-energy systems.

Model-based dual-energy tomographic image reconstruction of objects containing known metal components

Dual-energy (DE) decomposition has been adopted in orthopedic imaging to measure bone composition and visualize intraarticular contrast enhancement. One of the potential applications involves monitoring of callus mineralization for longitudinal assessment of fracture healing. However, fracture repair usually involves internal fixation hardware that can generate significant artifacts in reconstructed images. To address this challenge, we develop a novel algorithm that combines simultaneous reconstruction-decomposition using a previously reported method for model-based material decomposition (MBMD) augmented by the known-component (KC) reconstruction framework to mitigate metal artifacts. We apply the proposed algorithm to simulated DE data representative of a dedicated extremity cone-beam CT (CBCT) employing an x-ray unit with three vertically arranged sources. The scanner generates DE data with non-coinciding high- and low-energy projection rays when the central source is operated at high tube potential and the peripheral sources at low potential. The proposed algorithm was validated using a digital extremity phantom containing varying concentrations of Ca-water mixtures and Ti implants. Decomposition accuracy was compared to MBMD without the KC model. The proposed method suppressed metal artifacts and yielded estimated Ca concentrations that approached the reconstructions of an implant-free phantom for most mixture regions. In the vicinity of simple components, the errors of Ca density estimates obtained by incorporating KC in MBMD were ∼1.5–5× lower than the errors of conventional MBMD; for cases with complex implants, the errors were ∼3–5× lower. In conclusion, the proposed method can achieve accurate bone mineral density measurements in the presence of metal implants using non-coinciding DE projections acquired on a multisource CBCT system.

Model-based Material Decomposition with System Blur Modeling.

In this work, we present a novel model-based material decomposition (MBMD) approach for x-ray CT that includes system blur in the measurement model. Such processing has the potential to extend spatial resolution in material density estimates - particularly in systems where different spectral channels exhibit different spatial resolutions. We illustrate this new approach for a dual-layer detector x-ray CT and compare MBMD algorithms with and without blur in the reconstruction forward model. Both qualitative and quantitative comparisons of performance with and without blur modeling are reported. We find that blur modeling yields images with better recovery of high-resolution structures in an investigation of reconstructed line pairs as well as lower cross-talk bias between material bases that is ordinarily found due to mismatches in spatial resolution between spectral channels. The extended spatial resolution of the material decompositions has potential application in a range of high-resolution clinical tasks and spectral CT systems where spectral channels exhibit different spatial resolutions.

Prospective Prediction and Control of Image Properties in Model-based Material Decomposition for Spectral CT.

Model-based material decomposition (MBMD) directly estimates the material densities from the spectral CT data and has found opportunities for dose reduction via physical and statistical modeling and advanced regularization. However, image properties such as spatial resolution, noise, and cross-basis response in the context of material decomposition are dependent on regularization, and high-dimensional exhaustive sweeping of regularization parameters is suboptimal. In this work, we proposed a set of prediction tools for generalized local impulse response (LIR) that characterizes both in-basis spatial resolution and cross-basis response, and noise correlation prospectively. The accuracy of noise predictor was validated in a simulation study, comparing predicted and measured in- and cross-basis noise correlations. Employing these predictors, we composed a specialized regularization for cross-talk reduction and showed that such prediction tools are promising for task-based optimization in spectral CT applications.

Combining Spectral CT Acquisition Methods for High-Sensitivity Material Decomposition.

Quantitative estimation of contrast agent concentration is made possible by spectral CT and material decomposition. There are several approaches to modulate the sensitivity of the imaging system to obtain the different spectral channels required for decomposition. Spectral CT technologies that enable this varied sensitivity include source kV-switching, dual-layer detectors, and source-side filtering (e.g., tiled spatial-spectral filters). In this work, we use an advanced physical model to simulate these three spectral CT strategies as well as hybrid acquisitions using all combinations of two or three strategies. We apply model-based material decomposition to a water-iodine phantom with iodine concentrations from 0.1 to 5.0 mg/mL. We present bias-noise plots for the different combinations of spectral techniques and show that combined approaches permit diversity in spectral sensitivity and improve low concentration imaging performance relative to the those strategies applied individually. Better ability to estimate low concentrations of contrast agent has the potential to reduce risks associated with contrast administration (by lowering dosage) or to extend imaging applications into targets with much lower uptake.

Known-Component Model-Based Material Decomposition for Dual Energy Imaging of Bone Compositions in the Presence of Metal Implant.

Dual energy computed tomography (DE CT) is a promising technology for the assessment of bone compositions. One of potential applications involves evaluations of fracture healing using longitudinal measurements of callus mineralization. However, imaging of fractures is often challenged by the presence of metal fixation hardware. In this work, we report on a new simultaneous DE reconstruction-decomposition algorithm that integrates the previously introduced Model-Based Material Decomposition (MBMD) with a Known-Component (KC) framework to mitigate metal artifacts. The algorithm was applied to the DE data obtained on a dedicated extremity cone-beam CT (CBCT) with capability for weight-bearing imaging. To acquire DE projections in a single gantry rotation, we exploited a unique multisource design of the system, where three X-ray sources were mounted parallel to the axis of rotation. The central source provided high energy (HE) data at 120 kVp, while the two remaining sources were operated at a low energy (LE) of 60 kVp. This novel acquisition trajectory further motivates the use of MBMD to accommodate this complex DE sampling pattern. The algorithm was validated in a simulation study using a digital extremity phantom. The phantom consisted of a water background with an insert containing varying concentrations of calcium (50 - 175 mg/mL). Two configurations of titanium implants were considered: a fixation plate and an intramedullary nail. The accuracy of calcium-water decompositions obtained with the proposed KC-MBMD algorithm was compared to MBMD without metal component model. Metal artifacts were almost completely removed by KC-MBMD. Relative absolute errors of calcium concentration in the vicinity of metal were 6% - 31% for KC-MBMD (depending on the calcium insert and implant configuration), compared favorably to 48% - 273% for MBMD. Moreover, accuracy of concentration estimates for KC-MBMD in the presence of metal implant approached that of MBMD in a configuration without implant (6%-23%). The proposed algorithm achieved accurate DE material decomposition in the presence of metal implants using a non-conventional, axial multisource DE acquisition pattern.

