A simulation-based phantom model for generating synthetic mitral valve image data-application to MRI acquisition planning.

PURPOSE: Numerical phantom methods are widely used in the development of medical imaging methods. They enable quantitative evaluation and direct comparison with controlled and known ground truth information. Cardiac magnetic resonance has the potential for a comprehensive evaluation of the mitral valve (MV). The goal of this work is the development of a numerical simulation framework that supports the investigation of MRI imaging strategies for the mitral valve. METHODS: We present a pipeline for synthetic image generation based on the combination of individual anatomical 3D models with a position-based dynamics simulation of the mitral valve closure. The corresponding images are generated using modality-specific intensity models and spatiotemporal sampling concepts. We test the applicability in the context of MRI imaging strategies for the assessment of the mitral valve. Synthetic images are generated with different strategies regarding image orientation (SAX and rLAX) and spatial sampling density. RESULTS: The suitability of the imaging strategy is evaluated by comparing MV segmentations against ground truth annotations. The generated synthetic images were compared to ones acquired with similar parameters, and the result is promising. The quantitative analysis of annotation results suggests that the rLAX sampling strategy is preferable for MV assessment, reaching accuracy values that are comparable to or even outperform literature values. CONCLUSION: The proposed approach provides a valuable tool for the evaluation and optimization of cardiac valve image acquisition. Its application to the use case identifies the radial image sampling strategy as the most suitable for MV assessment through MRI.

Deep Learning Segmentation of the Right Ventricle in Cardiac MRI: The M&Ms Challenge.

In recent years, several deep learning models have been proposed to accurately quantify and diagnose cardiac pathologies. These automated tools heavily rely on the accurate segmentation of cardiac structures in MRI images. However, segmentation of the right ventricle is challenging due to its highly complex shape and ill-defined borders. Hence, there is a need for new methods to handle such structure's geometrical and textural complexities, notably in the presence of pathologies such as Dilated Right Ventricle, Tricuspid Regurgitation, Arrhythmogenesis, Tetralogy of Fallot, and Inter-atrial Communication. The last MICCAI challenge on right ventricle segmentation was held in 2012 and included only 48 cases from a single clinical center. As part of the 12th Workshop on Statistical Atlases and Computational Models of the Heart (STACOM 2021), the M&Ms-2 challenge was organized to promote the interest of the research community around right ventricle segmentation in multi-disease, multi-view, and multi-center cardiac MRI. Three hundred sixty CMR cases, including short-axis and long-axis 4-chamber views, were collected from three Spanish hospitals using nine different scanners from three different vendors, and included a diverse set of right and left ventricle pathologies. The solutions provided by the participants show that nnU-Net achieved the best results overall. However, multi-view approaches were able to capture additional information, highlighting the need to integrate multiple cardiac diseases, views, scanners, and acquisition protocols to produce reliable automatic cardiac segmentation algorithms.

CT-Based Analysis of Left Ventricular Hemodynamics Using Statistical Shape Modeling and Computational Fluid Dynamics.

Background: Cardiac computed tomography (CCT) based computational fluid dynamics (CFD) allows to assess intracardiac flow features, which are hypothesized as an early predictor for heart diseases and may support treatment decisions. However, the understanding of intracardiac flow is challenging due to high variability in heart shapes and contractility. Using statistical shape modeling (SSM) in combination with CFD facilitates an intracardiac flow analysis. The aim of this study is to prove the usability of a new approach to describe various cohorts. Materials and Methods: CCT data of 125 patients (mean age: 60.6 ± 10.0 years, 16.8% woman) were used to generate SSMs representing aneurysmatic and non-aneurysmatic left ventricles (LVs). Using SSMs, seven group-averaged LV shapes and contraction fields were generated: four representing patients with and without aneurysms and with mild or severe mitral regurgitation (MR), and three distinguishing aneurysmatic patients with true, intermediate aneurysms, and globally hypokinetic LVs. End-diastolic LV volumes of the groups varied between 258 and 347 ml, whereas ejection fractions varied between 21 and 26%. MR degrees varied from 1.0 to 2.5. Prescribed motion CFD was used to simulate intracardiac flow, which was analyzed regarding large-scale flow features, kinetic energy, washout, and pressure gradients. Results: SSMs of aneurysmatic and non-aneurysmatic LVs were generated. Differences in shapes and contractility were found in the first three shape modes. Ninety percent of the cumulative shape variance is described with approximately 30 modes. A comparison of hemodynamics between all groups found shape-, contractility- and MR-dependent differences. Disturbed blood washout in the apex region was found in the aneurysmatic cases. With increasing MR, the diastolic jet becomes less coherent, whereas energy dissipation increases by decreasing kinetic energy. The poorest blood washout was found for the globally hypokinetic group, whereas the weakest blood washout in the apex region was found for the true aneurysm group. Conclusion: The proposed CCT-based analysis of hemodynamics combining CFD with SSM seems promising to facilitate the analysis of intracardiac flow, thus increasing the value of CCT for diagnostic and treatment decisions. With further enhancement of the computational approach, the methodology has the potential to be embedded in clinical routine workflows and support clinicians.

