Comprehensive 4 D velocity mapping of the heart and great vessels by cardiovascular magnetic resonance

Background: Phase contrast cardiovascular magnetic resonance (CMR) is able to measure all three directional components of the velocities of blood flow relative to the three spatial dimensions and the time course of the heart cycle. In this article, methods used for the acquisition, visualization, and quantification of such datasets are reviewed and illustrated. Methods: Currently, the acquisition of 3D cine (4D) phase contrast velocity data, synchronized relative to both cardiac and respiratory movements takes about ten minutes or more, even when using parallel imaging and optimized pulse sequence design. The large resulting datasets need appropriate post processing for the visualization of multidirectional flow, for example as vector fields, pathlines or streamlines, or for retrospective volumetric quantification. Applications: Multidirectional velocity acquisitions have provided 3D visualization of large scale flow features of the healthy heart and great vessels, and have shown altered patterns of flow in abnormal chambers and vessels. Clinically relevant examples include retrograde streams in atheromatous descending aortas as potential thromboembolic pathways in patients with cryptogenic stroke and marked variations of flow visualized in common aortic pathologies. Compared to standard clinical tools, 4D velocity mapping offers the potential for retrospective quantification of flow and other hemodynamic parameters. Conclusions: Multidirectional, 3D cine velocity acquisitions are contributing to the understanding of normal and pathologically altered blood flow features. Although more rapid and user-friendly strategies for acquisition and analysis may be needed before 4D velocity acquisitions come to be adopted in routine clinical CMR, their capacity to measure multidirectional flows throughout a study volume has contributed novel insights into cardiovascular fluid dynamics in health and disease. Introduction Phase contrast (PC) cardiovascular magnetic resonance (CMR) can measure, non-invasively, all three directional components of the velocities of blood flow relative to all four spatio-temporal dimensions of the heart and great vessels. The underlying principles have been known and applied over several decades [1-6]. The mapping of just the component of time-resolved velocity directed perpendicularly through a 2D plane is widely used for clinical measurements of volume flow [7-10]. This approach allows measurements of forward, regurgitant and shunt flows in congenital and acquired heart disease [11-14], and in certain circumstances, measurements of jet velocity. However, such acquisitions require appropriate placement of the velocity mapping plane, and clearly have limitations relative to the multiple directions of flow through the heart and large vessels [15]. Alternatively, Doppler ultrasound can be employed to assess regional blood flow velocities. The technique is widely and routinely used in numerous applications and cardiovascular pathologies and has a number of advantages compared to MRI including widespread availability, ease of use, and no contraindications in case of pacemakers or metallic implants. However, Doppler * Correspondence: michael.markl@uniklinik-freiburg.de Department of Radiology, Medical Physics, University Hospital Freiburg, Germany Full list of author information is available at the end of the article Markl et al. Journal of Cardiovascular Magnetic Resonance 2011, 13:7 http://www.jcmr-online.com/content/13/1/7 © 2011 Markl et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ultrasound is also limited by its inter-observer variability and by detecting only the component of velocity directed to or from the transducer. Computed tomography provides relatively rapid 3D scans with excellent spatial resolution that can show the intravascular distribution of contrast agent at a given moment, but without being able to measure the velocities of blood flow. This review paper deals principally with the methods and applications of the more comprehensive, 3 dimensional, 3 directionally encoded, time resolved (cine) velocity acquisition[16,17], which we will refer to as 4D velocity acquisition. The concise naming of such acquisitions has varied between groups. While ‘4D’ has come to be widely used and recognized, having the advantage of brevity, use of ‘3D cine’ is arguably more correct and consistent with the use of ‘2D cine’ to describe routine velocity mapping (see table 1 for a definition of terminology). It is important to be aware that the time dimension of this type of cine velocity acquisitions does not represent real time, but rather the time course of an effectively averaged heart cycle. Any instabilities or beat-to-beat variations of blood flow are not represented, as data contributing to each phase is gathered, by ECG triggering, from many heart cycles. Recent methodological advances including improved respiratory navigation, parallel imaging, or efficient radial k-space sampling allow good 4D velocity acquisition quality in acceptable time periods [18-20]. In combination with advanced flow visualization and quantification software, partially adapted from automotive and aerospace engineering, a tool for the studying multidirectional flow characteristics in the individual patients has been established [21-24]. In this article, the CMR methods used for 4D velocity acquisition, and the subsequent visualization and quantification of blood flow are reviewed. The value and limitations of this approach are considered in relation to a number of proposed clinical applications. We will focus on studies of blood flow in the thorax, although multidirectional velocity acquisitions can also be applied in other parts of the body such as the neck [25,26], brain [27,28] or liver [29], and, using a suitably low velocity encoding range, to studies of ventricular function [30-34].

