The accuracy of magnetic resonance phase velocity measurements in stenotic flow

Pergamon

PII: S0021-9290(96)00032-2

TECHNICAL

J. Biomechanics, Vol. 29, No. 12, pp. 1665 1672, 1996 Copyright (c% 1996 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0021 9290/96 $15.00 + .00

NOTE

THE ACCURACY OF MAGNETIC RESONANCE PHASE VELOCITY MEASUREMENTS IN STENOTIC FLOW J o h n M. Siegel, J r , * t J o h n N. Oshinski,:~ Roderic I. Pettigrew:~ a n d D a v i d N. Ku* *George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405, U.S.A.; and ~Department of Radiology, Emory University School of Medicine, Atlanta, GA 30322, U.S.A. Abstract--Nuclear magnetic resonance (MR) Can be used to measure velocities in fluid flow using the technique of phase velocity mapping. Advantages of MR velocimetry include the simultaneous mapping of the entire flow field through a non-contacting, magnetic window. The phase velocity mapping technique assumes that velocity is constant over the measurement time (typically around 10 ms). For many fluid flows, this assumption is not valid. The current study showed that MR phase velocity measurements of velocity through stenotic flow can be in error by over 100% immediately upstream and downstream of the stenosis throat and by 20% far downstream of the throat in comparison with laser Doppler anemometer measurements taken at the same location. Highly turbulent flow also led to significant errors in velocity measurement. These errors can be attributed to several sources including low signal-to-noise ratio, additional phase shifts due to non-constant velocities, and non-stationary transit-time effects. Velocity measurement errors could be reduced to under 3 0 o at all measurement locations through the use of MR sequences with high signal-to-noise ratios, low echo times, and thick slices. Copyright © 1996 Elsevier Science Ltd. Keywords: Phase velocity mapping; Magnetic resonance; MRI; Stenosis; Acceleration; LDA.

INTRODUCTION In vivo magnetic resonance phase velocity mapping has the

potential to provide critical physiologic data such as flow and shear rates within diseased vessels. Others have extensively discussed the utility of MR PVM of diseased vessels as a diagnostic tool (e.g. Levin et al., 1994; Underwood et al., 1987). However, the lack of a consistent, objective method for determining reference velocities in vivo has led to an increased role for in vitro models in the assessment of the accuracy of phase velocity mapping. Several previous studies (e.g. Bryant et al., 1984; Firmin et al., 1990; Meier et al., 1988) have shown that MR phase velocity measurements of straight tube laminar and turbulent flows can be excellent. Phase velocity measurements have also been shown to be accurate in more complex situations such as curved tubes (Ku et al., 1990) and slow moving retrograde flows (Mostbeck et al., 1993). Phase velocity mapping has been shown to overestimate flow rates in the upstream (accelerating) portion of a cosine shaped stenosis (Oshinski et al., 1992) and PVM profiles have been shown to differ from independent laser Doppler anemometry profiles distal to the stenosis throat (Oshinski, 1993). Extremely short (3-5 ms) echo time sequences have been used to take accurate velocity measurements in orifice-type stenoses and heart valves, but at a tradeoff with poor spatial resolution (Kilner et al., 1991; Sondergaard et al., 1992, 1993). It was necessary to use slice thicknesses of 6-15 mm in 2 and 5 mm long stenoses to obtain these echo times. A recent study advocated the use of a new 'free induction decay acquired echo'

Received in final f o r m 7 January 1996.

tPresent address: CFD Research Corporation, Hunstville, AL 38505, U.S.A.

sequence for a reduction in echo time without a corresponding reduction in spatial resolution (Boesinger et al., 1992). The imaging technique proved accurate in the in vivo imaging of normal aortic blood flow, but validation of the technique on a stenotic model was not performed. The current study was undertaken for the purpose of providing an assessment of the accuracy of MR phase velocity mapping throughout a 90% area reduction stenotic flow using typical clinical imaging times and spatial resolutions. Specifically, this study compared laser Doppler anemometry (LDA) measurements with MR measurements in the following sites: (1) Poiseuille flow upstream of the stenosis, (2) accelerating flow proximal to the stenosis throat, (3) separated flow distal to the stenosis throat, and (4) turbulent flow downstream of the stenosis. The current study also examined the effects of signal-to-noise ratio, slice thickness, and gradient switching vibration upon the measured PVM profiles.

