The measurement of volumetric blood flow has

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1 Volumetric Blood Flow Measurement with Color Doppler Ultrasonography: The Importance of Visual Clues Mark F. Fillinger, MD, Robert A. Schwartz, MD Volumetric flow rates were obtained in an in vivo canine pulsatile flow model using color Doppler ultrasonography (CDUS) and timed collection (TC) over a range which included laminar and turbulent flow. CDUS demonstrated increasing flow disturbance as flow rates increased, with effects on velocity profile, diameter measurements, and flow symmetry. Data comparing CDUS and TC showed marked differences in laminar flow (regression: slope = 1.02;,-2 = 0.93; mean error, 11%) and nonlaminar flow (slope = 0.53;,-2 = 0.78; mean error, 26%). Assigning the angle of insonation precisely was crucial to measurement accuracy. CDUS quantitates volumetric blood flow with a reasonable degree of accuracy under laminar flow conditions. Visual dues provided by CDUS can help avoid errors associated with deviations from laminar flow. KEY WORDS: Ultrasound artifacts; Color Doppler; Flow measurement. The measurement of volumetric blood flow has a number of clinical and research applications, including the serial evaluation of atheroscle, rotic disease, angioplasty, surgical grafts, and transplanted organs. The historical standards for flow measurement have been TC and electromagnetic probe systems, but these invasive methods are not useful for clinical applications. Duplex ultrasono graphic systems are noninvasive, but they generally require cumbersome and time consuming calculations for volumetric blood flow. ABBREVIATIONS CDUS, Color Doppler ultrasonography; TC, Timed collection Received November 20, 1990, from the Dartmouth-Hitchcock Medical Center, Lebanon, New Hampshire (M.F.F.), and SUNY Health Science Center, Syracuse, New York (R.A.S.). Revised manuscript accepted for publication September 22, Address correspondence and reprint requests to Mark F. Fillinger, MD, Section of Vascular Surgery, Dartmouth-Hitchcock Medical Center, One Medical Center Drive, Lebanon, NH Acknowledgment: We would like to thank Andrew Paskanik and David Bruch, MS, for their technical assistance on this project. A previous study has explored the utility of a CDUS system that allows volume flow to be recorded in a simple manner without additional calculations. 1 Keagy and associates indicated that this system may be an accurate method of quantitating in vivo volumetric blood flow in relatively large vessels at phys iologic flow rates. In many clinical and research applications, however, conditions are encountered that may adversely affect flow quantitation. Blood flow can be disturbed by atherosclerotic lesions, vessel branches, surgical anastomoses, or abnormally high flow rates (as in arteriovenous fistulas or grafts). Because abnormal flow conditions are encountered frequently in clinical and laboratory settings,2- o this study explores the accuracy of CDUS versus the gold standard of TC over a wide range of flow conditions, including nonlaminar flow. METHODS An in vivo flow model was constructed using mongrel dogs weighing 17 to 20 kg under general anesthesia. The femoral artery and vein were left in situ by the American Institute of Ultrasound in Medicine I Ultrasound Med 3: , /$3.50

2 124 VOLUMETRIC BLOOD FLOW MEASUREMENT and cannulated distally so that at least 8 em of vessel was available for color Doppler imaging. The vessels were immediately subcutaneous in the location chosen for study, at a depth of 3 to 5 mm. If necessary, branches were ligated (not divided) several millimeters away from the study area so that the vessel could remain in situ with intact skin as an imaging window. Plasma and coagulated blood were used to avoid air spaces in adjacent areas. The cannulas were connected to a pulsatile pump, which was placed more than 35 em (i.e., over 50 vessel diameters) away from the measurement area. The pump allowed precise control of flow rates (± 1%) without appreciably altering arterial velocity and flow waveforms. The pump was placed "downstream" from the artery and "upstream" from the vein, producing venous waveforms with minor variation at low flow rates and sinusoidal waveforms similar to arteriovenous grafts at high flow rates. At each pump setting, volumetric flow rate measurements were obtained from the femoral vessels using CDUS and TC. In addition, flow rates were monitored with an in-line flow probe (Transonic Systems, Ithaca, NY) to ensure that pump flow remained stable. By allowing control of flow rates to ± 1%, this system followed the general rule that a calibration standard be 10 times as accurate as the instrument being calibrated.s CDUS imaging was performed using a Quantum QADI scanner (Siemens Quantum, Issaquah, WA) using a 7.5 MHz transducer. This equipment has several features that are useful for experimental purposes, including the capability of quantitating volumetric blood flow as an average over multiple cardiac cycles. This begins by processing signals from throughout the scanning field for amplitude, phase, and frequency so that each image pixel can be updated on a real-time format. 