Combined analysis of spatial and velocity displacement artifacts in phase contrast measurements of complex flows

Four-dimensional flow MRI for quantitative assessment of cerebrospinal fluid dynamics: Status and opportunities

Neurological disorders can manifest with altered neurofluid dynamics in different compartments of the central nervous system. These include alterations in cerebral blood flow, cerebrospinal fluid (CSF) flow, and tissue biomechanics. Noninvasive quantitative assessment of neurofluid flow and tissue motion is feasible with phase contrast magnetic resonance imaging (PC MRI). While two-dimensional (2D) PC MRI is routinely utilized in research and clinical settings to assess flow dynamics through a single imaging slice, comprehensive neurofluid dynamic assessment can be limited or impractical. Recently, four-dimensional (4D) flow MRI (or time-resolved three-dimensional PC with three-directional velocity encoding) has emerged as a powerful extension of 2D PC, allowing for large volumetric coverage of fluid velocities at high spatiotemporal resolution within clinically reasonable scan times. Yet, most 4D flow studies have focused on blood flow imaging. Characterizing CSF flow dynamics with 4D flow (i.e., 4D CSF flow) is of high interest to understand normal brain and spine physiology, but also to study neurological disorders such as dysfunctional brain metabolite waste clearance, where CSF dynamics appear to play an important role. However, 4D CSF flow imaging is challenged by the long T1 time of CSF and slower velocities compared with blood flow, which can result in longer scan times from low flip angles and extended motion-sensitive gradients, hindering clinical adoption. In this work, we review the state of 4D CSF flow MRI including challenges, novel solutions from current research and ongoing needs, examples of clinical and research applications, and discuss an outlook on the future of 4D CSF flow.

CMRsim-A python package for cardiovascular MR simulations incorporating complex motion and flow

PURPOSE

To present an open-source MR simulation framework that facilitates the incorporation of complex motion and flow for studying cardiovascular MR (CMR) acquisition and reconstruction.

METHODS

CMRsim is a Python package that allows simulation of CMR images using dynamic digital phantoms with complex motion as input. Two simulation paradigms are available, namely, numerical and analytical solutions to the Bloch equations, using a common motion representation. Competitive simulation speeds are achieved using TensorFlow for GPU acceleration. To demonstrate the capability of the package, one introductory and two advanced CMR simulation experiments are presented. The latter showcase phase-contrast imaging of turbulent flow downstream of a stenotic section and cardiac diffusion tensor imaging on a contracting left ventricle. Additionally, extensive documentation and example resources are provided.

RESULTS

The Bloch simulation with turbulent flow using approximately 1.5 million particles and a sequence duration of 710 ms for each of the seven different velocity encodings took a total of 29 min on a NVIDIA Titan RTX GPU. The results show characteristic phase contrast and magnitude modulation present in real data. The analytical simulation of cardiac diffusion tensor imaging with bulk-motion phase sensitivity took approximately 10 s per diffusion-weighted image, including preparation and loading steps. The results exhibit the expected alteration of diffusion metrics due to strain.

CONCLUSION

CMRsim is the first simulation framework that allows one to feasibly incorporate complex motion, including turbulent flow, to systematically study advanced CMR acquisition and reconstruction approaches. The open-source package features modularity and transparency, facilitating maintainability and extensibility in support of reproducible research.

Toward accurate and fast velocity quantification with 3D ultrashort TE phase-contrast imaging

PURPOSE

Traditional phase-contrast MRI is affected by displacement artifacts caused by non-synchronized spatial- and velocity-encoding time points. The resulting inaccurate velocity maps can affect the accuracy of derived hemodynamic parameters. This study proposes and characterizes a 3D radial phase-contrast UTE (PC-UTE) sequence to reduce displacement artifacts. Furthermore, it investigates the displacement of a standard Cartesian flow sequence by utilizing a displacement-free synchronized-single-point-imaging MR sequence (SYNC-SPI) that requires clinically prohibitively long acquisition times.

METHODS

3D flow data was acquired at 3T at three different constant flow rates and varying spatial resolutions in a stenotic aorta phantom using the proposed PC-UTE, a Cartesian flow sequence, and a SYNC-SPI sequence as reference. Expected displacement artifacts were calculated from gradient timing waveforms and compared to displacement values measured in the in vitro flow experiments.

RESULTS

The PC-UTE sequence reduces displacement and intravoxel dephasing, leading to decreased geometric distortions and signal cancellations in magnitude images, and more spatially accurate velocity quantification compared to the Cartesian flow acquisitions; errors increase with velocity and higher spatial resolution.

CONCLUSION

PC-UTE MRI can measure velocity vector fields with greater accuracy than Cartesian acquisitions (although pulsatile fields were not studied) and shorter scan times than SYNC-SPI. As such, this approach is superior to traditional Cartesian 3D and 4D flow MRI when spatial misrepresentations cannot be tolerated, for example, when computational fluid dynamics simulations are compared to or combined with in vitro or in vivo measurements, or regional parameters such as wall shear stress are of interest.

Accelerated sequences of 4D flow MRI using GRAPPA and compressed sensing: A comparison against conventional MRI and computational fluid dynamics

PURPOSE

To evaluate hemodynamic markers obtained by accelerated GRAPPA (R = 2, 3, 4) and compressed sensing (R = 7.6) 4D flow MRI sequences under complex flow conditions.

METHODS

The accelerated 4D flow MRI scans were performed on a pulsatile flow phantom, along with a nonaccelerated fully sampled k-space acquisition. Computational fluid dynamics simulations based on the experimentally measured flow fields were conducted for additional comparison. Voxel-wise comparisons (Bland-Altman analysis, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>L</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {L}_2 $$</mml:annotation></mml:semantics> </mml:math> -norm metric), as well as nonderived quantities (velocity profiles, flow rates, and peak velocities), were used to compare the velocity fields obtained from the different modalities.

RESULTS

4D flow acquisitions and computational fluid dynamics depicted similar hemodynamic patterns. Voxel-wise comparisons between the MRI scans highlighted larger discrepancies at the voxels located near the phantom's boundary walls. A trend for all MR scans to overestimate velocity profiles and peak velocities as compared to computational fluid dynamics was noticed in regions associated with high velocity or acceleration. However, good agreement for the flow rates was observed, and eddy-current correction appeared essential for consistency of the flow rates measurements with respect to the principle of mass conservation.

CONCLUSION

GRAPPA (R = 2, 3) and highly accelerated compressed sensing showed good agreement with the fully sampled acquisition. Yet, all 4D flow MRI scans were hampered by artifacts inherent to the phase-contrast acquisition procedure. Computational fluid dynamics simulations are an interesting tool to assess these differences but are sensitive to modeling parameters.

