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Quantitative study of steady flow using color doppler ultrasound
Ultrasound in Med. & Biol. Vol. 17, No. 6, pp. 595-605, 1991 Printed in the U.S.A.
0301-5629/91 $3.00 + .00 © 1991 Pergamon Press plc
OOriginal Contribution QUANTITATIVE COLOR
STUDY OF STEADY FLOW DOPPLER ULTRASOUND
USING
TADASHI TAMURA, RICHARD S. C. COBBOLD a n d K. WAYNE JOHNSTON Institute of Biomedical Engineering and Department of Surgery, University of Toronto, Toronto M5S 1A4, Canada (Received 20 September 1990; in final form 21 January 1991) Abstract--The use of color Doppler flow mapping systems for quantitative in vitro studies of flow fields is examined and illustrated. A 5-MHz color Doppler system was used, and the resolution was determined by comparing the results of flow-field measurement for steady parabolic pipe flow with calculated values. The velocity accuracy was about 6% of the velocity corresponding to half the pulse repetition frequency, and the spatial resolution was better than 1 mm. Frame frequency limitations permitted only partial tracking of fast temporal changes in the flow field. However, detection of vortices downstream from a small cylinder placed in the flow tube was significantly enhanced by synchronizing the frame frequency with the vortex shedding frequency and using a velocity-variance mode. Color Doppler aliasing was found to be useful to define streamlines and determine whether the flow was laminar or turbulent. The color Doppler system clearly imaged Poiseuille, transitional and turbulent flow and vortex shedding in vitro. It is concluded that color Doppler ultrasound flow mapping can enable large, complex flow fields to be quantitatively studied in vitro. Key Words: Color Doppler ultrasound, Steady flow, Laminar, Turbulence, Transitional flow, Streamline, Spectral broadening, Variance.
INTRODUCTION
tion. On the other hand, color Doppler systems provide a virtually instantaneous noninvasive image of the flow field in a quantitative manner. While the temporal resolution of color Doppler flow mapping is inferior to alternative methods of flow velocity measurement, the ability to visualize a complex flow field over a relatively large area and to follow how it changes in time could be of considerable significance. For example, in the study of nonperiodic flow phenomena, such as may occur distal to a stenosis, the development of techniques for off-line computer analysis of the recorded frames may prove to be an effective means of understanding the dynamic properties of the flow field. It is the purpose of this article to illustrate the application of color Doppler flow mapping for quantitative studies of fluid phenomena that may have some relevance to understanding in vivo blood flow. Initially, we discuss some aspects of the spatial, velocity and temporal resolution of color Doppler systems relevant to our studies. We then describe the results of some preliminary investigations of steady and transitional flow in a straight tube and show how velocity profiles can be obtained directly from a color-flow system.
Color Doppler flow mapping has become an important noninvasive ultrasound method for the clinical diagnosis of cardiac (Assmann and Roelandt 1987; Sahn 1985; Swensson et al. 1987; Switzer and Nanda 1985; Valdes-Cruz et al. 1986), arterial (Zierler et al. 1987), venous (Foley et al. 1989) and fetal and maternal circulatory diseases (Kurjak et al. 1988). As a measurement technique for investigating pulsatile and steady flow fields and phenomena in basic and applied research, color Doppler ultrasound may have certain significant advantages over other well-known methods such as laser Doppler anemometry, single and multigate pulsed Doppler ultrasound, hot film anemometry and various flow visualization techniques. Multigate pulsed Doppler systems (Reneman et al. 1986) can determine velocity profiles with better velocity and temporal resolution than is possible with current color Doppler systems. However, they yield only one-dimensional velocity informa-
Address correspondence to: Richard S. C. Cobbold, Institute of Biomedical Engineering, University of Toronto, Toronto, M5S 1A4, Canada. 595
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BACKGROUND
Color Dopplerflow mapping The principles underlining color Doppler flow mapping have been described in a number of publications (Cobbold et al. 1989; Evans et al. 1989; Kasai et al. 1985; Magnin 1987; Namekawa et al. 1982; Omoto 1984). An essential feature of color Doppler systems is the ability to estimate quickly the mean velocity component along the beam direction for each incremental volume~ along a given transmitted beam direction; thus, considerable effort has been devoted to the development and comparison of various mean frequency estimators (Kristoffersen 1988). Generally, such systems process the received signals by removing the clutter signals originating from fixed and slowly moving interfaces. This can be achieved by using delay-line cancellation, whereby the received signals from two successive transmissions along the same direction are subtracted. The mean velocity arising from a given sample volume can be estimated either from the time shift or frequency shift. In the time-shift method, a cross-correlator is used to determine the mean time shift of the scattered signal that occurs over the time interval between successive transmissions. Since the time shift is inversely proportional to the velocity component in the beam direction, this technique provides a direct estimate of the mean velocity (Bonnefous and Pesque 1986). This method, which requires direct digitization of the RF signal, can, in principle, avoid the problems created by aliasing. In the frequency shift approach, the RF signal is first demodulated, followed by clutter removal and detection of the Doppler frequency shift. In the system described by Kasai et al. (1985), an autocorrelator, followed by some simple approximate computations, enables fast estimates to be made of both the mean Doppler frequency and the variance. This avoids the comparatively complex (and potentially time-consuming) task of performing a full spectral estimation (e.g., an FFT) for every sample volume along the transmitted beam path. The variance a 2 of the Doppler frequency is a measure of the velocity distribution and is defined by ~2=
f S(f)(f_f)2df/ f S(f)df
(1)
where f is the Doppler frequency, f is the mean Doppler frequency and S(f) is the Doppler power spectral density. Thus, the variance should contain t The incremental volume is similar to the sample volume for a pulsed Doppler system. Subsequently, we refer to this volume as the sample volume even though there are some subtle distinctions.
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information reflecting the effects of flow disturbances that may be present. In color-flow Doppler systems, a phased array transducer is generally used to generate a scan line pattern throughout the region under examination. Each line consists of the information received from N ultrasound transmissions (typically 6 to 12) along that line. One complete image consists of between 20 and 50 ultrasound scan line paths. Typically, a frame frequency of from 5 to 30 Hz is used, depending on the pulse repetition frequency (PRF). For example, for a frame frequency of 10 Hz, N = 12 and 40 different paths, the pulse repetition frequencyfpRF is 4.8 kHz. From Shannon's theorem, the frequency resolution Af, which is limited by the duration of the observation, depends on the number of times the same scan can be repeated and is given approximately by Af =
fI'RF/(N-- 1).
(2)
From the Doppler equation, the velocity resolution Av is given by AV = 2 V N y q , l s t / ( N - -
1),
(3)
where VNyq.~,tis the velocity corresponding to half the PRF and is called the Nyquist velocity. In practice, noise, the effects of signal bandwidth and the statistical nature of the Doppler signal cause both Afand &v to be degraded in the manner described by Kristofferson (1988). The resolution is significantly worse than that attainable with a conventional pulsed Doppler system due to the smaller value of Nthat must be used. However, a significant improvement in both the velocity and spatial resolution may be achieved through the use of a spatial convolution filter, as is used in some commercial systems. For quasi-stationary flow conditions, temporal averaging can also be used to achieve significant improvements in velocity resolution, but this is at the cost of temporal resolution.
Laminar, transitional and turbulentflow It is well known that for steady pipe flow below a certain critical Reynolds number Re (typically 2000), any perturbations in the fluid motion are damped out by viscous effect and laminar flow results. There exists both an upper and lower critical Reynolds number at which the flow regime changes from laminar to turbulent or turbulent to laminar flows, respectively. Experiments have shown that there exists a range of Reynolds numbers between which the flow exhibits some of the characteristics of laminar and some of turbulent flow. In this flow regime, commonly re-
Quantitative study of steady flow @T. TAMLrRAet al.
