30th Annual International IEEE EMBS Conference Vancouver, British Columbia, Canada, August 20-24, 2008
In vivo Velocity and Flow Errors Quantification by PhaseContrast Magnetic Resonance Imaging J. García, L. Kadem, E. Larose and P. Pibarot Abstract -- Magnetic resonance imaging is a very efficient tool for assessing velocity and flow in the cardiovascular system under normal and pathological conditions. However, this technique still has some limitations that produce different type of errors. In this study, velocities and flow were measured in vivo using phase-contrast method to determine the optimal number of phases allowing the minimization of the errors. The effect of velocity encoding upsampling was also investigated. The results showed that a number of phases between 1624 is a good compromise to accurately estimate both ejection and regurgitant flows. Furthermore, a time shift effect caused by velocity encoding upsampling was found and a corrective linear model was proposed. These considerations may reduce flow and velocity measurement errors in normal and pathological conditions.
Figure 1. Peak and mean flow downstream a mechanical heart valve for the selected region of interest (ROI).
I INTRODUCTION Although Doppler echocardiography is predominantly used to study blood flow dynamics in the heart and great vessels and to assess cardiovascular diseases, this technique however does not provide satisfactory results in about 20-30 % of the patients due to inadequate acoustic window, angledependency of flow velocity measurement and other technical pitfalls [1-5]. Cardiovascular magnetic resonance imaging (CMRI) techniques may help to overcome Doppler echocardiography limitations because it enables the acquisition of the complete flow map within the heart and great vessels. Hence, CMRI may allow for accurate description and quantification of blood flow pattern in a variety of pathological conditions [1, 2-7]. In particular, information about the flow velocity and volume is crucial for the assessment of valvular heart diseases such as aortic valve stenosis.
velocities by CMRI; phase-contrast is one of them and is widely used in current MRI systems [1, 6-8]. However, MRI has some technical limitations such as temporal and spatial resolutions, signal-to-noise constrains and T2 dependency [9-10]. It is, therefore, important to identify the limitations of this technique as well as to quantify its errors in the determination of transvalvular flow rate. In this study, we analyzed the effect of different temporal resolutions on the estimation of ejected and regurgitant flows in vivo as well as the effect of encoding velocity upsampling on peak velocity computation.
II METHOD
Different techniques have been developed to measure
Phase-Contrast Acquisition Imaging
_______________________________
A clinical 1.5 Tesla MRI scanner with a dedicated cardiac phase-array receiver coil (Achieva, Philips Medical Systems, Best, Netherlands) was used to determine velocity maps using phase-contrast technique. An Electrocardiographic gating was used, with cine images acquired during expiratory breath-holds. Phase-Contrast (sQFlow Phase SENSE) examination in standard short and long axis planes at aortic valve level was performed by one experienced CMR cardiologist. The following imaging parameters were used: echo time (2.4 - 2.5 ms), flip angle (15°), phases per slice location (24 - 194), velocity encoding (100 - 300), pixel
J. García, Laval Hospital Research Center, Laval University, Quebec, Canada and Laboratory for Cardiovascular Fluid Dynamics, Concordia University, Montreal, Canada. (Corresponding author’s phone: 418656-8711 #3117; e-mail:
[email protected]). L. Kadem, Laboratory for Cardiovascular Fluid Dynamics, Concordia University, Montreal, Canada (e-mail :
[email protected]). E. Larose, Laval Hospital Research Center, Laval University, Quebec, Canada (e-mail :
[email protected]). P. Pibarot, Laval Hospital Research Center, Laval University, Quebec, Canada (e-mail :
[email protected]).
978-1-4244-1815-2/08/$25.00 ©2008 IEEE.
