CT Reconstruction using Diffusion Posterior Sampling conditioned on a Nonlinear Measurement Model.

Diffusion models have been demonstrated as powerful deep learning tools for image generation in CT reconstruction and restoration. Recently, diffusion posterior sampling, where a score-based diffusion prior is combined with a likelihood model, has been used to produce high quality CT images given low-quality measurements. This technique is attractive since it permits a one-time, unsupervised training of a CT prior; which can then be incorporated with an arbitrary data model. However, current methods rely on a linear model of x-ray CT physics to reconstruct or restore images. While it is common to linearize the transmission tomography reconstruction problem, this is an approximation to the true and inherently nonlinear forward model. We propose a new method that solves the inverse problem of nonlinear CT image reconstruction via diffusion posterior sampling. We implement a traditional unconditional diffusion model by training a prior score function estimator, and apply Bayes rule to combine this prior with a measurement likelihood score function derived from the nonlinear physical model to arrive at a posterior score function that can be used to sample the reverse-time diffusion process. This plug-and-play method allows incorporation of a diffusion-based prior with generalized nonlinear CT image reconstruction into multiple CT system designs with different forward models, without the need for any additional training. We develop the algorithm that performs this reconstruction, including an ordered-subsets variant for accelerated processing and demonstrate the technique in both fully sampled low dose data and sparse-view geometries using a single unsupervised training of the prior.

Lifelike PixelPrint phantoms for assessing clinical image quality and dose reduction capabilities of a deep learning CT reconstruction algorithm.

Deep learning CT reconstruction (DLR) has become increasingly popular as a method for improving image quality and reducing radiation exposure. Due to their nonlinear nature, these algorithms result in resolution and noise performance which are object-dependent. Therefore, traditional CT phantoms, which lack realistic tissue morphology, have become inadequate for assessing clinical imaging performance. We propose to utilize 3D-printed PixelPrint phantoms, which exhibit lifelike attenuation profiles, textures, and structures, as a better tool for evaluating DLR performance. In this study, we evaluate a DLR algorithm (Precise Image (PI), Philips Healthcare) using a custom PixelPrint lung phantom and perform head-to-head comparisons between DLR, iterative reconstruction, and filtered back projection (FBP) with scans acquired at a broad range of radiation exposures (CTDIvol: 0.5, 1, 2, 4, 6, 9, 12, 15, 19, and 20 mGy). We compared the performance of each resultant image using noise, peak signal to noise ratio (PSNR), structural similarity index (SSIM), feature-based similarity index (FSIM), information theoretic-based statistic similarity measure (ISSM) and universal image quality index (UIQ). Iterative reconstruction at 9 mGy matches the image quality of FBP at 12 mGy (diagnostic reference level) for all metrics, demonstrating a dose reduction capability of 25%. Meanwhile, DLR matches the image quality of diagnostic reference level FBP images at doses between 4 - 9 mGy, demonstrating dose reduction capabilities between 25% and 67%. This study shows that DLR allows for reduced radiation dose compared to both FBP and iterative reconstruction without compromising image quality. Furthermore, PixelPrint phantoms offer more realistic testing conditions compared to traditional phantoms in the evaluation of novel CT technologies. This, in turn, promotes the translation of new technologies, such as DLR, into clinical practice.

Hybrid spectral CT system with clinical rapid kVp-switching x-ray tube and dual-layer detector for improved iodine quantification.

Spectral computed tomography (CT) is a powerful diagnostic tool offering quantitative material decomposition results that enhance clinical imaging by providing physiologic and functional insights. Iodine, a widely used contrast agent, improves visualization in various clinical contexts. However, accurately detecting low-concentration iodine presents challenges in spectral CT systems, particularly crucial for conditions like pancreatic cancer assessment. In this study, we present preliminary results from our hybrid spectral CT instrumentation which includes clinical-grade hardware (rapid kVp-switching x-ray tube, dual-layer detector). This combination expands spectral datasets from two to four channels, wherein we hypothesize improved quantification accuracy for low-dose and low-iodine concentration cases. We modulate the system duty cycle to evaluate its impact on quantification noise and bias. We evaluate iodine quantification performance by comparing two hybrid weighting strategies alongside rapid kVp-switching. This evaluation is performed with a polyamide phantom containing seven iodine inserts ranging from 0.5 to 20 mg/mL. In comparison to alternative methodologies, the maximum separation configuration, incorporating data from both the 80 kVp, low photon energy detector layer and the 140 kVp, high photon energy detector layer produces spectral images containing low quantitative noise and bias. This study presents initial evaluations on a hybrid spectral CT system, leveraging clinical hardware to demonstrate the potential for enhanced precision and sensitivity in spectral imaging. This research holds promise for advancing spectral CT imaging performance across diverse clinical scenarios.

