Effects of intravoxel velocity distributions on the accuracy of the phase-mapping method in phase-contrast MR angiography

Impact of turbulence-induced asymmetric propagators on the accuracy of phase-contrast velocimetry

Phase-contrast magnetic resonance velocimetry (PC-MRI) has been widely used to investigate flow properties in numerous systems. In a horizontal cylindrical pipe (3 mm diameter), we investigated the accuracy of PC-MRI as the flow transitioned from laminar to turbulent flow (Reynolds number 352-2708). We focus primarily on velocimetry errors introduced by skewed intra-voxel displacement distributions, a consequence of PC-MRI theory assuming symmetric distributions. We demonstrated how rapid fluctuations in the velocity field, can produce broad asymmetric intravoxel displacement distributions near the wall. Depending on the shape of the distribution, this resulted in PC-MRI measurements under-estimating (positive skewness) or over-estimating (negative skewness) the true mean intravoxel velocity, which could have particular importance to clinical wall shear stress measurements. The magnitude of these velocity errors was shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution. These experimental results confirm our previous theoretical analysis, which gives a relationship for PC-MRI velocimetry errors, as a function of the higher moments of the intravoxel displacement distribution (skewness, variance, and kurtosis) and the experimental parameters q and Δ. This suggests that PC-MRI errors in such unsteady/turbulent flow conditions can potentially be reduced by employing lower q values or shorter observation times Δ.

Heart applications of 4D flow

Four-dimensional (4D) flow sequences are an innovative type of MR sequences based upon phase contrast (PC) sequences which are a type of application of Angio-MRI together with the Time of Flight (TOF) sequences and Contrast-Enhanced Magnetic Resonance Acquisition (CE-MRA). They share the basic principles of PC, but unlike PC sequences, 4D flow has velocity encoding along all three flow directions and three-dimensional (3D) anatomic coverage. They guarantee the analysis of flow with multiplanarity on a post-processing level, which is a unique feature among MR sequences. Furthermore, this technique provides a completely new level to the in vivo flow analysis as it allows measurements in never studied districts such as intracranial applications or some parts of the heart never studied with echo-color-doppler, which is its sonographic equivalent. Furthermore, this technique provides a completely new level to the in vivo flow analysis as it allows accurate measurement of the flows in different districts (e.g., intracranial, cardiac) that are usually studied with echo-color-doppler, which is its sonographic equivalent. Of note, the technique has proved to be affected by less inter and intra-observer variability in several application. 4D-flow basic principles, advantages, limitations, common pitfalls and artefacts are described. This review will outline the basis of the formation of PC image, the construction of a 4D-flow and the huge impact the technique is having on the cardiovascular non-invasive examination. It will be then studied how this technique has had a huge impact on cardiovascular examinations especially on a central heart level.

Accuracy of phase-contrast velocimetry in systems with skewed intravoxel velocity distributions

Phase contrast velocimetry (PCV) has been widely used to investigate flow properties in numerous systems. Several authors have reported errors in velocity measurements and have speculated on the sources, which have ranged from eddy current effects to acceleration artefacts. An often overlooked assumption in the theory of PCV, which may not be met in complex or unsteady flows, is that the intravoxel displacement distributions (propagators) are symmetric. Here, the effect of the higher moments of the displacement distribution (variance, skewness and kurtosis) on the accuracy of PCV is investigated experimentally and theoretically. Phase and propagator measurements are performed on tailored intravoxel distributions, achieved using a simple phantom combined with a single large voxel. Asymmetric distributions (Skewness ≠ 0) are shown to generate important phase measurement errors that lead to significant velocimetry errors. Simulations of the phase of the spin vector sum, based on experimentally measured propagators, are shown to quantitatively reproduce the relationship between measured phase and experimental parameters. These allow relating the observed velocimetry errors to a discrepancy between the average phase of intravoxel spins considered in PCV theory and the vector phase actually measured by a PFG experiment. A theoretical expression is derived for PCV velocimetry errors as a function of the moments of the displacement distribution. Positively skewed distributions result in an underestimation of the true mean velocity, while negatively skewed distributions result in an overestimation. The magnitude of these errors is shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution.