Synthesis of patient-specific multipoint 4D flow MRI data of turbulent aortic flow downstream of stenotic valves

We propose to synthesize patient-specific 4D flow MRI datasets of turbulent flow paired with ground truth flow data to support training of inference methods. Turbulent blood flow is computed based on the Navier-Stokes equations with moving domains using realistic boundary conditions for aortic shapes, wall displacements and inlet velocities obtained from patient data. From the simulated flow, synthetic multipoint 4D flow MRI data is generated with user-defined spatiotemporal resolutions and reconstructed with a Bayesian approach to compute time-varying velocity and turbulence maps. For MRI data synthesis, a fixed hypothetical scan time budget is assumed and accordingly, changes to spatial resolution and time averaging result in corresponding scaling of signal-to-noise ratios (SNR). In this work, we focused on aortic stenotic flow and quantification of turbulent kinetic energy (TKE). Our results show that for spatial resolutions of 1.5 and 2.5 mm and time averaging of 5 ms as encountered in 4D flow MRI in practice, peak total turbulent kinetic energy downstream of a 50, 75 and 90% stenosis is overestimated by as much as 23, 15 and 14% (1.5 mm) and 38, 24 and 23% (2.5 mm), demonstrating the importance of paired ground truth and 4D flow MRI data for assessing accuracy and precision of turbulent flow inference using 4D flow MRI exams.

Virtual injections using 4D flow MRI with displacement corrections and constrained probabilistic streamlines

PURPOSE

Streamlines from 4D-flow MRI have been used clinically for intracranial blood-flow tracking. However, deterministic and stochastic errors degrade streamline quality. The purpose of this study is to integrate displacement corrections, probabilistic streamlines, and novel fluid constraints to improve selective blood-flow tracking and emulate "virtual bolus injections."

METHODS

Both displacement artifacts (deterministic) and velocity noise (stochastic) inherently occur during phase-contrast MRI acquisitions. Here, two displacement correction methods, single-step and iterative, were tested in silico with simulated displacements and were compared with ground-truth velocity fields. Next, the effects of combining displacement corrections and constrained probabilistic streamlines were performed in 10 healthy volunteers using time-averaged 4D-flow data. Measures of streamline length and depth into vasculature were then compared with streamlines generated with no corrections and displacement correction alone using one-way repeated-measures analysis of variance and Friedman's tests. Finally, virtual injections with improved streamlines were generated for three intracranial pathology cases.

RESULTS

Iterative displacement correction outperformed the single-step method in silico. In volunteers, the combination of displacement corrections and constrained probabilistic streamlines allowed for significant improvements in streamline length and increased the number of streamlines entering the circle of Willis relative to streamlines with no corrections and displacement correction alone. In the pathology cases, virtual injections with improved streamlines were qualitatively similar to dynamic arterial spin labeling images and allowed for forward/reverse selective flow tracking to characterize cerebrovascular malformations.

CONCLUSION

Virtual injections with improved streamlines from 4D-flow MRI allow for flexible, robust, intracranial flow tracking.

Toward an accurate estimation of wall shear stress from 4D flow magnetic resonance downstream of a severe stenosis

PURPOSE

First, to investigate the agreement between velocity, velocity gradient, and Reynolds stress obtained from four-dimensional flow magnetic resonance (4D flow MRI) measurements and direct numerical simulation (DNS). Second, to propose and optimize based on DNS, 2 alternative methods for the accurate estimation of wall shear stress (WSS) when the resolution of the flow measurements is limited. Thirdly, to validate the 2 methods based on 4D flow MRI data.

METHODS

In vitro 4D MRI has been conducted in a realistic rigid stenosed aorta model under a constant flow rate of 12 L/min. A DNS of transitional stenotic flow has been performed using the same geometry and boundary conditions.

RESULTS

Time-averaged velocity and Reynolds stresses are in good agreement between in vitro 4D MRI data and DNS (errors between 2% and 8% of the reference downsampled data). WSS estimation based on the 2 proposed methods applied to MRI data provide good agreement with DNS for slice-averaged values (maximum error is less than 15% of the mean reference WSS for the first method and 25% for the second method). The performance of both models is not strongly sensitive to spatial resolution up to 1.5 mm voxel size. While the performance of model 1 deteriorates appreciably at low signal-to-noise ratios, model 2 remains robust.

CONCLUSIONS

The 2 methods for WSS magnitude give an overall better agreement than the standard approach used in the literature based on direct calculation of the velocity gradient close to the wall (relative error of 84%).

Numerical simulation of time-resolved 3D phase-contrast magnetic resonance imaging

A numerical approach is presented to efficiently simulate time-resolved 3D phase-contrast Magnetic resonance Imaging (or 4D Flow MRI) acquisitions under realistic flow conditions. The Navier-Stokes and Bloch equations are simultaneously solved with an Eulerian-Lagrangian formalism. A semi-analytic solution for the Bloch equations as well as a periodic particle seeding strategy are developed to reduce the computational cost. The velocity reconstruction pipeline is first validated by considering a Poiseuille flow configuration. The 4D Flow MRI simulation procedure is then applied to the flow within an in vitro flow phantom typical of the cardiovascular system. The simulated MR velocity images compare favorably to both the flow computed by solving the Navier-Stokes equations and experimental 4D Flow MRI measurements. A practical application is finally presented in which the MRI simulation framework is used to identify the origins of the MRI measurement errors.

The impact of 4D flow displacement artifacts on wall shear stress estimation

PURPOSE

To investigate the amplitude and spatial distribution of errors in wall shear stress (WSS) values derived from 4D flow measurements caused by displacement artifacts intrinsic to the 4D flow acquisition.

METHODS

Phase-contrast MRI velocimetry was performed in a model of a stenotic aorta using two different timing schemes, both of which are commonly applied in vivo but differ in their resulting displacement artifacts. Whereas one scheme is optimized to minimize the duration of the encoding gradients (herein called FAST), the other aims to specifically minimize displacement artifacts by synchronizing all three spatial-encoding time points (called ECHO). WSS estimates were calculated and compared to unbiased WSS values obtained by a 5-hour single-point imaging acquisition. In addition, MRI simulations based on computational fluid dynamics data were carried out to investigate the impact of gradient timings corresponding to different spatial resolutions.

RESULTS

4D flow displacement artifacts were found to have an impact on the quantified WSS peak values, spatial location, and overall WSS pattern. FAST leads to the underestimation of local WSS values in the phantom arch by up to 90%. Moreover, the corresponding WSS estimates depend on the image orientation. This effect was avoided using ECHO, which, however, results in biased WSS values within the stenosis, yielding an underestimation of peak WSS by up to 17%. Computational fluid dynamics-based simulation results show that the bias in WSS due to displacement artifacts increases with increasing spatial resolution, thus counteracting the resolution benefit for WSS due to reduced partial volume effects and segmentation errors.

CONCLUSIONS

4D flow displacement artifacts can significantly impact the WSS estimates and depend on the timing scheme as well as potentially the image orientation. Whereas FAST might allow correct WSS estimation for lower resolutions, ECHO is recommended especially when spatial resolutions of 1 mm and smaller are used. Users need to be aware of this nonnegligible effect, particularly when conducting inter-site studies or studies between vendors. The timing scheme should thus be explicitly mentioned in publications.

On the limitations of echo planar 4D flow MRI

PURPOSE

To compare EPI and GRE readout in high-flow velocity regimes and evaluate their impact on measurement accuracy in silico and in vitro.

THEORY AND METHODS

Phase-contrast sequences for EPI and GRE were simulated using CFD velocity data to assess displacement artifacts as well as effective spatial resolution. In silico findings were validated experimentally using a steady flow phantom.

RESULTS

For EPI factor 5 and simulated stenotic flow with peak velocity of 2.2 m s - 1 , displacement artifacts resulted in misregistration of 7.3 mm at echo time and the effective resolution was locally reduced by factors 5 and 8 compared to GRE for flow along phase and frequency encoding directions, respectively. In vitro, a maximum velocity difference between EPI factor 5 and GRE of 0.97 m s - 1 was found.