MATERIALSAND METHODS The basic flow model for this study was a 2.54 cm upstream diameter silicone cast of a 90% area reduction cosine shaped stenosis (Fig. 1). The large diameter stenotic flow model was chosen for signal-to-noise considerations downstream of the stenosis. Smaller models typically exhibit complete turbulent signal loss downstream of the stenosis and therefore velocity measurements are difficult or impossible to obtain. This model was placed in a recirculating flow loop driven by a centrifugal pump. A long, straight inlet length preceded the stenosis in order to assure a fully developed entrance profile. The working fluid was an undoped glycerin-water mix (T t = 1100 ms; T~ = 100 ms) with a viscosity approximating that of blood (v = - 0.0375 cm 2 s- l ). Flow rates ranged from 1.1 to 6.8 l min-1 to create Reynolds numbers between 250 and 1500, based upon upstream diameter. Velocity profiles were

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Technical Note

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measured 3.0 and 0.5 diameters upstream of the stenosis and 1.5 and 6 diameters downstream of the stenosis. MR angiographic images of the stenoses were obtained using a Philips 1.5 T Gyroscan system (Philips Medical Systems North America, Shelton, CT). The flow was measured using 2D phase contrast processing of a gradient echo sequence. The baseline parameters included an echo time of 8 ms, a repetition time of 37 ms, a slice thickness of 3 mm, a flip angle of 45 °, 12 signals averaged, a field of view of 256 x 256 mm and a reconstruction matrix of 256 × 256. Flow encoding was achieved in the axial (flow) direction (left to right in Fig. 1). The maximum phase contrast velocity setting was varied from 25 to 175 cm s - 1, dependent upon the measurement location and Reynolds number. The selection of the appropriate value for this setting was determined from the LDA measurements. Slices were taken transverse to the flow direction. The full body coil was used for excitation gradients while a rectangular surface coil was placed upon the model to enhance the detection of the echo signal. The MR sequence used two-dimensional Fourier encoding for spatial positioning of the image. In this reconstruction process, images are created by performing a two-dimensional Fourier transform upon the signal in k-space (phase-frequency space). Each image requires 256 phase-encoding steps and velocity is assumed to be constant over all these steps. Signal averaging can be performed either in k-space (before reconstruction) or by averaging multiple reconstructed images. The 'NSA' (number of signals averaged) imaging parameter indicates averaging of multiple images in k-space before reconstruction. Motion in the direction of an applied gradient induces a phase shift in magnetic resonance images: dp(T) = ?

fo

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(1)

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(2)

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This assumption forms the basis for clinical MR phase velocity mapping. Firmin et al. (1990) provides an excellent discussion of the theory and history of MR phase velocity mapping.

Laser Doppler anemometry was chosen as a gold-standard based upon previous studies which showed LDA to be highly accurate in the measurement of complex and stenotic flow (Ahmed and Giddens, 1983; Ku and Giddens, 1985; Lieber, 1986). The laser Doppler anemometry (LDA) measurements were taken using an Aerometrics fiber-optic system interfaced to a FFT-based real-time signal analyzer. The LDA system incorporated a 4 W Argon-ion, multi-line laser coupled to a fiber drive color separator/frequency shift unit. The fiber drive unit split the incoming multi-line laser beam and applied a 40 MHz frequency shift to one of the split beams. The transmitting optics provided an ellipsoidal measurement volume with an 18.5 pm diameter and a length of 100 pln. The real-time signal analyzer was interfaced to a Gateway 486 DX-2 50 MHz microprocessor for on-line data acquisition. At least 20,000 Doppler bursts were evaluated at each measurement location. The accuracy of the LDA measurements was verified at all profile locations by the accurate determination of flow rate through integration of the profiles (reference flow rates were obtained by direct 'bucket and stopwatch' measurements). In addition, LDA velocity profiles from the current study were in agreement with LDA profiles from Lieber (1986).