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.

Application of flow sensitive gradients for improved measures of metabolism using hyperpolarized (13) c MRI

PURPOSE

To develop the use of bipolar gradients to suppress partial-volume and flow-related artifacts from macrovascular, hyperpolarized spins.

THEORY AND METHODS

Digital simulations were performed over a range of spatial resolutions and gradient strengths to determine the optimal bipolar gradient strength and duration to suppress flowing spins while minimizing signal loss from static tissue. In vivo experiments were performed to determine the efficacy of this technique to suppress vascular signal in the study of hyperpolarized [1-(13)C]pyruvate renal metabolism.

RESULTS

Digital simulations showed that in the absence of bipolar gradients, partial-volume artifacts from the vasculature were still present, causing underestimation of the apparent reaction rate of pyruvate to lactate (kP). The addition of a bipolar gradient with b = 32 s/mm(2) sufficiently suppressed the vascular signal without a substantial decrease in signal from static tissue. In vivo results corroborate digital simulations, with similar peak lactate signal to noise ratio (SNR) but substantially different kP in the presence of bipolar gradients.

CONCLUSION

The proposed approach suppresses signal from flowing spins while minimizing signal loss from static tissue, removing contaminating signal from the vasculature and increasing kinetic modeling accuracy without substantially sacrificing SNR or temporal resolution.

Assessment of flow and hemodynamics in the carotid artery using a reduced TE 4D flow spiral phase-contrast MRI

4D flow MRI is a powerful technique for quantitative flow assessment and visualization of complex flow patterns and hemodynamics of cardiovascular flows. This technique results in more anatomical information and comprehensive assessment of blood flow. However, conventional 4D PC MRI suffers from a few obstacles for clinical applications. The total scan time is long, especially in large volumes with high spatial resolutions. Inaccuracy of conventional Cartesian PC MRI in the setting of atherosclerosis and in general, disturbed and turbulent blood flow is another important challenge. This inaccuracy is the consequence of signal loss, intravoxel dephasing and flow-related artifact in the presence of disturbed and turbulent flow. Spiral k-space trajectory has valuable attributes which can help overcome some of the problems with 4D flow Cartesian acquisitions. Spiral trajectory benefits from shorter TE and reduces the flow-related artifacts. In addition, short spiral readouts with spiral interleaves can significantly reduce the total scan time, reducing the chances of patient motion which may also corrupt the data in the form of motion artifacts. In this paper, the accuracy of flow assessment and flow visualization with reduced TE 4D Spiral PC was investigated and good agreement was observed between the spiral and conventional technique. The systolic mean velocity, peak flow and the average flow in CCA and ICA of normal volunteers using 4D spiral PC MRI showed errors less than 10% compared to conventional 4D PC MRI. In addition, the scan time using spiral sequence was 3∶31 min which is half of the time using conventional sequence.

4D UTE flow: a phase-contrast MRI technique for assessment and visualization of stenotic flows

PURPOSE

Inaccuracy of conventional four-dimensional (4D) flow MR imaging in the presence of random unsteady and turbulent blood flow distal to a narrowing has been an important challenge. Previous investigations have revealed that shorter echo times (TE) decrease the errors, leading to more accurate flow assessments.

METHODS

In this study, as part of a 4D flow acquisition, an Ultra-Short TE (UTE) method was adopted. UTE works based on a center-out radial k-space trajectory that inherently has a short TE. By employing free induction decay sampling starting from read-out gradient ramp-up, and by combining the refocusing lobe of the slice select gradient with the bipolar flow encoding gradient, TEs of ≈1 msec may be achieved.

RESULTS

Both steady and pulsatile flow regimes, and in each case a range of Reynolds numbers, were studied in an in-vitro model. Flow assessment at low and medium flow rates demonstrated a good agreement between 4D UTE and conventional 4D flow techniques. However, 4D UTE flow significantly outperformed conventional 4D flow, at high flow rates for both steady and pulsatile flow regimes. Feasibility of the method in one patient with Aortic Stenosis was also demonstrated.

