Phase-contrast virtual chest radiography.

Respiratory X-ray imaging enhanced by phase contrast has shown improved airway visualization in animal models. Limitations in current X-ray technology have nevertheless hindered clinical translation, leaving the potential clinical impact an open question. Here, we explore phase-contrast chest radiography in a realistic in silico framework. Specifically, we use preprocessed virtual patients to generate in silico chest radiographs by Fresnel-diffraction simulations of X-ray wave propagation. Following a reader study conducted with clinical radiologists, we predict that phase-contrast edge enhancement will have a negligible impact on improving solitary pulmonary nodule detection (6 to 20 mm). However, edge enhancement of bronchial walls visualizes small airways (< 2 mm), which are invisible in conventional radiography. Our results show that phase-contrast chest radiography could play a future role in observing small-airway obstruction (e.g., relevant for asthma or early-stage chronic obstructive pulmonary disease), which cannot be directly visualized using current clinical methods, thereby motivating the experimental development needed for clinical translation. Finally, we discuss quantitative requirements on distances and X-ray source/detector specifications for clinical implementation of phase-contrast chest radiography.

The Effects of Free Breathing on Cerebral Venous Flow: A Real-Time Phase Contrast MRI Study in Healthy Adults.

Quantifying the effects of free breathing on cerebral venous flow is crucial for understanding cerebral circulation mechanisms and clinical applications. Unlike conventional cine phase-contrast MRI sequences (CINE-PC), real-time phase-contrast MRI sequences (RT-PC) can provide a continuous beat-to-beat flow signal that makes it possible to quantify the effect of breathing on cerebral venous flow. In this study, we examined 28 healthy human participants, comprising of 14 males and 14 females. Blood flows in the right/left internal jugular veins in the extracranial plane and the superior sagittal sinus (SSS) and straight sinus in the intercranial plane were quantified using CINE-PC and RT-PC. The first objective of this study was to determine the accuracy of RT-PC in quantifying cerebral venous flow, relative to CINE-PC. The second, and main objective, was to quantify the effect of free breathing on cerebral venous flow, using a time-domain multiparameter analysis method. Our results showed that RT-PC can accurately quantify cerebral venous flow with a 2 × 2 mm2 spatial resolution and 75 ms/image time resolution. The mean flow rate, amplitude, stroke volume, and cardiac period of cerebral veins were significantly higher from the mid-end phase of expiration to the mid-end phase of inspiration. Breathing affected the mean flow rates in the jugular veins more than those in the SSS and straight sinus. Furthermore, the effects of free breathing on the flow rate of the left and right jugular veins were not synchronous. These new findings provide a useful reference for better understanding the mechanisms of cerebral circulation.

Obliteration of portal venules contributes to portal hypertension in biliary cirrhosis.

The effects of the obliteration of portal venules (OPV) in cirrhotic portal hypertension are poorly understood. To investigate its contribution to portal hypertension in biliary cirrhosis and its underlying mechanism, we evaluated OPV using two-dimensional (2D) histopathology in liver explants from patients with biliary atresia (BA, n = 63), primary biliary cholangitis (PBC, n = 18), and hepatitis B-related cirrhosis (Hep-B-cirrhosis, n = 35). Then, three-dimensional (3D) OPV was measured by X-ray phase-contrast CT in two parallel models in rats following bile duct ligation (BDL) or carbon tetrachloride (CCl4) administration, representing biliary cirrhosis and post-necrotic cirrhosis, respectively. The portal pressure was also measured in the two models. Finally, the effects of proliferative bile ducts on OPV were investigated. We found that OPV was significantly more frequent in patients with biliary cirrhosis, including BA (78.57 ± 16.45%) and PBC (60.00 ± 17.15%), than that in Hep-B-cirrhotic patients (29.43 ± 14.94%, p < 0.001). OPV occurred earlier, evidenced by the paired liver biopsy at a Kasai procedure (KP), and was irreversible even after a successful KP in the patients with BA. OPV was also significantly more frequent in the BDL models than in the CCl4 models, as shown by 2D and 3D quantitative analysis. Portal pressure was significantly higher in the BDL model than that in the CCl4 model. With the proliferation of bile ducts, portal venules were compressed and irreversibly occluded, contributing to the earlier and higher portal pressure in biliary cirrhosis. OPV, as a pre-sinusoidal component, plays a key role in the pathogenesis of portal hypertension in biliary cirrhosis. The proliferated bile ducts and ductules gradually take up the 'territory' originally attributed to portal venules and compress the portal venules, which may lead to OPV in biliary cirrhosis. © 2024 The Pathological Society of Great Britain and Ireland.