CONCLUSIONS

Four-dimensional flow MRI using EPI readout results not only in considerable velocity misregistration but also in spatially varying degradation of resolution. The proposed work indicates that EPI is inferior to standard GRE for 4D flow MRI.

Four-Dimensional Flow Magnetic Resonance Imaging for Assessment of Velocity Magnitudes and Flow Patterns in The Human Carotid Artery Bifurcation: Comparison with Computational Fluid Dynamics

Purpose: Knowledge of the hemodynamics in the vascular system is important to understand and treat vascular pathology. The present study aimed to evaluate the hemodynamics in the human carotid artery bifurcation measured by four-dimensional (4D) flow magnetic resonance imaging (MRI) as compared to computational fluid dynamics (CFD). Methods: This protocol used MRI data of 12 healthy volunteers for the 3D vascular models and 4D flow MRI measurements for the boundary conditions in CFD simulation. We compared the velocities measured at the carotid bifurcation and the 3D velocity streamlines of the carotid arteries obtained by these two methods. Results: There was a good agreement for both maximum and minimum velocity values between the 2 methods for velocity magnitude at the bifurcation plane. However, on the 3D blood flow visualization, secondary flows, and recirculation regions are of poorer quality when visualized through the 4D flow MRI. Conclusion: 4D flow MRI and CFD show reasonable agreement in demonstrated velocity magnitudes at the carotid artery bifurcation. However, the visualization of blood flow at the recirculation regions and the assessment of secondary flow characteristics should be enhanced for the use of 4D flow MRI in clinical situations.

Reconciling PC-MRI and CFD: An in-vitro study

Several well-resolved 4D Flow MRI acquisitions of an idealized rigid flow phantom featuring an aneurysm, a curved channel as well as a bifurcation were performed under pulsatile regime. The resulting hemodynamics were processed to remove MRI artifacts. Subsequently, they were compared with CFD predictions computed on the same flow domain, using an in-house high-order low dissipative flow solver. Results show that reaching a good agreement is not straightforward but requires proper treatments of both techniques. Several sources of discrepancies are highlighted and their impact on the final correlation evaluated. While a very poor correlation (r²  = 0.63) is found in the entire domain between raw MRI and CFD data, correlation as high as r²  = 0.97 is found when artifacts are removed by post-processing the MR data and down sampling the CFD results to match the MRI spatial and temporal resolutions. This work demonstrates that, in a well-controlled environment, both PC-MRI and CFD might bring reliable and correlated flow quantities when a proper methodology to reduce the errors is followed.

Comparison of MR flow quantification in peripheral and main pulmonary arteries in patients after right ventricular outflow tract surgery: A retrospective study

PURPOSE

To compare the quantification of pulmonary stroke volume (SV) by phase contrast magnetic resonance (PC-MR) in the main pulmonary artery (MPA) to the sum of SVs in both peripheral pulmonary arteries (PPA) in different right ventricular (RV) outflow pathologies.

MATERIALS AND METHODS

Pulmonary SV was determined by PC-MR in the MPA and the PPA in healthy individuals (H, n = 54), patients after correction for tetralogy of Fallot with significant pulmonary regurgitation and without pulmonary or RV outflow tract stenosis (PR, n = 50), and in patients with RV outflow tract or pulmonary valve stenosis (PS, n = 50). Resulting SVs were compared to aortic SV in the ascending aorta.

RESULTS

Mean age was similar between the groups: H 28 ± 17 vs. PR 24 ± 11 vs. PS 22 ± 10 years. Bland-Altman analyses revealed in all groups a relatively small systemic (bias) but large random error (limits of agreement) for pulmonary SV determined in the MPA as compared to summed SVs in the PPA. The largest limits of agreement were present in PS patients: H: MPA 3.9% (-11, + 19) vs. PPA 0.4% (-15, + 15); PR: MPA 5.2% (-25, + 36) vs. PPA 0.6% (-24, + 26); PS: MPA 5% (-36; + 46), PPA -0.03% (-34, + 35).

CONCLUSION

The accuracy of PC-MR in the MPA is reasonable; however, a large random error (precision) is observed that is most pronounced in PS patients. This potential error should be taken into consideration when interpreting MPA flow measurements.

LEVEL OF EVIDENCE

3 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2017;46:1839-1845.

Cerebrovascular MRI: a review of state-of-the-art approaches, methods and techniques

Cerebrovascular imaging is of great interest in the understanding of neurological disease. MRI is a non-invasive technology that can visualize and provide information on: (i) the structure of major blood vessels; (ii) the blood flow velocity in these vessels; and (iii) the microcirculation, including the assessment of brain perfusion. Although other medical imaging modalities can also interrogate the cerebrovascular system, MR provides a comprehensive assessment, as it can acquire many different structural and functional image contrasts whilst maintaining a high level of patient comfort and acceptance. The extent of examination is limited only by the practicalities of patient tolerance or clinical scheduling limitations. Currently, MRI methods can provide a range of metrics related to the cerebral vasculature, including: (i) major vessel anatomy via time-of-flight and contrast-enhanced imaging; (ii) blood flow velocity via phase contrast imaging; (iii) major vessel anatomy and tissue perfusion via arterial spin labeling and dynamic bolus passage approaches; and (iv) venography via susceptibility-based imaging. When designing an MRI protocol for patients with suspected cerebral vascular abnormalities, it is appropriate to have a complete understanding of when to use each of the available techniques in the 'MR angiography toolkit'. In this review article, we: (i) overview the relevant anatomy, common pathologies and alternative imaging modalities; (ii) describe the physical principles and implementations of the above listed methods; (iii) provide guidance on the selection of acquisition parameters; and (iv) describe the existing and potential applications of MRI to the cerebral vasculature and diseases. The focus of this review is on obtaining an understanding through the application of advanced MRI methodology of both normal and abnormal blood flow in the cerebrovascular arteries, capillaries and veins.

Volumetric velocity measurements in restricted geometries using spiral sampling: a phantom study

OBJECT

The aim of this study was to evaluate the accuracy of maximum velocity measurements using volumetric phase-contrast imaging with spiral readouts in a stenotic flow phantom.

MATERIALS AND METHODS

In a phantom model, maximum velocity, flow, pressure gradient, and streamline visualizations were evaluated using volumetric phase-contrast magnetic resonance imaging (MRI) with velocity encoding in one (extending on current clinical practice) and three directions (for characterization of the flow field) using spiral readouts. Results of maximum velocity and pressure drop were compared to computational fluid dynamics (CFD) simulations, as well as corresponding low-echo-time (TE) Cartesian data. Flow was compared to 2D through-plane phase contrast (PC) upstream from the restriction.

RESULTS

Results obtained with 3D through-plane PC as well as 4D PC at shortest TE using a spiral readout showed excellent agreements with the maximum velocity values obtained with CFD (<1 % for both methods), while larger deviations were seen using Cartesian readouts (-2.3 and 13 %, respectively). Peak pressure drop calculations from 3D through-plane PC and 4D PC spiral sequences were respectively 14 and 13 % overestimated compared to CFD.

