DOI: 10.1148/radiol.2321030783
(Radiology 2004;232:289-294.)
© RSNA, 2004
Arterial MR Imaging Phase-Contrast Flow Measurement: Improvements with Varying Velocity Sensitivity during Cardiac Cycle1
Steffen Ringgaard, PhD,
Sten A. Oyre, MD and
Erik M. Pedersen, PhD, DMSc
1 From the MR Center, Institute of Experimental Clinical Research, Aarhus University Hospital, Skejby Sygehus, Brendstrupgaardsvej, DK-8200 Aarhus N, Denmark. Received May 19, 2003; revision requested August 6; revision received October 13; accepted December 9. Supported by Danish Medical Research Council grant 9902664, Danish Heart Foundation grant 97–2-1–5-22549, and the Kirsten Antonius Foundation. Address correspondence to S.R. (e-mail: steffen@mr.au.dk).
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ABSTRACT
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To reduce noise in velocity images of magnetic resonance (MR) phase-contrast measurements, the authors implemented and evaluated a pulse sequence that enables automatic optimization of the velocity-encoding parameter Venc for individual heart phases in pulsatile flow on the basis of a rapid prescan. This sequence was prospectively evaluated by comparing velocity-to-noise ratios with those from a standard MR flow scan obtained in the carotid artery in eight volunteers. This sequence was shown to improve velocity-to-noise ratios by a factor of 2.0–6.0 in all but the systolic heart phase and was determined to be an effective technique for reducing noise in phase-contrast velocity measurements.
© RSNA, 2004
Index terms: Coronary vessels, flow dynamics, 54.12144 • Coronary vessels, MR, 54.12144 • Heart, flow dynamics, 51.12144 • Magnetic resonance (MR), noise reduction, 54.12144 • Magnetic resonance (MR), phase imaging, 54.12144 • Magnetic resonance (MR), vascular studies, 54.12144
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INTRODUCTION
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Optimization of the velocity image signal-to-noise ratio in magnetic resonance (MR) phase-contrast velocity measurements with high spatial resolution or a short image time is an important issue. It is particularly crucial when detailed velocity maps from throughout the cardiac cycle are needed (eg, to calculate wall shear stress [1]) or when accurate determination of low diastolic velocities is important (eg, to determine diastolic valvular regurgitation).
The so-called velocity-to-noise ratio (VNR) is defined by V/
V, where V is the velocity SD. Because the velocity V is determined by the physiology, an improvement in VNR is equivalent to a reduction in V. The velocity SD depends on the signal-to-noise ratio (SNR) of the modulus images and the velocity sensitivity (Venc) (2), as follows:
so v can be reduced by increasing SNR or reducing the velocity-encoding factor Venc. The factor 
2 is a result of the subtraction of two phase images obtained with different velocity sensitivities.
Image signal-to-noise ratio can be increased by means of signal averaging. However, this increase is at the expense of prolonged imaging times, and VNR still increases only by the square root of imaging time.
By decreasing Venc below the actual peak velocities, the phase wraps in images obtained during systolic heart phases. If the flow is not too complicated and the signal-to-noise ratio is high, the aliased pixels can be unwrapped, but this complicates the analysis procedure. Because of the large difference between systolic and diastolic velocities, the diastolic velocities cannot be fully optimized without introducing multiple phase wraps.
The VNR can be improved with multistep acquisition, where more than two velocity sensitivities are used (3). In general, VNR is improved more effectively with such techniques than with signal averaging (3). For many purposes, however, this method is too time-consuming.
Another approach is application of different velocity sensitivities in the different phases of the cardiac cycle. Buonocore (4) previously presented a pulse sequence where two velocity sensitivities for systole and diastole were implemented for quantitative flow measurements in a retrospectively gated pulse sequence. The two sensitivities were based on assumptions about the velocity range in the vessel of interest. Findings in that study showed substantially smaller variation in repeated flow measurements in diastole with the higher velocity sensitivity.
Variation of velocity encoding through the cardiac cycle has also been used to optimize small vessel contrast in phase-contrast (PC) MR angiography (5,6). Findings in these studies showed that both large and small vessels were better visualized with the variable velocity-encoding method than with standard PC MR angiography. The contrast-to-noise ratio in these studies was increased between 17% and 149%.