ferred to as transitional pipe flow, the flow consists of turbulent regions interspersed with regions of laminar flow. The turbulent regions for transitional flow in a straight circular tube have been characterized as puffs or slugs whose creation depends on the smoothness of the entrance condition and the Reynolds number. Puffs can be generated when the entry flow to the pipe is highly disturbed and the Reynolds number lies between 2000 and 2700 (Wygnanski and Champagne 1973). Their primary properties have been carefully studied by Wygnanski et al. (1975) and Bandyopadhyay (1986). In a Lagrangian coordinate system, they typically consist of a relatively sharp upstream (trailing) front of between 3 and 4 tube diameters (D) in length, a fully turbulent region of about 5D, and a long rather poorly defined downstream (leading) region over which turbulent fluid is detrained and relaminarized. Furthermore, at about Re = 2450, the intermittency factor (fraction of time for which the flow is turbulent) is about 0.45 and the laminar and turbulent regions each occupy roughly 15-20D (Coles 1981). After their formation and fairly far from the entrance (> 100D), puffs reach an equilibrium state and propagate with a velocity very close to that of the mean flow velocity. On the other hand, slugs are produced when the entrance region is relatively smooth and the Reynolds number is greater than about 3200. Unlike equilibrium puffs, the trailing front of slugs has a propagation velocity less than the mean flow velocity, while the leading front velocity is greater; consequently, they grow in length with distance from the entrance at a rate that increases with Re. The trailing fronts of slugs appear to be similar to those of puffs--involving breakdown of upstream laminar fluid jetting into the turbulent region--but the leading fronts of slugs involve intense, large-scale vortex entanglement, downstream laminar fluid engulfment and breakdown. The trailing fronts of puffs and slugs and the leading fronts of slugs, even though sharp, are not flat, smooth surfaces perpendicular to the pipe axis; rather, they are highly contorted interfaces that occupy several diameters in their extent. METHODS
Color Dopperflow recording and analysis An Acuson color Doppler flow mapping system (Model 128, Mountain View, CA) with a 38-mm aperture, 7-MHz linear array transducer (L738) was used in all the experiments. For B-mode imaging the transducer operates at 7 MHz, while in the color and pulsed Doppler modes the frequency is 5.0 MHz. The transmitting power was set to yield the best apparent color flow image for a Doppler angle of approxi-
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mately 70 ° and with the transmitting focal point set to near the center of the flow tube. The gain setting was optimized to just eliminate background color noise on the screen. The persistence setting, which determines the number of video frames to be averaged in a weighted manner, can be set between 0 and 3. Unless stated to the contrary, a setting of 0 corresponding to no averaging was used. The color flow imaging frame frequency (i.e., the actual rate at which the flow field is scanned) was generally in the range 8 to 10 Hz. The B-mode imaging frame frequency is indicated on the screen: The color flow frame frequency is exactly half this value. For most of our experiments, the color Doppler system was set to the lower line density setting such that the number of bursts was 11 per line with about 30 lines across the 3.8-cm field of view, as measured with the help of two moveable miniature hydrophone detectors. The color Doppler system has two basic modes of color coding: the velocity mode and the velocity-variance mode, both of which were used in this study. In the velocity mode, the saturation of the displayed color can be used to indicate the flow velocity, with separate colors being used for flow toward and away from the transducer. Alternatively, fully saturated colors can be used with the hue indicating the velocity. In the velocity-variance mode, the variance is displayed by modulating the basic velocity color with green. The system can be used in a mode whereby the pulsed Doppler signal from a defined region can be displayed along with a frozen color flow image. Specifically, the sample volume length and position can be adjusted to obtain a Doppler signal from any given region, and the Doppler spectrogram displayed in grey-scale. Both the color Doppler images and the Doppler audio signal were recorded on videotapes using the high-quality VHS VCRs (Panasonic, Models 7300, 6400). The frequency response of the audio channels was virtually fiat from 50 Hz to 12 kHz with a 40-dB dynamic range for normal recording and 20 Hz to 20 kHz for hi-fi channels with an 80-dB dynamic range. The Doppler shift audio signal was digitized at a sampling rate of 10 kHz, and the Hanning windowed data were analyzed using a 256-point fast Fourier transform (FFT). Doppler power spectra were obtained and the mean and maximum frequencies calculated. Since the signal to noise ratio (SNR) was good in all the experiments, a simple percentile method (97%) was used to calculate the maximum.
Steady flow model A suspension of 0.1-0,3% cornstarch (Tamura, Yoganathan and Sahn 1987) either in 0.9% saline or
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in a 25% glycerol-saline mixture was used in the experiments as a test fluid. Unless stated otherwise, latex tubing with a nominal internal diameter of 7.9 m m (~ inch) and a wall thickness of 1.6 mm (1 inch) was immersed in a large water bath. Latex has an acoustic impedance that is reasonably close to that of water, thereby ensuring good acoustic coupling on both sides of the tube. The average internal diameter was measured by filling a known length of tubing with water and measuring the increase in mass. It was found to be 7.5 mm. To ensure that the latex tubing was fairly straight with a circular cross-section, some longitudinal tension was applied. Also, a thread loop was used to provide slight support of the central section, and adjustments were made to achieve a symmetrical flow image. To achieve a somewhat smoother wall surface and better geometric symmetry, an acrylic tube with an internal diameter of 6.35 mm (¼ inch) and a wall thickness of 1.6 mm (~6 inch) was also used for the creation of turbulent slugs. For all the experiments, the entrance length was approximately 150 tube diameters, and steady flow was maintained by keeping a constant fluid level in a reservoir by means of a roller pump. During the experiments, the flow rate was monitored continuously by means of an electromagnetic flow meter (Gould, Models SP2202, SP2204) with a cannulating flow probe. Calibration was performed using timed collection of the fluid.
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peated for over 50 frames. In this way, it was possible to ensure that measurements were made at identical radial positions. This process was repeated for increments of 0.5 mm in the radial direction across the vessel diameter.
Speed of sound A small correction must be made to account for the difference in the speed of ultrasound in the glycerol-saline mixture with that assumed in the color Doppler system. To determine the speed of ultrasound assumed in the system, measurements were made on two wires spaced 5.0 cm apart in water. These showed that the assumed speed was close to 1560 m/s, which is 4% greater than that of water. A similar measurement made in the glycerol-saline mixture showed that the speed was approximately 1680 m/s (i.e., 8% greater than that assumed by the system). Thus, both the speed and the distance values, as measured by the instrument, were corrected.
Vortex shedding model Vortices involve radial velocity components, which can be detected by Doppler ultrasound (Cisneros et al. 1985; D'Luna et al. 1982; Tamura and Fronek 1990). Thus, vortices exhibit many velocity
Velocity accuracy The velocity can be determined at a given point on the frozen color Doppler image by means of an adjustable cursor. Velocity profiles were obtained using this facility by moving the cursor on a point-bypoint basis at right angles across the tube axis. To determine the velocity accuracy, the cursor function was used to read velocities from flow images obtained from parabolic flow (the gold standard) at an optimum setting and persistence of 0 (no averaging). Steady laminar flow of a 25% glycerol-saline mixture was created at a flow rate of 0.471/min, corresponding to a Reynolds number of 740. The angle between the beam and vessel axis was determined by aligning the cursor in the flow image. This allowed the system to calculate the axial velocity component. Measurements were made by positioning one cursor at the inner edge of the near wall and then placing a second cursor at a fixed radial position across the vessel with the help of a ruler placed on the display screen. The distance of the second cursor with respect to the first was displayed along with the velocity. Leaving the positions of the two cursors fixed and by freezing and unfreezing the system, this measurement was re-
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Relative Radial Position, mm Fig. 1. Velocity profile of laminar parabolic flow in a 7.5mm diameter latex tube for a flow rate of 0.47 l/rain (Re = 740). Each point represents from between 52 and 102 individual readings obtained from different frames. The mean and standard deviation is given. The broken line is that calculated from the measured flowrate and tube diameter; the solid curve is a least-squares fitted parabola.
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Relotive Rediel Position, mm Fig. 2. Velocity profile for turbulent flow in the 7.5-ram latex tube with a flow rate 1.70 l/rain (Re = 5300). Each point represents more than 70 measurements, for which the mean and standard deviation are plotted. The solid line corresponds to the equation given in the text. Note that the standard deviations are significantly greater than those of laminar flow in Fig. 1. A slight overestimation of the tube diameter for the experimental results should also be noted.
vectors, a n d color D o p p l e r should enable these velocity c o m p o n e n t s to be detected as eddy-like shapes with color grading.
Fig. 3. Example of a pulsed Doppler spectrogram obtained using a sample volume of 1.5 m m length placed close to the center of the 6.35-mm acrylic tube for R e = 3230 (0.87 l/min) and a pulsed Doppler angle of 53 °. The time scale is 1 s/division (total record length = 4.6 s). The dynamic range of the spectrogram is 25 dB. Note the inverted velocity scale and that it must be divided by 0.6 (1.04 cos 53 ° ) to obtain the correct velocity along the tube axis. The relatively rapid upstream and downstream transitions suggest that the changes are caused by turbulent slugs.
Fig. 4. Pulsed Doppler spectrogram was obtained with a sample volume length of 1.5 mm placed near the center of the 7.5-mm latex tube for R e = 2500 (0.79 1/min). The dynamic range was 25 dB. The transitions seen in the recording are characterized by a slow leading edge and a rapid transition of the trailing edge, suggesting the occurrence of turbulent puffs. Time scale: 1 s/division; the inverted velocity scale must be divided by 1.02 (1.04 cos 52°/cos 51 °) to account for the angle inaccuracy and the speed of ultrasound.
Since vortices o c c u r in flow disturbances (e.g., poststenotic flow or turbulence), vortex shedding experiments were p e r f o r m e d using a 25% glycerol-saline mixture to assess the sensitivity o f the color D o p p l e r system for detection o f vortices. A 2 . 5 - m m cylinder was inserted into a 9 - r a m latex tube to create a condition similar to the classical two-dimensional vortex shedding experiments (Schlichting 1979).
Fig. 5. Illustration of the effect of aliasing in a color-flow Doppler image for laminar flow in the 7.5-ram latex tube with R e = 740 (0.47 l/rain; the value given in the image is incorrect due to zero drift in the EM flowmeter). The boundary between the two regions defines a streamline for laminar flow. A persistence setting of 3 was used.