CONCLUSION

Identification of the maximum velocity location, as well as the accurate velocity quantification can be obtained in stenotic regions using short-TE spiral volumetric PC imaging.

A methodology to detect abnormal relative wall shear stress on the full surface of the thoracic aorta using four-dimensional flow MRI

PURPOSE

To compute cohort-averaged wall shear stress (WSS) maps in the thoracic aorta of patients with aortic dilatation or valvular stenosis and to detect abnormal regional WSS.

METHODS

Systolic WSS vectors, estimated from four-dimensional flow MRI data, were calculated along the thoracic aorta lumen in 10 controls, 10 patients with dilated aortas, and 10 patients with aortic valve stenosis. Three-dimensional segmentations of each aorta were coregistered by group and used to create a cohort-specific aortic geometry. The WSS vectors of each subject were interpolated onto the corresponding cohort-specific geometry to create cohort-averaged WSS maps. A Wilcoxon rank sum test was used to generate aortic P-value maps (P<0.05) representing regional relative WSS differences between groups.

RESULTS

Cohort-averaged systolic WSS maps and P-value maps were successfully created for all cohorts and comparisons. The dilation cohort showed significantly lower WSS on 7% of the ascending aorta surface, whereas the stenosis cohort showed significantly higher WSS on 34% of the ascending aorta surface.

CONCLUSIONS

The findings of this study demonstrated the feasibility of generating cohort-averaged WSS maps for the visualization and identification of regionally altered WSS in the presence of disease, compared with healthy controls.

In vivo validation of numerical prediction for turbulence intensity in an aortic coarctation

This paper compares numerical predictions of turbulence intensity with in vivo measurement. Magnetic resonance imaging (MRI) was carried out on a 60-year-old female with a restenosed aortic coarctation. Time-resolved three-directional phase-contrast (PC) MRI data was acquired to enable turbulence intensity estimation. A contrast-enhanced MR angiography (MRA) and a time-resolved 2D PCMRI measurement were also performed to acquire data needed to perform subsequent image-based computational fluid dynamics (CFD) modeling. A 3D model of the aortic coarctation and surrounding vasculature was constructed from the MRA data, and physiologic boundary conditions were modeled to match 2D PCMRI and pressure pulse measurements. Blood flow velocity data was subsequently obtained by numerical simulation. Turbulent kinetic energy (TKE) was computed from the resulting CFD data. Results indicate relative agreement (error ≈10%) between the in vivo measurements and the CFD predictions of TKE. The discrepancies in modeled vs. measured TKE values were within expectations due to modeling and measurement errors.

Computational simulations and experimental studies of 3D phase-contrast imaging of fluid flow in carotid bifurcation geometries

PURPOSE

To evaluate the use of computational fluid dynamic (CFD)-based magnetic resonance imaging (MRI) simulations to predict the image appearance and velocity measurement of fluid flow in human carotid bifurcation geometries, and to compare the results with images from experimental MRI studies.

MATERIALS AND METHODS

Simulated particle paths were calculated from available CFD datasets of normal and moderately stenosed carotid bifurcation geometries. An MRI simulator based on the spin isochromat method was used to generate images corresponding to a 3D phase-contrast sequence with velocity encoding in three orthogonal directions. The resulting images were compared qualitatively with experimental MRI scans of the corresponding physical models.

RESULTS

The simulations predicted the main features observed in experimental studies, such as the low image intensity in regions of complex flow and the position and bright appearance of the jet in the stenosed bifurcation. Simulated velocity images also agreed well with experimental results. The effects of sequence parameters such as repetition time (TR) and echo time (TE) were readily demonstrated by the simulations.

CONCLUSION

CFD-based MRI simulations can be used to predict the appearance of MRI images of regions of physiological flow, and may be useful in the development of improved pulse sequences for flow measurement.

Comparative velocity investigations in cerebral arteries and aneurysms: 3D phase-contrast MR angiography, laser Doppler velocimetry and computational fluid dynamics

In western populations, cerebral aneurysms develop in approximately 4% of humans and they involve the risk of rupture. Blood flow patterns are of interest for understanding the pathogenesis of the lesions and may eventually contribute to deciding on the most efficient treatment procedure for a specific patient. Velocity mapping with phase-contrast magnetic resonance angiography (PC-MRA) is a non-invasive method for performing in vivo measurements on blood velocity. Several hemodynamic properties can either be derived directly from these measurements or a flow field with all its parameters can be simulated on the basis of the measurements. For both approaches, the accuracy of the PC-MRA data and subsequent modeling must be validated. Therefore, a realistic transient flow field in a well-defined patient-specific silicone phantom was investigated. Velocity investigations with PC-MRA in a 3 Tesla MR scanner, laser Doppler velocimetry (LDV) and computational fluid dynamics (CFD) were performed in the same model under equal flow conditions and compared to each other. The results showed that PC-MRA was qualitatively similar to LDV and CFD, but showed notable quantitative differences, while LDV and CFD agreed well. The accuracy of velocity quantification by PC-MRA was best in straight artery regions with the measurement plane being perpendicular to the primary flow direction. The accuracy decreased in regions with disturbed flow and in cases where the measurement plane was not perpendicular to the primary flow. Due to these findings, it is appropriate to use PC-MRA as the inlet and outlet conditions for numerical simulations to calculate velocities and shear stresses in disturbed regions like aneurysms, rather than derive these values directly from the full PC-MRA measured velocity field.

Quantifying coronary sinus flow and global LV perfusion at 3T

Background

Despite the large availability of 3T MR scanners and the potential of high field imaging, this technical platform has yet to prove its usefulness in the cardiac MR setting, where 1.5T remains the established standard. Global perfusion of the left ventricle, as well as the coronary flow reserve (CFR), can provide relevant diagnostic information, and MR measurements of these parameters may benefit from increased field strength. Quantitative flow measurements in the coronary sinus (CS) provide one method to investigate these parameters. However, the ability of newly developed faster MR sequences to measure coronary flow during a breath-hold at 3T has not been evaluated.

Methods

The aim of this work was to measure CS flow using segmented phase contrast MR (PC MR) on a clinical 3T MR scanner. Parallel imaging was employed to reduce the total acquisition time. Global LV perfusion was calculated by dividing CS flow with left ventricular (LV) mass. The repeatability of the method was investigated by measuring the flow three times in each of the twelve volunteers. Phantom experiments were performed to investigate potential error sources.

Results

The average CS flow was determined to 88 ± 33 ml/min and the deduced LV perfusion was 0.60 ± 0.22 ml/min·g, in agreement with published values. The repeatability (1-error) of the three repeated measurements in each subject was on average 84%.

Conclusion

This work demonstrates that the combination of high field strength (3T), parallel imaging and segmented gradient echo sequences allow for quantification of the CS flow and global perfusion within a breath-hold.

Laser Doppler velocimetry (LDV) and 3D phase-contrast magnetic resonance angiography (PC-MRA) velocity measurements: validation in an anatomically accurate cerebral artery aneurysm model with steady flow

PURPOSE

To verify the accuracy of velocity mapping with three-dimensional (3D) phase-contrast magnetic resonance angiography (PC-MRA) for steady flow in a realistic model of a cerebral artery aneurysm at a 3T scanner.