CONCLUSION

For both steady and pulsatile high flow rates, the measured flow distal to the stenotic narrowing using conventional 4D flow revealed more than 20% error compared to the ground-truth flow. This error was reduced to less than 5% using the 4D UTE flow technique.

A novel phase-corrected 3D cine ultra-short te (UTE) phase-contrast MRI technique

Phase-contrast (PC) MRI is a non-invasive technique to assess cardiovascular blood flow. However, this technique is not accurate for instance at the carotid bifurcation due to turbulent and disturbed blood flow in atherosclerotic disease. Flow quantification using conventional PC MRI distal to stenotic vessels suffers from intravoxel dephasing and flow artifacts. Previous studies have shown that short echo time (TE) potentially decreases the phase errors. In this work, a novel 3D cine UTE-PC imaging method is designed to measure the blood velocity in the carotid bifurcation using a UTE center-out radial trajectory and short TE time compared to standard PC MRI sequences. With a new phase error correction technique based on autocorrelation method, the proposed 3D cine UTE-PC has the potential to achieve high accuracy for quantification and visualization of velocity jet distal to a stenosis. Herein, we test the feasibility of the method in determining accurate flow waveforms in normal volunteers.

A novel MRI framework for the quantification of any moment of arbitrary velocity distributions

MRI can measure several important hemodynamic parameters but might not yet have reached its full potential. The most common MRI method for the assessment of flow is phase-contrast MRI velocity mapping that estimates the mean velocity of a voxel. This estimation is precise only when the intravoxel velocity distribution is symmetric. The mean velocity corresponds to the first raw moment of the intravoxel velocity distribution. Here, a generalized MRI framework for the quantification of any moment of arbitrary velocity distributions is described. This framework is based on the fact that moments in the function domain (velocity space) correspond to differentials in the Fourier transform domain (kv-space). For proof-of-concept, moments of realistic velocity distributions were estimated using finite difference approximations of the derivatives of the MRI signal. In addition, the framework was applied to investigate the symmetry assumption underlying phase-contrast MRI velocity mapping; we found that this assumption can substantially affect phase-contrast MRI velocity estimates and that its significance can be reduced by increasing the velocity encoding range.

Assessment of left ventricular diastolic function by MR: why, how and when

Cardiovascular magnetic resonance (CMR), a valuable non-invasive technique for the evaluation of the cardiovascular system, has already been accepted as the "gold standard" for the assessment of systolic function. The assessment of diastolic function is important not only for diagnosis purposes, but also in terms of prognosis. ECG-triggering phase-contrast (PC) CMR allows the routine assessment of diastolic function by measuring the transmitral and pulmonary venous flow with high accuracy and reproducibility, using morphological and quantitative parameters similar to those obtained by transthoracic echocardiography, which are so familiar to general cardiologists. Therefore, the increasing role of CMR in the assessment of the cardiovascular system requires a greater awareness and knowledge of this condition by radiologists. The aim of this study is to review the main mechanisms and common causes of left ventricle diastolic dysfunction, provide a practical approach for the assessment of LV diastolic function and illustrate the different degrees of diastolic dysfunction.

Cardiac flow component analysis

In a chamber of the heart, large-scale vortices are shown to exist as the result of the dynamic blood flow and unique morphological changes of the chamber wall. As the cardiovascular flow varies over a cardiac cycle, there is a need for a robust quantification method to analyze its vorticity and circulation. We attempt to measure vortex characteristics by means of two-dimensional vorticity maps and vortex circulation. First, we develop vortex component analysis by segmenting the vortices using an data clustering algorithm before histograms of their vorticity distribution are generated. The next stage is to generate the statistics of the vorticity maps for each phase of the cardiac cycle to allow analysis of the flow. This is followed by evaluating the circulation of each segmented vortex. The proposed approach is dedicated to examining vortices within the human heart chamber. The vorticity field can indicate the strength and number of large-scale vortices in the chamber. We provide the results of the flow analysis after vorticity map segmentation and the statistical properties that characterize the vorticity components. The success of the cardiac measurement and analysis is illustrated by a case study of the right atrium. Our investigation shows that it is possible to utilize a data clustering algorithm to segment vortices after vorticity mapping, and that the vorticity and circulation analysis of a chamber vorticity can provide new insights into the blood flow within the cardiovascular structure.