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RESULTS AND DISCUSSION
Steady laminar flow-velocity accuracy The results are shown in Fig. 1 along with the least-square fitted parabolic profile (solid line) and the ideal profile calculated from the measured flow rate and vessel diameter (dashed line). It is clear that the fitted curve is in reasonably good agreement with the ideal profile. When corrected for the effects of refraction and the speed of propagation, the Doppler angle was found to be 68.5 ° with an error of 1°, which resuits in a 5% error in the velocity. Errors arising from slight deviations in the tube symmetry and the 4% error in the flowmeter reading (2% of the full-scale reading of 1.0 l/min) contribute to uncertainty in the ideal curve. The standard deviation (SD) ranges from 2.0 to 4.4 cm/s (6% to 13% of the Nyquist velocity) with an average of 2.5 cm/s over all the measurement positions. The Nyquist velocity was 12 cm/s, but at the Doppler angle of 68.5 ° this value translates to 33 cm/s along the vessel axis. Since a baseline offset of 6 cm/s was used, the maximum velocity was thereby increased from 12 to 18 cm/s, corresponding to 49 cm/s along the vessel axis. This ensured that no aliasing occurred in the measurements. The Nyquist velocity differs from the maximum velocity that can be measured without ambiguity due to the offset. The fractional velocity resolution (ml)/1)Nyquist) can be calculated from eqn 3 for N = 11 to be 20%. From this experiment, the smallest standard deviation of the velocity data was 6% of the Nyquist velocity. Evidently, effects arising from the many factors that govern the velocity resolution should also be present. The variation in standard deviation across the tube diameter indicates the dependency of the accuracy on the sample volume size (transmit focus), velocity gradients, velocity magnitude (intrinsic broadening), SNR and the MTI filter. As discussed, all these factors degrade the velocity resolution, and thus the 6% accuracy indicates that the effects of image processing (i.e., a spatial convolution filter) may be present. Finally, for the experimental conditions described in this article, it was concluded that the accuracy of the color Doppler system is about 6% of the Nyquist velocity.
Turbulent flow profile Turbulent flow measurements at a Reynolds number of 5300 ( 1.70 l/rain) were made using saline and the same method as described for Fig. 1. The mean velocity and standard deviation are shown in Fig. 2 for more than 70 individual measurements at each radial position in 0.4-ram steps across the tube.
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It can be seen that the profile is blunt with a maximum velocity of 92 cm/s. As expected, this is less than the peak velocity ( 128 cm/s) ofthe corresponding parabolic flow profile based on the measured flow rate. For fully developed turbulent flow in a smooth pipe, the velocity profile can be represented by the empirical formula v(y) = V~[I - (y/R)] t/", where Is,, is the centerline velocity, R is the tube radius, y is the radial distance and n is a parameter that depends weakly on the Reynolds number (Schlichting 1979). Schlichting gives the value n = 6 for Re = 4000, which together with the measured flow rate was used to calculate the solid line curve.* Two aspects of the results should be noted. The first is that the SDs for the turbulent flow observations are substantially greater than those for parabolic flow (Fig. ! ), even if normalized by the Nyquist velocity. This difference was caused partly by the turbulent velocity fluctuations. The second concerns the observation that the measured mean velocities in the central tube region are about 15% higher than those predicted; the reason for which is not fully understood. For both Figs. l and 2, the apparent flow diameters are about 0.5 mm larger than the actual values. This most likely arises from the effects of the finite sample volume size. Even when the center of the sample volume lies outside the actual flow region, a portion of the sample volume can lie within the vessel, depending on the sample volume dimensions. Because the effective size of the sample volume depends on the color gain, the apparent size of the imaged flow region will depend on the gain setting. A higher gain apparently overestimates the actual flow diameter while a lower gain can result in a diameter reduction. Based on these observations, it was concluded that for our in vitro experiments the effective spatial resolution of the 5-MHz linear array was in the neighborhood of 0.5 mm.
Transitional flow observations Pulsed Doppler spectra. To create turbulent slugs, saline flow in an acrylic tube of 6.35 mm ID with a smooth wall surface was used. For a range of Reynolds numbers from 3000-3400, it was found that the turbulence intermittency factor varied from 10 to 90%. To determine the variations in the maximum centerline velocity as the characteristics of the flow changed, the pulsed Doppler was used. The Doppler spectrogram shown in Fig. 3 was obtained for Re * Except near the center of the tube, the agreement of this empirical formula with the experimental results of others is good.
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Fig. 6. Sequence of transitional flow images for R e = 2200 (0.71 l/min) for a Doppler flow imaging angle of 72 ° and a frame frequency of approximately 9 Hz. The persistence setting was 0. The MTI filter was set to the lowest value, and the transmitting power was set to Normal. (a) "Laminar" flow zone; (b) frame at 0.56 s later showing evidence for the presence of a turbulent puff (note patchy nature of image); (c) frame 0.2 s later; the image shows evidence of a laminar flow zone (note the streamlined aliased nature of the image).
(b)
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Fig. "7.(a) Color image of vortex shedding downstream from a 2.5-mm cylinder in a 9-ram latextube. The velocity-variance mode (VV5) was used, and the frame rate was 8.5 Hz. The cylinder is positioned in the upper leftcorner just upstream from the separated flow region, which isimaged as the dark blue color. The vortices captured in this frame are indicated by the bright yellow regions. Mean flow velocity was 12 cm/s upstream from the obstruction and was 18 cm/s at the obstruction. Thus, based on the mean velocity and the diameter of the obstruction R e = 250 at the obstruction. (b) Pulsed Doppler spectrogram obtained from a streak of vortices, showing a vortex shedding frequency of 17 Hz. One division is 1 s, and a total of about 2.6 s is displayed.
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= 3200 with a sample volume of 1.5 mm length placed near the center of the tube at a Doppler angle of 53 ° . At this Reynolds number, the turbulent intermittency factor was found to be approximately 50%. Note that the recording shows increasing velocity in the downward direction. The color-flow image was obtained using a Doppler angle of 73 ° and was frozen prior to entering the pulsed Doppler mode. As with all the color flow images presented in this article, flow is from left to right and the color flow velocity scale gives the velocity component along the beam axis. The sharp and relatively large changes of the centerline maximum velocity are well delineated, suggesting that turbulent slugs were present in this relatively smooth acrylic tube. Moreover, the durations were approximately 0.7 s, corresponding to a length of 50D. Ultrasonic interference effects arising from the poor acoustic match between water and the acrylic walls of the tube gave rise to severe distortion of the color Doppler image. However, in the pulsed Doppler mode, with the sample volume near the center of the tube, the maximum velocity waveform does not appear to be affected. Observations were also made with the 7.5-mm latex tube using a range of Reynolds numbers suitable for observing transitional flow. Figure 4 shows the Doppler spectrogram for Re = 2500 (0.79 1/min) and a Doppler angle of 52 °. The transition from laminar to turbulent flow is relatively slow compared to that in the reverse direction. Specifically, the total duration of a puff was around 0.6 s, corresponding to a length of 24D. Moreover, it was found that this phenomenon was clearly present for Reynolds numbers in the range of 2200 to 2700, which is consistent with the known properties of puffs as described earlier.
Color Doppler flow images. Figure 5 shows a color image taken with the 7.5-mm latex tube for laminar flow at a Reynolds number of 740 (0.47 1/min), which is identical to the flow conditions used to obtain the parabolic profile in Fig. 1. For this color coding scheme, if the color image is not aliased, shades of blue-green indicate velocities toward the transducer, and shades of red-yellow away from the transducer. The blue central region, which was intentionally aliased by using a low PRF, actually has higher velocities than the surrounding yellow region. Since aliasing occurs at a specific velocity, for laminar flow the aliasing points define a boundary on which the velocity components along the ultrasound beam are identical. Thus, for laminar flow, in a straight tube, the boundary corresponds to a streamline. In fact, due to the abrupt change in color, single or multiple aliasing provides a means for more clearly identifying regions that
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have nearly the same velocity. Figure 5, which was obtained with some frame averaging, shows reasonably straight streamlines, suggesting laminar flow. The sequence of color flow images shown in Fig. 6 was obtained under similar conditions to Fig. 4, but with Re = 2200. This sequence describes the temporal characteristics of turbulent puffs. In Fig. 6a, aliased regions can be seen near the tube center with doubly aliased narrow patches. Consequently, the velocity in the center must be somewhat higher than 52 cm/s (i.e., (12 + 4)/cos 72 ° cm/s). Based on the measured flow rate and tube diameter, the maximum velocity would be 54 cm/s for a parabolic velocity profile, which is close to that estimated. Moreover, the lines of the single aliased image are relatively straight, although some irregularities are seen in this figure as well as in Fig. 5. Thus, it seems reasonable to conclude that flow was close to laminar at this moment. Figure 6b shows a color Doppler image approximately 0.56 s later. Based on the measured mean flow velocity, this figure corresponds to a region of the flow field that existed approximately 20 diameters upstream from the image of Fig. 6a, although there are some changes due to the transit time. Evidence of turbulent flow is indicated by the patchy nature of the image and the lack of consistent aliased regions in the center. Figure 6c, which was obtained approximately 0.2 s later and corresponds to about 7 diameters upstream from the image of Fig. 6b, suggests the presence of laminar flow, similar to Fig. 6a.