[1]  C L Dumoulin,et al.  Three‐dimensional phase contrast angiography , 1989, Magnetic resonance in medicine.

[2]  R. Pettigrew,et al.  Determination of wall shear stress in the aorta with the use of MR phase velocity mapping , 1995, Journal of magnetic resonance imaging : JMRI.

[3]  Cornelius Weiller,et al.  In Vivo Wall Shear Stress Distribution in the Carotid Artery: Effect of Bifurcation Geometry, Internal Carotid Artery Stenosis, and Recanalization Therapy , 2010, Circulation. Cardiovascular imaging.

[4]  T Ebbers,et al.  Estimation of relative cardiovascular pressures using time‐resolved three‐dimensional phase contrast MRI , 2001, Magnetic resonance in medicine.

[5]  F. Korosec,et al.  PC VIPR: a high-speed 3D phase-contrast method for flow quantification and high-resolution angiography. , 2005, AJNR. American journal of neuroradiology.

[6]  C Mistretta,et al.  Physiologic and anatomic assessment of a canine carotid artery stenosis model utilizing phase contrast with vastly undersampled isotropic projection imaging. , 2007, AJNR. American journal of neuroradiology.

[7]  Michael Markl,et al.  MR‐based visualization and quantification of three‐dimensional flow characteristics in the portal venous system , 2010, Journal of magnetic resonance imaging : JMRI.

[8]  M. Alley,et al.  Bicuspid Aortic Valve : Four-dimensional MR Evaluation of Ascending Aortic Systolic Flow Patterns 1 , 2010 .

[9]  Jeroen J. Bax,et al.  Flow Assessment Through Four Heart Valves Simultaneously Using 3-Dimensional 3-Directional Velocity-Encoded Magnetic Resonance Imaging With Retrospective Valve Tracking in Healthy Volunteers and Patients With Valvular Regurgitation , 2009, Investigative radiology.

[10]  J. Hennig,et al.  Sclerotic aortic valve: flow-sensitive 4-dimensional magnetic resonance imaging reveals 3 distinct flow-pattern changes. , 2007, Circulation.

[11]  T. Schaeffter,et al.  Four‐dimensional (4D) flow of the whole heart and great vessels using real‐time respiratory self‐gating , 2009, Magnetic resonance in medicine.

[12]  Michael Markl,et al.  Time-resolved three-dimensional magnetic resonance velocity mapping of aortic flow in healthy volunteers and patients after valve-sparing aortic root replacement. , 2005, The Journal of thoracic and cardiovascular surgery.

[13]  P. Kilner,et al.  Our tortuous heart in dynamic mode — an echocardiographic study of mitral flow and movement in exercising subjects , 2007, Heart and Vessels.

[14]  Reto Meuli,et al.  Estimation of local aortic elastic properties with MRI , 2002, Magnetic resonance in medicine.

[15]  T Ebbers,et al.  Pitfalls in Doppler evaluation of diastolic function: insights from 3-dimensional magnetic resonance imaging. , 1999, Journal of the American Society of Echocardiography : official publication of the American Society of Echocardiography.

[16]  P. Walker,et al.  Semiautomated method for noise reduction and background phase error correction in MR phase velocity data , 1993, Journal of magnetic resonance imaging : JMRI.

[17]  Michael Markl,et al.  Estimation of global aortic pulse wave velocity by flow‐sensitive 4D MRI , 2010, Magnetic resonance in medicine.

[18]  Petter Dyverfeldt,et al.  Semi-automatic quantification of 4D left ventricular blood flow , 2010, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[19]  Maxim Zaitsev,et al.  Visualization of iliac and proximal femoral artery hemodynamics using time‐resolved 3D phase contrast MRI at 3T , 2007, Journal of magnetic resonance imaging : JMRI.