To our knowledge, no previous investigators have addressed the use of variable velocity encoding throughout the entire cardiac cycle to optimize quantitative blood velocity mapping, and no quantitative data on the expected improvement in VNR throughout the cardiac cycle are available. Thus, on the basis of theory (Eq [1]), the purpose of our study was to prospectively determine if variation of velocity sensitivity during the cardiac cycle would improve arterial MR imaging PC flow measurements.
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Materials and Methods
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Volunteer imaging examinations were approved by the local ethics committee, and informed written consent was obtained from each participant. Eight healthy volunteers (six men and two women; mean age, 24.9 years ± 3.9; age range, 21–33 years) participated in the study.
Implementation
The variable PC method was implemented with a 1.5-T MR imaging system (NT; Philips, Best, the Netherlands) equipped with gradients with peak strength of 21 mT/m, slew rate of 105 mT/m/msec, and Cardiac Patch software, version 6. The pulse sequence parameter Venc was expanded into an array with one element for each heart phase. To simplify the timing of the sequence, the echo time was kept constant for all heart phases. Because the gradient moment demand for the velocity-encoding segment increases with lower Venc values, the shortest possible echo time was defined by the heart phase with the lowest Venc value.
Velocity sensitivity (Venc) for each heart phase could be input manually or loaded automatically from a velocity prescan (Fig 1). This prescan could be a fast scan (eg, obtained with segmented k-space or echo-planar type sequences with low spatial and temporal resolution). On the resulting prescans, the artery of interest was marked with a circle with a diameter of half the vessel diameter. This circle was automatically copied to all heart phases, and the highest velocity for each cardiac phase was automatically determined. The resulting peak velocity curve was interpolated and stored to a text file. Interpolation permitted use of a different number of heart phases and different heart phase intervals for the prescan and the subsequent variable PC scan.
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Figure 1. Schematic of automatic variable PC procedure. A, Approximate peak velocities throughout heart cycle of artery of interest are measured with fast low-spatial-resolution imaging. B, Measured peak velocities are interpolated with cubic-spline algorithm to allow different heart phase intervals in prescan and final scan. C, Peak velocity curves are filtered with a multiplication factor, an addition value, and a minimum value. D, Resulting values are used as Venc values in final variable PC scan.
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When the variable PC imaging was initialized, the peak velocity curve was automatically loaded into the Venc array of the sequence. The loaded Venc values could be modified in three ways: (a) by multiplying by a factor (typically 1.1), (b) by adding a velocity (typically 0 cm/sec), and (c) by setting a minimum Venc velocity (typically 10 cm/sec) to not induce a critically long echo time for the entiresequence. The only user inputs were the acquisition of the prescan, the setting of a circle, and the adjustment of parameters. Imaging time for the variable PC scan was unchanged compared with that for the standard PC scan.
Evaluation
Velocity patterns were studied in a cross section of the right common carotid artery 2 cm upstream from the carotid bifurcation. The through-plane velocity components were quantified on the basis of two similar velocity images obtained with the fixed Venc and variable PC sequences. MR imaging was performed by one of the authors (S.R. or E.M.P.), who had 4 and 8 years, respectively, of experience with cardiovascular MR imaging.
Initially, scout images and a three-dimensional PC MR angiographic scan were acquired to determine vessel geometry. Then, the velocity prescan (1-minute gradient-echo MR scan) was acquired with echo time of 3.2 msec, 128 x 69 matrix, 128 x 77-mm field of view, and 25 heart phases with an interval of 30 msec. In all volunteers, the variable PC setup time was estimated as the time between the start of acquisition of the prescan and the start of acquisition of the variable PC scan.
In both the standard fixed Venc and variable PC scans, the short echo time, free-induction-decay, acquired-echo pulse sequence was used (7). Both scans were obtained with a matrix of 256 x 180, field of view of 102 x 71 mm (pixel size of 0.40 x 0.40 mm), section thickness of 6 mm, and heart phase interval of 35 msec. For the standard PC velocity scans, Venc was set to 110 cm/sec, which was the approximate maximum peak velocity during systole. The echo time was 2.7 msec. For the variable PC scans, Venc varied between approximately 15 and 115 cm/sec, and echo time was approximately 3.9 msec. The Venc multiplication and addition parameters in the variable PC scan were set to 1.1 and 0 cm/sec, respectively, and we used a minimum Venc value of 10 cm/sec. After reconstruction, the velocity images were corrected for offset errors by means of subtraction of a plane fitted through stationary tissue, according to our normal procedure.
