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This work uses a recently developed MRI method to measure the solid fraction and velocity in three-dimensional (3D) hoppers quantitatively. We demonstrate that the measurements are quantitative by calculating the mass flow rate within the hopper using MRI and show good agreement with the mass flow rate measured gravimetrically. We study the velocity and solid fraction in hoppers with various angles and outlet sizes. We show that the solid fraction decreases smoothly from the bulk value above the outlet, indicating that the assumption of a "free-fall arch" used in some mass flow correlations is invalid. Furthermore, we show that the solid fraction, velocity and vertical evolution of the acceleration are all self-similar when normalised by the value at the centre of the outlet in a 3D hopper, in agreement with recent studies of 2D hoppers. Thus, these quantitative measurements enable evaluation of phenomenological models describing the flow rate from hoppers. [Display omitted] • We present quantitative measurements of solid fraction and velocity in 3D hoppers. • The velocity and solid fraction profiles scale with outlet size. • There is no "empty annulus" at the outlet of a hopper. • Acceleration increases towards the outlet and there is no "free fall arch". [ABSTRACT FROM AUTHOR]

Abstract Background Volumetric quantification of mean and fluctuating velocity components of transient and turbulent flows promises a comprehensive characterization of valvular and aortic flow characteristics. Data acquisition using standard navigator-gated 4D Flow cardiovascular magnetic resonance (CMR) is time-consuming and actual scan times depend on the breathing pattern of the subject, limiting the applicability of the method in a clinical setting. We sought to develop a 5D Flow CMR framework which combines undersampled data acquisition including multipoint velocity encoding with low-rank image reconstruction to provide cardiac- and respiratory-motion resolved assessment of velocity maps and turbulent kinetic energy in fixed scan times. Methods Data acquisition and data-driven motion state detection was performed using an undersampled Cartesian tiny Golden angle approach. Locally low-rank (LLR) reconstruction was implemented to exploit correlations among heart phases and respiratory motion states. To ensure accurate quantification of mean and turbulent velocities, a multipoint encoding scheme with two velocity encodings per direction was incorporated. Velocity-vector fields and turbulent kinetic energy (TKE) were obtained using a Bayesian approach maximizing the posterior probability given the measured data. The scan time of 5D Flow CMR was set to 4 min. 5D Flow CMR with acceleration factors of 19 .0 ± 0.21 (mean ± std) and velocity encodings (VENC) of 0.5 m/s and 1.5 m/s per axis was compared to navigator-gated 2x SENSE accelerated 4D Flow CMR with VENC = 1.5 m/s in 9 subjects. Peak velocities and peak flow were compared and magnitude images, velocity and TKE maps were assessed. Results While net scan time of 5D Flow CMR was 4 min independent of individual breathing patterns, the scan times of the standard 4D Flow CMR protocol varied depending on the actual navigator gating efficiency and were 17.8 ± 3.9 min on average. Velocity vector fields derived from 5D Flow CMR in the end-expiratory state agreed well with data obtained from the navigated 4D protocol (normalized root-mean-square error 8.9 ± 2.1%). On average, peak velocities assessed with 5D Flow CMR were higher than for the 4D protocol (3.1 ± 4.4%). Conclusions Respiratory-motion resolved multipoint 5D Flow CMR allows mapping of mean and turbulent velocities in the aorta in 4 min.

The rope-driven snake manipulator is a bionic mechanism with hyper redundant DOFs and can be applied in narrow and confined environments, such as surgery, spacecraft, nuclear plant, etc. The kinematic mapping expressed by the rope length, joint angle and end pose is highly nonlinear and difficult to be calculated. Moreover, the control methods with rope length as input are prone to redundant driving ropes getting stuck due to differences in model and actual mechanism. Therefore, the perfect kinematic mapping of the rope-driven snake manipulator is necessary for designing high-efficiency motion controllers. In this paper, an analytical mapping about the velocities of ropes, joints and end is established and verified. Firstly, a prototype inspired by the biological snake spine is designed. And then the Jacobian matrix representing the velocity mapping is derived and analyzed in detail. The joint and rope velocities are optimized by configuring the null space vector of the Jacobian matrix. Based on the velocity mapping and optimization, a motion control scheme for the snake manipulator is established to realize servo control of the joints and end. Finally, the trajectory tracking simulation and experiment are executed to verify the velocity mapping theory and control scheme. This research can provide solutions for the complex motion control problems of subsequent snake manipulators. [ABSTRACT FROM AUTHOR]