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spacing (1.56 – 1.64 mm), repetition time (4.2 – 4.5 ms), slice thickness (10 mm), acquisition matrix (64 – 160 x 52 128) and time resolution (4.6 – 37.8 ms). Velocity and Flow Measurements By performing two measurements, with and without the magnetic gradient field, the phase shift due to spin motion alone can be computed. Phase shift values are in the range of ± 90°. The constant that links velocity and phase shift angle is the encoding velocity or Venc, which specifies the maximum velocity that will be encoded by the sequence acquisition [4, 8]. The Venc adjusts the strength of bipolar gradient so that maximum velocity selected corresponds to a 90° phase shift in the data and to the maximal velocity measured, figure 2. Pixel velocity measured is represented by a gray level value in the phase contrast image or velocity map [12]. We calculated image velocity using equation 1.
V=
2 Venc I − Venc Max I
Image Cases Two different cases were considered in this study: flow through a mechanical heart valve (St-Jude 25 mm) and flow in the right pulmonary artery. The flow downstream of the mechanical heart valve was acquired in vivo using 194 phases. Then, the number of phases was decreased to determine the optimal range allowing a minimization of the
[1]
Figure 2. Shift angle caused by vessel blood flow motion.
Where V is the image matrix with velocities calculated in cm/s, Venc is the velocity encoding in cm/s, I is the image matrix with gray levels, velocity map, and Max I is the maximum gray value that can be represented in gray level in the velocity map. Region of interest was obtained by level set active contour method [13]. Figure 1 shows velocity and mean flow calculations for the selected valvular region or ROI downstream of a mechanical heart valve. For all images, the velocity is perpendicular to pixel area, so we estimated the flow by multiplying pixel velocity by pixel area for all pixels in the ROI [2, 11, 14]. Then mean flow is given by equation 2.
Figure 3. Jet velocity distribution downstream of a mechanical heart valve during cardiac cycle. Q194 600
Q97 500
[2]
Q49
400
Where n is the number of pixels in the ROI, Vi is the calculated velocity at pixel i and Ai is the pixel area. So we can obtain Q for all phases during a cardiac cycle. Ejected volume is estimated by the integral area of Q during systolic period and regurgitant volume during diastolic period. Mean ejected flow rate, Qmean, was estimated by the mean of Q during systolic period [8, 15]. Images were processed using a home-made research application, Marevel v02, developed using Matlab software (Mathworks, Natick, MA).
Q (mL/s)
1 n Q = ∑ Vi Ai n i =1
Q25
300
Q15
200
Q8
100 0 ‐100 ‐200 0
200
400
600
800
Time (ms)
Figure 4. Reconstruction of the flow waveform downstream of the mechanical heart valve using different number of phases.
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error in the determination of ejected and regurgitant flows, while keeping clinically realistic measurement conditions. To investigate the effect of upsampling velocity encoding on the determination of peak velocity, two encoding velocities were used (100 and 300 cm/s).
TABLE 1 Volume (mL)\Phases
194
97
49
25
15
8
Error Average
Ejected
133
133 (0%)
132 (1%)
130 (2%)
137 (3%)
123 (8%)
4.64 (3%)
21
21 (0%)
22 (7%)
23 (1%)
21 (3%)
25 (22%)
1.75 (9%)
Regurgitant / Ejected % 16 16 (0%) 17 (8%) 18 (13%) Relative Errors of computed values are between brackets.
16 (0%)
21 (32%)
1.97 (13%)
Regurgitant
III RESULTS
Figure 6 shows the peak velocity measured with two different encoding velocities (100 and 300 cm/s) at the pulmonary artery level. A time shift effect was observed. Time difference at same phase was computed to estimate the time shift tendency between encoding velocity cases, both cases were acquire with 24 phases/cardiac cycle. Figure 7 represents the time shift computed between 100 and 300 cm/s encoding velocities and a linear model allowing a compensation for this error.
Qmean/Qmean194
1.3
Qmean / Qmean194
24 phases 37 phases
1.2
50 phases 100 phases
1.1
0.95 1
0.9
0.8 0
20
40
60
80
100
120
140
160
180
200
Phases
Figure 5. Normalized Qmean flow quantification with different number of phases during a cardiac cycle. 100 Venc = 100 cm/s
80
Venc = 300 cm/s
60
Peak Velocity (cm/s)
Figure 3 shows the velocity distribution downstream of a mechanical heart valve during the cardiac cycle. Figure 4 shows the effect of the variation in the number of phases on the reconstruction of the flow waveform downstream of the mechanical heart valve. Table 1 summarizes the values of ejected and regurgitant volumes for different number of phases. Figure 5 shows the effect of the number of phases on the mean transvalvular flow rate (in comparison with a reference flow rate computed with 194 phases). This plot is very useful for the determination of the optimal range for the number of phases in terms of minimizing the errors, while keeping realistic clinical settings.