6 The Doppler information is converted mathematically to velocity information that can be displayed in real time or averaged over time. The diameter of the vessel is measured in real time as the distance across all the pixels in which the returning signal indicates motion. Thus the "functional" diameter is calculated instead of the gray scale diameter. Because the area of the vessel changes with pressure throughout the cardiac cycle, this method may be superior to conventional techniques, as the functional lumen diameter and velocity information are assessed simultaneously,t The diameter is used to calculate vessel area, assuming a cylindrical vessel. At the same time, velocity data from the scanning plane at the cross-section of interest is used to calculate mean velocity or "spatial average velocity." In brief, the system automatically. selects the center of flow and calculates an average velocity starting with the center pixel and working outward, layer by Jayer.t This method thereby takes the velocity profile into account when calculating net flow. The spatial average velocity and vessel diameter waveforms can be displayed simultaneously with the color flow image for direct comparison in real time. The information can also be averaged over time for use in the equation "volume flow = area X mean velocity." Another useful feature of this equipment (for experimental purposes) is that raw data can be recorded digitally on videotape, allowing data to be acquired without recording the color Doppler-derived volumetric flow ra te during data collection. The flow measurements could thus be performed in a blinded fashion at another time and location. Recorded data included the assigned angle of insonation, volumetric flow rate, vessel diameter (maximum, minimum, and mean), velocity profile, and a qualitative visual impression of the color flow image (laminar flow, disturbed flow, vessel walj motion). Volumetric flow rate data were recorded as an average value obtained from a segment of tape spanning six to ten cardiac cycles. The angle of insonation was assigned by placing an adjustable computer-generated line directly over the color flow image on the monitor. The angle was checked at both normal and four times magnification to determine the angle that provided the best visual fit (i.e., most closely parallel to vessel walls or flow streamlines). The flow rate was then obtained at the "best visual fit" angle and at angles 3 degrees higher and 3 degrees lower, using the same segment of videotape data each time. Actual flow rates as determined by timed collection varied from 0 to 900 cd min in an effort to produce a wide range of flow conditions, including laminar and nonlaminar flow. A total of 68 data points were obtained for each method in four different subjects. Statistical evaluation was performed using a microcomputer and commercial software to perform linear regression analysis of color Doppler ultrasound flow rates versus timed collection. Error was also calculated for each data point as a percentage of the actual value (percentage error). The mean percentage error was used for comparison to the "probable" error and 95% confidence limits calculated from the standard deviation of the regression data. 5 Animal care complied at all times with the "Principles of Laboratory Animal Care" and the "Guide for the Care and Use of Laboratory Animals" (NIH Publication No , revised 1985).

3 FILLINGER AND SCHWARTZ 125 A A B B Figure 2 A, CDUS image demonstrating green color "tag" and a typical velocity profile at the limit of laminar flow conditions. Flow rate = 240 cd min. The velocity profile is located at the bottom of the figure. B, CDUS image demonstrating green color "tag" and a typical velocity profile for nonlaminar flow conditions. Same vessel as in A. Flow rate = 500 cc/min. The velocity profile is located at the bottom of the figure. Figure 1 A, CDUS image demonstrating the limit of laminar flow conditions. Flow rate = 240 cc/min. B, CDUS image demonstrating nonlaminar flow conditions. Same vessel as in A. Flow rate = 500 cc/min. RESULTS Flow images and velocity profiles produced a clear distinction between laminar and nonlaminar flow (Figs. 1-3). As flow rates increase, the visual signs of flow disturbance or turbulence increase. The first sign of nonlaminar flow generally is the appearance of eddy currents and other types of asymmetrical retrograde flow, which clearly differ from the retrograde flow patterns of physiologic pulsatile flow. These patterns begin to appear at flow rates near 250 cdmin for the vessel sizes in this study, which is approximately three times the normal flow rate. Abnormal patterns are easily seen due to the portrayal of forward and retrograde flow in contrasting colors (red and blue). As flow rates increase, high velocity flow becomes abnormally distributed throughout the ves sel (Fig. lb), as demonstrated by varying color saturation (lighter shades portraying higher velocities). The equipment used for this study can portray up to 64 different saturations or shades of color at one time, with a spatial resolution of 0.2 mm, which is sufficient to distinguish high velocity jets and the random velocity patterns characteristic of disturbed or turbulent flow (Fig. lb). When more contrast is needed, discrete velocities can be tagged in green using the post+processing capabilities of the equipment (Fig. 2A,B). Tagging high or low velocities with a high contrast color facilitates the recognition of abnormal velocity distributions.