Magnetic resonance imaging (MRI) is a non-invasive and non-optical measurement technique, which makes it a promising method for studying delicate and opaque samples, such as foam. Another key benefit of MRI is its sensitivity to different nuclei in a sample. The research presented in this article focuses on the use of MRI to measure density and velocity of foam as it passes through a pipe constriction. The foam was created by bubbling fluorinated gas through an aqueous solution. This allowed for the liquid and gas phases to be measured separately by probing the 1H and 19F behavior of the same foam. Density images and velocity maps of the gas and liquid phases of foam flowing through a pipe constriction are presented. In addition, results of computational fluid dynamics simulations of foam flow in the pipe constriction are compared with experimental results.

The pressure variations experienced by a liquid flowing through a pipe constriction can, in some cases, result in the formation of a bubble cloud (i.e., hydrodynamic cavitation). Due to the nature of the bubble cloud, it is ideally measured through the use of non-optical and non-invasive techniques; therefore, it is well-suited for study by magnetic resonance imaging. This paper demonstrates the use of Conical SPRITE (a 3D, centric-scan, pure phase-encoding pulse sequence) to acquire time-averaged void fraction and velocity information about hydrodynamic cavitation for water flowing through a pipe constriction. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this study was to evaluate timed-resolved three-dimensional (3D) magnetic resonance (MR) velocity mapping as a method for investigation of cerebrospinal fluid (CSF) flow changes in patients with aqueductal stenosis (AS) treated by endoscopic third ventriculostomy (ETV).Methods: The MR velocity mapping was performed in 12 AS patients before and after ETV and in 10 healthy volunteers by using a 3-Tesla MR system. Time-resolved 3D MR velocity mapping data were acquired with a standard 3D phase contrast (PC) sequence with cardiac triggering. Values of mean (vmean) and maximum (vpeak) velocity were measured at several ventricular structures using dedicated software.Results: Of the patients 11 showed a satisfactory clinical improvement after ETV, whereas one patient needed subsequent shunt implantation. All AS patients showed significant hypomotile CSF flow dynamics in the third ventricle when compared to healthy subjects before surgery (p < 0.05). In contrast, CSF flow velocity was increased within the Foramen of Monro in AS patients. After ETV, all AS patients showed a decrease of CSF flow dynamics within the third ventricle. Mean and peak CSF flow velocities through the ventriculostomy were 1.72 ± 0.59 cm/s (vmean) and 3.53 ± 0.79 cm/s (vpeak), respectively after ETV. The patient who needed shunt implantation after ETV had the lowest flow velocities through the ventriculostomy.Conclusion: This study demonstrates that timed-resolved 3D MR velocity mapping is a useful imaging investigation for diagnostics and follow-up in patients with AS. This new technique provides an insight into the physiological CSF flow changes related with AS and its treatment. [ABSTRACT FROM AUTHOR]

LSPIV (Large Scale Particle Image Velocimetry) and LSPTV (Large Scale Particle Tracking Velocimetry) are used as relatively low-cost and non-intrusive techniques for water-surface velocity analysis and flow discharge measurements in rivers or large-scale hydraulic models. This paper describes a methodology based on state-of-the-art tools (for example, that apply classical PIV/PTV analysis) resulting in large-scale surface-flow characterization according to the first operational version of the RIVeR (Rectification of Image Velocity Results). RIVeR is developed in Matlab and is designed to be user-friendly. RIVeR processes large-scale water-surface characterization such as velocity fields or individual trajectories of floating tracers. This work describes the wide range of application of the techniques for comparing measured surface flows in hydraulic physical models to flow discharge estimates for a wide range of flow events in rivers (for example, low and high flows). [ABSTRACT FROM AUTHOR]