[20]  T. Ebbers,et al.  Assessment of fluctuating velocities in disturbed cardiovascular blood flow: In vivo feasibility of generalized phase‐contrast MRI , 2008, Journal of magnetic resonance imaging : JMRI.

[21]  Matthias Gutberlet,et al.  In vitro validation of phase‐contrast flow measurements at 3 T in comparison to 1.5 T: Precision, accuracy, and signal‐to‐noise ratios , 2005, Journal of magnetic resonance imaging : JMRI.

[22]  René M. Botnar,et al.  Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulations and in vitro MRI measurements. , 2000, Journal of biomechanics.

[23]  D. Laidlaw,et al.  Three‐dimensional, time‐resolved (4D) relative pressure mapping using magnetic resonance imaging , 2000, Journal of magnetic resonance imaging : JMRI.

[24]  Patrick A Turski,et al.  Improved 3D phase contrast MRI with off‐resonance corrected dual echo VIPR , 2008, Magnetic resonance in medicine.

[25]  Tino Ebbers,et al.  Improving computation of cardiovascular relative pressure fields from velocity MRI , 2009, Journal of magnetic resonance imaging : JMRI.

[26]  D N Firmin,et al.  Magnetic resonance velocity vector mapping of blood flow in thoracic aortic aneurysms and grafts. , 1995, The Journal of thoracic and cardiovascular surgery.

[27]  M. Buonocore,et al.  4D magnetic resonance velocity mapping of blood flow patterns in the aorta in young vs. elderly normal subjects , 1999, Journal of magnetic resonance imaging : JMRI.

[28]  O Wieben,et al.  Noninvasive Measurement of Intra-Aneurysmal Pressure and Flow Pattern Using Phase Contrast with Vastly Undersampled Isotropic Projection Imaging , 2007, American Journal of Neuroradiology.

[29]  B. Wranne,et al.  Temporally resolved 3D phase‐contrast imaging , 1996, Magnetic resonance in medicine.

[30]  Jürgen Hennig,et al.  Detailed analysis of myocardial motion in volunteers and patients using high‐temporal‐resolution MR tissue phase mapping , 2006, Journal of magnetic resonance imaging : JMRI.

[31]  M. Buonocore,et al.  Four‐dimensional magnetic resonance velocity mapping of blood flow patterns in the aorta in patients with atherosclerotic coronary artery disease compared to age‐matched normal subjects , 2004, Journal of magnetic resonance imaging : JMRI.

[32]  Alex Frydrychowicz,et al.  Images in Cardiovascular Medicine. Scimitar syndrome: added value by isotropic flow-sensitive four-dimensional magnetic resonance imaging with PC-VIPR (phase-contrast vastly undersampled isotropic projection reconstruction). , 2010, Circulation.

[33]  Peter Boesiger,et al.  Accelerating cine phase‐contrast flow measurements using k‐t BLAST and k‐t SENSE , 2005, Magnetic resonance in medicine.

[34]  Philipp Beerbaum,et al.  Noninvasive Quantification of Left-to-Right Shunt in Pediatric Patients: Phase-Contrast Cine Magnetic Resonance Imaging Compared With Invasive Oximetry , 2001, Circulation.

[35]  D. Pennell,et al.  MR blood flow measurement. Clinical application in the heart and circulation. , 1998, Cardiology clinics.

[36]  W. I. Tseng,et al.  Estimation of pulse wave velocity in main pulmonary artery with phase contrast MRI: Preliminary investigation , 2006, Journal of magnetic resonance imaging : JMRI.

[37]  N J Pelc,et al.  Concomitant gradient terms in phase contrast MR: Analysis and correction , 1998, Magnetic resonance in medicine.

[38]  N J Pelc,et al.  Minimizing TE in moment‐nulled or flow‐encoded two‐and three‐dimensional gradient‐echo imaging , 1992, Journal of magnetic resonance imaging : JMRI.

[39]  Alastair J. Martin,et al.  Phase‐contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: Comparison with computational fluid dynamics , 2009, Magnetic resonance in medicine.

[40]  J. Hennig,et al.  Quantitative 2D and 3D phase contrast MRI: Optimized analysis of blood flow and vessel wall parameters , 2008, Magnetic resonance in medicine.