A Collaborative Approach for the Development and Application of Machine Learning Solutions for CMR-Based Cardiac Disease Classification.

The quality and acceptance of machine learning (ML) approaches in cardiovascular data interpretation depends strongly on model design and training and the interaction with the clinical experts. We hypothesize that a software infrastructure for the training and application of ML models can support the improvement of the model training and provide relevant information for understanding the classification-relevant data features. The presented solution supports an iterative training, evaluation, and exploration of machine-learning-based multimodal data interpretation methods considering cardiac MRI data. Correction, annotation, and exploration of clinical data and interpretation of results are supported through dedicated interactive visual analytics tools. We test the presented concept with two use cases from the ACDC and EMIDEC cardiac MRI image analysis challenges. In both applications, pre-trained 2D U-Nets are used for segmentation, and classifiers are trained for diagnostic tasks using radiomics features of the segmented anatomical structures. The solution was successfully used to identify outliers in automatic segmentation and image acquisition. The targeted curation and addition of expert annotations improved the performance of the machine learning models. Clinical experts were supported in understanding specific anatomical and functional characteristics of the assigned disease classes.

CT-Based Simulation of Left Ventricular Hemodynamics: A Pilot Study in Mitral Regurgitation and Left Ventricle Aneurysm Patients.

Background: Cardiac CT (CCT) is well suited for a detailed analysis of heart structures due to its high spatial resolution, but in contrast to MRI and echocardiography, CCT does not allow an assessment of intracardiac flow. Computational fluid dynamics (CFD) can complement this shortcoming. It enables the computation of hemodynamics at a high spatio-temporal resolution based on medical images. The aim of this proposed study is to establish a CCT-based CFD methodology for the analysis of left ventricle (LV) hemodynamics and to assess the usability of the computational framework for clinical practice. Materials and Methods: The methodology is demonstrated by means of four cases selected from a cohort of 125 multiphase CCT examinations of heart failure patients. These cases represent subcohorts of patients with and without LV aneurysm and with severe and no mitral regurgitation (MR). All selected LVs are dilated and characterized by a reduced ejection fraction (EF). End-diastolic and end-systolic image data was used to reconstruct LV geometries with 2D valves as well as the ventricular movement. The intraventricular hemodynamics were computed with a prescribed-motion CFD approach and evaluated in terms of large-scale flow patterns, energetic behavior, and intraventricular washout. Results: In the MR patients, a disrupted E-wave jet, a fragmentary diastolic vortex formation and an increased specific energy dissipation in systole are observed. In all cases, regions with an impaired washout are visible. The results furthermore indicate that considering several cycles might provide a more detailed view of the washout process. The pre-processing times and computational expenses are in reach of clinical feasibility. Conclusion: The proposed CCT-based CFD method allows to compute patient-specific intraventricular hemodynamics and thus complements the informative value of CCT. The method can be applied to any CCT data of common quality and represents a fair balance between model accuracy and overall expenses. With further model enhancements, the computational framework has the potential to be embedded in clinical routine workflows, to support clinical decision making and treatment planning.

Cascaded neural network-based CT image processing for aortic root analysis.