Purpose: To correct background phase errors in phase-contrast magnetic resonance imaging (MRI), image-based correction by referencing through stationary tissue is widely used. The aim of the present study was a detailed assessment of background phase errors in 4D Flow MRI and limitations of image-based correction.Materials and Methods: In a phantom study, 4D Flow MRI data were acquired for typical settings on two clinical 3T MR systems. Background errors were analyzed with respect to their spatial order and minimum requirements regarding the signal-to-noise ratio (SNR) and the amount of stationary tissue for image-based correction were assessed. For in vivo evaluation, data of the aorta were acquired on one 3T MR system in five healthy subjects including subsequent scans on the stationary phantom as reference.Results: Background errors were found to exhibit spatial variation of first- to third-order. For correction, a minimum SNR of 20 was needed to achieve an error of less than 0.4% of the encoding velocity. The minimum amount of stationary tissue was strongly dependent on the spatial order requiring at least 25%, 60%, and 75% of stationary tissue for first-, second-, and third-order correction. In vivo evaluation showed that with 35-41% of stationary tissue available only first-order correction yielded a significant reduction (P < 0.01).Conclusion: Background phase errors can range from first to third spatial order in 4D Flow MRI requiring correction with appropriate polynomials. At the same time, the limited amount of stationary tissue available in vivo limits image-based background phase correction to first spatial order.Level Of Evidence: 1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1516-1525. [ABSTRACT FROM AUTHOR]

Purpose In various cerebrovascular diseases the visualization of individual arteries and knowledge about their hemodynamic properties, like flow velocity and direction, can become important for an accurate diagnosis. Magnetic resonance angiography methods are intended to acquire this information, but often a single acquisition is not sufficient to retrieve all of this desired information. Methods Using selective arterial spin labeling (ASL) methods, a single artery of interest can be tagged and visualized, whereas quantitative information about hemodynamics can be retrieved using phase-contrast techniques that are often limited regarding their selectivity. In this study, a method that allows for velocity mapping of individual arteries by incorporating phase-contrast preparation into selective ASL angiography measurements is presented. Several postprocessing steps are required to generate velocity and directional-encoded maps of selected arteries from the data acquired in a single scan. Results The method was successfully evaluated in healthy volunteers, and a first application in two selected patients is presented. In one patient, an aneurysm of the middle cerebral artery is investigated, and in the second patient it is used to visualize an arterio-venous malformation. Conclusion Selective ASL imaging in conjunction with phase-contrast acquisition allows for investigating hemodynamic properties of individual arteries. Magn Reson Med 78:1469-1475, 2017. © 2016 International Society for Magnetic Resonance in Medicine. [ABSTRACT FROM AUTHOR]

In the last few years, wall shear stress (WSS) has arisen as a new diagnostic indicator in patients with arterial disease. There is a substantial evidence that the WSS plays a significant role, together with hemodynamic indicators, in initiation and progression of the vascular diseases. Estimation of WSS values, therefore, may be of clinical significance and the methods employed for its measurement are crucial for clinical community. Recently, four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) has been widely used in a number of applications for visualization and quantification of blood flow, and although the sensitivity to blood flow measurement has increased, it is not yet able to provide an accurate three-dimensional (3D) WSS distribution. The aim of this work is to evaluate the aortic blood flow features and the associated WSS by the combination of 4D flow cardiovascular magnetic resonance (4D CMR) and computational fluid dynamics technique. In particular, in this work, we used the 4D CMR to obtain the spatial domain and the boundary conditions needed to estimate the WSS within the entire thoracic aorta using computational fluid dynamics. Similar WSS distributions were found for cases simulated. A sensitivity analysis was done to check the accuracy of the method. 4D CMR begins to be a reliable tool to estimate the WSS within the entire thoracic aorta using computational fluid dynamics. The combination of both techniques may provide the ideal tool to help tackle these and other problems related to wall shear estimation. [ABSTRACT FROM AUTHOR]

Sprays are dynamic collections of droplets dispersed in a gas, with many industrial and agricultural applications. Quantitative characterization is essential for understanding processes of spray formation and dynamics. There exists a wide range of measurement techniques to characterize sprays, from direct imaging to phase Doppler interferometry to X-rays, which provide detailed information on spray characteristics in the “far-nozzle” region (≫10 diameters of the nozzle). However, traditional methods are limited in their ability to characterize the “near-nozzle” region where the fluid may be inside the nozzle, optically dense, or incompletely atomized. Magnetic Resonance Imaging (MRI) presents potential as a non-invasive technique that is capable of measuring optically inaccessible fluid in a quantitative fashion. In this work, MRI measurements of the spray generated by ceramic flat-fan nozzles were performed. A wide range of flow speeds in the system (0.2 to >25 m/s) necessitated short encoding times. A 3D Conical SPRITE and motion-sensitized 3D Conical SPRITE were employed. The signal from water inside the nozzle was well-characterized, both via proton density and velocity measurements. The signal outside the nozzle, in the near-nozzle region, was detectable, corresponding to the expected flat-fan spray pattern up to 3 mm away. The results demonstrate the potential of MRI for measuring spray characteristics in areas inaccessible by other methods. [ABSTRACT FROM AUTHOR]