[41]  T. Ebbers,et al.  Particle trace visualization of intracardiac flow using time‐resolved 3D phase contrast MRI , 1999, Magnetic resonance in medicine.

[42]  Einar Heiberg,et al.  Design and validation of Segment - freely available software for cardiovascular image analysis , 2010, BMC Medical Imaging.

[43]  R. Mohiaddin,et al.  Cine MR fourier velocimetry of blood flow through cardiac valves: Comparison with doppler echocardiography , 1997, Journal of magnetic resonance imaging : JMRI.

[44]  M. Yacoub,et al.  Asymmetric redirection of flow through the heart , 2000, Nature.

[45]  S. Riederer,et al.  Navigator-echo-based real-time respiratory gating and triggering for reduction of respiration effects in three-dimensional coronary MR angiography. , 1996, Radiology.

[46]  Jürgen Hennig,et al.  Highly k‐t‐space–accelerated phase‐contrast MRI , 2008, Magnetic resonance in medicine.

[47]  Charles A Mistretta,et al.  Transstenotic pressure gradients: measurement in swine--retrospectively ECG-gated 3D phase-contrast MR angiography versus endovascular pressure-sensing guidewires. , 2007, Radiology.

[48]  Cornelius Weiller,et al.  In vivo assessment of wall shear stress in the atherosclerotic aorta using flow‐sensitive 4D MRI , 2010, Magnetic resonance in medicine.

[49]  R. Edelman,et al.  Cineangiography of the heart in a single breath hold with a segmented turboFLASH sequence. , 1991, Radiology.

[50]  R. Herfkens,et al.  Phase contrast cine magnetic resonance imaging. , 1991, Magnetic resonance quarterly.

[51]  John N Oshinski,et al.  Three-directional myocardial phase-contrast tissue velocity MR imaging with navigator-echo gating: in vivo and in vitro study. , 2008, Radiology.

[52]  Petter Dyverfeldt,et al.  In vitro assessment of flow patterns and turbulence intensity in prosthetic heart valves using generalized phase‐contrast MRI , 2010, Journal of magnetic resonance imaging : JMRI.

[53]  J. Hennig,et al.  4D phase contrast MRI at 3 T: Effect of standard and blood‐pool contrast agents on SNR, PC‐MRA, and blood flow visualization , 2010, Magnetic resonance in medicine.

[54]  Jan Engvall,et al.  Flow patterns in the aortic root and the aorta studied with time-resolved, 3-dimensional, phase-contrast magnetic resonance imaging: implications for aortic valve-sparing surgery. , 2004, The Journal of thoracic and cardiovascular surgery.

[55]  David N. Firmin,et al.  Rapid 7-dimensional imaging of pulsatile flow , 1993, Proceedings of Computers in Cardiology Conference.

[56]  Horst Olschewski,et al.  Magnetic Resonance–Derived 3-Dimensional Blood Flow Patterns in the Main Pulmonary Artery as a Marker of Pulmonary Hypertension and a Measure of Elevated Mean Pulmonary Arterial Pressure , 2008, Circulation. Cardiovascular imaging.

[57]  D N Firmin,et al.  Computation of flow pressure fields from magnetic resonance velocity mapping , 1996, Magnetic resonance in medicine.

[58]  Guang-Zhong Yang,et al.  Helical and Retrograde Secondary Flow Patterns in the Aortic Arch Studied by Three‐Directional Magnetic Resonance Velocity Mapping , 1993, Circulation.

[59]  D N Firmin,et al.  Blood flow imaging by cine magnetic resonance. , 1986, Journal of computer assisted tomography.

[60]  J. Hennig,et al.  Time‐resolved 3D MR velocity mapping at 3T: Improved navigator‐gated assessment of vascular anatomy and blood flow , 2007, Journal of magnetic resonance imaging : JMRI.

[61]  AlexFrydrychowicz,et al.  In Vivo 3-Dimensional Flow Connectivity Mapping After Extracardiac Total Cavopulmonary Connection , 2008 .

[62]  R. Mohiaddin,et al.  Applications of phase-contrast flow and velocity imaging in cardiovascular MRI , 2005, European Radiology.

[63]  Daniel B Vigneron,et al.  Evaluation of intracranial stenoses and aneurysms with accelerated 4D flow. , 2010, Magnetic resonance imaging.