Fully automatic online geometric calibration for non-circular cone-beam CT orbits using fiducials with unknown placement.

BACKGROUND: Cone-beam CT (CBCT) with non-circular scanning orbits can improve image quality for 3D intraoperative image guidance. However, geometric calibration of such scans can be challenging. Existing methods typically require a prior image, specialized phantoms, presumed repeatable orbits, or long computation time. PURPOSE: We propose a novel fully automatic online geometric calibration algorithm that does not require prior knowledge of fiducial configuration. The algorithm is fast, accurate, and can accommodate arbitrary scanning orbits and fiducial configurations. METHODS: The algorithm uses an automatic initialization process to eliminate human intervention in fiducial localization and an iterative refinement process to ensure robustness and accuracy. We provide a detailed explanation and implementation of the proposed algorithm. Physical experiments on a lab test bench and a clinical robotic C-arm scanner were conducted to evaluate spatial resolution performance and robustness under realistic constraints. RESULTS: Qualitative and quantitative results from the physical experiments demonstrate high accuracy, efficiency, and robustness of the proposed method. The spatial resolution performance matched that of our existing benchmark method, which used a 3D-2D registration-based geometric calibration algorithm. CONCLUSIONS: We have demonstrated an automatic online geometric calibration method that delivers high spatial resolution and robustness performance. This methodology enables arbitrary scan trajectories and should facilitate translation of such acquisition methods in a clinical setting.

Patient-derived PixelPrint phantoms for evaluating clinical imaging performance of a deep learning CT reconstruction algorithm.

Objective. Deep learning reconstruction (DLR) algorithms exhibit object-dependent resolution and noise performance. Thus, traditional geometric CT phantoms cannot fully capture the clinical imaging performance of DLR. This study uses a patient-derived 3D-printed PixelPrint lung phantom to evaluate a commercial DLR algorithm across a wide range of radiation dose levels.Method. The lung phantom used in this study is based on a patient chest CT scan containing ground glass opacities and was fabricated using PixelPrint 3D-printing technology. The phantom was placed inside two different size extension rings to mimic a small- and medium-sized patient and was scanned on a conventional CT scanner at exposures between 0.5 and 20 mGy. Each scan was reconstructed using filtered back projection (FBP), iterative reconstruction, and DLR at five levels of denoising. Image noise, contrast to noise ratio (CNR), root mean squared error, structural similarity index (SSIM), and multi-scale SSIM (MS SSIM) were calculated for each image.Results.DLR demonstrated superior performance compared to FBP and iterative reconstruction for all measured metrics in both phantom sizes, with better performance for more aggressive denoising levels. DLR was estimated to reduce dose by 25%-83% in the small phantom and by 50%-83% in the medium phantom without decreasing image quality for any of the metrics measured in this study. These dose reduction estimates are more conservative compared to the estimates obtained when only considering noise and CNR.Conclusion. DLR has the capability of producing diagnostic image quality at up to 83% lower radiation dose, which can improve the clinical utility and viability of lower dose CT scans. Furthermore, the PixelPrint phantom used in this study offers an improved testing environment with more realistic tissue structures compared to traditional CT phantoms, allowing for structure-based image quality evaluation beyond noise and contrast-based assessments.

Patient-derived PixelPrint phantoms for evaluating clinical imaging performance of a deep learning CT reconstruction algorithm.