Purpose To extend SPIRiT to additionally exploit temporal correlations for highly accelerated generalized phase-contrast MRI and to compare the performance of the proposed radial k-t SPIRiT method relative to frame-by-frame SPIRiT and radial k-t GRAPPA reconstruction for velocity and turbulence mapping in the aortic arch. Theory and Methods Free-breathing navigator-gated two-dimensional radial cine imaging with three-directional multi-point velocity encoding was implemented and fully sampled data were obtained in the aortic arch of healthy volunteers. Velocities were encoded with three different first gradient moments per axis to permit quantification of mean velocity and turbulent kinetic energy. Velocity and turbulent kinetic energy maps from up to 14-fold undersampled data were compared for k-t SPIRiT, frame-by-frame SPIRiT, and k-t GRAPPA relative to the fully sampled reference. Results Using k-t SPIRiT, improvements in magnitude and velocity reconstruction accuracy were found. Temporally resolved magnitude profiles revealed a reduction in spatial blurring with k-t SPIRiT compared with frame-by-frame SPIRiT and k-t GRAPPA for all velocity encodings, leading to improved estimates of turbulent kinetic energy. Conclusion k-t SPIRiT offers improved reconstruction accuracy at high radial undersampling factors and hence facilitates the use of generalized phase-contrast MRI for routine use. Magn Reson Med 72:1233-1245, 2014. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Aortic root dilation and propensity to dissection are typical manifestations of the Marfan Syndrome (MS), a genetic defect leading to the degeneration of the elastic fibres. Dilation affects the structure of the flow and, in turn, altered flow may play a role in vessel dilation, generation of aneurysms, and dissection. The aim of the present work is the investigation in-vitro of the fluid dynamic modifications occurring as a consequence of the morphological changes typically induced in the aortic root by MS. A mock-loop reproducing the left ventricle outflow tract and the aortic root was used to measure time resolved velocity maps on a longitudinal symmetry plane of the aortic root. Two dilated model aortas, designed to resemble morphological characteristics typically observed in MS patients, have been compared to a reference, healthy geometry. The aortic model was designed to quantitatively reproduce the change of aortic distensibility caused by MS. Results demonstrate that vorticity released from the valve leaflets, and possibly accumulating in the root, plays a fundamental role in redirecting the systolic jet issued from the aortic valve. The altered systolic flow also determines a different residual flow during the diastole. [ABSTRACT FROM AUTHOR]