A high-resolution phase-contrast microscopy system for label-free imaging in living cells.

Cell biologists have long sought the ability to observe intracellular structures in living cells without labels. This study presents procedures to adjust a commercially available apodized phase-contrast (APC) microscopy system for better visualizing the dynamic behaviors of various subcellular organelles in living cells. By harnessing the versatility of this technique to capture sequential images, we could observe morphological changes in cellular geometry after virus infection in real time without probes or invasive staining. The tune-up APC microscopy system is a highly efficient platform for simultaneously observing the dynamic behaviors of diverse subcellular structures with exceptional resolution.

Deep learning-based segmentation of subcellular organelles in high-resolution phase-contrast images.

Although quantitative analysis of biological images demands precise extraction of specific organelles or cells, it remains challenging in broad-field grayscale images, where traditional thresholding methods have been hampered due to complex image features. Nevertheless, rapidly growing artificial intelligence technology is overcoming obstacles. We previously reported the fine-tuned apodized phase-contrast microscopy system to capture high-resolution, label-free images of organelle dynamics in unstained living cells (Shimasaki, K. et al. (2024). Cell Struct. Funct., 49: 21-29). We here showed machine learning-based segmentation models for subcellular targeted objects in phase-contrast images using fluorescent markers as origins of ground truth masks. This method enables accurate segmentation of organelles in high-resolution phase-contrast images, providing a practical framework for studying cellular dynamics in unstained living cells.Key words: label-free imaging, organelle dynamics, apodized phase contrast, deep learning-based segmentation.

DFT-Assisted Investigation of the Electric Field and Charge Density Distribution of Pristine and Defective 2D WSe2 by Differential Phase Contrast Imaging.

Most properties of solid materials are defined by their internal electric field and charge density distributions which so far are difficult to measure with high spatial resolution. Especially for 2D materials, the atomic electric fields influence the optoelectronic properties. In this study, the atomic-scale electric field and charge density distribution of WSe2 bi- and trilayers are revealed using an emerging microscopy technique, differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). For pristine material, a higher positive charge density located at the selenium atomic columns compared to the tungsten atomic columns is obtained and tentatively explained by a coherent scattering effect. Furthermore, the change in the electric field distribution induced by a missing selenium atomic column is investigated. A characteristic electric field distribution in the vicinity of the defect with locally reduced magnitudes compared to the pristine lattice is observed. This effect is accompanied by a considerable inward relaxation of the surrounding lattice, which according to first principles DFT calculation is fully compatible with a missing column of Se atoms. This shows that DPC imaging, as an electric field sensitive technique, provides additional and remarkable information to the otherwise only structural analysis obtained with conventional STEM imaging.

High-angular-sensitivity X-ray phase-contrast microtomography of soft tissue through a two-directional beam-tracking synchrotron set-up.

Two-directional beam-tracking (2DBT) is a method for phase-contrast imaging and tomography that uses an intensity modulator to structure the X-ray beam into an array of independent circular beamlets that are resolved by a high-resolution detector. It features isotropic spatial resolution, provides two-dimensional phase sensitivity, and enables the three-dimensional reconstructions of the refractive index decrement, δ, and the attenuation coefficient, µ. In this work, the angular sensitivity and the spatial resolution of 2DBT images in a synchrotron-based implementation is reported. In its best configuration, angular sensitivities of ∼20 nrad and spatial resolution of at least 6.25 µm in phase-contrast images were obtained. Exemplar application to the three-dimensional imaging of soft tissue samples, including a mouse liver and a decellularized porcine dermis, is also demonstrated.