PURPOSE: Careful assessment of the aortic root is paramount to select an appropriate prosthesis for transcatheter aortic valve implantation (TAVI). Relevant information about the aortic root anatomy, such as the aortic annulus diameter, can be extracted from pre-interventional CT. In this work, we investigate a neural network-based approach for segmenting the aortic root as a basis for obtaining these parameters. METHODS: To support valve prosthesis selection, geometric measures of the aortic root are extracted from the patient's CT scan using a cascade of convolutional neural networks (CNNs). First, the image is reduced to the aortic root, valve, and left ventricular outflow tract (LVOT); within that subimage, the aortic valve and ascending aorta are segmented; and finally, the region around the aortic annulus. From the segmented annulus region, we infer the annulus orientation using principal component analysis (PCA). The area-derived diameter of the annulus is approximated based on the segmentation of the aortic root and LVOT and the plane orientation resulting from the PCA. RESULTS: The cascade of CNNs was trained using 90 expert-annotated contrast-enhanced CT scans routinely acquired for TAVI planning. Segmentation of the aorta and valve within the region of interest achieved an F1 score of 0.94 on the test set of 36 patients. The area-derived diameter within the annulus region was determined with a mean error below 2 mm between the automatic measurement and the diameter derived from annotations. The calculated diameters and resulting errors are comparable to published results of alternative approaches. CONCLUSIONS: The cascaded neural network approach enabled the assessment of the aortic root with a relatively small training set. The processing time amounts to 30 s per patient, facilitating time-efficient, reproducible measurements. An extended training data set, including different levels of calcification or special cases (e.g., pre-implanted valves), could further improve this method's applicability and robustness.

Interactive editing of virtual chordae tendineae for the simulation of the mitral valve in a decision support system.

PURPOSE: Decision support systems for mitral valve disease are an important step toward personalized surgery planning. A simulation of the mitral valve apparatus is required for decision support. Building a model of the chordae tendineae is an essential component of a mitral valve simulation. Due to image quality and artifacts, the chordae tendineae cannot be reliably detected in medical imaging. METHODS: Using the position-based dynamics framework, we are able to realistically simulate the opening and closing of the mitral valve. Here, we present a heuristic method for building an initial chordae model needed for a successful simulation. In addition to the heuristic, we present an interactive editor to refine the chordae model and to further improve pathology reproduction as well as geometric approximation of the closed valve. RESULTS: For evaluation, five mitral valves were reconstructed based on image sequences of patients scheduled for mitral valve surgery. We evaluated the approximation of the closed valves using either just the heuristic chordae model or a manually refined model. Using the manually refined models, prolapse was correctly reproduced in four of the five cases compared to two of the five cases when using the heuristic. In addition, using the editor improved the approximation in four cases. CONCLUSIONS: Our approach is suitable to create realistically parameterized mitral valve apparatus reconstructions for the simulation of normally and abnormally closing valves in a decision support system.

Analysis of three-chamber view conventional and tagged cine MRI in patients with suspected hypertrophic cardiomyopathy.

OBJECTIVES: To investigate the potential value of adding a tagged three-chamber (3Ch) cine to clinical hypertrophic cardiomyopathy (HCM) magnetic resonance imaging (MRI) protocols, including to help distinguish HCM patients with regionally impaired cardiac function. METHODS: Forty-eight HCM patients, five patients with "septal knuckle" (SK), and 20 healthy volunteers underwent MRI at 1.5T; a tagged 3Ch cine was added to the protocol. Regional strain, myocardial wall thickness, and mitral valve leaflet lengths were measured in the 3Ch view. RESULTS: In HCM, we found a reduced tangential strain with decreased diastolic relaxation in both hypertrophied (p = 0.003) and remote segments (p = 0.035). Strain in the basal septum correlated with the length of the coaptation zone + residual leaflet (r = 0.48, p < 0.001). In the basal free wall, patients with SK had faster relaxation compared to HCM patients with septal hypertrophy. DISCUSSION: The 3Ch tagged MRI sequence provides useful information for the examination of suspected HCM patients, with minimal additional time cost. Local wall function is closely associated with morphological changes of the mitral apparatus measured in the same plane and may provide insights into mechanisms of obstruction. The additional strain information may be helpful when analyzing local myocardial wall motion patterns in the presence of SK.

An extensible software platform for interdisciplinary cardiovascular imaging research.