Objective: Deep learning reconstruction (DLR) algorithms exhibit object-dependent resolution and noise performance. Thus, traditional geometric CT phantoms cannot fully capture the clinical imaging performance of DLR. This study uses a patient-derived 3D-printed PixelPrint lung phantom to evaluate a commercial DLR algorithm across a wide range of radiation dose levels. Approach: The lung phantom used in this study is based on a patient chest CT scan containing ground glass opacities and was fabricated using PixelPrint 3D-printing technology. The phantom was placed inside two different sized extension rings to mimic a small and medium sized patient and was scanned on a conventional CT scanner at exposures between 0.5 and 20 mGy. Each scan was reconstructed using filtered back projection (FBP), iterative reconstruction, and DLR at five levels of denoising. Image noise, contrast to noise ratio (CNR), root mean squared error (RMSE), structural similarity index (SSIM), and multi-scale SSIM (MS SSIM) were calculated for each image. Main Results: DLR demonstrated superior performance compared to FBP and iterative reconstruction for all measured metrics in both phantom sizes, with better performance for more aggressive denoising levels. DLR was estimated to reduce dose by 25-83% in the small phantom and by 50-83% in the medium phantom without decreasing image quality for any of the metrics measured in this study. These dose reduction estimates are more conservative compared to the estimates obtained when only considering noise and CNR with a non-anatomical physics phantom. Significance: DLR has the capability of producing diagnostic image quality at up to 83% lower radiation dose which can improve the clinical utility and viability of lower dose CT scans. Furthermore, the PixelPrint phantom used in this study offers an improved testing environment with more realistic tissue structures compared to traditional CT phantoms, allowing for structure-based image quality evaluation beyond noise and contrast-based assessments.

Notice of Removal: Fourier Diffusion Models: A Method to Control MTF and NPS in Score-Based Stochastic Image Generation.

Removed.

Three-material decomposition using a dual-layer flat panel detector in the presence of soft tissue motion.

Digital subtraction angiography (DSA) is a widely used technique for the visualization of contrast-enhanced structures. However, temporal subtraction DSA is challenged by misregistration artifacts due to patient motion and incomplete separation of iodine contrast agent from background soft tissue and bone. In this work, we propose an approach that allows three-material decomposition using a dual-layer flat panel detector in the presence of soft tissue motion. We assume the calcium signal (bone) remains stationary in the pre- and post-contrast images but allow soft tissues to move freely (e.g. cardiac motion). The dual-layer pre- and post-injection images form and ensemble of four measurements that permits material decomposition of four bases (pre- and post-injection soft tissue, calcium, and iodine). We apply two different processing techniques: 1) a modified lookup table and; 2) a model-based material estimation. These are compared with previously proposed DSA methods using temporal subtraction and hybrid (dual-energy) subtraction. Investigations were performed using an XCAT thorax phantom simulating a breath-hold. The pre- and post-contrast measurements were simulated at different time points within a cardiac cycle. Both the lookup table and model-based algorithms eliminate motion artifact as a result of soft tissue motion and allow good separation of iodine, bone, and soft tissue. While the lookup table algorithm contains high noise at the simulated dose level, the model-based algorithm produced iodine images that allow the visualization of major vessels around the heart. In contrast, traditional temporal DSA is susceptible to subtraction artifacts and hybrid DSA shows increased noise.

PixelPrint: A collection of three-dimensional printed CT phantoms of different respiratory diseases.

Imaging is often a first-line method for diagnostics and treatment. Radiological workflows increasingly mine medical images for quantifiable features. Variability in device/vendor, acquisition protocol, data processing, etc., can dramatically affect quantitative measures, including radiomics. We recently developed a method (PixelPrint) for 3D-printing lifelike computed tomography (CT) lung phantoms, paving the way for future diagnostic imaging standardization. PixelPrint generates phantoms with accurate attenuation profiles and textures by directly translating clinical images into printer instructions that control density on a voxel-by-voxel basis. The present study introduces a library of 3D printed lung phantoms covering a wide range of lung diseases, including usual interstitial pneumonia with advanced fibrosis, chronic hypersensitivity pneumonitis, secondary tuberculosis, cystic fibrosis, Kaposi sarcoma, and pulmonary edema. CT images of the patient-based phantom are qualitatively comparable to original CT images, both in texture, resolution and contrast levels allowing for clear visualization of even subtle imaging abnormalities. The variety of cases chosen for printing include both benign and malignant pathology causing a variety of alveolar and advanced interstitial abnormalities, both clearly visualized on the phantoms. A comparison of regions of interest revealed differences in attenuation below 6 HU. Identical features on the patient and the phantom have a high degree of geometrical correlation, with differences smaller than the intrinsic spatial resolution of the scans. Using PixelPrint, it is possible to generate CT phantoms that accurately represent different pulmonary diseases and their characteristic imaging features.