4 126 VOLUMETRIC BLOOD FLOW MEASUREMENT y L02X 11.4 r" c:.. I 200 ii: " > 'ii. ii Q c Figure 3 CDUS demonstrating fluctua tions in vessel diameter and mean flow velocity signals that are typical of severely disturbed or turbulent flow conditions. The signals are at the bottom of the figure with the diameter tracings just above the mean velocity tracings. Flow rate "' 500 cdmin. Velocity profiles generated by internal computer software also are useful in determining the nature of the flow conditions. The lower portion of Figure 2A shows a typical velocity profile near the limit of laminar conditions. Note that it is symmetrical and smooth, without retrograde vectors or evidence of aliasing. Contrast this with Figure 28, demonstrating the irregular velocity profile associated with disturbed flow. Note the retrograde flow, evidence of aliasing, and the nonzero flow velocity at the right flow delimiter. At higher flow rates the flow disturbances are severe enough to cause rapid movements or vibration of the vessel wall and perivascular tissue. These movements become more severe as flow rates increase and can be palpated as a characteristic "thrill." Interestingly, this phenomenon can be detected visually with CDUS imaging (Figs. 18, 28, 3). The moving tissue specular reflectors apparently are detected and portrayed by color. With the appearance of these vibrations, signal tracings for vessel diameter and "spatial average" flow velocity begin to demonstrate marked fluctuations as well (Fig. 3). Results for the linear regression of CDUS versus TC data are shown in Figures 4 and 5. Data were divided into laminar and nonlaminar categories by using visual signs of disturbed flow, such as eddy currents, asymmetrical velocity profiles, abnormally distributed high velocity signals, abnormal vessel motion, or perivascular vibration (Figs. 1 to 3). The point of division was chosen as 250 cdmin (corresponding to a Reynolds number of 300). Figure 4 demonstrates Timed Ca lectlan, cc/mln Figure 4 Volumetric flow rate by CDUS imaging versus TC for laminar flow conditions. The equation of the linear regression and the r value are shown. Regression P < the relative accuracy of CDUS for laminar flow conditions. Note that the slope for laminar flow is nearly unity (1.02 ± 0.09, ± SO). Mean percentage error was 11% for data in this range. This compares to a "prob able" error (number used to bracket the actual value 50% of the time) of ± 14.0 cdmin. If 95% confidence is desired, the bracketing value calculated from standard methods5 would be ±41.6 cdmin in this flow range. Data analysis was repeated for both arterial and venous-arteriovenous waveforms. No statistical Figure 5 Volumetric flow rate by CDUS imaging versus timed collection for nonlaminar flow conditions. The equa tion of the linear regression and the r value are shown. Regression P < E 400. y 0.528X r" II Q ii: " 'i > 'ii. Q, c Q 200 II II BOO Timed Collection, cclmln 10 00

5 FILLINGER AND SCHWARTZ Table 1: Effect of Error in the Assignment of lnsonation Angle Data Set Slope Optimum angle +3 degrees -3 degrees 1.02 ± ± ± 0.09 Error % 14% Data for laminar flow conditions (flow rates less than 250 cd min). Slope and,2 refer to values for the linear regression of CDUS volume flow measurements versus TC. P value for each regression was < Slope is : standard deviation. Optimum angle refers to the "best visual fit" for the assigned angle of insonation (see Methods). "+3 degrees" and " -3 degrees" refer to deviations from the optimum angle. Error refers to the percentage change caused solely by changing the angle from optimum. or graphical distinction was found between results for the different waveforms, and therefore the data were not separated on this basis. The results for laminar flow are in distinct contrast to those obtained for nonlaminar flow conditions. Although the regression line for nonlaminar flow demonstrates a strong correlation and a highly significant P value (Fig. 5), the slope of the line is 0.53 ± 0.11, indicating that relying on the measured value could result in a large measurement error. The mean error for these data was 26% when compared to TC data. If the regression line of Figure 5 were used to calibrate the equipment for turbulent flow conditions, the "probable" error would be ±68 cd min. This would lower the mean error to approximately 17%, but 95% confidence values would be ± 201 cd min. The latter values apply only if the equipment is calibrated and used in conditions closely reproducing those outlined earlier. The higher values would more likely represent the error for disturbed or turbulent flow conditions in the clinical setting. The effect of error in the assignment of insonation angle is reported in Table 1. The data were calculated using