To evaluate whether the theoretically predicted gain in VNR of the variable PC scan compared with that of the fixed Venc scan was found, we calculated VNR directly from the velocity images. Mean velocity inside a region of interest in the common carotid artery with a diameter of half the vessel diameter was divided by the SD calculated from an equally sized region of interest positioned on stationary tissue with signal intensity in the same range as that of the artery.
To estimate the influence of the variable PC technique on the assessment of wall shear stress, which is the tangential force on the vessel wall exerted by the flowing blood, circumferentially averaged shear stresses were calculated by means of the three-dimensional paraboloid method (1). Also, the root mean square errors of the three-dimensional paraboloid modeling were obtained. The root mean square error is a measure of noise level in the velocity images.
To evaluate images from the eight patients at functionally equivalent time points, five time points during the cardiac cycle were defined: (a) at end diastole immediately after the R wave of the electrocardiogram, (b) at peak systole, (c) at early diastole before the "dicrotic notch" peak, (d) at the dicrotic notch peak, and (e) at late diastole 200 msec after the dicrotic notch peak (Fig 2). The mean and SD of results from all examinations were calculated.
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Figure 2. Typical flow curve in common carotid artery. Measurements were analyzed at five time points: 1 = end diastole immediately before R wave of electrocardiogram, 2 = peak systole, 3 = early diastole before dicrotic notch peak, 4 = dicrotic notch peak, and 5 = late diastole 200 msec after dicrotic notch peak.
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To assess the quality of variable PC imaging in combination with fast MR imaging, we compared fixed Venc and variable PC scans for flow measurements in the abdominal aorta immediately after exercise by using an ergometer (8). The sequence was a hybrid segmented k-space echo-planar MR imaging sequence (matrix of 128 x 128, pixel size of 1.1 x 1.1 mm, and section thickness of 7 mm) that allowed acquisition of a PC flow image in 12 heartbeats. Fifteen heart phases with an interval of 50 msec were acquired. For the standard PC velocity scan, Venc was 100 cm/sec, and the echo time was 5.8 msec. For the variable PC scan, Venc was between 30 and 101 cm/sec, and echo time was approximately 6.6 msec. The Venc multiplication and addition parameters of the variable PC scan were 1.1 and 0 cm/sec, respectively, and we used a minimum Venc of 30 cm/sec. VNRs were calculated for both scans, and results were compared with expected values.
Statistical Analysis
Differences in VNRs between the standard and variable PC high-spatial-resolution carotid artery MR images were tested with the Wilcoxon signed rank sum test. Results of wall shear stress analyses were given as the mean plus or minus standard error of the mean, and differences in both mean and standard error of the mean values between the two methods were tested with the Wilcoxon signed rank sum test. Finally, the three-dimensional paraboloid wall shear stress analysis provided the root mean square error of the fittings. These were plotted, and differences between root mean square errors for the two imaging methods were also tested with the Wilcoxon signed rank sum test. All tests were performed for each of the five time points during the cardiac cycle. Differences with a P value of .05 were considered to be statistically significant. Statistical software (Analyse-it, version 1.60; Analyse-It Software, Leeds, England) was used for all tests.
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Results
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Setup time for all variable PC scans was less than 3 minutes. After visual inspection of velocity images obtained from the high-spatial-resolution variable PC scans, it was seen that velocities in the artery were equally close to Venc in all heart phases (Fig 3). In some cases, a few pixels in the vessel center were aliased in most of the heart phases, but these were easily unwrapped by using a semiautomatic approach.