[64]  T Ebbers,et al.  Noninvasive measurement of time-varying three-dimensional relative pressure fields within the human heart. , 2002, Journal of biomechanical engineering.

[65]  M H Buonocore,et al.  Visualizing blood flow patterns using streamlines, arrows, and particle paths , 1998, Magnetic resonance in medicine.

[66]  J. Felmlee,et al.  Adaptive technique for high-definition MR imaging of moving structures. , 1989, Radiology.

[67]  M. Alley,et al.  Comparison of flow patterns in ascending aortic aneurysms and volunteers using four‐dimensional magnetic resonance velocity mapping , 2007, Journal of magnetic resonance imaging : JMRI.

[68]  H. W. Korin,et al.  Adaptive motion compensation in MRI: Accuracy of motion measurement , 1991, Magnetic resonance in medicine.

[69]  G. Glover,et al.  Generalized reconstruction of phase contrast MRI: Analysis and correction of the effect of gradient field distortions , 2003, Magnetic resonance in medicine.

[70]  C Thomsen,et al.  A segmented k‐space velocity mapping protocol for quantification of renal artery blood plow during breath‐holding , 1995, Journal of magnetic resonance imaging : JMRI.

[71]  T Ebbers,et al.  Three dimensional flow in the human left atrium , 2001, Heart.

[72]  Einar Heiberg,et al.  Transit of blood flow through the human left ventricle mapped by cardiovascular magnetic resonance. , 2007, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[73]  Jürgen Hennig,et al.  Three‐dimensional analysis of segmental wall shear stress in the aorta by flow‐sensitive four‐dimensional‐MRI , 2009, Journal of magnetic resonance imaging : JMRI.

[74]  Steffen Ringgaard,et al.  Three dimensional three component whole heart cardiovascular magnetic resonance velocity mapping: comparison of flow measurements from 3D and 2D acquisitions , 2009, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[75]  K. Scheffler,et al.  In vivo assessment and visualization of intracranial arterial hemodynamics with flow-sensitized 4D MR imaging at 3T. , 2007, AJNR. American journal of neuroradiology.

[76]  David Atkinson,et al.  Retrospective respiratory motion correction for navigated cine velocity mapping. , 2004, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[77]  M. Alley,et al.  Time-Resolved 3-Dimensional Velocity Mapping in the Thoracic Aorta: Visualization of 3-Directional Blood Flow Patterns in Healthy Volunteers and Patients , 2004, Journal of computer assisted tomography.

[78]  Jan Engvall,et al.  Three-directional myocardial motion assessed using 3D phase contrast MRI. , 2004, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[79]  P Boesiger,et al.  Visualization of flow patterns distal to aortic valve prostheses in humans using a fast approach for cine 3D velocity mapping , 2001, Journal of magnetic resonance imaging : JMRI.

[80]  J. Hennig,et al.  3D blood flow characteristics in the carotid artery bifurcation assessed by flow‐sensitive 4D MRI at 3T , 2009, Magnetic resonance in medicine.

[81]  A. G. Collins,et al.  Respiratory ordered phase encoding (ROPE): a method for reducing respiratory motion artefacts in MR imaging. , 1985, Journal of computer assisted tomography.

[82]  Jürgen Hennig,et al.  Journal of Cardiovascular Magnetic Resonance Open Access Multidirectional Flow Analysis by Cardiovascular Magnetic Resonance in Aneurysm Development following Repair of Aortic Coarctation , 2008 .

[83]  Cornelius Weiller,et al.  Complex Plaques in the Proximal Descending Aorta: An Underestimated Embolic Source of Stroke , 2010, Stroke.

[84]  R. Herfkens,et al.  Evaluation of Myocardial Motion Tracking With Cine-Phase Contrast Magnetic Resonance Imaging , 1994, Investigative radiology.

[85]  S. Alper,et al.  Hemodynamic shear stress and its role in atherosclerosis. , 1999, JAMA.

[86]  T. Ebbers,et al.  Quantification of intravoxel velocity standard deviation and turbulence intensity by generalizing phase‐contrast MRI , 2006, Magnetic resonance in medicine.

[87]  Johan H C Reiber,et al.  Mitral valve and tricuspid valve blood flow: accurate quantification with 3D velocity-encoded MR imaging with retrospective valve tracking. , 2008, Radiology.