Signal-to-noise and spatial resolution in in-line imaging. 1. Basic theory, numerical simulations and planar experimental images.

Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to the detector plane, followed by phase retrieval in accordance with Paganin's method, can increase the signal-to-noise in the resultant images without deteriorating the spatial resolution. This results in violation of the noise-resolution uncertainty principle and demonstrates `unreasonable' effectiveness of the method. On the other hand, when the process of free-space propagation is performed in software, using the detected intensity distribution in the object plane, it cannot reproduce the same effectiveness, due to the amplification of photon shot noise. Here, it is shown that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the real decrement to the imaginary part of the refractive index of the imaged object. The relevant theoretical analysis is performed first, followed by computer simulations and then by a brief test using experimental images collected at a synchrotron beamline. More extensive experimental tests will be presented in the second part of this paper.

High Throughput Tomography (HiTT) on EMBL beamline P14 on PETRA III.

Here, high-throughput tomography (HiTT), a fast and versatile phase-contrast imaging platform for life-science samples on the EMBL beamline P14 at DESY in Hamburg, Germany, is presented. A high-photon-flux undulator beamline is used to perform tomographic phase-contrast acquisition in about two minutes which is linked to an automated data processing pipeline that delivers a 3D reconstructed data set less than a minute and a half after the completion of the X-ray scan. Combining this workflow with a sophisticated robotic sample changer enables the streamlined collection and reconstruction of X-ray imaging data from potentially hundreds of samples during a beam-time shift. HiTT permits optimal data collection for many different samples and makes possible the imaging of large sample cohorts thus allowing population studies to be attempted. The successful application of HiTT on various soft tissue samples in both liquid (hydrated and also dehydrated) and paraffin-embedded preparations is demonstrated. Furthermore, the feasibility of HiTT to be used as a targeting tool for volume electron microscopy, as well as using HiTT to study plant morphology, is demonstrated. It is also shown how the high-throughput nature of the work has allowed large numbers of `identical' samples to be imaged to enable statistically relevant sample volumes to be studied.

X-ray phase-contrast tomography of cells manipulated with an optical stretcher.

X-rays can penetrate deeply into biological cells and thus allow for examination of their internal structures with high spatial resolution. In this study, X-ray phase-contrast imaging and tomography is combined with an X-ray-compatible optical stretcher and microfluidic sample delivery. Using this setup, individual cells can be kept in suspension while they are examined with the X-ray beam at a synchrotron. From the recorded holograms, 2D phase shift images that are proportional to the projected local electron density of the investigated cell can be calculated. From the tomographic reconstruction of multiple such projections the 3D electron density can be obtained. The cells can thus be studied in a hydrated or even living state, thus avoiding artifacts from freezing, drying or embedding, and can in principle also be subjected to different sample environments or mechanical strains. This combination of techniques is applied to living as well as fixed and stained NIH3T3 mouse fibroblasts and the effect of the beam energy on the phase shifts is investigated. Furthermore, a 3D algebraic reconstruction scheme and a dedicated mathematical description is used to follow the motion of the trapped cells in the optical stretcher for multiple rotations.

BEATS: BEAmline for synchrotron X-ray microTomography at SESAME.