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Figure 3a. Transverse velocity images obtained through the neck in a typical study include (a) fixed Venc and variable PC scans (b) before and (c) after unwrapping of phase aliasing. In a, signal intensity of common carotid artery (bottom vessel in each image in a-c) varies throughout cardiac cycle, while that of jugular vein (top vessel in each image in a-c) is almost constant. In b and c, however, signal intensity of carotid artery was almost constant, while that of jugular vein varied. Notice the high spatial resolution (0.4 x 0.4 mm).
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Figure 3b. Transverse velocity images obtained through the neck in a typical study include (a) fixed Venc and variable PC scans (b) before and (c) after unwrapping of phase aliasing. In a, signal intensity of common carotid artery (bottom vessel in each image in a-c) varies throughout cardiac cycle, while that of jugular vein (top vessel in each image in a-c) is almost constant. In b and c, however, signal intensity of carotid artery was almost constant, while that of jugular vein varied. Notice the high spatial resolution (0.4 x 0.4 mm).
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Figure 3c. Transverse velocity images obtained through the neck in a typical study include (a) fixed Venc and variable PC scans (b) before and (c) after unwrapping of phase aliasing. In a, signal intensity of common carotid artery (bottom vessel in each image in a-c) varies throughout cardiac cycle, while that of jugular vein (top vessel in each image in a-c) is almost constant. In b and c, however, signal intensity of carotid artery was almost constant, while that of jugular vein varied. Notice the high spatial resolution (0.4 x 0.4 mm).
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For the high-spatial-resolution scans, VNR was between 2.50 and 6.10 times higher for the variable PC scans than for the fixed Venc scans for all time points except the systolic phase (Table 1, Fig 4). The differences were statistically significant (P < .01), except for the systolic heart phase. These values were compared with the theoretic gain in VNR (Eq [1]). The difference between theoretic and experimental VNR gain was less than 12%.
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Figure 4. Line graph depicts measured VNRs of variable PC (VARPC) and fixed Venc images compared with Venc ratios of the two image sets. Data were averaged for eight high-spatial-resolution studies. Error bars indicate SDs. Gain in VNR with variable PC imaging is highest in cardiac phases with low velocities (eg, time point 3), with no gain in systole (time point 2). Measured VNR gain (experimental) matched theoretic value well.
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The wall shear stress curve throughout the cardiac cycle was qualitatively similar to the flow curve, as was shown previously (1). The circumferentially averaged wall shear stresses with corresponding standard errors of the mean for the five time points are listed in Table 2. There was no significant difference between the mean wall shear stress values obtained with the two methods, but the standard errors of the mean values were significantly different (P < .05) except at time point 2. Root mean square errors of the three-dimensional paraboloid modeling were significantly improved (P < .05) with variable PC imaging in all but the systolic phase (Fig 5). Data in Figures 4 and 5 are averages for the eight volunteers.
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Figure 5. Line graph depicts root mean square errors (RMSE) for VNR obtained with three-dimensional paraboloid fitting for scans without (Non VARPC) and those with (VARPC) variable PC. Data were averaged for eight high-spatial-resolution studies. Error bars indicate SDs. With variable PC imaging, errors were significantly (P < .05) reduced, except at systole.
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For the fast low-spatial-resolution scan, the ratio of VNR between the variable PC and fixed Venc images varied between 0.83 and 3.8 except for a single heart phase, where a ratio of 8.1 was seen (Fig 6). This difference was due to very low velocities in that phase. The difference between theoretic and experimental gain in VNR varied between 0% and 74%, with an average of 17.2%.
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Figure 6. Line graph shows relative VNR data for a fast exercise scan, with ratio between measured VNR for variable PC (VARPC) and fixed Venc scans compared with Venc ratio for the two scans. With variable PC, VNR more than tripled in part of cardiac cycle. Theoretic and measured (experimental) VNR gains matched reasonably well, except at one point where measured VNR gain was inaccurate because of very low velocities.