[Analysis of flow in artificial stenosis models of mid-sized arteries using 3D PC-MRI]

Phase contrast MRI allows access to tri-directional encoded velocity information and therefore, measurement of flow in the human hemodynamic system. The aim of this work was to investigate whether this technology could be applied to support the grading of stenosis in mid-size arteries. Using a specially constructed flow phantom and a stenosis model with tube diameter of 5mm and 8mm and a stenosis of 50%, experiments at different flow rates (180-640 ml/min), slice thickness (1-4 mm), field strength (1.5 and 3.0 T), and multi-slice as well as 3D volume acquisition were performed. The observations were assessed visually and evaluated by signal-to-noise (SNR) ratios in regions before and after the stenosis. The obtained results show that examinations should be performed at high field (3.0 T) and at flow rates up to 500 ml/min without hampering the measurements by areas of signal loss. In comparison, no detectable differences in the flow patterns of the two acquisition schemes could be observed. However, the SNR was higher using the 3D volume acquisition and thick slices. In summary, 3D PC-MRI of mid-size vessels with stenosis is feasible for certain flow rates. The presented results could be seen as guidance for in vivo situations to assess if an examination of a patient is reasonable in terms of outcome.

Aortic valve stenotic area calculation from phase contrast cardiovascular magnetic resonance: the importance of short echo time

BACKGROUND

Cardiovascular magnetic resonance (CMR) can potentially quantify aortic valve area (AVA) in aortic stenosis (AS) using a single-slice phase contrast (PC) acquisition at valve level: AVA = aortic flow/aortic velocity-time integral (VTI). However, CMR has been shown to underestimate aortic flow in turbulent high velocity jets, due to intra-voxel dephasing. This study investigated the effect of decreasing intra-voxel dephasing by reducing the echo time (TE) on AVA estimates in patients with AS.

METHOD

15 patients with moderate or severe AS, were studied with three different TEs (2.8 ms/2.0 ms/1.5 ms), in the main pulmonary artery (MPA), left ventricular outflow tract (LVOT) and 0 cm/1 cm/2.5 cm above the aortic valve (AoV). PC estimates of stroke volume (SV) were compared with CMR left ventricular SV measurements and PC peak velocity, VTI and AVA were compared with Doppler echocardiography. CMR estimates of AVA obtained by direct planimetry from cine acquisitions were also compared with the echoAVA.

RESULTS

With a TE of 2.8 ms, the mean PC SV was similar to the ventricular SV at the MPA, LVOT and AoV0 cm (by Bland-Altman analysis bias +/- 1.96 SD, 1.3 +/- 20.2 mL/-6.8 +/- 21.9 mL/6.5 +/- 50.7 mL respectively), but was significantly lower at AoV1 and AoV2.5 (-29.3 +/- 31.2 mL/-21.1 +/- 35.7 mL). PC peak velocity and VTI underestimated Doppler echo estimates by approximately 10% with only moderate agreement. Shortening the TE from 2.8 to 1.5 msec improved the agreement between ventricular SV and PC SV at AoV0 cm (6.5 +/- 50.7 mL vs 1.5 +/- 37.9 mL respectively) but did not satisfactorily improve the PC SV estimate at AoV1 cm and AoV2.5 cm. Agreement of CMR AVA with echoAVA was improved at TE 1.5 ms (0.00 +/- 0.39 cm2) versus TE 2.8 (0.11 +/- 0.81 cm2). The CMR method which agreed best with echoAVA was direct planimetry (-0.03 cm2 +/- 0.24 cm2).