The ID10 beamline of the SESAME (Synchrotron-light for Experimental Science and Applications in the Middle East) synchrotron light source in Jordan was inaugurated in June 2023 and is now open to scientific users. The beamline, which was designed and installed within the European Horizon 2020 project BEAmline for Tomography at SESAME (BEATS), provides full-field X-ray radiography and microtomography imaging with monochromatic or polychromatic X-rays up to photon energies of 100 keV. The photon source generated by a 2.9 T wavelength shifter with variable gap, and a double-multilayer monochromator system allow versatile application for experiments requiring either an X-ray beam with high intensity and flux, and/or a partially spatial coherent beam for phase-contrast applications. Sample manipulation and X-ray detection systems are designed to allow scanning samples with different size, weight and material, providing image voxel sizes from 13 µm down to 0.33 µm. A state-of-the-art computing infrastructure for data collection, three-dimensional (3D) image reconstruction and data analysis allows the visualization and exploration of results online within a few seconds from the completion of a scan. Insights from 3D X-ray imaging are key to the investigation of specimens from archaeology and cultural heritage, biology and health sciences, materials science and engineering, earth, environmental sciences and more. Microtomography scans and preliminary results obtained at the beamline demonstrate that the new beamline ID10-BEATS expands significantly the range of scientific applications that can be targeted at SESAME.

Deep learning to overcome Zernike phase-contrast nanoCT artifacts for automated micro-nano porosity segmentation in bone.

Bone material contains a hierarchical network of micro- and nano-cavities and channels, known as the lacuna-canalicular network (LCN), that is thought to play an important role in mechanobiology and turnover. The LCN comprises micrometer-sized lacunae, voids that house osteocytes, and submicrometer-sized canaliculi that connect bone cells. Characterization of this network in three dimensions is crucial for many bone studies. To quantify X-ray Zernike phase-contrast nanotomography data, deep learning is used to isolate and assess porosity in artifact-laden tomographies of zebrafish bones. A technical solution is proposed to overcome the halo and shade-off domains in order to reliably obtain the distribution and morphology of the LCN in the tomographic data. Convolutional neural network (CNN) models are utilized with increasing numbers of images, repeatedly validated by `error loss' and `accuracy' metrics. U-Net and Sensor3D CNN models were trained on data obtained from two different synchrotron Zernike phase-contrast transmission X-ray microscopes, the ANATOMIX beamline at SOLEIL (Paris, France) and the P05 beamline at PETRA III (Hamburg, Germany). The Sensor3D CNN model with a smaller batch size of 32 and a training data size of 70 images showed the best performance (accuracy 0.983 and error loss 0.032). The analysis procedures, validated by comparison with human-identified ground-truth images, correctly identified the voids within the bone matrix. This proposed approach may have further application to classify structures in volumetric images that contain non-linear artifacts that degrade image quality and hinder feature identification.

Denoising of dual-VENC PC-MRI with large high/low VENC ratios.

PURPOSE: Dual velocity encoding PC-MRI can produce spurious artifacts when using high ratios of velocity encoding values (VENCs), limiting its ability to generate high-quality images across a wide range of encoding velocities. This study aims to propose and compare dual-VENC correction methods for such artifacts. THEORY AND METHODS: Two denoising approaches based on spatiotemporal regularization are proposed and compared with a state-of-the-art method based on sign correction. Accuracy is assessed using simulated data from an aorta and brain aneurysm, as well as 8 two-dimensional (2D) PC-MRI ascending aorta datasets. Two temporal resolutions (30,60) ms and noise levels (9,12) dB are considered, with noise added to the complex magnetization. The error is evaluated with respect to the noise-free measurement in the synthetic case and to the unwrapped image without additional noise in the volunteer datasets. RESULTS: In all studied cases, the proposed methods are more accurate than the Sign Correction technique. Using simulated 2D+T data from the aorta (60 ms, 9 dB), the Dual-VENC (DV) error 0 . 82 ± 0 . 07 $$ 0.82\pm 0.07 $$ is reduced to: 0 . 66 ± 0 . 04 $$ 0.66\pm 0.04 $$ (Sign Correction); 0 . 34 ± 0 . 04 $$ 0.34\pm 0.04 $$ and 0 . 32 ± 0 . 04 $$ 0.32\pm 0.04 $$ (proposed techniques). The methods are found to be significantly different (p-value < 0 . 05 $$ <0.05 $$ ). Importantly, brain aneurysm data revealed that the Sign Correction method is not suitable, as it increases error when the flow is not unidirectional. All three methods improve the accuracy of in vivo data. CONCLUSION: The newly proposed methods outperform the Sign Correction method in improving dual-VENC PC-MRI images. Among them, the approach based on temporal differences has shown the highest accuracy.