only laminar flow measurements to eliminate the variables associated with nonlaminar flow. The mean assigned angle for all data points was 69 ± 4.4 degrees (SD). As seen in Table 1, a change in angle assignment of ;t; 3 degrees at a mean angle of 69 degrees resulted in an error of 14 to 19% under laminar flow conditions. DISCUSSION The results of this study indicate that CDUS imaging quantitates volume flow with a reasonable degree of accuracy under laminar, physiologic flow conditions. In contrast, disturbed or turbulent flow conditions cause significant measurement error with this tech- 127 nique. Fortunately, color flow imaging provides vi sual clues and "warning signs," which can help the user avoid potential error. To understand potential sources of measurement error, the investigator must first understand the method used to calculate volume flow by the equation "volume flow - area x mean velocity" (see Methods). Understanding this, it should not be surprising that the CDUS imaging data presented here are relatively accurate at physiologic flow rates when flow is laminar (Fig. 4). In laminar flow the angle of insonation can be set along the parallel streamlines visualized during peak systole and the majority of the velocity vectors for the individual red blood cells will be in alignment with each other and with the vessel wall. The velocity profile generally is symmetrical (Fig. 2A), so the calculated mean velocity should be representative of the entire vessel cross section at that point. Thus, the values calculated from the equation for volumetric blood flow should have a relatively high degree of precision if flow remains laminar. Even if flow conditions remain laminar, however, the imprecise assignment of insonation angle can be a clinically relevant source of error.7 When frequency shift data are converted to velocity data, the cosine of the angle of insonation is included in the calculation using the well-known Doppler equation, V f0(2f cos f/>). When the angle of insonation q, approaches 0 degrees, small misassignments of the angle are insignificant. In contrast, when the assigned angle of insonation approaches 80 to 90 degrees, small deviations cause large errors in the velocity calculation owing to the nature of the cosine function. Because Doppler derived velocities often are acquired at angles of insonation greater than 60 degrees, small aberrations lead to clinically significant errors. Our data suggest that a 3 degree error in angle assignment will cause an error of 14 to 19 percent in volumetric flow rate measurements when the presumed angle of insonation nears 70 degrees. The expected error would be 13 to 17% on the basis of the cosine function alone. Interestingly, the automatic diameter calculation also depends on the angle of insonation. In this case, however, the value varies with the sine function (the diameter is at right angles to the flow). Thus, mathematically the expected diameter error would be 1.7 to 2.1% in the situation described. It also is noteworthy that a 3 degree angle discrepancy is barely perceptible at normal magnification. We required a four times magnified display and numerical angle readout to recognize a 3 degree angle change clearly. Because volume flow calculations with any system require visual angle assignment, the clinician and researcher should bracket flow calculations with a percentage error based on the angle of =

6 128 VOLUMETRIC BLOOD FLOW MEASUREMENT J Ultrasound Med 3 :1130, 1993 insonation at which the data are acquired (unless calibration curves are available). The physical and mathematical aspects of flow angle are even important in highly regulated measurement systems using string phantoms, as demonstrated by Goldstein.u The potential error of flow measurements becomes even more important when flow rates become unusually high and flow patterns are no longer laminar. Note that we generally have described the flow patterns seen in this study as "nonlaminar" or "disturbed" rather than "turbulent." Although often these terms are used interchangeably, technically this is not correct. Laminar flow is a state in which fluid flows in smooth streamlines and particle paths do not cross. Turbulence is a flow state in which fluid elements move in a random fashion and quantities such as pressure and velocity fluctuate randomly with respect to time and spatial coordinates (although distinct average values can be obtained). "Disturbed" flow is a transient response of laminar flow to a source of instability causing it to deviate from streamlined motion. to Reynolds demonstrated that the point at which the flow changes from laminar to turbulent is related to a dimensionless constant (Reynolds number). Fully developed turbulent flow generally is stated to occur at