BACKGROUND AND OBJECTIVE: Cardiovascular imaging is an exponentially growing field with aspects ranging from image acquisition and analysis to disease characterization, and evaluation of therapy approaches.The transfer of innovative new technological and algorithmic solutions into clinical practice is still slow. In addition to the verification of solutions, their integration in the clinical processing workflow must be enabled for the assessment of clinical impact and risks. The goal of our software platform for cardiac image processing - CAIPI - is to support researchers from different specialties such as imaging physics, computer science, and medicine by a common extensible platform to address typical challenges and hurdles in interdisciplinary cardiovascular imaging research. It provides an integrated solution for method comparison, integrated analysis, and validation in the clinical context. The interface concept enables a combination with existing frameworks that address specific aspects of the pipeline, such as modeling (e.g., OpenCMISS, CARP) or image reconstruction (Gadgetron). METHODS: In our platform, we developed a concept for import, integration, and management of cardiac image data. The integration approach considers the spatiotemporal properties of the beating heart through a specific data model. The solution is based on MeVisLab and provides functionalities for data retrieval and storage. Two types of plugins can be added. While ToolPlugins usually provide processing algorithms such as image correction and segmentation, AnalysisPlugins enable interactive data exploration and reporting. GUI integration concepts are presented for both plugin types. We developed domain-specific reporting and visualization tools (e.g., AHA segment model) to enable validation studies by clinical experts. The platform offers plugins for calculating and reporting quantitative parameters such as cardiac function, which can be used to, e.g., evaluate the effect of processing algorithms on clinical parameters. Export functionalities include quantitative measurements to Excel, image data to PACS, and STL models to modeling and simulation tools. RESULTS: To demonstrate the applicability of this concept both for method development and clinical application, we present use cases representing different problems along the innovation chain in cardiac MR imaging. Validation of an image reconstruction method (MRI T1 mapping) Validation of an image correction method for real-time 2D-PC MRI Comparison of quantification methods for blood flow analysis Training and integration of machine learning solutions with expert annotations Clinical studies with new imaging techniques (flow measurements in the carotid arteries and peripheral veins as well as cerebral spinal fluid). CONCLUSION: The presented platform can be used in interdisciplinary teams, in which engineers or data scientists perform the method validation, followed by clinical research studies in patient collectives. The demonstrated use cases show how it enables the transfer of innovations through validation in the cardiovascular application context.

Combining position-based dynamics and gradient vector flow for 4D mitral valve segmentation in TEE sequences.

PURPOSE: For planning and guidance of minimally invasive mitral valve repair procedures, 3D+t transesophageal echocardiography (TEE) sequences are acquired before and after the intervention. The valve is then visually and quantitatively assessed in selected phases. To enable a quantitative assessment of valve geometry and pathological properties in all heart phases, as well as the changes achieved through surgery, we aim to provide a new 4D segmentation method. METHODS: We propose a tracking-based approach combining gradient vector flow (GVF) and position-based dynamics (PBD). An open-state surface model of the valve is propagated through time to the closed state, attracted by the GVF field of the leaflet area. The PBD method ensures topological consistency during deformation. For evaluation, one expert in cardiac surgery annotated the closed-state leaflets in 10 TEE sequences of patients with normal and abnormal mitral valves, and defined the corresponding open-state models. RESULTS: The average point-to-surface distance between the manual annotations and the final tracked model was [Formula: see text]. Qualitatively, four cases were satisfactory, five passable and one unsatisfactory. Each sequence could be segmented in 2-6 min. CONCLUSION: Our approach enables to segment the mitral valve in 4D TEE image data with normal and pathological valve closing behavior. With this method, in addition to the quantification of the remaining orifice area, shape and dimensions of the coaptation zone can be analyzed and considered for planning and surgical result assessment.

User-dependent variability in mitral valve segmentation and its impact on CFD-computed hemodynamic parameters.

PURPOSE: While novel tools for segmentation of the mitral valve are often based on automatic image processing, they mostly require manual interaction by a proficient user. Those segmentations are essential for numerical support of mitral valve treatment using computational fluid dynamics, where the reconstructed geometry is incorporated into a simulation domain. To quantify the uncertainty and reliability of hemodynamic simulations, it is crucial to examine the influence of user-dependent variability in valve segmentation. METHODS: Previously, the inter-user variability of landmarks in mitral valve segmentation was investigated. Here, the inter-user variability of geometric parameters of the mitral valve, projected orifice area (OA) and projected annulus area (AA), is investigated for 10 mitral valve geometries, each segmented by three users. Furthermore, the propagation of those variations into numerically calculated hemodynamics, i.e., the blood flow velocity, was investigated. RESULTS: Among the three geometric valve parameters, AA was least user-dependent. Almost all deviations to the mean were below 10%. Larger variations were observed for OA. Variations observed for the numerically calculated hemodynamics were in the same order of magnitude as those of geometric parameters. No correlation between variation of geometric parameters and variation of calculated hemodynamic parameters was found. CONCLUSION: Errors introduced due to the user-dependency were of the same size as the variations of calculated hemodynamics. The variation was thereby of the same scale as deviations in clinical measurements of blood flow velocity using Doppler echocardiography. Since no correlation between geometric and hemodynamic uncertainty was found, further investigation of the complex relationship between anatomy, leaflet shape and flow is necessary.