K-t PCA accelerated in-plane balanced steady-state free precession phase-contrast (PC-SSFP) for all-in-one diastolic function evaluation.

PURPOSE: Diastolic function evaluation requires estimates of early and late diastolic mitral filling velocities (E and A) and of mitral annulus tissue velocity (e'). We aimed to develop an MRI method for simultaneous all-in-one diastolic function evaluation in a single scan by generating a 2D phase-contrast (PC) sequence with balanced steady-state free precession (bSSFP) contrast (PC-SSFP). E and A could then be measured with PC, and e' estimated by valve tracking on the magnitude images, using an established deep learning framework. METHODS: Our PC-SSFP used in-plane flow-encoding, with zeroth and first moment nulling over each TR. For further acceleration, different k-t principal component analysis (PCA) methods were investigated with both retrospective and prospective undersampling. PC-SSFP was compared to separate balanced SSFP cine and PC-gradient echo acquisitions in phantoms and in 10 healthy subjects. RESULTS: Phantom experiments showed that PC-SSFP measured accurate velocities compared to PC-gradient echo (r = 0.98 for a range of pixel-wise velocities -80 cm/s to 80 cm/s). In subjects, PC-SSFP generated high SNR and myocardium-blood contrast, and excellent agreement for E (limits of agreement [LOA] 0.8 ± 2.4 cm/s, r = 0.98), A (LOA 2.5 ± 4.1 cm/s, r = 0.97), and e' (LOA 0.3 ± 2.6 cm/s, r = 1.00), versus the standard methods. The best k-t PCA approach processed the complex difference data and substituted in raw k-space data. With prospective k-t PCA acceleration, higher frame rates were achieved (50 vs. 25 frames per second without k-t PCA), yielding a 13% higher e'. CONCLUSION: The proposed PC-SSFP method achieved all-in-one diastolic function evaluation.

Inline automatic quality control of 2D phase-contrast flow MRI for subject-specific scan time adaptation.

PURPOSE: To develop an inline automatic quality control to achieve consistent diagnostic image quality with subject-specific scan time, and to demonstrate this method for 2D phase-contrast flow MRI to reach a predetermined SNR. METHODS: We designed a closed-loop feedback framework between image reconstruction and data acquisition to intermittently check SNR (every 20 s) and automatically stop the acquisition when a target SNR is achieved. A free-breathing 2D pseudo-golden-angle spiral phase-contrast sequence was modified to listen for image-quality messages from the reconstructions. Ten healthy volunteers and 1 patient were imaged at 0.55 T. Target SNR was selected based on retrospective analysis of cardiac output error, and performance of the automatic SNR-driven "stop" was assessed inline. RESULTS: SNR calculation and automated segmentation was feasible within 20 s with inline deployment. The SNR-driven acquisition time was 2 min 39 s ± 67 s (aorta) and 3 min ± 80 s (main pulmonary artery) with a min/max acquisition time of 1 min 43 s/4 min 52 s (aorta) and 1 min 43 s/5 min 50 s (main pulmonary artery) across 6 healthy volunteers, while ensuring a diagnostic measurement with relative absolute error in quantitative flow measurement lower than 2.1% (aorta) and 6.3% (main pulmonary artery). CONCLUSION: The inline quality control enables subject-specific optimized scan times while ensuring consistent diagnostic image quality. The distribution of automated stopping times across the population revealed the value of a subject-specific scan time.

Phase contrast MRI with minimized background phase errors.