a Reynolds number greater than 2,000 for steady flow in a rigid, circular pipe. n Pulsatile flow in a distensible tube is inherently less stable, however, so it is not surprising that nonlaminar flow occurred at a Reynolds number of 300 in this study. Disturbed flow has been noted at Reynolds numbers as low as J We also have noted deviations from laminar flow at low Reynolds numbers in previous studies using phonoangiography and pressure measurements." H Although many of the qualities of turbulent flow were seen at higher flow rates, we found that the measurement errors described in this study did not require fully developed turbulent flow. Why does CDUS imaging become Jess accurate with deviations from laminar flow? This result is predictable when the investigator understands the basic assumptions made in the flow calculations. For instance, use of the Doppler equation to calculate velocity generally assumes that flow is laminar with streamlines parallel to the vessel wall. This assumption alone can lead to large measurement errors. 7 Even if the color image is used to align the insonation angle with the main streamline, disturbed flow can cause significant portions of the flow to deviate from the main streamline.ts In addition, aligning the angle of insonation with the main streamline will create an error in measurement of diameter in the system tested. Although the magnitude of this error would likely be much smaller owing to the angles involved (see earlier discussion), it would be squared in the area calculation. Thus, the angle of flow relative to the vessel wall and indications of flow disturbances are important visual clues provided by CDUS. Similarly, the transmitted ultrasound beam is assumed to intersect the center of the vessel, generating a representative velocity profile at the selected cross section (Fig. 2A,8). The calculation of volume flow assumes that the mean velocity over the entire vessel cross section is the same as the mean velocity for that particular velocity profile. Thus asymmetrical or nonaxial flow patterns generally will result in measurement error. Several clues may help to avoid this error: the color Doppler image itself; volume flow waveforms; the velocity profile generated at the cross section in question; and post-processed color "tags" of specific frequencies or velocities that aid in the identification of asymmetrical flow. Another source of error at high flow rates is aliasing-very high velocities causing frequency shifts that exceed the pulse repetition frequency of the imaging transducer. When this occurs the flow velocity can be underestimated by limiting the recorded frequency to the pulse repetition frequency of the transducer or by interpreting a large positive vector as a small negative vector.16 Increasing the angle of insonation can reduce aliasing,t 6 but this may increase angle assignment error, as discussed previously. It should be noted, however, that aliasing was an infrequent problem in this study, possibly because the equipment used aliases at the pulse repetition frequency, rather than at one half of the pulse repetition frequency. Another interesting phenomenon that may occur at high flow rates is the detection and processing of the kinetic energy released with extremely disturbed blood flow. This kinetic energy causes vibration of the vessel wall and adjacent soft tissue. Although the visual image resulting from this vibration (Figs. 18, 28, 3) might be interpreted as artifact, the vibration can be palpated manually. In addition, acoustic measurements with phonoangiography in our laboratory and those of others confirm the presence of abnormal spectra associated with turbulence. 17 The tissue movement apparently is the result of pressure variations within the vessel secondary to turbulence.to,t8-2o We also have confirmed this type of intraluminal pressure variation in areas where turbulence and tissue vibration are displayed by CDUS. These pressure fluctuations can set up characteristic movements of the vessel wall, including vibration.t9,2t The resultant movement of tissue specular reflectors apparently causes a frequency shift in the