Vortex shedding Figure 7a shows flow in a tube with a 2.5-mm cylindrical obstruction that is perpendicular to the field of view in the upper left corner. The flow rate was 0.441/min, corresponding to mean flow velocity of 12 cm/s in the unobstructed tube and 18 cm/s (Re = 250) at the obstruction. Flow separation appears as the dark blue color region just downstream from the obstruction. Several bright yellow regions are present. The velocity-variance mode (VV5) used in this experiment apparently enabled vortices being shed to be clearly enhanced as bright yellow regions. The vortices are partially dissipated about 4 diameters downstream from the cylinder. In fact, this image was obtained by synchronizing the vortex shedding frequency with the frame frequency of the color Doppler. A pulsed Doppler spectrogram was obtained from a streak of vortices at a Doppler angle of 90 o, as shown in Fig. 7b. The alternating direction of the radial velocities is clearly depicted at a frequency of 17 Hz, which is exactly double the color Doppler frame frequency. Consequently, the color image of Fig. 7a shows just half of the vortices actually present in the
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driven by the hydrostatic pressure difference between the upper and lower reservoirs, was analyzed. The equation governing the system performance is simply the extended form of Bernoullis' equation, that is, Ap = 0v2/2 + Ly(v) + L(I) 2) = kinetic energy gained
+ frictional loss + other loss,
Fig. 8. Color Doppler flow image of fully turbulent flow in the 7.5-mm latex tube obtained using the velocity-variance mode (VVl). Flow rate was 1.42 l/rain (Re = 4500). The frame frequency was half the 17 Hz indicated in the figure. Small vortices are clearly imaged and enhanced by the use of the variance mode. Large velocity distributions in vortices seem to create the high variance.
where Ap is the pressure difference, p is the fluid density and v o is the velocity at the outlet to the lower reservoir. To determine the contribution of L/(proportional to v and viscosity) to the right-hand side of this equation, the fluid viscosity was experimentally increased by a factor of 4. It was found that the flow rate changed by about 10%, which indicates that the Ly term contribution is small (10%) compared to the other two terms. Thus, although there should be substantial changes in the wall shear stress with changes
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tube. From this experiment, it was concluded that the color Doppler, especially when used in the velocityvariance mode, is sensitive to the detection of vortices. The velocity-variance mode (VVI) and R e = 4500 was used to obtain the turbulent flow image shown in Fig. 8. Vortices in the turbulent flow are clearly seen and enhanced by color Doppler variance. The variance coded by the green color superimposed on the directional flow information of blue or red is useful for indicating the velocity distribution in each color Doppler sample volume.
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Mean and m a x i m u m Doppler frequencies The mean and m a x i m u m Doppler shift frequencies computed from the Doppler power spectra are shown in Fig. 9. The mean frequency variation for a small (1.5-mm) pulsed Doppler sample volume (Fig. 9a) shows significant changes as the flow regimes changed. However, with the large (12-mm) sample volume (Fig. 9b), mean frequency changes are not evident, while the m a x i m u m frequency changes substantially. Since the mean frequency is more closely related to flow rate than is the m a x i m u m frequency, the results indicate that little if any changes in volumetric flow occur, even though the m a x i m u m frequency waveform indicates the passage of slugs. This was confirmed by the electromagnetic flowmeter reading, which changed with time by less than 2% of the mean value. To understand the reasons for the preceding observation, the flow system, in which the flow was
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Fig. 9. Maximum and mean pulsed Doppler frequency variations for transitional flow, indicating the passage of slugs. (a) Small sample volume, flow rate, 0.851/min (Re = 3200). Significant fluctuations in mean and maximum frequencies are observed as the flow regime changes. (b) Large sample volume, flow rate, 0.80 1/min (Re = 3000). As the flow regime changes, the mean frequency obtained with the large sample volume shows little change as compared to that obtained with the small sample volume.
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in the flow regime, the volumetric flow changes should be small.
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formed under ideal in vitro conditions, and it remains to be shown if similar quantitative information can be obtained in vivo.
CONCLUSIONS The color-flow mapping system used in this study had a velocity accuracy corresponding to about 6% of the Nyquist velocity. Spatial resolution, which is a function of the beam profile, gain and other factors, was approximately 0.5 mm and was satisfactory for studies of flow in tubes larger than 7.5 mm diameter and even for the detection of vortices. Understanding the factors that govern the temporal resolution is complex and has not been investigated in this study. The temporal resolution proved to be adequate for the detection of transitional flow but may not be sufficient to follow the rapid changes of the flow phenomena. Some color Doppler systems provide color Mmode (so-called M-Q mode) that is indeed similar to the multigate pulsed Doppler (Reneman et al. 1986) but uses colors to display velocities. The M-Q mode yields better velocity and temporal resolutions, although it is only one dimensional. Furthermore, a narrower color Doppler window could be provided to increase the temporal resolution. The velocity-variance mode enhanced detection of flow disturbances (Tamura, Elias et al. 1987) as illustrated by the vortex shedding experiments. In clinical studies, this feature may provide a useful map of the spatial distribution of spectral broadening in poststenotic regions and be an alternative to the measurement of spectral broadening index (Johnston et al. 1986). Alternatively, it may be possible to detect turbulence by the use of the power mode (Tamura et al. 1988), which has been shown to increase under turbulent flow conditions (Bascom et al. 1988). The power mode has been applied to diagnosis in the fetal circulation. Since the system resolution is good, the video color-flow images can be digitized and further processed (Krabill et al. 1987) to obtain velocity information. Through postprocessing, velocity profiles can be displayed at any point in the flow field. Further, if color-flow maps are obtained at two different angles, a two-dimensional flow velocity vector field can be displayed (Tamura et al. 1990). In conclusion, these studies have demonstrated that color Doppler flow mapping is useful for quantitative hemodynamic studies in vitro. Furthermore, we have shown that qualitative aspects of the flow field can be enhanced by displaying the variance and through the use of an aliased image which can display streamlines and which can also be used to estimate velocity values. These experiments have been per-
Acknowledgements--The authors thank the Canadian Heart and Stroke Foundation and NSERC for financial grant support. They are grateful to Bach Vinh for helpful discussions and also to William Gibson for help in determining the color Doppler system transmission parameters.
REFERENCES Assmann, P. E.; Roelandt, J. R. T. C. Two-dimensional and Doppler echocardiography in acute myocardial infarction and its complications. Ultrasound Med. BioL 13:507-517; 1987. Bandyopadhyay, P. Aspects of the equilibrium puff in transitional pipe flow. J. Fluid Mech. 163:439-458; 1986. Bascom, P. A. J.; Routh, H. F.; Cobbold, R. S. C. Interpretation of power changes in Doppler signals from human blood--in vitro studies. IEEE ultrasonics symposium proc.; 1988:985-988. Bonnefous, O.; Pesque, P. Time domain formulation of pulseDoppler ultrasound and blood velocity estimation by cross correlation. Ultrasonic lmag. 8:73-85; 1986. Cisneros, J. A.; Newhouse, V. L.; Goldberg, B. Doppler spectral characterization of flow disturbances in the carotid with the Doppler probe at right angles to the vessel axis. Ultrasound Med. Biol. 11:319-328; 1985. Cobbold, R. S. C.; Mo, L. Y. L.; Johnston, K. W. Methods for processing, displaying, and recording Doppler signals. In: Nicolaides, A.; Salmasi, A. M., eds. Cardiovascular Applications of Doppler Ultrasonography. Edinburgh: Churchill Livingstone; 1989:43-70. Coles, D. Prospects for useful research on coherent structure in turbulent shear flow. Proc. Indian Acad. Sci. 4:111-127; 1981. D'Luna, L. J.; Newhouse, V. L.; Giddens, D. P. In vitro Doppler detection of axisymmetric stenoses from transverse velocity measurements. J. Biomechanics 15:647-660; 1982. Evans, D. H.; McDicken, W. N.; Skidmore, R.; Woodcock, J. P. Doppler ultrasound, physics, instrumentation and clinical application. New York; Wiley; 1989:102-105. Foley, W. D.; Middleton, W. D.; Lawson, T. L.; Erickson, S.; Quiroz, F. A.; Macrander, S. Color Doppler ultrasound imaging of lower-extremity venous disease. Am. J. Radiology 152:371376; 1989. Johnston, K. W.; Baker, W. H.; Burnham, S. J.; Hayes, A. C.; Kupper, C. A.; Poole, M. A. Quantitative analysis of continuouswave Doppler spectral broadening for the diagnosis of carotid disease: Results of a multicenter study. J. Vascular Surgery 4:493-504; 1986. Kasai, C.; Namekawa, K.; Koyano, A.; Omoto, R. Real-time twodimensional blood flow imaging using an autocorrelation technique. IEEE Trans. Sonics Ultrasonics 32:458-464; 1985. Krabill, K.; Tamura, T.; Sahn, D. Verification of velocity assignment by color Doppler flow mapping: Development of a computer method for angle correction of color Doppler velocities. J. Am. College Cardiology 9:65A; 1987. Kristoffersen, K. Time-domain estimation of the center frequency and spread of Doppler spectra in diagnostic ultrasound. IEEE Trans. Ultrasonics, Ferroelectrics Freq. Control 35:685-700; 1988. Kurjak, A.; Alfirevic, Z.; Miljan, M. Conventional and color Doppler in the assessment of fetal and maternal circulation, Ultrasound Med. Biol. 14:337-354; 1988. Magnin, P. A review of Doppler flow mapping techniques. IEEE ultrasonics symposium proc.; 1987:969-977. Namekawa, K.; Kasai, C.; Tsukamoto, M.; Koyano, A. Real-time blood flow imaging system utilizing autocorrelation techniques. In: Lerski, R. A.; Morley, P., eds. Ultrasound '82. Elmsford, NY: Pergamon Press; 1982:203-208.