PURPOSE: Phase contrast MRI (PC-MRI) is used clinically to measure velocities in the body, but systematic background phase errors caused by magnetic field imperfections corrupt the velocity measurements with offsets that limit clinical utility. This work aims to minimize systematic background phase errors in PC-MRI, thereby maximizing the accuracy of velocity measurements. METHODS: The MRI scanner's background phase errors from eddy currents and mechanical oscillations were modeled using the gradient impulse response function (GIRF). Gradient waveforms were then numerically optimized using the GIRF to create pulse sequences that minimize the background phase errors. The pulse sequences were tested in a static phantom where the predicted response could be compared directly to the measured background velocity. The optimized acquisitions were then tested in human subjects, where flow rates and background errors were compared to conventional PC-MRI. RESULTS: When using the GIRF-optimized gradient waveforms, the predicted background phase was within 0.6 [95% CI = -3.4, 5.4] mm/s of the measured background phase in a static phantom. Excellent agreement was seen for in vivo blood flow values (flow rate agreement r 2 $$ {r}^2 $$ = 0.96), and the background phase was reduced by 78.8 ± $$ \pm $$ 18.7%. CONCLUSION: This work shows that using a GIRF to model the effects of magnetic field imperfections combined with numerically optimized gradient waveforms enables PC-MRI waveforms to be designed to produce a minimal background phase in the most time-efficient manner. The methodology could be adapted for other MRI sequences where similar magnetic field errors affect measurements.

Tricuspid valve flow measurement using a deep learning framework for automated valve-tracking 2D phase contrast.

PURPOSE: Tricuspid valve flow velocities are challenging to measure with cardiovascular MR, as the rapidly moving valvular plane prohibits direct flow evaluation, but they are vitally important to diastolic function evaluation. We developed an automated valve-tracking 2D method for measuring flow through the dynamic tricuspid valve. METHODS: Nine healthy subjects and 2 patients were imaged. The approach uses a previously trained deep learning network, TVnet, to automatically track the tricuspid valve plane from long-axis cine images. Subsequently, the tracking information is used to acquire 2D phase contrast (PC) with a dynamic (moving) acquisition plane that tracks the valve. Direct diastolic net flows evaluated from the dynamic PC sequence were compared with flows from 2D-PC scans acquired in a static slice localized at the end-systolic valve position, and also ventricular stroke volumes (SVs) using both planimetry and 2D PC of the great vessels. RESULTS: The mean tricuspid valve systolic excursion was 17.8 ± 2.5 mm. The 2D valve-tracking PC net diastolic flow showed excellent correlation with SV by right-ventricle planimetry (bias ± 1.96 SD = -0.2 ± 10.4 mL, intraclass correlation coefficient [ICC] = 0.92) and aortic PC (-1.0 ± 13.8 mL, ICC = 0.87). In comparison, static tricuspid valve 2D PC also showed a strong correlation but had greater bias (p = 0.01) versus the right-ventricle SV (10.6 ± 16.1 mL, ICC = 0.61). In most (8 of 9) healthy subjects, trace regurgitation was measured at begin-systole. In one patient, valve-tracking PC displayed a high-velocity jet (380 cm/s) with maximal velocity agreeing with echocardiography. CONCLUSION: Automated valve-tracking 2D PC is a feasible route toward evaluation of tricuspid regurgitant velocities, potentially solving a major clinical challenge.

GRASP reconstruction amplified with view-sharing and KWIC filtering reduces underestimation of peak velocity in highly-accelerated real-time phase-contrast MRI: A preliminary evaluation in pediatric patients with congenital heart disease.