CONCLUSION

Agreement of CMR AVA at the aortic valve level with echo AVA improves with a reduced TE of 1.5 ms. However, flow measurements in the aorta (AoV 1 and 2.5) are underestimated and 95% limits of agreement remain large. Further improvements or novel, more robust techniques are needed in the CMR PC technique in the assessment of AS severity in patients with moderate to severe aortic stenosis.

Quantification of intravoxel velocity standard deviation and turbulence intensity by generalizing phase-contrast MRI

Turbulent flow, characterized by velocity fluctuations, is a contributing factor to the pathogenesis of several cardiovascular diseases. A clinical noninvasive tool for assessing turbulence is lacking, however. It is well known that the occurrence of multiple spin velocities within a voxel during the influence of a magnetic gradient moment causes signal loss in phase-contrast magnetic resonance imaging (PC-MRI). In this paper a mathematical derivation of an expression for computing the standard deviation (SD) of the blood flow velocity distribution within a voxel is presented. The SD is obtained from the magnitude of PC-MRI signals acquired with different first gradient moments. By exploiting the relation between the SD and turbulence intensity (TI), this method allows for quantitative studies of turbulence. For validation, the TI in an in vitro flow phantom was quantified, and the results compared favorably with previously published laser Doppler anemometry (LDA) results. This method has the potential to become an important tool for the noninvasive assessment of turbulence in the arterial tree.

Rapid cardiac-output measurement with ungated spiral phase contrast

An ungated spiral phase-contrast (USPC) method was used to measure cardiac output (CO) rapidly and conveniently. The USPC method, which was originally designed for small peripheral vessels, was modified to assess CO by measuring flow in the ascending aorta (AA). The modified USPC used a 12-interleaf spiral trajectory to acquire full-image data every 283 ms with 2-mm spatial resolution. The total scan time was 5 s. For comparison, a triggered real-time (TRT) method was used to indirectly calculate CO by measuring left-ventricular (LV) volume. The USPC and TRT measurements from all normal volunteers agreed. In a patient with patent ductus arteriosus (PDA), high CO was measured with USPC, which agreed well with the invasive cardiac-catheterized measurement. In normal volunteers, CO dropped about 20-30% with Valsalva maneuvering, and increased about 100% after exercise. Continuous 28-s cycling between Valsalva maneuvering and free-breathing showed that USPC can temporally resolve physiological CO changes.

Rapid mapping of flow velocity using a new PARSE method

A new method for flow velocity mapping is presented here. Instead of the conventional approach of employing two images (velocity sensitive and control) to generate velocity information, in the new method one determines the velocity directly from a single-shot acquisition by solving an inverse problem. This technique is a variant of single-shot parameter assessment by retrieval from signal encoding (SS-PARSE). The results of simulation and phantom studies show strong agreement with the actual velocities. The prototype method can measure velocities in the range of -50 to 50 cm/s, which is roughly appropriate for future applications in dynamic blood flow measurement in carotid arteries.

Rapid MR elastography using selective excitations

Rapid MR elastography (MRE) techniques using spatially-selective excitations to reduce acquisition times to a few seconds or less were devised and tested. The techniques included reduced field of view (rFOV) MRE and 1D MRE (beam MRE) using 2D spatially selective RF excitations for gradient-echo (GRE) applications and intersecting 90 degrees and 180 degrees slice-selective excitations for spin-echo (SE) applications. It was shown that scan times could be reduced by a factor of 8 using rFOV MRE, and by 64 using beam MRE, while still obtaining stiffness estimates comparable to full-FOV MRE. Results were shown in gel phantom experiments as well as in the case of a preserved postmortem breast tissue specimen with a stiff lesion. These methods can be used to more rapidly interrogate regions of interest (ROIs) in tissue to quickly obtain information about the viscoelastic properties of that tissue.