40 20 0 ‐20 ‐40 ‐60
IV DISCUSSION
‐80 ‐100 0
100
200
300
400
Time (ms)
500
600
700
Figure 6. Peak Velocity reconstruction in a right pulmonary artery. Time shift due to Venc is observed. 35
Time shift Venc=300 vs Venc=100 (ms)
In this study, we considered the flow downstream of a mechanical heart valve. The flow was determined in vivo using phase contrast method with 194 phases. Then, we modified the number of phases (temporal resolution) to assess the dependence of reconstructed flow waveform upon the number of phases considered. It appears that, the reconstructed flow waveforms with 25 to 194 phases are similar and that small differences appear with 8 to 15 phases. However, phase-contrast sequences are usually acquired with 24 phases per cardiac cycle, for this case we estimated an error in Qmean of about of 5%. Our results for temporal flow representation are in agreement with Lotz et al. [4] who reported good velocity measurement in a range of 16 to 24 phases and significant partial volume effects with phases under 16 phases for healthy aortic valves. Hence, ejection and regurgitant volumes were calculated with small relative errors of 3% and 9 % respectively. The error in regurgitant fraction determination was around 13%. These results confirm a good concordance for ejected and
30
y = 1.2631x ‐ 1E‐13
25 20 15
T300‐T100
10 5 0 0
5
10
15
20
Phases
Figure 7. Time shift due to Venc upsampling and linear model
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25
regurgitant volumes as [17-20]. Figure 4 shows normalized Qmean (with respect to the mean flow rate obtained using 194 phases) for different phase cases. An error of 0.5 % was estimated from using 24 phases. Higher number of phases (37, 50 and 100) led to the same Qmean than the one computed using 194 phases. These results allow the determination of the optimal number of phases in terms of temporal and spatial resolution measurements. This is an important issue since the temporal resolution is limited by the heart rate. We also determined the effect of encoding velocity upsampling on the peak velocity measurement using two encoding velocities (100 and 300 cm/s). A time shift effect was observed despite similar velocity amplitudes. Temporal time shift followed a linear and predictable model which is showed in Figure 6. A Venc higher than two times the maximal velocity is usually recommended for velocity acquisition. This is in order to avoid aliasing in velocity magnitude. However this case shows a time shift effect along phase acquisition caused by upsampling of maximal velocity. We suggested then a linear model that could correct this error. We considered 100 cm/s encoding velocity as reference for this case because velocity magnitude did not seem aliasing but the ideal reference is a 200 cm/s encoding velocity sequence. We observed that the time shift is more significant during diastolic period. This correction could be used, then, only during this period. However, other studies are still required to investigate the dependence of this model upon different flow configurations.
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
V CONCLUSIONS Temporal resolution corresponding to measurements with a number of phases > 24 induced small errors in volume quantification. We found similar Qmean using different number of phases, or temporal resolution. These results may be useful for the evaluation of turbulent flows and for the determination of the optimal number of phases. Encoding velocity upsampling of maximal velocity introduced a time shift and a linear model was introduced to correct this error, leading to a reduction in the effects introduced by a Venc > 2 Vmax. These considerations may reduce flow and velocity errors quantification in different cardiovascular diseases and turbulent flow quantification.
[16] [17] [18] [19] [20] [21]
[22]
ACKNOWLEDGMENTS
[23]
This work was supported by a NSERC grant (343165-07). Dr. Pibarot is the director of the Canada Research Chair in Valvular Heart Diseases, Canadian Institutes of Health Research, Ottawa, Ontario, Canada. J. García is supported by CONACYT (Mexico City, Mexico, grant 208171) at Laval University.
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