[88]  M. McConnell,et al.  Comparison of respiratory suppression methods and navigator locations for MR coronary angiography. , 1997, AJR. American journal of roentgenology.

[89]  Michael Markl,et al.  Time‐resolved three‐dimensional phase‐contrast MRI , 2003, Journal of magnetic resonance imaging : JMRI.

[90]  A P Yoganathan,et al.  Left ventricular blood flow patterns in normal subjects: a quantitative analysis by three-dimensional magnetic resonance velocity mapping. , 1995, Journal of the American College of Cardiology.

[91]  Importance of different correction methods for optimized 3 D visualization of 3-directional MR velocity data , 2009 .

[92]  D. Firmin,et al.  Measurement of Flow with NMR Imaging Using a Gradient Pulse and Phase Difference Technique , 1984, Journal of computer assisted tomography.

[93]  D. Didier Assessment of valve disease: qualitative and quantitative. , 2003, Magnetic resonance imaging clinics of North America.

[94]  Eric Laffon,et al.  Feasibility of aortic pulse pressure and pressure wave velocity MRI measurement in young adults , 2005, Journal of magnetic resonance imaging : JMRI.

[95]  Andrew C Larson,et al.  Self‐gated cardiac cine MRI , 2004, Magnetic resonance in medicine.

[96]  P. R. Moran A flow velocity zeugmatographic interlace for NMR imaging in humans. , 1982, Magnetic resonance imaging.

[97]  P Boesiger,et al.  Automatic accurate non-invasive quantitation of blood flow, cross-sectional vessel area, and wall shear stress by modelling of magnetic resonance velocity data. , 1998, European journal of vascular and endovascular surgery : the official journal of the European Society for Vascular Surgery.

[98]  D N Firmin,et al.  Blood flow patterns in the thoracic aorta studied with three‐directional MR velocity mapping: The effects of age and coronary artery disease , 1997, Journal of magnetic resonance imaging : JMRI.

[99]  A. Bolger,et al.  Passing strange: flow in the failing ventricle. , 2010, Circulation. Heart failure.

[100]  Murat Aksoy,et al.  Time‐resolved 3D quantitative flow MRI of the major intracranial vessels: Initial experience and comparative evaluation at 1.5T and 3.0T in combination with parallel imaging , 2007, Magnetic resonance in medicine.

[101]  Petter Dyverfeldt,et al.  On MRI turbulence quantification. , 2009, Magnetic resonance imaging.

[102]  Raad Mohiaddin,et al.  How we perform cardiovascular magnetic resonance flow assessment using phase-contrast velocity mapping. , 2005, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[103]  N J Pelc,et al.  Reconstructions of phase contrast, phased array multicoil data , 1994, Magnetic resonance in medicine.

[104]  C L Dumoulin,et al.  Phase contrast MR angiography techniques. , 1995, Magnetic resonance imaging clinics of North America.

[105]  Kieran Clarke,et al.  Longitudinally and circumferentially directed movements of the left ventricle studied by cardiovascular magnetic resonance phase contrast velocity mapping , 2010, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[106]  Matts Karlsson,et al.  Quantifying turbulent wall shear stress in a stenosed pipe using large eddy simulation. , 2010, Journal of biomechanical engineering.

[107]  D N Firmin,et al.  Magnetic resonance velocity mapping. , 1990, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[108]  Maxim Zaitsev,et al.  Time-resolved, 3-Dimensional Magnetic Resonance Flow Analysis at 3 T: Visualization of Normal and Pathological Aortic Vascular Hemodynamics , 2007, Journal of computer assisted tomography.

[109]  P. Dijk Direct cardiac NMR imaging of heart wall and blood flow velocity. , 1984 .

[110]  G. Glover,et al.  Encoding strategies for three‐direction phase‐contrast MR imaging of flow , 1991, Journal of magnetic resonance imaging : JMRI.

[111]  Andreas Stadlbauer,et al.  Accelerated time-resolved three-dimensional MR velocity mapping of blood flow patterns in the aorta using SENSE and k-t BLAST. , 2010, European journal of radiology.

[112]  M. Alley,et al.  Clinical Evaluation of Aortic Coarctation With 4D , 2010 .