Applications of phase-contrast flow and velocity imaging in cardiovascular MRI

A review of cardiovascular clinical and research applications of MRI phase-contrast velocity imaging, also known as velocity mapping or flow imaging. Phase-contrast basic principles, advantages, limitations, common pitfalls and artefacts are described. It can measure many different aspects of the complicated blood flow in the heart and vessels: volume flow (cardiac output, shunt, valve regurgitation), peak blood velocity (for stenosis), patterns and timings of velocity waveforms and flow distributions within heart chambers (abnormal ventricular function) and vessels (pulse-wave velocity, vessel wall disease). The review includes phase-contrast applications in cardiac function, heart valves, congenital heart diseases, major blood vessels, coronary arteries and myocardial wall velocity.

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.

Cardiovascular flow measurement with phase-contrast MR imaging: basic facts and implementation

Phase-contrast magnetic resonance (MR) imaging is a well-known but undervalued method of obtaining quantitative information on blood flow. Applications of this technique in cardiovascular MR imaging are expanding. According to the sequences available, phase-contrast measurement can be performed in a breath hold or during normal respiration. Prospective as well as retrospective gating techniques can be used. Common errors in phase-contrast imaging include mismatched encoding velocity, deviation of the imaging plane, inadequate temporal resolution, inadequate spatial resolution, accelerated flow and spatial misregistration, and phase offset errors. Flow measurements are most precise if the imaging plane is perpendicular to the vessel of interest and flow encoding is set to through-plane flow. The sequence should be repeated at least once, with a high encoding velocity used initially. If peak velocity has to be estimated, flow measurement is repeated with an adapted encoding velocity. The overall error of a phase-contrast flow measurement comprises errors during prescription as well as errors that occur during image analysis of the flow data. With phase-contrast imaging, the overall error in flow measurement can be reduced to less than 10%, an acceptable level of error for routine clinical use.

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.

In vitro validation of MR measurements of arterial pulse-wave velocity in the presence of reflected waves

A magnetic resonance imaging projective velocity encoding sequence was used to determine the pulse-wave velocity in an artery model. To this end, a well-defined flow phantom simulating flow propagation in large arteries was used. In order to validate the measurement method in the presence of large reflected waves, these were deliberately created in the phantom. The projective sequence was applied to two measurement sites and the wave velocity was determined from the spatial and temporal separations of the foot of the velocity waveform. A theoretical model describing reflection and attenuation phenomena was compared with experimental velocity waveforms. The model showed that reflections and attenuation can explain the important changes in velocity waveforms. The model also confirmed that in the presence of reflecting waves, the foot of the waveform can be used as a characteristic point for measurements through changes in the waveform.

Preferential arterial imaging using gated thick-slice gadolinium-enhanced phase-contrast acquisition in peripheral MRA

PURPOSE

To investigate the feasibility of preferential arterial imaging using gadolinium-enhanced thick-slice phase-contrast imaging.

METHODS

Six healthy volunteers were studied using a peripheral-gated segmented k-space CINE phase-contrast pulse sequence using four views per RR interval with flow encoding in the superior-inferior direction. Images at the level of the popiteal trifurcation were acquired postcontrast with different section thicknesses (4-8 cm) and VENC values (20-150 cm/sec), and phase-difference processing.

RESULTS

The post-gadolinium contrast-enhanced thick-slice phase-contrast acquisitions demonstrated the ability to visualize the tibio-peroneal (trifurcation) arteries, especially in systole. With MR contrast agents, the signal from blood is raised significantly above that of stationary tissue from T(1) shortening such that the partial volume artifact is reduced in thick-slice acquisitions. Furthermore, by selecting the VENC value as a function of the cardiac cycle, the noise floor can be raised to selectively suppress flow values less than that of the noise threshold, allowing better accentuation of arterial structures at systole.

CONCLUSIONS

Thick-slice phase-contrast acquisition with phase-difference processing has been observed to reduce partial volume artifacts when an MR contrast agent substantially increases signal in the vasculature over that of normal background tissue. Preferential arterial images can be obtained by either increasing the VENC value to selectively suppress signal from slow flow in the veins or by subtracting the diastolic phase image from the peak systolic phase image. J. Magn. Reson. Imaging 2001;13:714-721.