Local response prediction in model-based CT material decomposition.

Spectral CT is an emerging modality that permits material decomposition and density estimation through the use of energy-dependent information in measurements. Direct model-based material decomposition algorithms have been developed that incorporate statistical models and advanced regularization schemes to improve density estimates and lower exposure requirements. However, understanding and control of the relationship between regularization and image properties is complex with interactions between spectral channels and material bases. In particular, regularization in one material basis can affect the image properties of other material bases, and vice versa. In this work, we derived a closed-form set of local impulse responses for the solutions to a general, regularized, model-based material decomposition (MBMD) objective. These predictors quantify both the spatial resolution in each material image as well as the influence of regularization of one material basis on other material images. This information can be used prospectively to tune regularization parameters for specific imaging goals.

Physical Modeling and Performance of Spatial-Spectral Filters for CT Material Decomposition.

Material decomposition for imaging multiple contrast agents in a single acquisition has been made possible by spectral CT: a modality which incorporates multiple photon energy spectral sensitivities into a single data collection. This work presents an investigation of a new approach to spectral CT which does not rely on energy-discriminating detectors or multiple x-ray sources. Instead, a tiled pattern of K-edge filters are placed in front of the x-ray to create spatially encoded spectra data. For improved sampling, the spatial-spectral filter is moved continuously with respect to the source. A model-based material decomposition algorithm is adopted to directly reconstruct multiple material densities from projection data that is sparse in each spectral channel. Physical effects associated with the x-ray focal spot size and motion blur for the moving filter are expected to impact overall performance. In this work, those physical effects are modeled and a performance analysis is conducted. Specifically, experiments are presented with simulated focal spot widths between 0.2 mm and 4.0 mm. Additionally, filter motion blur is simulated for a linear translation speeds between 50 mm/s and 450 mm/s. The performance differential between a 0.2 mm and a 1.0 mm focal spot is less than 15% suggesting feasibility of the approach with realistic x-ray tubes. Moreover, for reasonable filter actuation speeds, higher speeds are shown to decrease error (due to improved sampling) despite motion-based spectral blur.

Model-based material decomposition with a penalized nonlinear least-squares CT reconstruction algorithm

Spectral information in CT may be used for material decomposition to produce accurate reconstructions of material density and to separate materials with similar overall attenuation. Traditional methods separate the reconstruction and decomposition steps, often resulting in undesirable trade-offs (e.g. sampling constraints, a simplified spectral model). In this work, we present a model-based material decomposition algorithm which performs the reconstruction and decomposition simultaneously using a multienergy forward model. In a kV-switching simulation study, the presented method is capable of reconstructing iodine at 0.5 mg ml−1 with a contrast-to-noise ratio greater than two, as compared to 3.0 mg ml−1 for image domain decomposition. The presented method also enables novel acquisition methods, which was demonstrated in this work with a combined kV-switching/split-filter acquisition explored in simulation and physical test bench studies. This novel design used four spectral channels to decompose three materials: water, iodine, and gadolinium. In simulation, the presented method accurately reconstructed concentration value estimates with RMSE values of 4.86 mg ml−1 for water, 0.108 mg ml−1 for iodine and 0.170 mg ml−1 for gadolinium. In test-bench data, the RMSE values were 134 mg ml−1, 5.26 mg ml−1 and 1.85 mg ml−1, respectively. These studies demonstrate the ability of model-based material decomposition to produce accurate concentration estimates in challenging spatial/spectral sampling acquisitions.

A General CT Reconstruction Algorithm for Model-Based Material Decomposition.

Material decomposition in CT has the potential to reduce artifacts and improve quantitative accuracy by utilizing spectral models and multi-energy scans. In this work we present a novel Model-Based Material Decomposition (MBMD) method based on an existing iterative reconstruction algorithm derived from a general non-linear forward model. A digital water phantom with inserts containing different concentrations of calcium was scanned on a kV switching system. We used the presented method to simultaneously reconstruct water and calcium material density images, and compared the results to an image domain and a projection domain decomposition method. When switching voltage every other frame, MBMD resulted in more accurate water and calcium concentration values than the image domain decomposition method, and was just as accurate as the projection domain decomposition method. In a second, slower, kV switching scheme (changing voltage every ten frames) which precluded the use of traditional projection domain based methods, MBMD continued to produce quantitatively accurate reconstructions. Finally, we present a preliminary study applying MBMD to a water phantom containing vials of different concentrations of K2HPO4 which was scanned on a cone-beam CT test bench. Both the fast and slow (emulated) kV switching schemes resulted in similar reconstructions, indicating MBMD's robustness to challenging acquisition schemes. Additionally, the K2HPO4 concentration ratios between the vials were accurately represented in the reconstructed K2HPO4 density image.