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Purpose To demonstrate the use of temporal averaging with radial 4D flow magnetic resonance imaging (MRI) to reduce scan time for quantification and visualization of flow in the portal circulation. This study compared phase-contrast MR angiography, 3D flow visualization, and flow quantification of portal venous hemodynamics of time-averaged vs. time-resolved reconstructions. Materials and Methods Time-resolved 3D radial ('4D') phase contrast data were acquired from 44 subjects (15 volunteers, 29 cirrhosis patients) at 3T. Images were reconstructed as a fully sampled time-resolved reconstruction and multiple time-averaged reconstructions using a variable number of acquired projections to simulate different scan times. Images from each reconstruction were evaluated to compare the quality of anatomical and hemodynamic visualization. Results Time-averaged reconstructions outperformed time-resolved reconstructions for flow quantification (3.9 ± 3.1% error vs. 5.2 ± 4.4% error), average streamline length (47 ± 7 mm vs. 34 ± 15 mm), and visualization quality (average grading = 3.7 ± 0.5 vs. 2.2 ± 0.9). In addition, excellent visualization quality was achieved using fewer acquired projections. Conclusion Reductions in scan time can be achieved through time-averaging while still providing excellent visualization and quantification in the portal circulation. Scan time reduction of up to 70%-80% was possible for high-quality assessment, translating into a reduction in scan time from 10-12 minutes to ∼3-4 minutes. J. Magn. Reson. Imaging 2014;39:819-826. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The aim of this study was to quantify changes in thoracic aortic wall shear stress (WSS) in asymptomatic patients with Marfan syndrome (MFS) compared with healthy controls. WSS in the thoracic aorta was quantified based on time-resolved 3D phase contrast MRI with three-directional velocity encoding (4D flow MRI, temporal resolution ∼44 ms, spatial resolution ∼2.5 mm) in 24 patients with confirmed MFS (age = 18 ± 12 years) and in 12 older healthy volunteers (age = 25 ± 3 years). Diameters of the thoracic aorta normalized to body surface area were similar for both groups. Peak systolic velocity, absolute WSS, time-averaged WSS, circumferential WSS, peak systolic WSS, and WSS eccentricity were calculated in eight analysis planes distributed along the thoracic aorta. Plane-wise comparison revealed significant differences between MFS patients and volunteers in the proximal ascending aorta for peak systolic velocities (1.11 ± 0.23 m/s vs. 1.34 ± 0.18 m/s, P = 0.004) and circumferential WSS (0.14 ± 0.03 N/m2 vs. 0.11 ± 0.02 N/m2, P = 0.007). WSS eccentricity was altered in most of the ascending aorta and proximal arch ( P = 0.009-0.020). MFS patients demonstrated segmental differences in peak systolic WSS with a significantly higher WSS at the inner curvature in the proximal ascending aorta and at the anterior part in the more distal ascending aorta ( P < 0.01). These findings indicate differences in WSS associated with MFS despite similar aortic dimensions compared to controls. Magn Reson Med, 70:1137-1144, 2013. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

An approach to efficiently measure three-dimensional velocity vector fields and turbulent kinetic energy of blood flow is presented. Multipoint phase-contrast imaging is used in combination with Bayesian analysis to map both mean and fluctuating velocities over a large dynamic range and for practically relevant signal-to-noise ratios. It is demonstrated that the approach permits significant spatiotemporal undersampling to allow for clinically acceptable scan times. Using numerical simulations and in vitro measurements in aortic valve phantoms, it is shown that for given scan time, Bayesian multipoint velocity encoding provides consistently lower errors of velocity and turbulent kinetic energy over a larger dynamic range relative to previous methods. In vitro, significant differences in both peak velocity and turbulent kinetic energy between the aortic CoreValve (150 cm/s, 293 J/m3) and the St. Jude Medical mechanical valve (120 cm/s, 149 J/m3) were found. Comparison of peak turbulent kinetic energy measured in a patient with aortic stenosis (950 J/m3) and in a patient with an implanted aortic CoreValve (540 J/m3) revealed considerable differences relative to the values detected in healthy subjects (149 ± 12 J/m3) indicating the potential of the method to provide a comprehensive hemodynamic assessment of valve performance in vivo. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Electron capture at the carbon–fluorine σ* antibonding orbital accounts for the vector correlations between fragments F− and CF3 or F and CF3− in two complementary dissociation pathways after electron attachment to CF4. An orientation effect in the low‐energy electron attachment is observed by velocity mapping (see picture; C black, F blue). [ABSTRACT FROM AUTHOR]