Fast measurements of the motion and velocity spectrum of blood using MR tagging

A new method is presented for tracking the motion of blood and determining its velocity spectrum from magnetic resonance data collected within a single heartbeat. The method begins by tagging a column of blood in a vessel by combining a 1D SPAMM excitation with a 2D cylindrical excitation. A series of 1D projections of the tagging pattern is acquired from a train of gradient echoes. The influence of specific excitation profiles and velocity profiles on the motion of the tags is explored for steady flow. It is shown mathematically, and confirmed with phantom experiments, that the velocity of a tag equals the mean velocity of the excited fluid when the velocity spectrum is symmetric about its mean velocity. The velocity spectrum is derived by analyzing the interference between tags moving at different velocities. This appears to be the first use of magnitude tagging to obtain velocity spectra. Representative measurements in a human aorta are presented to assess feasibility in vivo. Magn Reson Med 45:461-469, 2001.

Improved phase-contrast flow quantification by three-dimensional vessel localization

In this paper, a method of three-dimensional (3D) vessel localization is presented to allow the identification of a vessel of interest, the selection of a vessel segment, and the determination of a slice orientation to improve the accuracy of phase-contrast magnetic resonance (PCMR) angiography. A marching-cube surface-rendering algorithm was used to reconstruct the 3D vasculature. Surface-rendering was obtained using an iso-surface value determined from a maximum intensity projection (MIP) image. This 3D vasculature was used to find a vessel of interest, select a vessel segment, and to determine the slice orientation perpendicular to the vessel axis. Volumetric flow rate (VFR) was obtained in a phantom model and in vivo using 3D localization with double oblique cine PCMR scanning. PCMR flow measurements in the phantom showed 5. 2% maximum error and a standard deviation of 9 mL/min during steady flow, 7.9% maximum error and a standard deviation of 13 mL/min during pulsatile flow compared with measurements using an ultrasonic transit-time flowmeter. PCMR VFR measurement error increased with misalignment at 10, 20, and 30 degrees oblique to the perpendicular slice in vitro and in vivo. The 3D localization technique allowed precise localization of the vessel of interest and optimal placement of the slice orientation for minimum error in flow measurements.

Estimation of pressure gradients in pulsatile flow from magnetic resonance acceleration measurements

A method for estimating pressure gradients from MR images is demonstrated. Making the usual assumption that the flowing medium is a Newtonian fluid, and with appropriate boundary conditions, the inertial forces (or acceleration components of the flow) are proportional to the pressure gradients. The technique shown here is based on an evaluation of the inertial forces from Fourier acceleration encoding. This method provides a direct measurement of the total acceleration defined as the sum of the velocity derivative vs. time and the convective acceleration. The technique was experimentally validated by comparing MR and manometer pressure gradient measurements obtained in a pulsatile flow phantom. The results indicate that the MR determination of pressure gradients from an acceleration measurement is feasible with a good correlation with the true measurements (r = 0.97). The feasibility of the method is demonstrated in the aorta of a normal volunteer. Magn Reson Med 44:66-72, 2000.

Flow quantification using low-spatial-resolution and low-velocity-resolution velocity images

In this report, a flow-quantification method using Fourier velocity encoding (FVE) with limited spatial and velocity resolution is presented. The total flow rate in a vessel corresponds to the first moment of the velocity histogram of spins in the vessel, whereas the spin density of flowing spins is the normalization constant. Because the measured histogram using FVE is distorted by RF saturation effects, the RF saturation effects are first estimated and then accurately compensated by acquiring five velocity-encoded images. The spatial resolution in each image can be relatively low because all stationary spins vanish in the resultant flow map. In a phantom study, the errors in measured flow rates were within +/-10% even when the pixel size was greater than the vessel size. This method was also successfully applied to measure flow in the femoral artery. In general, this method constitutes a basis for analyzing multiple velocity-encoded images and is particularly useful for quantifying slow flow or flow in small vessels. Magn Reson Med 42:682-690, 1999.