Approaches for Three Material Decomposition using a Triple-Layer Flat-Panel Detector.

X-ray spectral imaging has been increasingly investigated in radiography and interventional imaging. Flat-panel detectors with more than one detection layer have demonstrated advantages in providing separate soft tissue and bone images. Current dual-layer flat-panel detectors (DL-FPD) have limited capability to further differentiate between iodinated contrast agent and bony/calcified structures. In this work, we investigate a triple-layer flat-panel detector (TL-FPD) and the feasibility of three-material (water/calcium/iodine) decomposition. A physical model of TL-FPD, including system geometry, spectrum sensitivities, blur and noise models was developed. Using simulated triple-layer projections, three-material decompositions were performed using three different processing methods: polynomial-based, model-based, and a machine learning-based method (ResUnet). We find that the polynomial-based method leads to very noisy images with poor differentiation between calcium and iodine maps. The model-based method achieved much lower noise levels than the polynomial-based method but exhibited residual errors between the iodine and calcium channels. The ResUnet method offered the best decompositions among the investigated methods in terms of root mean square error from the ground truth and noise in the material maps. These preliminary results demonstrate the feasibility of three-material decomposition using TL-FPD and suggest a path for clinical translation of single-shot contrast/iodine differentiation in radiography and fluoroscopy.

Revealing pelvic structures in the presence of metal hip prothesis via non-circular CBCT orbits.

As the expansion of Cone Beam CT (CBCT) to new interventional procedures continues, the burdensome challenge of metal artifacts remains. Photon starvation and beam hardening from metallic implants and surgical tools in the field of view can result in the anatomy of interest being partially or fully obscured by imaging artifacts. Leveraging the flexibility of modern robotic CBCT imaging systems, implementing non-circular orbits designed for reducing metal artifacts by ensuring data-completeness during acquisition has become a reality. Here, we investigate using non-circular orbits to reduce metal artifacts arising from metallic hip prostheses when imaging pelvic anatomy. As a first proof-of-concept, we implement a sinusoidal and a double-circle-arc orbit on a CBCT test bench, imaging a physical pelvis phantom, with two metal hip prostheses, housing a 3D-printed iodine-filled radial line-pair target. A standard circular orbit implemented with the CBCT test bench acted as comparator. Imaging data collection and processing, geometric calibration and image reconstruction was completed using in-house developed software programs. Imaging with the standard circular orbit, image artifacts were observed in the pelvic bones and only 33 out of the possible 45 line-pairs of the radial line-pair target were partially resolvable in the reconstructed images. Comparatively, imaging with both the sinusoid and double-circle-arc orbits reduced artifacts in the surrounding anatomy and enabled all 45 line-pairs to be visibly resolved in the reconstructed images. These results indicate the potential of non-circular orbits to assist in revealing previously obstructed structures in the pelvic region in the presence of metal hip prosthesis.

Design and fabrication of 3D-printed patient-specific soft tissue and bone phantoms for CT imaging.