PURPOSE: To develop a highly-accelerated, real-time phase contrast (rtPC) MRI pulse sequence with 40 fps frame rate (25 ms effective temporal resolution). METHODS: Highly-accelerated golden-angle radial sparse parallel (GRASP) with over regularization may result in temporal blurring, which in turn causes underestimation of peak velocity. Thus, we amplified GRASP performance by synergistically combining view-sharing (VS) and k-space weighted image contrast (KWIC) filtering. In 17 pediatric patients with congenital heart disease (CHD), the conventional GRASP and the proposed GRASP amplified by VS and KWIC (or GRASP + VS + KWIC) reconstruction for rtPC MRI were compared with respect to clinical standard PC MRI in measuring hemodynamic parameters (peak velocity, forward volume, backward volume, regurgitant fraction) at four locations (aortic valve, pulmonary valve, left and right pulmonary arteries). RESULTS: The proposed reconstruction method (GRASP + VS + KWIC) achieved better effective spatial resolution (i.e., image sharpness) compared with conventional GRASP, ultimately reducing the underestimation of peak velocity from 17.4% to 6.4%. The hemodynamic metrics (peak velocity, volumes) were not significantly (p > 0.99) different between GRASP + VS + KWIC and clinical PC, whereas peak velocity was significantly (p < 0.007) lower for conventional GRASP. RtPC with GRASP + VS + KWIC also showed the ability to assess beat-to-beat variation and detect the highest peak among peaks. CONCLUSION: The synergistic combination of GRASP, VS, and KWIC achieves 25 ms effective temporal resolution (40 fps frame rate), while minimizing the underestimation of peak velocity compared with conventional GRASP.

4D flow MRI velocity uncertainty quantification.

PURPOSE: An automatic method is presented for estimating 4D flow MRI velocity measurement uncertainty in each voxel. The velocity distance (VD) metric, a statistical distance between the measured velocity and local error distribution, is introduced as a novel measure of 4D flow MRI velocity measurement quality. METHODS: The method uses mass conservation to assess the local velocity error variance and the standardized difference of means (SDM) velocity to estimate the velocity error correlations. VD is evaluated as the Mahalanobis distance between the local velocity measurement and the local error distribution. The uncertainty model is validated synthetically and tested in vitro under different flow resolutions and noise levels. The VD's application is demonstrated on two in vivo thoracic vasculature 4D flow datasets. RESULTS: Synthetic results show the proposed uncertainty quantification method is sensitive to aliased regions across various velocity-to-noise ratios and assesses velocity error correlations in four- and six-point acquisitions with correlation errors at or under 3.2%. In vitro results demonstrate the method's sensitivity to spatial resolution, venc settings, partial volume effects, and phase wrapping error sources. Applying VD to assess in vivo 4D flow MRI in the aorta demonstrates the expected increase in measured velocity quality with contrast administration and systolic flow. CONCLUSION: The proposed 4D flow MRI uncertainty quantification method assesses velocity measurement error owing to sources including noise, intravoxel phase dispersion, and velocity aliasing. This method enables rigorous comparison of 4D flow MRI datasets obtained in longitudinal studies, across patient populations, and with different MRI systems.

An Eulerian formulation for the computational modeling of phase-contrast MRI.

PURPOSE: Computational simulation of phase-contrast MRI (PC-MRI) is an attractive way to physically interpret properties and errors in MRI-reconstructed flow velocity fields. Recent studies have developed PC-MRI simulators that solve the Bloch equation, with the magnetization transport being modeled using a Lagrangian approach. Because this method expresses the magnetization as spatial distribution of particles, influences of particle densities and their spatial uniformities on numerical accuracy are well known. This study developed an alternative method for PC-MRI modeling using an Eulerian approach in which the magnetization is expressed as a spatially smooth continuous function. METHODS: The magnetization motion was described using the Bloch equation with an advection term and computed on a fixed grid using a finite difference method, and k-space sampling was implemented using the spoiled gradient echo sequence. PC-MRI scans of a fully developed flow in straight and stenosed cylinders were acquired to provide numerical examples. RESULTS: Reconstructed flow in a straight cylinder showed excellent agreement with input velocity profiles and mean errors were less than 0.5% of the maximum velocity. Numerical cases of flow in a stenosed cylinder successfully demonstrated the velocity profiles, with displacement artifacts being dependent on scan parameters and intravoxel dephasing due to flow disturbances. These results were in good agreement with those obtained using the Lagrangian approach with a sufficient particle density. CONCLUSION: The feasibility of the Eulerian approach to PC-MRI modeling was successfully demonstrated.