Motion measurements from individual MR signals using volume localization

A novel method is presented for measuring motion using individual magnetic resonance (MR) signals. This method uses a volume-localized excitation with reduced spatial encoding to measure displacement with a temporal resolution of several milliseconds. The trajectory of the excited volume is derived from the time-dependent frequency of the MR signal, which changes as the volume moves through a magnetic-field gradient. Phantom and in vivo experiments confirm that this method can monitor the trajectory of plug-like structures accurately, with T2* decay limiting the measurement period. The displacement of flowing blood in a human aorta has been measured for 65 msec from one MR signal, with a theoretical accuracy of 0.25 mm and an effective time resolution of 2 msec. The high temporal resolution of this method is useful for capturing rapid motions. An interesting property of this method is that it measures motion from the reference frame of the moving anatomy.

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.

Transplant renal artery stenosis. Evaluation of diagnosis with magnetic resonance angiography compared with color duplex sonography and arteriography

The goal of this study was to assess the value of a three-dimensional phase contrast magnetic resonance angiography (3D PC MRA) for diagnosing transplant renal artery stenosis (TRAS). Twelve consecutive patients clinically suspected of having TRAS were prospectively enrolled during a period of 18 months. Delays from transplantation varied from 3 months to 4 years (mean: 18.3 months). Patients first had color Doppler sonography, then MRA-and, on the following day, intraarterial digital subtraction angiography (IADSA). The site of the maximum peak systolic velocity was noted when doing the report of each color Doppler sonogram. On MRA images, any signal cutoff or any vascular narrowing of more than 50% of the diameter of the vessel was considered to be a significant stenosis. Eight patients were considered to have TRAS on MRA, but only two stenoses were noted on IADSA. The six false-positive results of MRA (due to major intravoxel phase dispersion) were observed when elevated peak systolic velocities were noted on doppler sonograms (mean: 214 cm/sec). These elevated peak systolic velocities were noted in the proximal part of the renal artery when there was a tortuous vessel or a sharp angle between the renal artery and the parent vessel. It is our opinion that 3D PC MRA is of limited value for the diagnosis of renal transplant artery stenosis because of a high number of false-positive results.

Effects of intravoxel velocity distributions on the complex difference method of phase-contrast MR angiography

The complex difference method of phase-contrast MR angiography is affected not only by the degree of velocity encoding applied during the scan but also by the variance of the intravoxel velocity distribution. The reconstructed intensities of voxels with the same average flow rate but different variances of the velocity distribution can differ significantly. Mathematical analysis and scanner phantom experiments confirm this conclusion.

Motion induced phase shifts in MR: acceleration effects in quantitative flow measurements--a reconsideration

Magnetic resonance phase difference techniques are commonly used to study flow velocities in the human body. Acceleration is often present, either in the form of pulsatile flow, or in the form of convective acceleration. Questions have arisen about the exact time point at which the velocity is encoded, and also about the sensitivity to (convective) acceleration and higher order motion derivatives. It has become common practice to interpret the net phase shifts measured with a phase difference velocity technique as being the velocity at a certain (Taylor) expansion time point, chosen somewhere between the RF excitation and the echo readout. However, phase shifts are developed over the duration of the encoding magnetic field gradient wave form, and should therefore be interpreted as a more or less time-averaged velocity. It will be shown that the phase shift as measured with a phase difference velocity technique represents the velocity at the "gravity" center of the encoding bipolar gradient (difference) function, without acceleration contribution. Any attempt to interpret the measured phase shift in terms of velocity on any other time point than the gradient gravity point will automatically introduce acceleration sensitivity.

Correction of partial volume inaccuracies in quantitative phase contrast MR angiography

The phase difference method of phase contrast MR angiography provides a means of measuring the average velocity in each voxel of an MR scan. When static tissue is present in a voxel containing flow, the measured velocity is not the average velocity of the flow alone, but is lower due to the partial volume effect of the static tissue. We present a preprocessing technique that removes the contribution of static tissue in each voxel prior to calculation of average velocity, resulting in more accurate velocity measurements and better lumen definition. Results of flow tube experiments are presented which confirm the improvement in measurement accuracy.