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Discussion
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The hypothesis of the current study was proved because this approach for optimization of VNR throughout the cardiac cycle yielded up to sixfold increase in VNR for arterial flow. Clearly, this is beyond what can be achieved with signal averaging, as this would require up to 36-fold longer scan times. Furthermore, the setup time for variable PC imaging was less than 3 minutes in this first implementation. The variable PC method is conceptually uncomplicated, and the only disadvantages are the need to acquire a velocity prescan and the need to use longer echo times because of the increased gradient moments with higher velocity sensitivity. Because only a rough estimate of peak velocity is necessary, the prescan can be acquired with a fast technique, such as segmented gradient-echo or echo-planar sequences, or with coarse spatial resolution. Thus, a scan with acceptable quality can be acquired in 10–15 seconds. If a specific vascular region is imaged frequently, the interpolated peak velocity–time curve could be saved to a computer file and used for the following examinations if a less velocity optimized scan is acceptable.
Wall shear stresses in the arteries are important because they are known to be linked to atherogenesis. Measurement of wall shear stress necessitates use of axial velocity components of the flow field (1). Because the parabolic boundary layer, which can be used for data fitting, is very narrow, measurements with high spatial resolution are required. Because high spatial resolution is accompanied by reduced signal-to-noise ratio, the improvement in VNR provided with the variable PC method is particularly important, as demonstrated by the significantly lower SDs and root mean square errors for the wall shear stress values calculated from variable PC scans. Findings in a previous study (9) showed the potential of the variable PC method for assessment of wall shear stress in the complicated flow in the carotid bifurcation.
To control the Venc settings, we introduced three parameters for manipulation of the Venc values loaded automatically from the prescan. A minimum value was used to ensure that very low Venc values did not increase the echo time to critically high values, and the multiplication and addition parameters could be used either to ensure that no phase wraps were encountered in any heart phases or to permit the use of controlled phase wrapping to further increase VNR. These parameters allowed a high degree of flexibility and were crucial for the efficiency and practical use of the technique.
A noise reduction efficiency parameter E was defined by Lamothe and Rutt (3) as the inverse of noise variance per scan time, as follows:
If the scan time of the velocity prescan is taken to be one-fourth the time of the variable PC scan, we find that the ratio of this efficiency parameter for the variable PC method compared with the standard PC method is as follows:
where NSA is the number of signals averaged. The VNR of the variable (VARPC) and standard (PC) methods (PC/VARPC) is approximately 1 at systole and is 3–6 at diastole. Thus, for one signal average, Er is 0.8 at systole and is 7–28 at diastole. The efficiency at diastole is greater than that obtained with the multistep phase difference method with fewer than eight signal averages (3).
The main limitation of the present implementation is that variable PC imaging is accompanied by increased minimum echo times, since the minimum echo time increases with lower Venc values. This can lead to signal loss in regions with complicated or disturbed flow patterns. To reduce this disadvantage in the future, echo time should be allowed to vary throughout the cardiac cycle.
In conclusion, we implemented and evaluated a variable velocity-encoding method for improving the quality of velocity quantification in arterial flow. Our results show that the method significantly increased VNR in all but the peak systolic heart phase beyond values that can be reasonably achieved by increasing scan times. Experimental results were in accordance with theoretic values. In this first implementation, variable PC setup time was reduced to less than 3 minutes, which makes the method clinically applicable. The method is of particular value when a very high-quality velocity image is needed and when image signal-to-noise ratio is low as a result of high-spatial-resolution or fast acquisition. Future clinical use could include quantification of valvular regurgitation and flow in small vessels (eg, coronary arteries, where low signal-to-noise ratio currently is a limiting factor for quantitative flow measurements).
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ACKNOWLEDGMENTS
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We thank Sebastian Kozerke, PhD, Institute of Biomedical Engineering, Zurich, Switzerland, for allowing us to use his STRACK program to extract peak velocities from the velocity prescans.
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FOOTNOTES
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Abbreviations: PC = phase contrast,
Venc = velocity-encoding parameter,
VNR = velocity-to-noise ratio
Author contributions: Guarantors of integrity of entire study, S.R., E.M.P.; study concepts, S.R., S.A.O., E.M.P.; study design, S.R., E.M.P.; literature research, S.R.; clinical studies, S.R., E.M.P.; data acquisition, S.R., E.M.P.; data analysis/interpretation, S.R., S.A.O., E.M.P.; statistical analysis, S.R., E.M.P.; manuscript preparation, definition of intellectual content, and editing, S.R., E.M.P.; manuscript revision/review and final version approval, S.R., S.A.O., E.M.P.
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REFERENCES
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