Virtual downsizing for decision support in mitral valve repair.

PURPOSE: Various options are available for the treatment of mitral valve insufficiency, including reconstructive approaches such as annulus correction through ring implants. The correct choice of general therapy and implant is relevant for an optimal outcome. Additional to guidelines, decision support systems (DSS) can provide decision aid by means of virtual intervention planning and predictive simulations. Our approach on virtual downsizing is one of the virtual intervention tools that are part of the DSS workflow. It allows for emulating a ring implantation based on patient-specific lumen geometry and vendor-specific implants. METHODS: Our approach is fully automatic and relies on a lumen mask and an annulus contour as inputs. Both are acquired from previous DSS workflow steps. A virtual surface- and contour-based model of a vendor-specific ring design (26-40 mm) is generated. For each case, the ring geometry is positioned with respect to the original, patient-specific annulus and additional anatomical landmarks. The lumen mesh is parameterized to allow for a vertex-based deformation with respect to the user-defined annulus. Derived from post-interventional observations, specific deformation schemes are applied to atrium and ventricle and the lumen mesh is altered with respect to the ring location. RESULTS: For quantitative evaluation, the surface distance between the deformed lumen mesh and segmented post-operative echo lumen close to the annulus was computed for 11 datasets. The results indicate a good agreement. An arbitrary subset of six datasets was used for a qualitative evaluation of the complete lumen. Two domain experts compared the deformed lumen mesh with post-interventional echo images. All deformations were deemed plausible. CONCLUSION: Our approach on virtual downsizing allows for an automatic creation of plausible lumen deformations. As it takes only a few seconds to generate results, it can be added to a virtual intervention toolset without unnecessarily increasing the pipeline complexity.

Extraction of open-state mitral valve geometry from CT volumes.

PURPOSE: The importance of mitral valve therapies is rising due to an aging population. Visualization and quantification of the valve anatomy from image acquisitions is an essential component of surgical and interventional planning. The segmentation of the mitral valve from computed tomography (CT) acquisitions is challenging due to high variation in appearance and visibility across subjects. We present a novel semi-automatic approach to segment the open-state valve in 3D CT volumes that combines user-defined landmarks to an initial valve model which is automatically adapted to the image information, even if the image data provide only partial visibility of the valve. METHODS: Context information and automatic view initialization are derived from segmentation of the left heart lumina, which incorporates topological, shape and regional information. The valve model is initialized with user-defined landmarks in views generated from the context segmentation and then adapted to the image data in an active surface approach guided by landmarks derived from sheetness analysis. The resulting model is refined by user landmarks. RESULTS: For evaluation, three clinicians segmented the open valve in 10 CT volumes of patients with mitral valve insufficiency. Despite notable differences in landmark definition, the resulting valve meshes were overall similar in appearance, with a mean surface distance of [Formula: see text] mm. Each volume could be segmented in 5-22 min. CONCLUSIONS: Our approach enables an expert user to easily segment the open mitral valve in CT data, even when image noise or low contrast limits the visibility of the valve.

Development of a modeling pipeline for the prediction of hemodynamic outcome after virtual mitral valve repair using image-based CFD.