MATERIALS AND METHODS

Steady flow through an original geometry model of a cerebral aneurysm was mapped at characteristic positions by state-of-the-art laser Doppler velocimetry (LDV) as well as 3D PC-MRA at 3T. The spatial distributions and local values of two velocity components obtained with these two measurement methods were compared.

RESULTS

The 3D PC-MRA velocity field distribution and mean velocity values exhibited only minor differences to compare to the LDV measurements in straight artery regions for both main and secondary velocities. The differences increased in regions with disturbed flow and in cases where the measurement plane was not perpendicular to the main flow direction.

CONCLUSION

3D PC-MRA can provide reliable measurements of velocity components of steady flow in small arteries. The accuracy of such measurements depends on the artery size and the measurement plane positioning.

A reconstruction method for gappy and noisy arterial flow data

Proper orthogonal decomposition (POD), Kriging interpolation, and smoothing are applied to reconstruct gappy and noisy data of blood flow in a carotid artery. While we have applied these techniques to clinical data, in this paper in order to rigorously evaluate their effectiveness we rely on data obtained by computational fluid dynamics (CFD). Specifically, gappy data sets are generated by removing nodal values from high-resolution 3-D CFD data (at random or in a fixed area) while noisy data sets are formed by superimposing speckle noise on the CFD results. A combined POD-Kriging procedure is applied to planar data sets mimicking coarse resolution "ultrasound-like" blood flow images. A method for locating the vessel wall boundary and for calculating the wall shear stress (WSS) is also proposed. The results show good agreement with the original CFD data. The combined POD-Kriging method, enhanced by proper smoothing if needed, holds great potential in dealing effectively with gappy and noisy data reconstruction of in vivo velocity measurements based on color Doppler ultrasound (CDUS) imaging or magnetic resonance angiography (MRA).

Numerical simulation of in vitro pulsatile flow and its study using FRISK, a rapid phase contrast technique

PURPOSE

To test the potential of a phase contrast magnetic resonance (PC-MR) sparse sampling technique, fragmented regional interpolation segmentation for k-space (FRISK), to capture complex flow features within a breathhold duration by using numerical simulations and experimental approaches.

MATERIALS AND METHODS

Computational fluid dynamics (CFD) data of three models were generated: a two-chamber orifice flow model simulating valvular regurgitation, a femoral artery model, and a U-shaped model simulating the aortic arch. These data were used to simulate conventional and FRISK PC-MR data acquisitions. FRISK parameters can be adapted for different flow fields to capture either high temporal information or complexly varying spatial information with a temporal component or a mixture of both. In vivo PC-MR images on a healthy volunteer were sampled to compare conventional PC-MR with novel FRISK imaging.

RESULTS

In our simulations of three representative models, when only the errors from different sampling sequences were considered, FRISK was shown to maintain or even improve data accuracy while cutting the scan time by at least 50% compared to corresponding conventional PC-MR. By adapting the FRISK parameters for flowfields with different features, FRISK was capable of capturing in-plane and through-plane velocity information with excellent detail in approximately 20 heartbeats breathhold duration. The results of the in vivo MR experiment were consistent with the simulation results, showing that breathhold FRISK imaging improved spatial resolution of the data and maintained adequate temporal resolution compared with breathhold conventional imaging.

CONCLUSION

FRISK, a new MRI sampling sequence that sparsely samples data and aligns acquired data during postprocessing, provides a scan time advantage of approximately a factor of 2 compared to conventional scans, and allowed rapid or breathhold scanning while obtaining acceptable accuracy.

Numerical simulations of phase contrast velocity mapping of complex flows in an anatomically realistic bypass graft geometry

Combined in vitro experiments and numerical simulations were performed to study flow artifacts in phase contrast (PC) velocity mapping of steady flow through an anatomically realistic aortocoronary bypass graft model. The geometry was obtained through imaging and computational reconstruction of a left anterior descending (LAD) coronary artery of a porcine heart. Simulated images of through-plane velocity were obtained at selected slices of the geometry. These were then compared and contrasted with velocity images of corresponding sites that were obtained from in vitro experiments. The shift and distortion of the measured velocity profile was well predicted by the simulation, while trajectories obtained from particle tracking were shown to be useful in understanding the origins of the flow artifacts that were observed.

Numerical simulation of magnetic resonance angiographies of an anatomically realistic stenotic carotid bifurcation

Magnetic Resonance Angiography (MRA) has become a routine imaging modality for the clinical evaluation of obstructive vascular disease. However, complex circulatory flow patterns, which redistribute the Magnetic Resonance (MR) signal in a complicated way, may generate flow artifacts and impair image quality. Numerical simulation of MRAs is a useful tool to study the mechanisms of artifactual signal production. The present study proposes a new approach to perform such simulations, applicable to complex anatomically realistic vascular geometries. Both the Navier-Stokes and the Bloch equations are solved on the same mesh to obtain the distribution of modulus and phase of the magnetization. The simulated angiography is subsequently constructed by a simple geometric procedure mapping the physical plane into the MRA image plane. Steady bidimensional numerical simulations of MRAs of an anatomically realistic severely stenotic carotid artery bifurcation are presented, for both time-of-flight and contrast-enhanced imaging modalities. These simulations are validated by qualitative comparison with flow phantom experiments performed under comparable conditions.

Extension of Rapid Phase-Contrast Magnetic Resonance Imaging Using BRISK in Multidirectional Flow

We developed BRISK-CON-VPS, a rapid phase-contrast cine approach that is a hybrid of the BRISK-VPS (Block Regional Interpolation Scheme for k-space) and conventional (CONV-VPS) scanning employing k-space views per segment (VPS). BRISK-CON-VPS allows data acquisition approximately four times faster than CONV-VPS imaging and has the advantage compared to BRISK-VPS that it can potentially be incorporated into real-time applications. In BRISK-CON-VPS contiguous regions of k-space are sampled using a views per segment factor that is varied as a function of distance from the k-space center. Computational fluid dynamics (CFD) data were used to simulate CONV-VPS, BRISK-VPS, and BRISK-CON-VPS. BRISK-CON-VPS was simulated by incrementing the VPS progressively with increasing distance from the k-space origin while BRISK-VPS was simulated using a uniform VPS applied to the sparse sampling scheme. Simulations showed that up to a base VPS of 5, both BRISK-CON-VPS and BRISK-VPS retained excellent axial-velocity accuracy. Secondary in-plane velocity flow fields were well represented with BRISK-CON-VPS and BRISK-VPS up to a base VPS of 3. CONV-VPS, BRISK-CON-VPS, and BRISK-VPS were applied in vivo and shown to provide comparable quantitative flow data. BRISK-CON-VPS accomplishes breath-hold acquisitions as efficiently as BRISK-VPS, but without requiring data interpolation or under-sampling k-space.

Multisite trial of MR flow measurement: Phantom and protocol design

PURPOSE

To describe a portable, easily assembled phantom with well-defined bore geometry together with a series of tests that will form the basis of a standardized quality assurance protocol in a multicenter trial of flow measurement by the MR phase mapping technique.

MATERIALS AND METHODS

The phantom consists of silicone polymer layers containing parallel straight and stenosed flow channels in one layer and a U-bend in a second layer, separated by hermetically sealed agarose slabs. The phantom is constructed by casting low melting-point metal in an aluminum mold precisely milled to the desired geometry, and then using the low melting-point metal core as a negative around which the silicone is allowed to set. By melting out the metal, the flow channels are established. The milled aluminum mold is reusable, ensuring faithful reproduction of the flow geometry for all phantoms thus produced. The agarose layers provide additional loading and static background signal for background correction. With the use of the described phantom, one can evaluate flow measurement accuracy and repeatability, as well as the influence of several imaging geometry factors: slice offset, in-plane position, and slice-flow obliquity.