The objective of this study is to create patient-specific phantoms for computed tomography (CT) that possess accurate densities and exhibit visually realistic image textures. These qualities are crucial for evaluating CT performance in clinical settings. The study builds upon a previously presented 3D printing method (PixelPrint) by incorporating soft tissue and bone structures. We converted patient DICOM images directly into 3D printer instructions using PixelPrint and utilized calcium-doped filament to increase the Hounsfield unit (HU) range. Density was modeled by controlling printing speed according to volumetric filament ratio to emulate attenuation profiles. We designed micro-CT phantoms to demonstrate the reproducibility, and to determine mapping between filament ratios and HU values on clinical CT systems. Patient phantoms based on clinical cervical spine and knee examinations were manufactured and scanned with a clinical spectral CT scanner. The CT images of the patient-based phantom closely resembled original CT images in visual texture and contrast. Micro-CT analysis revealed minimal variations between prints, with an overall deviation of ± 0.8% in filament line spacing and ± 0.022 mm in line width. Measured differences between patient and phantom were less than 12 HU for soft tissue and 15 HU for bone marrow, and 514 HU for cortical bone. The calcium-doped filament accurately represented bony tissue structures across different X-ray energies in spectral CT (RMSE ranging from ± 3 to ± 28 HU, compared to 400 mg/ml hydroxyapatite). In conclusion, this study demonstrated the possibility of extending 3D-printed patient-based phantoms to soft tissue and bone structures while maintaining accurate organ geometry, image texture, and attenuation profiles.

Consistency of spectral results in cardiac dual-source photon-counting CT.

We evaluate stability of spectral results at different heart rates, acquisition modes, and cardiac phases in first-generation clinical dual-source photon-counting CT (PCCT). A cardiac motion simulator with a coronary stenosis mimicking a 50% eccentric calcium plaque was scanned at five different heart rates (0, 60-100 bpm) with the three available cardiac scan modes (high pitch prospectively ECG-triggered spiral, prospectively ECG-triggered axial, retrospectively ECG-gated spiral). Subsequently, full width half max (FWHM) of the stenosis, Dice score (DSC) for the stenosed region, and eccentricity of the non-stenosed region were calculated for virtual monoenergetic images (VMI) at 50, 70, and 150 keV and iodine density maps at both diastole and systole. FWHM averaged differences of - 0.20, - 0.28, and - 0.15 mm relative to static FWHM at VMI 150 keV across acquisition parameters for high pitch prospectively ECG-triggered spiral, prospectively ECG-triggered axial, and retrospectively ECG-gated spiral scans, respectively. Additionally, there was no effect of heart rate and acquisition mode on FWHM at diastole (p-values < 0.001). DSC demonstrated similarity among parameters with standard deviations of 0.08, 0.09, 0.11, and 0.08 for VMI 50, 70, and 150 keV, and iodine density maps, respectively, with insignificant differences at diastole (p-values < 0.01). Similarly, eccentricity illustrated small differences across heart rate and acquisition mode for each spectral result. Consistency of spectral results at different heart rates and acquisition modes for different cardiac phase demonstrates the added benefit of spectral results from PCCT to dual-source CT to further increase confidence in quantification and advance cardiovascular diagnostics.

Tunable neural networks for CT image formation.

Optimization of CT image quality typically involves balancing variance and bias. In traditional filtered back-projection, this trade-off is controlled by the filter cutoff frequency. In model-based iterative reconstruction, the regularization strength parameter often serves the same function. Deep neural networks (DNNs) typically do not provide this tunable control over output image properties. Models are often trained to minimize the expected mean squared error, which penalizes both variance and bias in image outputs but does not offer any control over the trade-off between the two. We propose a method for controlling the output image properties of neural networks with a new loss function called weighted covariance and bias (WCB). Our proposed method uses multiple noise realizations of the input images during training to allow for separate weighting matrices for the variance and bias penalty terms. Moreover, we show that tuning these weights enables targeted penalization of specific image features with spatial frequency domain penalties. To evaluate our method, we present a simulation study using digital anthropomorphic phantoms, physical simulation of CT measurements, and image formation with various algorithms. We show that the WCB loss function offers a greater degree of control over trade-offs between variance and bias, whereas mean-squared error provides only one specific image quality configuration. We also show that WCB can be used to control specific image properties including variance, bias, spatial resolution, and the noise correlation of neural network outputs. Finally, we present a method to optimize the proposed weights for a spiculated lung nodule shape discrimination task. Our results demonstrate this new image quality can control the image properties of DNN outputs and optimize image quality for task-specific performance.

Design and fabrication of 3D-printed patient-specific soft tissue and bone phantoms for CT imaging.