PURPOSE: Severe mitral valve regurgitation can either be treated by a replacement or a repair of the valve. The latter is recommended due to lower perioperative mortality and better long-term survival. On the other hand, recurrence rates after mitral valve repair are high compared to those after replacements and the repair intervention can cause induced mitral valve stenosis. So far, there are no methods to predict the hemodynamic outcome of a chosen treatment or to compare different treatment options in advance. To overcome this, diastolic mitral valve hemodynamics are simulated using computational fluid dynamics after different virtual treatments of the valve. METHODS: The left ventricular geometry of one patient was reconstructed using trans-esophageal echocardiography and computed tomography data. Pre-op hemodynamics are simulated using a referenced wall model to avoid expansive modeling of wall motion. Subsequently, the flow structures are compared to in vivo measurements. After manipulating the patient-specific geometry in order to mimic a restrictive mitral annuloplasty as well as a MitraClip intervention, hemodynamics results are calculated. RESULTS: Good agreements exist between calculated pre-op hemodynamics and in vivo measurements. The virtual annuloplasty did not result in any remarkable change of hemodynamics. Neither the pressure drop nor the velocity field showed strong differences. In contrast, the virtual MitraClip intervention led to a complete change in blood flow structures as well as an elevated pressure drop across the valve. CONCLUSION: The presented approach allows fast simulation of the diastolic hemodynamic situation before and after treatment of a mitral valve insufficiency. However, this approach is limited to the early diastolic phase of the cardiac cycle and needs to be validated using a larger sample size.

An Open Benchmark Challenge for Motion Correction of Myocardial Perfusion MRI.

Cardiac magnetic resonance perfusion examinations enable noninvasive quantification of myocardial blood flow. However, motion between frames due to breathing must be corrected for quantitative analysis. Although several methods have been proposed, there is a lack of widely available benchmarks to compare different algorithms. We sought to compare many algorithms from several groups in an open benchmark challenge. Nine clinical studies from two different centers comprising normal and diseased myocardium at both rest and stress were made available for this study. The primary validation measure was regional myocardial blood flow based on the transfer coefficient (Ktrans), which was computed using a compartment model and the myocardial perfusion reserve (MPR) index. The ground truth was calculated using contours drawn manually on all frames by a single observer, and visually inspected by a second observer. Six groups participated and 19 different motion correction algorithms were compared. Each method used one of three different motion models: rigid, global affine, or local deformation. The similarity metric also varied with methods employing either sum-of-squared differences, mutual information, or cross correlation. There were no significant differences in Ktrans or MPR compared across different motion models or similarity metrics. Compared with the ground truth, only Ktrans for the sum-of-squared differences metric, and for local deformation motion models, had significant bias. In conclusion, the open benchmark enabled evaluation of clinical perfusion indices over a wide range of methods. In particular, there was no benefit of nonrigid registration techniques over the other methods evaluated in this study. The benchmark data and results are available from the Cardiac Atlas Project ( www.cardiacatlas.org).

Multi-cycle Reconstruction of Cardiac MRI for the Analysis of Inter-ventricular Septum Motion During Free Breathing.

Small variations in left-ventricular preload due to respiration produce measurable changes in cardiac function in normal subjects. We show that this mechanism is altered in patients with reduced ejection fraction (EF), hypertrophy, or volume-loaded right ventricle (RV). We propose a multi-dimensional retrospective image reconstruction, based on an adaptive, soft classification of data into respiratory and cardiac phases, to study these effects.

Spatiotemporal phase unwrapping for real-time phase-contrast flow MRI.

PURPOSE: To develop and evaluate a practical phase unwrapping method for real-time phase-contrast flow MRI using temporal and spatial continuity. METHODS: Real-time phase-contrast MRI of through-plane flow was performed using highly undersampled radial FLASH with phase-sensitive reconstructions by regularized nonlinear inversion. Experiments involved flow in a phantom and the human aorta (10 healthy subjects) with and without phase wrapping for velocity encodings of 100 cm·s(-1) and 200 cm·s(-1) . Phase unwrapping was performed for each individual cardiac cycle and restricted to a region of interest automatically propagated to all time frames. The algorithm exploited temporal continuity in forward and backward direction for all pixels with a "continuous" representation of blood throughout the entire cardiac cycle (inner vessel lumen). Phase inconsistencies were corrected by a comparison with values from direct spatial neighbors. The latter approach was also applied to pixels exhibiting a discontinuous signal intensity time course due to movement-induced spatial displacements (peripheral vessel zone). RESULTS: Phantom and human flow MRI data were successfully unwrapped. When halving the velocity encoding, the velocity-to-noise ratio (VNR) increased by a factor of two. CONCLUSION: The proposed phase unwrapping method for real-time flow MRI allows for measurements with reduced velocity encoding and increased VNR.