RESULTS

MR PVM velocity profiles three diameters upstream of the stenosis throat were in excellent agreement with the theoretical Poiseuille velocity profiles [Fig. 2(a)]. These measurements were confirmation of the accuracy of phase velocity measurements in regions of undisturbed flow. MR velocity measurements one-half diameter upstream of the stenosis throat were consistently greater than the velocity measurements by LDA at the same position [Fig. 2(b)]. As the flow rate was increased, the MR overestimation of velocity increased. The convective acceleration at this location represented a higher order of fluid motion which augmented the velocityinduced phase shift, thereby causing an overestimation of velocity. As the flow rate was increased, the convective acceleration increased and likewise the velocity error due to convective acceleration increased. Immediately downstream of the stenosis throat (1.5 diameters), MR underestimated LDA velocities in the core of the flow [Fig. 2(c)]. In the core of the flow, the decay of the stenotic jet caused fluid deceleration, while turbulent phase dispersion caused a low amplitude echo signal. This deceleration caused an underestimation in velocity measurements, just as acceleration caused an overestimation of velocity upstream of the throat. The near-wall region of separated flow moved with a relatively constant velocity over the echo time, and therefore MR PVM was able to make accurate measurements near the vessel wall. The MR PVM profiles six diameters downstream of the stenosis throat overestimated the LDA profiles by approximately

Technical Note

1667

increasing slice thickness as the measurement will be averaged over a larger volume.

12% at the centerline [Fig. 2(d)]. This overestimation remained relatively constant over the whole range of flow rates. This error was likely caused by the non-stationary characteristics of the turbulent flow (see the Discussion section). A comparison of the actual flow rate with the MR error in measured flow rate was used to summarize the information presented above (Fig. 3). Downstream of the stenosis, PVM velocity profiles decreased dramatically in magnitude with a decrease in the number of signals averaged (NSA) as shown in Fig. 4. The profiles shown in Fig. 4 represent (1) an average of 12 images each with an NSA of 1 (1 average in k-space), (2) an average of three images each with an NSA of 4 (4 averages in k-space), and (3) one image with an NSA of 12 (12 averages in k-space). This was done to assure that the total sampling time was constant as the NSA was changed. As the NSA was decreased from 12 to 1, the signal-to-noise ratio likewise decreased and the velocity measurement was underestimated. Increasing the slice thickness from 1 to 20 mm with a constant field of view caused a dramatic decrease in the MR PVM flow rate error (Fig. 5). The increase in slice thickness did several things to correct the M R velocimetry error: (1) the increase in slice thickness linearly increased the signal-to-noise ratio; (2) the increase in slice thickness decreased the echo time; and (3) the increase in slice thickness covered a flow domain in which the net acceleration/deceleration was reduced. It is important to note that the shape of the velocity profiles will differ with

DISCUSSION The error in magnetic resonance velocity measurement in the stenotic flow model raises serious concerns with similar in vivo measurements. The carotid arteries (6 mm diameter) and coronary arteries (4 mm diameter) are two sites which are predisposed to the formation of athromatous plaques. When imaging these smaller vessels, there is a tradeoff between signal-to-noise considerations and image resolution. If the pixel size is equivalent to that used in the current study, there is a poorer resolution of velocity measurements within a given cross-section. Furthermore, there is a wider range of velocities within a given pixel which results in a lower signal level due to increased phase dispersion. The resolution and phase dispersion can be improved by using smaller pixels, but, assuming that the M R hardware cannot produce larger magnetic gradient strengths, this typically lowers the signal-to-noise ratio as well. As the current study shows, low signal-to-noise ratios can significantly increase the errors which are inherent to phase velocity mapping of stenotic flow fields. Future improvements in MRI hardware may produce stronger magnetic fields and therefore higher signal-tonoise ratios; in the mean time, caution must be used in the interpretation of in vivo results.