Purpose: To evaluate accuracy and noise properties of a novel time-resolved, three-dimensional, three-directional phase contrast sequence with variable velocity encoding (denoted 4D-vPC) on a 3 Tesla MR system, and to investigate potential benefits and limitations of variable velocity encoding with respect to depicting blood flow patterns. Materials and Methods: A 4D PC-MRI sequence was modified to allow variable velocity encoding (VENC) over the cardiac cycle in all three velocity directions independently. 4D-PC sequences with constant and variable VENC were compared in a rotating phantom with respect to measured velocities and noise levels. Additionally, comparison of flow patterns in the ascending aorta was performed in six healthy volunteers. Results: Phantom measurements showed a linear relationship between velocity noise and velocity encoding. 4D-vPC MRI presented lower noise levels than 4D-PC both in phantom and in volunteer measurements, in agreement with theory. Volunteer comparisons revealed more consistent and detailed flow patterns in early diastole for the variable VENC sequences. Conclusion: Variable velocity encoding offers reduced noise levels compared with sequences with constant velocity encoding by optimizing the velocity-to-noise ratio (VNR) to the hemodynamic properties of the imaged area. Increased VNR ratios could be beneficial for blood flow visualizations of pathology in the cardiac cycle. J. Magn. Reson. Imaging 2012; 36:1450-1459. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Abstract: A time-efficient MRI method suitable for quantitative mapping of 3-D velocity fields in sedimentary rock cores, and granular samples is discussed. The method combines the 13-interval Alternating-Pulsed-Gradient Stimulated-Echo (APGSTE) scheme and three-dimensional Single Point Ramped Imaging with T 1 Enhancement (SPRITE). Collecting a few samples near the q-space origin and employing restricted k-space sampling dramatically improves the performance of the imaging method. The APGSTE–SPRITE method is illustrated through mapping of 3-D velocity field in a macroscopic bead pack and heterogeneous sandstone and limestone core plugs. The observed flow patterns are consistent with a general trend for permeability to increase with the porosity. Domains of low permeability obstruct the flow within the core volume. Water tends to flow along macroscopic zones of higher porosity and across zones of lower porosity. [Copyright &y& Elsevier]

Purpose: To validate a novel approach for accelerated four-dimensional phase contrast MR imaging (4D PC-MRI) with an extended range of velocity sensitivity. Materials and Methods: 4D PC-MRI data were acquired with a radially undersampled trajectory (PC-VIPR). A dual Venc (dVenc) processing algorithm was implemented to investigate the potential for scan time savings while providing an improved velocity-to-noise ratio. Flow and velocity measurements were compared with a flow pump, conventional 2D PC MR, and single Venc 4D PC-MRI in the chest of 10 volunteers. Results: Phantom measurements showed excellent agreement between accelerated dVenc 4D PC-MRI and the pump flow rate (R2 ≥ 0.97) with a three-fold increase in measured velocity-to-noise ratio (VNR) and a 5% increase in scan time. In volunteers, reasonable agreement was found when combining 100% of data acquired with Venc = 80 cm/s and 25% of the high Venc data, providing the VNR of a 80 cm/s acquisition with a wider velocity range of 160 cm/s at the expense of a 25% longer scan. Conclusion: Accelerated dual Venc 4D PC-MRI was demonstrated in vitro and in vivo. This acquisition scheme is well suited for vascular territories with wide ranges of flow velocities such as congenital heart disease, the hepatic vasculature, and others. J. Magn. Reson. Imaging 2012. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This is the second of two reviews that is intended to cover the essential aspects of cardiovascular magnetic resonance (CMR) physics in a way that is understandable and relevant to clinicians using CMR in their daily practice. Starting with the basic pulse sequences and contrast mechanisms described in part I, it briefly discusses further approaches to accelerate image acquisition. It then continues by showing in detail how the contrast behaviour of black blood fast spin echo and bright blood cine gradient echo techniques can be modified by adding rf preparation pulses to derive anumber of more specialised pulse sequences. The simplest examples described include T2-weighted oedema imaging, fat suppression and myocardial tagging cine pulse sequences. Two further important derivatives of the gradient echo pulse sequence, obtained by adding preparation pulses, are used in combination with the administration of a gadolinium-based contrast agent for myocardial perfusion imaging and the assessment of myocardial tissue viability using a late gadolinium enhancement (LGE) technique. These two imaging techniques are discussed in more detail, outlining the basic principles of each pulse sequence, the practical steps required to achieve the best results in a clinical setting and, in the case of perfusion, explaining some of the factors that influence current approaches toperfusion image analysis. The key principles of contrast-enhanced magnetic resonance angiography (CE-MRA) are also explained in detail, especially focusing on timing of the acquisition following contrast agent bolus administration, and current approaches to achieving time resolved MRA. Alternative MRA techniques that do not require the use of an endogenous contrast agent are summarised, and the specialised pulse sequence used to image the coronary arteries, using respiratory navigator gating, is described in detail. The article concludes by explaining the principle behind phase contrast imaging techniques which create images that represent the phase of the MR signal rather than the magnitude. It is shown how this principle can be used to generate velocity maps by designing gradient waveforms that give rise to a relative phase change that is proportional to velocity. Choice of velocity encoding range and key pitfalls in the use of this technique are discussed. [ABSTRACT FROM AUTHOR]