RESULTS

The new phantom is compact and portable, and is well suited for reassembly. We were able to demonstrate its facility in a battery of tests of interest in evaluating MR flow measurements.

CONCLUSION

The phantom is a robust standardized test object for use in a multicenter trial. Such a trial, to investigate the performance of MR flow measurement using the phantom and the tests we describe, has been initiated.

Magnetic resonance phase velocity mapping through NiTi stents in a flow phantom model

PURPOSE

To assess constant and pulsatile flow velocity within the lumen of a peripheral NiTi stent using phase velocity mapping for comparison with independent assessments of flow velocity in a phantom model.

MATERIALS AND METHODS

A 9 x 20-mm stent installed in flexible tubing was placed in a phantom filled with stationary fluid. Constant and pulsatile flow (produced by a pump programmed to produce a simulation of the carotid artery flow) was assessed using phase velocity mapping at 4.1 T (for constant flow) and at 1.5 T (for pulsatile flow). In all cases 256 x 256 gradient echo phase velocity maps were acquired. For the pulsatile flow condition, cine images with acquisition gated to the pump cycle were acquired with 40 msec temporal resolution across the simulated cardiac cycle. Computed flow volume rates were compared with fluid volume collection for the constant flow model, and with ultrasonic Doppler flow meter measurements for the pulsatile model.

RESULTS

The data showed that volume flow rate assessments by phase velocity mapping agreed with independent measurements within 10% to 15%.

CONCLUSION

Phase velocity mapping of the lumen of peripheral size NiTi stents is possible in an in vitro model.

Automated vessel edge detection in velocity-encoded cine-MR (VEC-MR) flow measurements: a retrospective evaluation in critically ill patients

OBJECTIVE

To assess feasibility of automated edge detection in magnetic resonance (MR) flow calculations in a clinical setting with critically ill patients.

MATERIAL AND METHODS

Velocity encoded cine-MR (VEC-MR) flow measurements cross-sectional area (CSA), mean spatial velocity (MSV), instantaneous flow (IF), flow (F), 0.5 T Philips, TR 800-800, TE=8 ms, 30 degrees flip angle, FOV 280 mm, 128 x 256 matrix, temporal resolution 16 time frames/RR, VENC=120 cm/s) were obtained in 20 major thoracic human vessels (ascending aorta, main, right and left pulmonary artery-AAO, MPA, RPA, LPA) of five patients, suffering from severe chronic thromboembolic pulmonary hypertension (CTEPH). Flow maps were evaluated by two independent observers using conventional manual edge detection (INTER m/m). Flow calculations were performed by one observer using both, manual and automated edge detection (INTRA m/a), by a second observer using automated edge detection two times (INTRA a/a) and by two independent observers using automated edge detection (INTER a/a). Evaluation time was measured. Linear regression analysis and Student's t-test were performed.

RESULTS

Overall regression coefficients (r2) for INTER m/m, INTRA m/a, INTER a/a and INTRA a/a, respectively, were as follows: CSA, 0.91, 0.91, 0.96, 0.98; MSV, 0.97, 0.99, 0.99, 0.99; IF, 0.98, 0.99, 0.99, 0.99; F, 0.98, 0.99, 0.99, 0.99. Manual CSA values differed significantly from automated data in MPA (P=0.01), RPA (P=0.0008) and LPA (P=0.02). No difference was found for the other assessed parameters of the pulmonary circulation. Average evaluation time per vessel was 20.2+/-2.6 min for manual and 2.1+/-0.7 min for automated edge detection (P<0.00001).

CONCLUSION

The software program used provided reproducible data, lead to a 90% reduction in evaluation and calculation time and, therefore, might excel the utilization of VEC-MR flow measurements. Despite variations in the evaluation of the pulmonary circulation CSAs, flow assessment is feasible in critically ill patients.

Computational modeling of arterial biomechanics: insights into pathogenesis and treatment of vascular disease

We review how advances in computational techniques are improving our understanding of the biomechanical behavior of the healthy and diseased cardiovascular system. Numerical modeling of biomechanics is being used in a wide variety of ways, including assessment of effects of mural and hemodynamically induced stresses on atherogenesis, development of risk measures for aneurysm rupture, improvement in interpretation of medical images, and quantification of oxygen transport in diseased and healthy arteries. Although not amenable to routine clinical use, numerical modeling of cardiovascular biomechanics is a powerful research tool.

MRI measurement of time-resolved wall shear stress vectors in a carotid bifurcation model, and comparison with CFD predictions

PURPOSE

To study pulsatile fluid flow in a physiologically realistic model of the human carotid bifurcation, and to derive wall shear stress (WSS) vectors.

MATERIALS AND METHODS

WSS vectors were calculated from time-resolved 3D phase-contrast (PC) MRI measurements of the velocity field. The technique was first validated with sinusoidal flow in a straight tube, and then used in a model of a healthy human carotid bifurcation. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for computational fluid dynamics (CFD) calculations of WSS, which were compared with those derived from MRI alone.

RESULTS

The straight tube measurements gave WSS results that were within 15% of the theoretical value. WSS results for the phantom showed the main features expected from fluid dynamics, notably the low values in the bulb region of the internal carotid artery, with a return to ordered flow further downstream. MRI was not able to detect the high WSS values along the divider wall that were predicted by the CFD model. Otherwise, there was good general agreement between MRI and CFD.

CONCLUSION

This is the first report of time-resolved WSS vectors estimated from 3D-MRI data. The technique worked well except in regions of disturbed flow, where the combination with CFD modeling is clearly advantageous.

Correction for displacement artifacts in 3D phase contrast imaging

PURPOSE

To correct for displacement artifacts in 3D phase contrast imaging.

MATERIALS AND METHODS

A 3D phase contrast pulse sequence was modified so that displacements of velocity measurements were restricted to one direction. By applying a postprocessing method, displaced measurements could be traced back to their accurate positions. Flow studies were performed using a phantom that generated flow through a stenosis, directed oblique relative to the phase and frequency encoding directions. Velocity profiles and streamline visualization were used to compare displaced and corrected velocity data to a reference.

RESULTS

Velocity profiles obtained from the original measurement showed skewed profiles due to the displacement artifact, both at close proximity to the orifice as well as further downstream. After correction, concordance with the reference improved considerably.

CONCLUSION

The displacement artifact, which restricts the accuracy of phase contrast measurements, can be corrected for using the proposed method. Correction of the phase contrast velocity data may improve the accuracy of subsequent flow analysis and visualization.

Effect of acquisition parameters on the accuracy of velocity encoded cine magnetic resonance imaging blood flow measurements

PURPOSE

To investigate the effect of acquisition parameters on the accuracy of 2D velocity encoded cine magnetic resonance imaging (VEC MRI) flow measurements.

MATERIALS AND METHODS

Using a pulsatile flow phantom, through-plane flow measurements were performed on a flexible vessel made of polyvinyl alcohol cryogel (PVA), a material that mimics the MR signal and biomechanical properties of aortic tissue.