Quantitative study of steady flow • T. TAMURAet al. Omoto, R. Color atlas of real-time two-dimensional Doppler echocardiography. Philadelphia: Lee & Febbinger; 1984: chap. 2. Reneman, R. S.; Merode, T. V.; Hick, P.; Hocks, A. P. G. Cardiovascular application of multi-gate pulsed Doppler systems. Ultrasound Med. Biol. 12:357-370; 1986. Sahn, D. J. Real-time two-dimensional Doppler echocardiographic flow mapping. Circulation 71:849-853; 1985. Schlichting, H. Boundary layer theory. New York: McGraw-Hill; 1979:18, 31-32, 599. Swensson, R.; Sahn, D.; Dembitsky, W.; Elias, W.; Tamura, T.; Sherman, F.; Valdes-Cruz, L. Color Doppler flow mapping of pulmonary artery flow in an animal model of patent ductus arteriosus (PDA). J. Am. College Cardiology 9:3A; 1987. Switzer, D. F.; Nanda, N. C. Doppler color flow mapping. Ultrasound. Med. Biol. 11:403-416; 1985. Tamura, T.; Cobbold, R. S. C.; Johnston, K, W. Determination of 2-D velocity vectors using color Doppler ultrasound. IEEE ultrasonic symposium proc.; 1990:1537-1540. Tamura, T.; Elias, W.; Gunday, E.; McMillan, S.; Jimoh, A.; Yoganathan, A.; Chung, K. In vitro studies of variance (turbulence) indicators in color flow mapping Doppler systems: Quantitative computer analysis of RGB digitized flow map images. Circulation 76:IV- 1411 ; 1987. Tamura, T.; Fronek, A. Determination of volume of vortices in
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poststenotic pulsatile flow by ultrasonic Doppler power ratio and spectrum analysis. J. Biomechanics 23:195-200; 1990. Tamura, T.; Sahn, D.; Krabill, K. Low flow velocity sensitivity in color flow mapping Doppler: Power mode vs dynamic range reallocation for display. J. Am. College Cardiology 11:98A; 1988. Tamura, T.; Yoganathan, A.; Sahn, D. In vitro methods for studying the accuracy of velocity determination and spatial resolution of a color Doppler flow mapping system. Am. Heart J. 114:152-158; 1987. Valdes-Cruz, L.: Tamura, T.; Dalton, N.; Elias, W. Color flow Doppler shunt areas as indicators of atrial septal defect shunting: Studies in an open chest animal model and initial clinical results. Circulation 74:II-145; 1986. Wygnanski, I. J.; Champagne, F. H. On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59:281-335; 1973. Wygnanski, I. J.; Sokolov, M.; Friedman, D. On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69:283-304: 1975. Zierler, R. E.; Phillips, D. J.; Beach, K. W.: Primozich, J. F,: Strandness, D. E., Jr. Noninvasive assessment of normal carotid bifurcation hemodynamics with color-flow ultrasound imaging. Ultrasound Med. Biol. 13:471-476; 1987.
0301-5629/91 $3.00 + .00 © 1991 Pergamon Press plc
OOriginal Contribution QUANTITATIVE COLOR
STUDY OF STEADY FLOW DOPPLER ULTRASOUND
USING
TADASHI TAMURA, RICHARD S. C. COBBOLD a n d K. WAYNE JOHNSTON Institute of Biomedical Engineering and Department of Surgery, University of Toronto, Toronto M5S 1A4, Canada (Received 20 September 1990; in final form 21 January 1991) Abstract--The use of color Doppler flow mapping systems for quantitative in vitro studies of flow fields is examined and illustrated. A 5-MHz color Doppler system was used, and the resolution was determined by comparing the results of flow-field measurement for steady parabolic pipe flow with calculated values. The velocity accuracy was about 6% of the velocity corresponding to half the pulse repetition frequency, and the spatial resolution was better than 1 mm. Frame frequency limitations permitted only partial tracking of fast temporal changes in the flow field. However, detection of vortices downstream from a small cylinder placed in the flow tube was significantly enhanced by synchronizing the frame frequency with the vortex shedding frequency and using a velocity-variance mode. Color Doppler aliasing was found to be useful to define streamlines and determine whether the flow was laminar or turbulent. The color Doppler system clearly imaged Poiseuille, transitional and turbulent flow and vortex shedding in vitro. It is concluded that color Doppler ultrasound flow mapping can enable large, complex flow fields to be quantitatively studied in vitro. Key Words: Color Doppler ultrasound, Steady flow, Laminar, Turbulence, Transitional flow, Streamline, Spectral broadening, Variance.
INTRODUCTION
tion. On the other hand, color Doppler systems provide a virtually instantaneous noninvasive image of the flow field in a quantitative manner. While the temporal resolution of color Doppler flow mapping is inferior to alternative methods of flow velocity measurement, the ability to visualize a complex flow field over a relatively large area and to follow how it changes in time could be of considerable significance. For example, in the study of nonperiodic flow phenomena, such as may occur distal to a stenosis, the development of techniques for off-line computer analysis of the recorded frames may prove to be an effective means of understanding the dynamic properties of the flow field. It is the purpose of this article to illustrate the application of color Doppler flow mapping for quantitative studies of fluid phenomena that may have some relevance to understanding in vivo blood flow. Initially, we discuss some aspects of the spatial, velocity and temporal resolution of color Doppler systems relevant to our studies. We then describe the results of some preliminary investigations of steady and transitional flow in a straight tube and show how velocity profiles can be obtained directly from a color-flow system.
Color Doppler flow mapping has become an important noninvasive ultrasound method for the clinical diagnosis of cardiac (Assmann and Roelandt 1987; Sahn 1985; Swensson et al. 1987; Switzer and Nanda 1985; Valdes-Cruz et al. 1986), arterial (Zierler et al. 1987), venous (Foley et al. 1989) and fetal and maternal circulatory diseases (Kurjak et al. 1988). As a measurement technique for investigating pulsatile and steady flow fields and phenomena in basic and applied research, color Doppler ultrasound may have certain significant advantages over other well-known methods such as laser Doppler anemometry, single and multigate pulsed Doppler ultrasound, hot film anemometry and various flow visualization techniques. Multigate pulsed Doppler systems (Reneman et al. 1986) can determine velocity profiles with better velocity and temporal resolution than is possible with current color Doppler systems. However, they yield only one-dimensional velocity informa-
Address correspondence to: Richard S. C. Cobbold, Institute of Biomedical Engineering, University of Toronto, Toronto, M5S 1A4, Canada. 595
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BACKGROUND
Color Dopplerflow mapping The principles underlining color Doppler flow mapping have been described in a number of publications (Cobbold et al. 1989; Evans et al. 1989; Kasai et al. 1985; Magnin 1987; Namekawa et al. 1982; Omoto 1984). An essential feature of color Doppler systems is the ability to estimate quickly the mean velocity component along the beam direction for each incremental volume~ along a given transmitted beam direction; thus, considerable effort has been devoted to the development and comparison of various mean frequency estimators (Kristoffersen 1988). Generally, such systems process the received signals by removing the clutter signals originating from fixed and slowly moving interfaces. This can be achieved by using delay-line cancellation, whereby the received signals from two successive transmissions along the same direction are subtracted. The mean velocity arising from a given sample volume can be estimated either from the time shift or frequency shift. In the time-shift method, a cross-correlator is used to determine the mean time shift of the scattered signal that occurs over the time interval between successive transmissions. Since the time shift is inversely proportional to the velocity component in the beam direction, this technique provides a direct estimate of the mean velocity (Bonnefous and Pesque 1986). This method, which requires direct digitization of the RF signal, can, in principle, avoid the problems created by aliasing. In the frequency shift approach, the RF signal is first demodulated, followed by clutter removal and detection of the Doppler frequency shift. In the system described by Kasai et al. (1985), an autocorrelator, followed by some simple approximate computations, enables fast estimates to be made of both the mean Doppler frequency and the variance. This avoids the comparatively complex (and potentially time-consuming) task of performing a full spectral estimation (e.g., an FFT) for every sample volume along the transmitted beam path. The variance a 2 of the Doppler frequency is a measure of the velocity distribution and is defined by ~2=
f S(f)(f_f)2df/ f S(f)df
(1)
where f is the Doppler frequency, f is the mean Doppler frequency and S(f) is the Doppler power spectral density. Thus, the variance should contain t The incremental volume is similar to the sample volume for a pulsed Doppler system. Subsequently, we refer to this volume as the sample volume even though there are some subtle distinctions.
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information reflecting the effects of flow disturbances that may be present. In color-flow Doppler systems, a phased array transducer is generally used to generate a scan line pattern throughout the region under examination. Each line consists of the information received from N ultrasound transmissions (typically 6 to 12) along that line. One complete image consists of between 20 and 50 ultrasound scan line paths. Typically, a frame frequency of from 5 to 30 Hz is used, depending on the pulse repetition frequency (PRF). For example, for a frame frequency of 10 Hz, N = 12 and 40 different paths, the pulse repetition frequencyfpRF is 4.8 kHz. From Shannon's theorem, the frequency resolution Af, which is limited by the duration of the observation, depends on the number of times the same scan can be repeated and is given approximately by Af =
fI'RF/(N-- 1).