7 returning ultrasound beam and is processed as a velocity vector. Because the diameter of the vessel is calculated as the distance across ail the pixels in which the returning signal indicates motion, the tissue moving immediately adjacent to the lumen may be included by the software as part of the diameter calculation. This was verified by observing the extent of recorded flow relative to the locations of flow delimiters on velocity profiles (compare Fig. 2B to 2A). The tissue reflectors move slowly relative to intraluminal blood flow, causing low velocity prograde and retrograde vectors to be added to the overall mean velocity. Thus, tissue vibration can cause underestimation of volumetric flow by adding in low velocity signals in an artifactually extended lumen. This error is limited to some extent by placing the flow delimiters just outside the vessel wall. If settings are altered to prevent these lower frequencies from being detected, low frequencies at the periphery of the vessel are likely to be missed, also resulting in error. The magnitude of the error caused solely by vibration could not be determined in the scope of this study. It is quite possible that the associated measurement error is largely due to the intraluminal flow disturbances that cause the vibration. Nonetheless, vascular and perivascular tissue vibration provides another visual clue to potential measurement error. Interestingly, many of the sources of error noted for nonlaminar flow can lead to artifactually low measurements. This may explain the results seen in Figures 4 and 5. To put the data into perspective, it should be pointed out that resting blood flow for these vessels is 75 to 100 cdmin. The information presented here is still clinically useful, however, as flow disturbances or abnormally high flow rates, or both, occur in numerous clinical situations.2-4 The more severe signs of turbulence in this study are associated with flow rates seen in arteriovenous fistulas or grafts. Vessel wall and tissue vibration can be seen in arteriovenous fistulas or immediately distal to a stenosis in a low resistance system such as the carotid or renal circulation.uo.t 7-2t Fortunately, color flow imaging provides visual "warning signs" in situations associated with measurement error. The potential for inaccurate data is clearly signaled by deviations from laminar flow, such as eddy currents, retrograde flow, asymmetrical velocity profiles, rapid vessel wall motion, or tissue vibration. When attempting to put a value on measurement error in the clinical situation, the special conditions of this study should be emphasized. The angle of insonation was examined under careful scrutiny in a magnified view. The locations used to measure flow FILLINGER AND SCHWARTZ 129 rates were not at branch points. Measurements were taken from an average over several cardiac cycles. The vessels were superficial and free of disease. Not ail of these precautions can be used for clinical measurements,22 so it is likely that this study represents a ''best case" scenario with regard to in vivo measurements. Even with these precautions, the 95% confidence limit for a measurement at the midpoint of the laminar flow range would be nearly 30% of the actual value. If measurements are made using improper Doppler angle assignment or a location with evidence of nonlaminar flow, the potential error is much larger. Lastly, it should be noted that there are several potential causes of measurement error with Doppler sonographic measurement that are beyond the scope of this study. 7,22,23 The goal of this study was to use commercially available equipment to determine the measurement error for pulsatile flow in vivo over a wide range of flow rates. By concentrating on the visual warning signs that accompany readily identifiable sources of error, this study identifies features that should be of benefit to those attempting to measure volumetric blood flow in the clinical or laboratory setting. We conclude that the color Doppler sonographic equipment used in this study measures volumetric blood flow with a reasonable degree of accuracy under physiologic, laminar flow conditions in vivo. As with other Doppler measurements, a great deal of attention should be given to the assignment of the insonation angle and to apparent deviations from laminar flow. Accuracy is affected significantly by nearly imperceptible changes in the angle of insonation, which must be considered when quantitating blood flow. Effects related to turbulence produce perceptible changes in flow images, velocity profiles, flow symmetry, vessel wall motion, and recorded lumen diameter. These effects are more pronounced at higher flow rates and appear to be responsible for the increased error noted with increasing volumetric flow. Each of these effects can be visualized with color Doppler imaging, thus providing "warning signs" of potential measurement error. If clinical decisions are to be made on the basis of serial volumetric blood flow measurements, it is crucial to know the relative error associated with these measurements and the situations in which measurements should be questioned. Reported volumetric flow rates for clinical or laboratory studies should include bracket values for estimated error, preferably determined by calibration studies performed for a similar setting.

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