RESULTS

Repeated VEC MRI flow measurements (N = 20) under baseline conditions yielded an error of 0.8 +/- 1.5%. Slice thickness, angle between flow and velocity encoding directions, spatial resolution, velocity encoding range, and radio frequency (RF) flip angles were varied over a clinically relevant range. Spatial resolution had the greatest impact on accuracy, with a 9% overestimation of flow at 16 pixels per vessel cross-section.

CONCLUSION

VEC MRI proved to be an accurate and reproducible technique for pulsatile flow measurements over the range of acquisition parameters examined as long as sufficient spatial resolution was prescribed.

Estimation and visualization of regional and global pulmonary perfusion with 3D magnetic resonance angiography

The purposes of this work were to estimate regional and global pulmonary perfusion and display pulmonary vasculature in 10 postoperative lung transplant patients using breath-hold, contrast-enhanced (0.2 mmol/kg, Gd DTPA-BMA, Omniscan, Nycomed, Inc., Princeton, NJ), three-dimensional (3D) magnetic resonance angiography (MRA) with specially designed double-variable-angle uniform signal excitation (VUSE) radio frequency (RF) pulses. Double-VUSE scans imaged both lungs simultaneously during contrast agent injection and provided both qualitative and quantitative information about pulmonary perfusion. Double-VUSE pulses clearly displayed healthy and diseased vessels. There was a strong correlation between contrast-enhanced double-VUSE MRA flow estimates and those measured from nuclear scans for global or whole lung (R(2) = 0.95; P = 0.000002) and upper, central, and lower thirds of the lung (R(2) = 0.89, 0.92, and 0.86, respectively; P < 0.001 for each region). In conclusion, 3D MRA using VUSE pulses in combination with a contrast agent is a valuable tool for the assessment of pulmonary perfusion that simultaneously acquires data for both the qualitative display of pulmonary vessels and the quantification of regional and global differential pulmonary blood flow.

Noninvasive Quantification of Left-to-Right Shunt in Pediatric Patients

Background —Blood flow can be quantified noninvasively by phase-contrast cine MRI (PC-MRI) in adults. Little is known about the feasibility of the method in children with congenital heart disease.

Methods and Results —In 50 children (mean age 6.2 years, range 1.1 to 17.7 years) with an atrial- or ventricular-level shunt, blood flow rate in the great vessels was determined by PC-MRI, and the ratio of pulmonary to aortic flow (Q̇p/Q̇s) was compared with Q̇p/Q̇s by oximetry. We found a difference of 2% and a range of −20% to +26% (limits of agreement, mean±2 SD). In another 7 children with congenital heart disease but no cardiac shunting (mean age 7.9 years, range 1.3 to 13.5 years), Q̇p/Q̇s by PC-MRI was 1.02 (SD ±0.06). No difference between systemic venous and aortic flow volumes was found (range −17% to +20%, n=37). Blood flow through a secundum atrial septal defect as assessed by PC-MRI (n=24) overestimated the shunt compared with the difference between pulmonary and aortic flows. The mean difference between 3 repeated PC-MRI measurements in each location was 5.3% (SD ±4.0%, n=522), demonstrating good precision. The interobserver variability was low. The accuracy of PC-MRI was confirmed by in vitro experiments.

Conclusions —Determination of Q̇p/Q̇s by PC-MRI in children is quick, safe, and reliable compared with oximetry. Systemic venous flow can be quantified by PC-MRI, whereas through-plane shunt measurement within an atrial septal defect is inaccurate.

Correction for acceleration-induced displacement artifacts in phase contrast imaging

The acceleration-induced displacement artifact impairs the accuracy of MR velocity measurements. This study proposes a post processing method for correction of this artifact. Velocity measurements were performed in a flow phantom containing a constriction. Velocity curves were obtained from streamlines parallel to the frequency, phase, and slice directions, respectively. The acceleration-induced displacement artifact was most prominent when the frequency encoding direction was aligned with the flow direction. After correction, velocity assignment improved and a more accurate description of the flow was obtained. In vivo measurements were performed in the aorta in a patient with a repaired aortic coarctation. The correction method was applied to velocity data along a streamline parallel to the frequency encoding direction. The result after correction was a new location of the peak velocity and improved estimates of the velocity gradients.

Reconstruction of blood flow patterns in a human carotid bifurcation: a combined CFD and MRI study

The carotid bifurcation is a common site for clinically significant atherosclerosis, and the development of this disease may be influenced by the local hemodynamic environment. It has been shown that vessel geometry and pulsatile flow conditions are the predominant factors that determine the detailed blood flow patterns at the carotid bifurcation. This study was initiated to quantify the velocity profiles and wall shear stress (WSS) distributions in an anatomically true model of the human carotid bifurcation using data acquired from magnetic resonance (MR) imaging scans of an individual subject. A numerical simulation approach combining the image processing and computational fluid dynamics (CFD) techniques was developed. Individual vascular anatomy and pulsatile flow conditions were all incorporated into the computer model. It was found that the geometry of the carotid bifurcation was highly complex, involving helical curvature and out-of-plane branching. These geometrical features resulted in patterns of flow and wall shear stress significantly different from those found in simplified planar carotid bifurcation models. Comparisons between the predicted flow patterns and MR measurement demonstrated good quantitative agreement.

Automatic vessel segmentation using active contours in cine phase contrast flow measurements

The segmentation of images obtained by cine magnetic resonance (MR) phase contrast velocity mapping using manual or semi-automated methods is a time consuming and observer-dependent process that still hampers the use of flow quantification in a clinical setting. A fully automatic segmentation method based on active contour model algorithms for defining vessel boundaries has been developed. For segmentation, the phase image, in addition to the magnitude image, is used to address image distortions frequently seen in the magnitude image of disturbed flow fields. A modified definition for the active contour model is introduced to reduce the influence of missing or spurious edge information of the vessel wall. The method was evaluated on flow phantom data and on in vivo images acquired in the ascending aorta of humans. Phantom experiments resulted in an error of 0.8% in assessing the luminal area of a flow phantom equipped with an artificial heart valve. Blinded evaluation of the volume flow rates from automatic vs. manual segmentation of gradient echo (FFE) phase contrast images obtained in vivo resulted in a mean difference of -0.9 +/- 3%. The mean difference from automatic vs. manual segmentation of images acquired with a hybrid phase contrast sequence (TFEPI) within a single breath-hold was -0.9 +/- 6%.

Particle trace visualization of intracardiac flow using time-resolved 3D phase contrast MRI

The flow patterns in the human heart are complex and difficult to visualize using conventional two-dimensional (2D) modalities, whether they depict a single velocity component (Doppler echocardiography) or all three components in a few slices (2D phase contrast MRI). To avoid these shortcomings, a temporally resolved 3D phase contrast technique was used to derive data describing the intracardiac velocity fields in normal volunteers. The MRI data were corrected for phase shifts caused by eddy currents and concomitant gradient fields, with improvement in the accuracy of subsequent flow visualizations. Pathlines describing the blood pathways through the heart were generated from the temporally resolved velocity data, starting from user-specified locations and time frames. Flow trajectories were displayed as 3D particle traces, with simultaneous demonstration of morphologic 2D slices. This type of visualization is intuitive and interactive and may extend our understanding of dynamic and previously unrecognized patterns of intracardiac flow.