(2)
From the Doppler equation, the velocity resolution Av is given by AV = 2 V N y q , l s t / ( N - -
1),
(3)
where VNyq.~,tis the velocity corresponding to half the PRF and is called the Nyquist velocity. In practice, noise, the effects of signal bandwidth and the statistical nature of the Doppler signal cause both Afand &v to be degraded in the manner described by Kristofferson (1988). The resolution is significantly worse than that attainable with a conventional pulsed Doppler system due to the smaller value of Nthat must be used. However, a significant improvement in both the velocity and spatial resolution may be achieved through the use of a spatial convolution filter, as is used in some commercial systems. For quasi-stationary flow conditions, temporal averaging can also be used to achieve significant improvements in velocity resolution, but this is at the cost of temporal resolution.
Laminar, transitional and turbulentflow It is well known that for steady pipe flow below a certain critical Reynolds number Re (typically 2000), any perturbations in the fluid motion are damped out by viscous effect and laminar flow results. There exists both an upper and lower critical Reynolds number at which the flow regime changes from laminar to turbulent or turbulent to laminar flows, respectively. Experiments have shown that there exists a range of Reynolds numbers between which the flow exhibits some of the characteristics of laminar and some of turbulent flow. In this flow regime, commonly re-
Quantitative study of steady flow @T. TAMLrRAet al.
ferred to as transitional pipe flow, the flow consists of turbulent regions interspersed with regions of laminar flow. The turbulent regions for transitional flow in a straight circular tube have been characterized as puffs or slugs whose creation depends on the smoothness of the entrance condition and the Reynolds number. Puffs can be generated when the entry flow to the pipe is highly disturbed and the Reynolds number lies between 2000 and 2700 (Wygnanski and Champagne 1973). Their primary properties have been carefully studied by Wygnanski et al. (1975) and Bandyopadhyay (1986). In a Lagrangian coordinate system, they typically consist of a relatively sharp upstream (trailing) front of between 3 and 4 tube diameters (D) in length, a fully turbulent region of about 5D, and a long rather poorly defined downstream (leading) region over which turbulent fluid is detrained and relaminarized. Furthermore, at about Re = 2450, the intermittency factor (fraction of time for which the flow is turbulent) is about 0.45 and the laminar and turbulent regions each occupy roughly 15-20D (Coles 1981). After their formation and fairly far from the entrance (> 100D), puffs reach an equilibrium state and propagate with a velocity very close to that of the mean flow velocity. On the other hand, slugs are produced when the entrance region is relatively smooth and the Reynolds number is greater than about 3200. Unlike equilibrium puffs, the trailing front of slugs has a propagation velocity less than the mean flow velocity, while the leading front velocity is greater; consequently, they grow in length with distance from the entrance at a rate that increases with Re. The trailing fronts of slugs appear to be similar to those of puffs--involving breakdown of upstream laminar fluid jetting into the turbulent region--but the leading fronts of slugs involve intense, large-scale vortex entanglement, downstream laminar fluid engulfment and breakdown. The trailing fronts of puffs and slugs and the leading fronts of slugs, even though sharp, are not flat, smooth surfaces perpendicular to the pipe axis; rather, they are highly contorted interfaces that occupy several diameters in their extent. METHODS
Color Dopperflow recording and analysis An Acuson color Doppler flow mapping system (Model 128, Mountain View, CA) with a 38-mm aperture, 7-MHz linear array transducer (L738) was used in all the experiments. For B-mode imaging the transducer operates at 7 MHz, while in the color and pulsed Doppler modes the frequency is 5.0 MHz. The transmitting power was set to yield the best apparent color flow image for a Doppler angle of approxi-
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mately 70 ° and with the transmitting focal point set to near the center of the flow tube. The gain setting was optimized to just eliminate background color noise on the screen. The persistence setting, which determines the number of video frames to be averaged in a weighted manner, can be set between 0 and 3. Unless stated to the contrary, a setting of 0 corresponding to no averaging was used. The color flow imaging frame frequency (i.e., the actual rate at which the flow field is scanned) was generally in the range 8 to 10 Hz. The B-mode imaging frame frequency is indicated on the screen: The color flow frame frequency is exactly half this value. For most of our experiments, the color Doppler system was set to the lower line density setting such that the number of bursts was 11 per line with about 30 lines across the 3.8-cm field of view, as measured with the help of two moveable miniature hydrophone detectors. The color Doppler system has two basic modes of color coding: the velocity mode and the velocity-variance mode, both of which were used in this study. In the velocity mode, the saturation of the displayed color can be used to indicate the flow velocity, with separate colors being used for flow toward and away from the transducer. Alternatively, fully saturated colors can be used with the hue indicating the velocity. In the velocity-variance mode, the variance is displayed by modulating the basic velocity color with green. The system can be used in a mode whereby the pulsed Doppler signal from a defined region can be displayed along with a frozen color flow image. Specifically, the sample volume length and position can be adjusted to obtain a Doppler signal from any given region, and the Doppler spectrogram displayed in grey-scale. Both the color Doppler images and the Doppler audio signal were recorded on videotapes using the high-quality VHS VCRs (Panasonic, Models 7300, 6400). The frequency response of the audio channels was virtually fiat from 50 Hz to 12 kHz with a 40-dB dynamic range for normal recording and 20 Hz to 20 kHz for hi-fi channels with an 80-dB dynamic range. The Doppler shift audio signal was digitized at a sampling rate of 10 kHz, and the Hanning windowed data were analyzed using a 256-point fast Fourier transform (FFT). Doppler power spectra were obtained and the mean and maximum frequencies calculated. Since the signal to noise ratio (SNR) was good in all the experiments, a simple percentile method (97%) was used to calculate the maximum.
Steady flow model A suspension of 0.1-0,3% cornstarch (Tamura, Yoganathan and Sahn 1987) either in 0.9% saline or
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in a 25% glycerol-saline mixture was used in the experiments as a test fluid. Unless stated otherwise, latex tubing with a nominal internal diameter of 7.9 m m (~ inch) and a wall thickness of 1.6 mm (1 inch) was immersed in a large water bath. Latex has an acoustic impedance that is reasonably close to that of water, thereby ensuring good acoustic coupling on both sides of the tube. The average internal diameter was measured by filling a known length of tubing with water and measuring the increase in mass. It was found to be 7.5 mm. To ensure that the latex tubing was fairly straight with a circular cross-section, some longitudinal tension was applied. Also, a thread loop was used to provide slight support of the central section, and adjustments were made to achieve a symmetrical flow image. To achieve a somewhat smoother wall surface and better geometric symmetry, an acrylic tube with an internal diameter of 6.35 mm (¼ inch) and a wall thickness of 1.6 mm (~6 inch) was also used for the creation of turbulent slugs. For all the experiments, the entrance length was approximately 150 tube diameters, and steady flow was maintained by keeping a constant fluid level in a reservoir by means of a roller pump. During the experiments, the flow rate was monitored continuously by means of an electromagnetic flow meter (Gould, Models SP2202, SP2204) with a cannulating flow probe. Calibration was performed using timed collection of the fluid.
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peated for over 50 frames. In this way, it was possible to ensure that measurements were made at identical radial positions. This process was repeated for increments of 0.5 mm in the radial direction across the vessel diameter.
Speed of sound A small correction must be made to account for the difference in the speed of ultrasound in the glycerol-saline mixture with that assumed in the color Doppler system. To determine the speed of ultrasound assumed in the system, measurements were made on two wires spaced 5.0 cm apart in water. These showed that the assumed speed was close to 1560 m/s, which is 4% greater than that of water. A similar measurement made in the glycerol-saline mixture showed that the speed was approximately 1680 m/s (i.e., 8% greater than that assumed by the system). Thus, both the speed and the distance values, as measured by the instrument, were corrected.
Vortex shedding model Vortices involve radial velocity components, which can be detected by Doppler ultrasound (Cisneros et al. 1985; D'Luna et al. 1982; Tamura and Fronek 1990). Thus, vortices exhibit many velocity
Velocity accuracy The velocity can be determined at a given point on the frozen color Doppler image by means of an adjustable cursor. Velocity profiles were obtained using this facility by moving the cursor on a point-bypoint basis at right angles across the tube axis. To determine the velocity accuracy, the cursor function was used to read velocities from flow images obtained from parabolic flow (the gold standard) at an optimum setting and persistence of 0 (no averaging). Steady laminar flow of a 25% glycerol-saline mixture was created at a flow rate of 0.471/min, corresponding to a Reynolds number of 740. The angle between the beam and vessel axis was determined by aligning the cursor in the flow image. This allowed the system to calculate the axial velocity component. Measurements were made by positioning one cursor at the inner edge of the near wall and then placing a second cursor at a fixed radial position across the vessel with the help of a ruler placed on the display screen. The distance of the second cursor with respect to the first was displayed along with the velocity. Leaving the positions of the two cursors fixed and by freezing and unfreezing the system, this measurement was re-
40t/I
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Relative Radial Position, mm Fig. 1. Velocity profile of laminar parabolic flow in a 7.5mm diameter latex tube for a flow rate of 0.47 l/rain (Re = 740). Each point represents from between 52 and 102 individual readings obtained from different frames. The mean and standard deviation is given. The broken line is that calculated from the measured flowrate and tube diameter; the solid curve is a least-squares fitted parabola.