The objective of this study is to create patient-specific phantoms for computed tomography (CT) that have realistic image texture and densities, which are critical in evaluating CT performance in clinical settings. The study builds upon a previously presented 3D printing method (PixelPrint) by incorporating soft tissue and bone structures. We converted patient DICOM images directly into 3D printer instructions using PixelPrint and utilized stone-based filament to increase Hounsfield unit (HU) range. Density was modeled by controlling printing speed according to volumetric filament ratio to emulate attenuation profiles. We designed micro-CT phantoms to demonstrate the reproducibility and to determine mapping between filament ratios and HU values on clinical CT systems. Patient phantoms based on clinical cervical spine and knee examinations were manufactured and scanned with a clinical spectral CT scanner. The CT images of the patient-based phantom closely resembled original CT images in texture and contrast. Measured differences between patient and phantom were less than 15 HU for soft tissue and bone marrow. The stone-based filament accurately represented bony tissue structures across different X-ray energies, as measured by spectral CT. In conclusion, this study demonstrated the possibility of extending 3D-printed patient-based phantoms to soft tissue and bone structures while maintaining accurate organ geometry, image texture, and attenuation profiles.

Design and fabrication of 3D-printed patient-specific soft tissue and bone phantoms for CT imaging.

The objective of this study is to create patient-specific phantoms for computed tomography (CT) that have realistic image texture and densities, which are critical in evaluating CT performance in clinical settings. The study builds upon a previously presented 3D printing method (PixelPrint) by incorporating soft tissue and bone structures. We converted patient DICOM images directly into 3D printer instructions using PixelPrint and utilized stone-based filament to increase Hounsfield unit (HU) range. Density was modeled by controlling printing speed according to volumetric filament ratio to emulate attenuation profiles. We designed micro-CT phantoms to demonstrate the reproducibility and to determine mapping between filament ratios and HU values on clinical CT systems. Patient phantoms based on clinical cervical spine and knee examinations were manufactured and scanned with a clinical spectral CT scanner. The CT images of the patient-based phantom closely resembled original CT images in texture and contrast. Measured differences between patient and phantom were less than 15 HU for soft tissue and bone marrow. The stone-based filament accurately represented bony tissue structures across different X-ray energies, as measured by spectral CT. In conclusion, this study demonstrated the possibility of extending 3D-printed patient-based phantoms to soft tissue and bone structures while maintaining accurate organ geometry, image texture, and attenuation profiles.

Three-dimensional printing of patient-specific computed tomography lung phantoms: a reader study.

In modern clinical decision-support algorithms, heterogeneity in image characteristics due to variations in imaging systems and protocols hinders the development of reproducible quantitative measures including for feature extraction pipelines. With the help of a reader study, we investigate the ability to provide consistent ground-truth targets by using patient-specific 3D-printed lung phantoms. PixelPrint was developed for 3D-printing lifelike computed tomography (CT) lung phantoms by directly translating clinical images into printer instructions that control density on a voxel-by-voxel basis. Data sets of three COVID-19 patients served as input for 3D-printing lung phantoms. Five radiologists rated patient and phantom images for imaging characteristics and diagnostic confidence in a blinded reader study. Effect sizes of evaluating phantom as opposed to patient images were assessed using linear mixed models. Finally, PixelPrint's production reproducibility was evaluated. Images of patients and phantoms had little variation in the estimated mean (0.03-0.29, using a 1-5 scale). When comparing phantom images to patient images, effect size analysis revealed that the difference was within one-third of the inter- and intrareader variabilities. High correspondence between the four phantoms created using the same patient images was demonstrated by PixelPrint's production repeatability tests, with greater similarity scores between high-dose acquisitions of the phantoms than between clinical-dose acquisitions of a single phantom. We demonstrated PixelPrint's ability to produce lifelike CT lung phantoms reliably. These phantoms have the potential to provide ground-truth targets for validating the generalizability of inference-based decision-support algorithms between different health centers and imaging protocols and for optimizing examination protocols with realistic patient-based phantoms. Classification: CT lung phantoms, reader study.