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nO Fig. 2. (a) MR phase velocity mapping and theoretical Poiseuille profiles were in excellent agreement 3.0 diameters upstream of the stenosis throat. (b) MR phase velocity mapping overestimated the LDA profiles in the converging section 0.5 diameters upstream of the stenosis throat, and (c) MR phase velocity mapping underestimated the LDA profiles in the decelerating jet 1.5 diameters downstream of the stenosis throat. (d) MR phase velocity mapping overestimated the LDA profiles by 25% 6.0 diameters downstream of the stenosis throat.

The accuracy of velocity measurements in laminar flow is consistent with previous studies of straight tube flows (Bryant et al., 1984; Firmin et al., 1990; Ku et al., 1990; Meier et al., 1988; Walker et al., 1988). Also, the overestimation of the velocity measurements agreed with the previous study of convectively accelerating flow (Oshinski et aL, 1992). The differences in flow rate accuracy with increased slice thickness explain some of the disagreement in the current literature regarding MR accuracy in stenotic flow: measurements taken with small voxel sizes and longer echo times can produce inaccurate results (Oshinski, 1993) while short echo time, low spatial resolution measurements can be more accurate (Kilner et al., 1991; Sondergaard et al., 1992, 1993). MR phase velocity images are actually composed of two images; the first image is velocity compensated and therefore provides a reference for the zero velocity phase value while the second image is velocity encoded. The zero velocity image is subtracted from the velocity encoded image to provide the net velocity shifts. With turbulent flow 6 diameters downstream of the stenosis, the smearing of the pixels across the image influenced the zero velocity reference image, thereby causing a constant offset over the entire image of approximately 10% of the maximum velocity mapping setting. It should be emphasized that 2D magnetic resonance phase velocity mapping represents a Lagrangian measurement. A 'slice' of the fluid is selected and the motion of the selected

fluid through magnetic gradients causes the phase shift which is indicative of the fluid velocity. Traditional MR motion compensation techniques attempt to nullify phase shifts due to acceleration by assuming that the acceleration is constant over the echo time. However, the convective acceleration seen immediately upstream and downstream of the stenosis throat represents a spatial, rather than a temporal variation, in velocity and is not constant over the imaging time. Acceleration-compensated gradient waveforms would therefore be ineffective in reducing convective acceleration errors. The short echo times seen with large slice thicknesses alleviate some of the problems with Lagrangian particle motion. As the echo time approaches zero, the Lagrangian description of the particle motion approaches the Eulerian description of the motion and the errors due to spatial velocity variations become small. In conclusion, magnetic resonance phase velocity mapping has great potential in the assessment of flow rate in the cardiovascular system. However, using typical imaging parameters, the only region of stenotic flow where PVM was consistently accurate was in the upstream, undisturbed flow; the converging section of the stenosis overestimated velocity measurements, the diverging section underestimated velocity measurements, and further downstream the velocity measurements were again overestimated. Velocity measurement errors can be reduced through the use of MR sequences with high signal-to-noise ratios, low echo times, and thick slices.

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Acknowledyement--Grateful acknowledgement is given for a Whitaker Foundation Bioengineering Fellowship (Siegel). REFERENCES

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Technical Note

Sondergaard, L., Thomsen, C., Stahlberg, F., Gymoese, E., Lindvig, K., Hildebrandt, P. and Henriksen, O. (1992) Mitral and aortic valvular flow: quantification with MR phase mapping. J M R I 2, 295-302. Underwood, S. R., Firmin, D. N., Klipstein, R. H., Rees, R. S. O. and Longmore, D. B. (1987) Magnetic resonance velocity mapping: clinical application of a new technique. Br. Heart J. 9, 530-536.

Walker, M. R., Souza, S. P. and Dumoulin, C. L. (1988) Quantitative flow measurement in phase contrast MR angiography. M R M 14, 230-241. Zananiri, F. V., Jackson, P. C., Halliwell, M., Harris, R. A., Hayward, J. K., Davies, E. R. and Wells, P. N. T. (1993) ' A comparative study of velocity measurements in major blood vessels using magnetic resonance imaging and-Doppler ultrasound. Br. J. Radiol. 66, 1128-1133.