Quantitative study of steady flow • T. TAMURAet al.
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Relotive Rediel Position, mm Fig. 2. Velocity profile for turbulent flow in the 7.5-ram latex tube with a flow rate 1.70 l/rain (Re = 5300). Each point represents more than 70 measurements, for which the mean and standard deviation are plotted. The solid line corresponds to the equation given in the text. Note that the standard deviations are significantly greater than those of laminar flow in Fig. 1. A slight overestimation of the tube diameter for the experimental results should also be noted.
vectors, a n d color D o p p l e r should enable these velocity c o m p o n e n t s to be detected as eddy-like shapes with color grading.
Fig. 3. Example of a pulsed Doppler spectrogram obtained using a sample volume of 1.5 m m length placed close to the center of the 6.35-mm acrylic tube for R e = 3230 (0.87 l/min) and a pulsed Doppler angle of 53 °. The time scale is 1 s/division (total record length = 4.6 s). The dynamic range of the spectrogram is 25 dB. Note the inverted velocity scale and that it must be divided by 0.6 (1.04 cos 53 ° ) to obtain the correct velocity along the tube axis. The relatively rapid upstream and downstream transitions suggest that the changes are caused by turbulent slugs.
Fig. 4. Pulsed Doppler spectrogram was obtained with a sample volume length of 1.5 mm placed near the center of the 7.5-mm latex tube for R e = 2500 (0.79 1/min). The dynamic range was 25 dB. The transitions seen in the recording are characterized by a slow leading edge and a rapid transition of the trailing edge, suggesting the occurrence of turbulent puffs. Time scale: 1 s/division; the inverted velocity scale must be divided by 1.02 (1.04 cos 52°/cos 51 °) to account for the angle inaccuracy and the speed of ultrasound.
Since vortices o c c u r in flow disturbances (e.g., poststenotic flow or turbulence), vortex shedding experiments were p e r f o r m e d using a 25% glycerol-saline mixture to assess the sensitivity o f the color D o p p l e r system for detection o f vortices. A 2 . 5 - m m cylinder was inserted into a 9 - r a m latex tube to create a condition similar to the classical two-dimensional vortex shedding experiments (Schlichting 1979).
Fig. 5. Illustration of the effect of aliasing in a color-flow Doppler image for laminar flow in the 7.5-ram latex tube with R e = 740 (0.47 l/rain; the value given in the image is incorrect due to zero drift in the EM flowmeter). The boundary between the two regions defines a streamline for laminar flow. A persistence setting of 3 was used.
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RESULTS AND DISCUSSION
Steady laminar flow-velocity accuracy The results are shown in Fig. 1 along with the least-square fitted parabolic profile (solid line) and the ideal profile calculated from the measured flow rate and vessel diameter (dashed line). It is clear that the fitted curve is in reasonably good agreement with the ideal profile. When corrected for the effects of refraction and the speed of propagation, the Doppler angle was found to be 68.5 ° with an error of 1°, which resuits in a 5% error in the velocity. Errors arising from slight deviations in the tube symmetry and the 4% error in the flowmeter reading (2% of the full-scale reading of 1.0 l/min) contribute to uncertainty in the ideal curve. The standard deviation (SD) ranges from 2.0 to 4.4 cm/s (6% to 13% of the Nyquist velocity) with an average of 2.5 cm/s over all the measurement positions. The Nyquist velocity was 12 cm/s, but at the Doppler angle of 68.5 ° this value translates to 33 cm/s along the vessel axis. Since a baseline offset of 6 cm/s was used, the maximum velocity was thereby increased from 12 to 18 cm/s, corresponding to 49 cm/s along the vessel axis. This ensured that no aliasing occurred in the measurements. The Nyquist velocity differs from the maximum velocity that can be measured without ambiguity due to the offset. The fractional velocity resolution (ml)/1)Nyquist) can be calculated from eqn 3 for N = 11 to be 20%. From this experiment, the smallest standard deviation of the velocity data was 6% of the Nyquist velocity. Evidently, effects arising from the many factors that govern the velocity resolution should also be present. The variation in standard deviation across the tube diameter indicates the dependency of the accuracy on the sample volume size (transmit focus), velocity gradients, velocity magnitude (intrinsic broadening), SNR and the MTI filter. As discussed, all these factors degrade the velocity resolution, and thus the 6% accuracy indicates that the effects of image processing (i.e., a spatial convolution filter) may be present. Finally, for the experimental conditions described in this article, it was concluded that the accuracy of the color Doppler system is about 6% of the Nyquist velocity.
Turbulent flow profile Turbulent flow measurements at a Reynolds number of 5300 ( 1.70 l/rain) were made using saline and the same method as described for Fig. 1. The mean velocity and standard deviation are shown in Fig. 2 for more than 70 individual measurements at each radial position in 0.4-ram steps across the tube.
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It can be seen that the profile is blunt with a maximum velocity of 92 cm/s. As expected, this is less than the peak velocity ( 128 cm/s) ofthe corresponding parabolic flow profile based on the measured flow rate. For fully developed turbulent flow in a smooth pipe, the velocity profile can be represented by the empirical formula v(y) = V~[I - (y/R)] t/", where Is,, is the centerline velocity, R is the tube radius, y is the radial distance and n is a parameter that depends weakly on the Reynolds number (Schlichting 1979). Schlichting gives the value n = 6 for Re = 4000, which together with the measured flow rate was used to calculate the solid line curve.* Two aspects of the results should be noted. The first is that the SDs for the turbulent flow observations are substantially greater than those for parabolic flow (Fig. ! ), even if normalized by the Nyquist velocity. This difference was caused partly by the turbulent velocity fluctuations. The second concerns the observation that the measured mean velocities in the central tube region are about 15% higher than those predicted; the reason for which is not fully understood. For both Figs. l and 2, the apparent flow diameters are about 0.5 mm larger than the actual values. This most likely arises from the effects of the finite sample volume size. Even when the center of the sample volume lies outside the actual flow region, a portion of the sample volume can lie within the vessel, depending on the sample volume dimensions. Because the effective size of the sample volume depends on the color gain, the apparent size of the imaged flow region will depend on the gain setting. A higher gain apparently overestimates the actual flow diameter while a lower gain can result in a diameter reduction. Based on these observations, it was concluded that for our in vitro experiments the effective spatial resolution of the 5-MHz linear array was in the neighborhood of 0.5 mm.
Transitional flow observations Pulsed Doppler spectra. To create turbulent slugs, saline flow in an acrylic tube of 6.35 mm ID with a smooth wall surface was used. For a range of Reynolds numbers from 3000-3400, it was found that the turbulence intermittency factor varied from 10 to 90%. To determine the variations in the maximum centerline velocity as the characteristics of the flow changed, the pulsed Doppler was used. The Doppler spectrogram shown in Fig. 3 was obtained for Re * Except near the center of the tube, the agreement of this empirical formula with the experimental results of others is good.
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(c)
Fig. 6. Sequence of transitional flow images for R e = 2200 (0.71 l/min) for a Doppler flow imaging angle of 72 ° and a frame frequency of approximately 9 Hz. The persistence setting was 0. The MTI filter was set to the lowest value, and the transmitting power was set to Normal. (a) "Laminar" flow zone; (b) frame at 0.56 s later showing evidence for the presence of a turbulent puff (note patchy nature of image); (c) frame 0.2 s later; the image shows evidence of a laminar flow zone (note the streamlined aliased nature of the image).
(b)
(a)
(b)
Fig. "7.(a) Color image of vortex shedding downstream from a 2.5-mm cylinder in a 9-ram latextube. The velocity-variance mode (VV5) was used, and the frame rate was 8.5 Hz. The cylinder is positioned in the upper leftcorner just upstream from the separated flow region, which isimaged as the dark blue color. The vortices captured in this frame are indicated by the bright yellow regions. Mean flow velocity was 12 cm/s upstream from the obstruction and was 18 cm/s at the obstruction. Thus, based on the mean velocity and the diameter of the obstruction R e = 250 at the obstruction. (b) Pulsed Doppler spectrogram obtained from a streak of vortices, showing a vortex shedding frequency of 17 Hz. One division is 1 s, and a total of about 2.6 s is displayed.
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= 3200 with a sample volume of 1.5 mm length placed near the center of the tube at a Doppler angle of 53 ° . At this Reynolds number, the turbulent intermittency factor was found to be approximately 50%. Note that the recording shows increasing velocity in the downward direction. The color-flow image was obtained using a Doppler angle of 73 ° and was frozen prior to entering the pulsed Doppler mode. As with all the color flow images presented in this article, flow is from left to right and the color flow velocity scale gives the velocity component along the beam axis. The sharp and relatively large changes of the centerline maximum velocity are well delineated, suggesting that turbulent slugs were present in this relatively smooth acrylic tube. Moreover, the durations were approximately 0.7 s, corresponding to a length of 50D. Ultrasonic interference effects arising from the poor acoustic match between water and the acrylic walls of the tube gave rise to severe distortion of the color Doppler image. However, in the pulsed Doppler mode, with the sample volume near the center of the tube, the maximum velocity waveform does not appear to be affected. Observations were also made with the 7.5-mm latex tube using a range of Reynolds numbers suitable for observing transitional flow. Figure 4 shows the Doppler spectrogram for Re = 2500 (0.79 1/min) and a Doppler angle of 52 °. The transition from laminar to turbulent flow is relatively slow compared to that in the reverse direction. Specifically, the total duration of a puff was around 0.6 s, corresponding to a length of 24D. Moreover, it was found that this phenomenon was clearly present for Reynolds numbers in the range of 2200 to 2700, which is consistent with the known properties of puffs as described earlier.