Deep Learning CT Image Restoration using System Blur Models.

Restoration of images contaminated by blur is an important processing tool across modalities including computed tomography where the blur induced by various system factors can be complex with dependencies on acquisition and reconstruction protocol, and even be patient-dependent. In many cases, such a blur can be modeled and predicted with high accuracy providing an important input to a classical deconvolution approach. While traditional deblurring methods tend to be highly noise magnifying, deep learning approaches have the potential to improve upon classic performance limits. However, most network architectures base their restoration on data inputs alone without knowledge of the system blur. In this work, we explore a deep learning approach that takes both image inputs as well as information that characterizes the system blur to combine modeling and deep learning approaches. We apply the approach to CT image restoration and compare with an image-only deep learning approach. We find that inclusion of the system blur model improves deblurring performance - suggesting the potential power of the combined modeling and deep learning technique.

Local Linearity Analysis of Deep Learning CT Denoising Algorithms.

The rapid development of deep-learning methods in medical imaging has called for an analysis method suitable for non-linear and data-dependent algorithms. In this work, we investigate a local linearity analysis where a complex neural network can be represented as piecewise linear systems. We recognize that a large number of neural networks consists of alternating linear layers and rectified linear unit (ReLU) activations, and are therefore strictly piecewise linear. We investigated the extent of these locally linear regions by gradually adding perturbations to an operating point. For this work, we explored perturbations based on image features of interest, including lesion contrast, background, and additive noise. We then developed strategies to extend these strictly locally linear regions to include neighboring linear regions with similar gradients. Using these approximately linear regions, we applied singular value decomposition (SVD) analysis to each local linear system to investigate and explain the overall nonlinear and data-dependent behaviors of neural networks. The analysis was applied to an example CT denoising algorithm trained on thorax CT scans. We observed that the strictly local linear regions are highly sensitive to small signal perturbations. Over a range of lesion contrast from 0.007 to 0.04 mm-1, there is a total of 33992 linear regions. The Jacobians are also shift-variant. However, the Jacobians of neighboring linear regions are very similar. By combining linear regions with similar Jacobians, we narrowed down the number of approximately linear regions to four over lesion contrast from 0.001 to 0.08 mm-1. The SVD analysis to different linear regions revealed denoising behavior that is highly dependent on the background intensity. Analysis further identified greater amount of noise reduction in uniform regions compared to lesion edges. In summary, the local linearity analysis framework we proposed has the potential for us to better characterize and interpret the non-linear and data-dependent behaviors of neural networks.

PixelPrint: Three-dimensional printing of realistic patient-specific lung phantoms for CT imaging.

Phantoms are essential tools for assessing and verifying performance in computed tomography (CT). Realistic patient-based lung phantoms that accurately represent textures and densities are essential in developing and evaluating novel CT hardware and software. This study introduces PixelPrint, a 3D-printing solution to create patient-specific lung phantoms with accurate contrast and textures. PixelPrint converts patient images directly into printer instructions, where density is modeled as the ratio of filament to voxel volume to emulate local attenuation values. For evaluation of PixelPrint, phantoms based on four COVID-19 pneumonia patients were manufactured and scanned with the original (clinical) CT scanners and protocols. Density and geometrical accuracies between phantom and patient images were evaluated for various anatomical features in the lung, and a radiomic feature comparison was performed for mild, moderate, and severe COVID-19 pneumonia patient-based phantoms. Qualitatively, CT images of the patient-based phantoms closely resemble the original CT images, both in texture and contrast levels, with clearly visible vascular and parenchymal structures. Regions-of-interest (ROIs) comparing attenuation demonstrated differences below 15 HU. Manual size measurements performed by an experienced thoracic radiologist revealed a high degree of geometrical correlation between identical patient and phantom features, with differences smaller than the intrinsic spatial resolution of the images. Radiomic feature analysis revealed high correspondence, with correlations of 0.95-0.99 between patient and phantom images. Our study demonstrates the feasibility of 3D-printed patient-based lung phantoms with accurate geometry, texture, and contrast that will enable protocol optimization, CT research and development advancements, and generation of ground-truth datasets for radiomic evaluations.