Construction of a protocol for measuring blood flow by two-dimensional phase-contrast MRA

Our aim is to describe and demonstrate the steps we have found to be useful in the construction and evaluation of protocols for triggered and nontriggered measurement of blood flow by two-dimensional phase-contrast magnetic resonance angiography (MRA). To achieve this goal, we start with a survey of factors governing the accuracy (validity) and precision (repeatability) of MR flow measurements. This knowledge, combined with prior information regarding the diameter of the target vessel and the prevailing flow conditions, is then employed to define a protocol for measuring flow with negligible systematic error. In the absence of a gold standard for in vivo flow measurements, the protocol is subsequently validated for a range of flow conditions by representative phantom experiments. Precision is then calculated from the signal-to-noise ratio (SNR) of blood in the accompanying magnitude images or, less conveniently, estimated from the standard deviation of repeated measurements. The desired precision is finally achieved by adjusting the appropriate SNR parameters. All steps involved in protocol development are demonstrated for both flow-independent and flow-dependent acquisitions.

A numerical study of magnetic resonance images of pulsatile flow in a two dimensional carotid bifurcation: a numerical study of MR images

A numerical method to simulate magnetic resonance angiographic images is proposed. The new method greatly simplifies the calculation of the average phase in a voxel, the bottleneck of previous simulations, and reduces the computation time by more than a factor of 5. Both the Navier-Stokes and the Bloch equations are solved on the same mesh to obtain the distributions of the modulus and phase of the magnetization. The data in the frequency domain are reordered according to the gating strategy to generate the final images. Pulsatile flow through a 2D normal carotid bifurcation is considered as a test case. Images for magnetic resonance angiography with an uncompensated gradient waveform, a velocity-compensated gradient waveform and an uncompensated short-TE gradient waveform are compared. Systolic gating images are shown to have degraded image quality. Images acquired with diastolic-gating have little variation in magnetization strength throughout the pulsatile cycle and provide a better representation of the vessel lumen.

Visualizing blood flow patterns using streamlines, arrows, and particle paths

A customized computer program (MRIView) is described for visualizing and quantifying complex blood flow patterns in major vessels, using nongated and cardiac-gated three-dimensional (3D) velocity data obtained with MR velocity-encoded phase pulse sequences. Streamlines, arrows, and particle paths (collectively referred to as "paths") can be computed interactively, using both forward and backward time integration of the velocity field. The program provides interactive cross-sectional and 3D perspective visualization of the paths, with quantification and statistical analysis of average speed, through-plane velocity, cross-sectional area, and flow. Normal flow patterns in the carotid artery, basilar artery tip, ascending aorta, coronary arteries, descending aorta, and renal arteries, as well as abnormal flow patterns in basilar tip aneurysms, have been investigated. The program revealed flow patterns in these regions with features that are well known from Doppler ultrasound and other features that have not been reported previously. The association between specific abnormal flow patterns and development of atherosclerosis suggests that particle paths can be used to assess risk of plaque formation and progression, as well as to evaluate flow dynamics and vascular patency before and after vascular interventions.

Hemodynamics of human carotid artery bifurcations: computational studies with models reconstructed from magnetic resonance imaging of normal subjects

PURPOSE

The precise role played by hemodynamics, particularly wall shear stress, in the development and progression of vascular disease remains unclear, in large part because of a lack of in vivo studies with humans. Although technical challenges remain for noninvasively imaging wall shear stresses in humans, vascular anatomy can be imaged with sufficiently high resolution to allow reconstruction of three-dimensional models for computational hemodynamic studies. In this paper we present an entirely noninvasive magnetic resonance imaging (MRI) protocol that provides carotid bifurcation geometry and flow rates from which the in vivo hemodynamics can be computed. Maps of average, oscillatory, and gradients of wall shear stress are presented for two normal human subjects, and their data are compared with those computed for an idealized carotid bifurcation model.

METHODS

An MRI protocol was developed to acquire all necessary image data in scan times suitable for patient studies. Three-dimensional models of the carotid bifurcation lumen were reconstructed from serial black blood MR images of two normal volunteers. Common and internal carotid artery flow rate waveforms were determined from MRI phase-contrast velocity imaging in the same subjects and were used to impose fully developed velocity boundary conditions for the computational model. Subject-specific time-resolved velocities and wall shear stresses were then computed with a finite element-based Navier-Stokes equation solver.

RESULTS

Models reconstructed from in vivo MRI of two subjects showed obvious differences in branch angle, bulb size and extent, and three-dimensional curvature. Maps of a variety of wall shear stress indices showed obvious qualitative differences in patterns between the in vivo models and between the in vivo models and the idealized model. Secondary, helical flow patterns, induced primarily by the asymmetric and curved in vivo geometries, were found to play a key role in determining the resulting wall shear stress patterns. The use of in vivo flow rate waveforms was found to play a minor but noticeable role in some of the wall shear stress behavior observed.

CONCLUSIONS

Conventional "averaged" carotid bifurcation models mask interesting hemodynamic features observed in realistic models derived from noninvasive imaging of normal human subjects. Observation of intersubject variations in the in vivo wall shear stress patterns supports the notion that more conclusive evidence regarding the role of hemodynamics in vascular disease may be derived from such individual studies. The techniques presented here, when combined with subject-specific MRI measurements of carotid artery plaque thickness and composition, provide the tools necessary for entirely noninvasive, prospective, in vivo human studies of hemodynamics and the relationship of hemodynamics to vascular disease.

On the nature and reduction of plaque-mimicking flow artifacts in black blood MRI of the carotid bifurcation

Cardiac-gated black blood MRI of the carotid artery bifurcation in normal human subjects shows signal within the lumen suggesting wall thickening or atherosclerotic plaque. This signal was believed to be artifactual, arising from complex flow patterns present at the carotid bifurcation. Computer simulation of the hemodynamics and black blood multislice image acquisition in a model of the carotid bifurcation showed that these artifacts arise from spins recovering their signal within the slow, recirculating flow of the carotid bulb. The computed hemodynamics also suggested that these artifacts could be minimized or eliminated entirely by gating the acquisition of slices in the most artifact-prone region of the carotid bulb within a 250-ms window after peak systole. Application of these predictions to studies of normal volunteers showed that, in most cases, these flow artifacts in black blood MRI can be eliminated simply by altering the phase of the cardiac cycle to which the image acquisition is gated. The observation that the size and placement of the saturation slabs had little effect on these artifacts suggested that, in those cases in which recirculation persists throughout the cardiac cycle, either inversion-recovery or presaturation within the bulb itself would be required to suppress them.

Tissue temperature monitoring with multiple gradient-echo imaging sequences

The inherent sensitivity of multiple gradient-echo sequences to the chemical shift is exploited to rapidly map muscle water frequency shifts caused by ultrasonic heating. The use of multiple echoes is shown to offer several advantages over single gradient-echo approaches previously proposed for temperature measurement. An increase in the effective bandwidth significantly reduces aliasing problems observed with single gradient-echo methods in high temperature applications. Of greater significance is the improved immunity to intrascan motion found for multi-echo versus single echo gradient methods, making the former more attractive for clinical applications. Finally, a sensitivity to the presence of multiple spectral components unavailable with single gradient-echo methods is obtained.