Color Doppler flow images. Figure 5 shows a color image taken with the 7.5-mm latex tube for laminar flow at a Reynolds number of 740 (0.47 1/min), which is identical to the flow conditions used to obtain the parabolic profile in Fig. 1. For this color coding scheme, if the color image is not aliased, shades of blue-green indicate velocities toward the transducer, and shades of red-yellow away from the transducer. The blue central region, which was intentionally aliased by using a low PRF, actually has higher velocities than the surrounding yellow region. Since aliasing occurs at a specific velocity, for laminar flow the aliasing points define a boundary on which the velocity components along the ultrasound beam are identical. Thus, for laminar flow, in a straight tube, the boundary corresponds to a streamline. In fact, due to the abrupt change in color, single or multiple aliasing provides a means for more clearly identifying regions that
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have nearly the same velocity. Figure 5, which was obtained with some frame averaging, shows reasonably straight streamlines, suggesting laminar flow. The sequence of color flow images shown in Fig. 6 was obtained under similar conditions to Fig. 4, but with Re = 2200. This sequence describes the temporal characteristics of turbulent puffs. In Fig. 6a, aliased regions can be seen near the tube center with doubly aliased narrow patches. Consequently, the velocity in the center must be somewhat higher than 52 cm/s (i.e., (12 + 4)/cos 72 ° cm/s). Based on the measured flow rate and tube diameter, the maximum velocity would be 54 cm/s for a parabolic velocity profile, which is close to that estimated. Moreover, the lines of the single aliased image are relatively straight, although some irregularities are seen in this figure as well as in Fig. 5. Thus, it seems reasonable to conclude that flow was close to laminar at this moment. Figure 6b shows a color Doppler image approximately 0.56 s later. Based on the measured mean flow velocity, this figure corresponds to a region of the flow field that existed approximately 20 diameters upstream from the image of Fig. 6a, although there are some changes due to the transit time. Evidence of turbulent flow is indicated by the patchy nature of the image and the lack of consistent aliased regions in the center. Figure 6c, which was obtained approximately 0.2 s later and corresponds to about 7 diameters upstream from the image of Fig. 6b, suggests the presence of laminar flow, similar to Fig. 6a.
Vortex shedding Figure 7a shows flow in a tube with a 2.5-mm cylindrical obstruction that is perpendicular to the field of view in the upper left corner. The flow rate was 0.441/min, corresponding to mean flow velocity of 12 cm/s in the unobstructed tube and 18 cm/s (Re = 250) at the obstruction. Flow separation appears as the dark blue color region just downstream from the obstruction. Several bright yellow regions are present. The velocity-variance mode (VV5) used in this experiment apparently enabled vortices being shed to be clearly enhanced as bright yellow regions. The vortices are partially dissipated about 4 diameters downstream from the cylinder. In fact, this image was obtained by synchronizing the vortex shedding frequency with the frame frequency of the color Doppler. A pulsed Doppler spectrogram was obtained from a streak of vortices at a Doppler angle of 90 o, as shown in Fig. 7b. The alternating direction of the radial velocities is clearly depicted at a frequency of 17 Hz, which is exactly double the color Doppler frame frequency. Consequently, the color image of Fig. 7a shows just half of the vortices actually present in the
Quantitative study of steady flow• T. TAMURAet al.
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driven by the hydrostatic pressure difference between the upper and lower reservoirs, was analyzed. The equation governing the system performance is simply the extended form of Bernoullis' equation, that is, Ap = 0v2/2 + Ly(v) + L(I) 2) = kinetic energy gained
+ frictional loss + other loss,
Fig. 8. Color Doppler flow image of fully turbulent flow in the 7.5-mm latex tube obtained using the velocity-variance mode (VVl). Flow rate was 1.42 l/rain (Re = 4500). The frame frequency was half the 17 Hz indicated in the figure. Small vortices are clearly imaged and enhanced by the use of the variance mode. Large velocity distributions in vortices seem to create the high variance.
where Ap is the pressure difference, p is the fluid density and v o is the velocity at the outlet to the lower reservoir. To determine the contribution of L/(proportional to v and viscosity) to the right-hand side of this equation, the fluid viscosity was experimentally increased by a factor of 4. It was found that the flow rate changed by about 10%, which indicates that the Ly term contribution is small (10%) compared to the other two terms. Thus, although there should be substantial changes in the wall shear stress with changes
4
tube. From this experiment, it was concluded that the color Doppler, especially when used in the velocityvariance mode, is sensitive to the detection of vortices. The velocity-variance mode (VVI) and R e = 4500 was used to obtain the turbulent flow image shown in Fig. 8. Vortices in the turbulent flow are clearly seen and enhanced by color Doppler variance. The variance coded by the green color superimposed on the directional flow information of blue or red is useful for indicating the velocity distribution in each color Doppler sample volume.
N
t
x- 3 >1
gl
kL~_
0
I
I
I
I
I
3
6
9
12
15
Time, (a)
s
4
Mean and m a x i m u m Doppler frequencies The mean and m a x i m u m Doppler shift frequencies computed from the Doppler power spectra are shown in Fig. 9. The mean frequency variation for a small (1.5-mm) pulsed Doppler sample volume (Fig. 9a) shows significant changes as the flow regimes changed. However, with the large (12-mm) sample volume (Fig. 9b), mean frequency changes are not evident, while the m a x i m u m frequency changes substantially. Since the mean frequency is more closely related to flow rate than is the m a x i m u m frequency, the results indicate that little if any changes in volumetric flow occur, even though the m a x i m u m frequency waveform indicates the passage of slugs. This was confirmed by the electromagnetic flowmeter reading, which changed with time by less than 2% of the mean value. To understand the reasons for the preceding observation, the flow system, in which the flow was
t
N
3 >i (1)
gl b_ I
I
I
I
I
3
6
9
12
15
Time,
s
(b)
Fig. 9. Maximum and mean pulsed Doppler frequency variations for transitional flow, indicating the passage of slugs. (a) Small sample volume, flow rate, 0.851/min (Re = 3200). Significant fluctuations in mean and maximum frequencies are observed as the flow regime changes. (b) Large sample volume, flow rate, 0.80 1/min (Re = 3000). As the flow regime changes, the mean frequency obtained with the large sample volume shows little change as compared to that obtained with the small sample volume.
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in the flow regime, the volumetric flow changes should be small.
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formed under ideal in vitro conditions, and it remains to be shown if similar quantitative information can be obtained in vivo.
CONCLUSIONS The color-flow mapping system used in this study had a velocity accuracy corresponding to about 6% of the Nyquist velocity. Spatial resolution, which is a function of the beam profile, gain and other factors, was approximately 0.5 mm and was satisfactory for studies of flow in tubes larger than 7.5 mm diameter and even for the detection of vortices. Understanding the factors that govern the temporal resolution is complex and has not been investigated in this study. The temporal resolution proved to be adequate for the detection of transitional flow but may not be sufficient to follow the rapid changes of the flow phenomena. Some color Doppler systems provide color Mmode (so-called M-Q mode) that is indeed similar to the multigate pulsed Doppler (Reneman et al. 1986) but uses colors to display velocities. The M-Q mode yields better velocity and temporal resolutions, although it is only one dimensional. Furthermore, a narrower color Doppler window could be provided to increase the temporal resolution. The velocity-variance mode enhanced detection of flow disturbances (Tamura, Elias et al. 1987) as illustrated by the vortex shedding experiments. In clinical studies, this feature may provide a useful map of the spatial distribution of spectral broadening in poststenotic regions and be an alternative to the measurement of spectral broadening index (Johnston et al. 1986). Alternatively, it may be possible to detect turbulence by the use of the power mode (Tamura et al. 1988), which has been shown to increase under turbulent flow conditions (Bascom et al. 1988). The power mode has been applied to diagnosis in the fetal circulation. Since the system resolution is good, the video color-flow images can be digitized and further processed (Krabill et al. 1987) to obtain velocity information. Through postprocessing, velocity profiles can be displayed at any point in the flow field. Further, if color-flow maps are obtained at two different angles, a two-dimensional flow velocity vector field can be displayed (Tamura et al. 1990). In conclusion, these studies have demonstrated that color Doppler flow mapping is useful for quantitative hemodynamic studies in vitro. Furthermore, we have shown that qualitative aspects of the flow field can be enhanced by displaying the variance and through the use of an aliased image which can display streamlines and which can also be used to estimate velocity values. These experiments have been per-
Acknowledgements--The authors thank the Canadian Heart and Stroke Foundation and NSERC for financial grant support. They are grateful to Bach Vinh for helpful discussions and also to William Gibson for help in determining the color Doppler system transmission parameters.
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