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In Vitro Analysis of Regurgitant Fraction Using Doppler Power-Weighted Sum of Velocities
In Vitro Analysis of Regurgitant Fraction Using Doppler Power-Weighted Sum of Velocities Theresa A. Tacy, MD, A. Rebecca Snider, MD, and Roger P. Vermilion, MD, Pittsburgh, Pennsylvania, Monmouth Junction, New Jersey, and Ann Arbor, Michigan
The power-weighted sum of velocities (PWS) is the sum of each velocity component of the Doppler signal multiplied by its power. The purpose of this study was to determine (1) whether PWS is linearly related to volume flow and (2) whether PWS can predict the regurgitant fraction in an in vitro pulsatile flow system simulating aortic regurgitation. Doppler analysis of aortic flow was performed with an intact valve and two regurgitant valves. For each valve a linear relation between the forward flow PWS and forward flow volume was demonstrated, with excel-
Ultrasound theory suggests that the volume flow through the ultrasound beam is proportional to the power of the received Doppler signal.1-5 The power is equivalent to the amplitude of the signal squared. Current ultrasound techniques process the received Doppler signal by fast Fourier transform analysis into a spectrum of frequencies that are displayed at their corresponding velocities. The power information of the returning signal is expressed on the Doppler display through the intensity of the gray scale corresponding to each velocity. Quantification of the power information currently encoded in the gray scale of the Doppler display may provide a means of volume flow estimation.1,2,5 Calculations of volume flow from Doppler echocardiography have usually involved determination of a velocity time integral multiplied by the flow cross-sectional area. If the velocity time integral is traced along its outermost edge, which is frequently recommended in clinical studies, its application to flow volume measurements may result in overestimation. The powerweighted mean velocity (PWMV) has been proposed as From Children’s Hospital of Pittsburgh, Division of Cardiology, University of Pittsburgh Medical Center, and C. S. Mott Children’s Hospital, Department of Pediatrics, University of Michigan Medical Center. Reprint requests: Theresa A. Tacy, MD, Division of Cardiology, Children’s Hospital of Pittsburgh, 3705 Fifth Ave., Pittsburgh, PA 15213. Copyright © 1998 by the American Society of Echocardiography. 0894-7317/98 $5.00 1 0 27/1/87809
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lent correlation (r 5 0.99). For the valves with regurgitant orifices, the values for the PWS-derived regurgitant fraction were compared with measured regurgitant fraction. A fair correlation was demonstrated (r 5 0.59), with low accuracy in prediction (error 44% 6 24%). The PWS was inaccurate in predicting flow ratios in our in vitro system despite the strong relation with forward flow volume. The error incurred may be due to effects of filters that remove low velocity and low amplitude information. (J Am Soc Echocardiogr 1998;11:266-73.)
a means for more accurate flow volume determination. The PWMV is the sum of individual velocities multiplied by their respective power fractions (the power of that signal divided by the total instantaneous power). The accuracy of this method in measuring volume flow in a laminar in vitro flow system has been reported.6 Both the power-weighted and amplitude-weighted mean velocities were accurate predictors of the volume flow for the flow conditions tested. Thus the PWMV estimation of flow volume is useful in applications wherein the cross-sectional area of flow can be measured with a reasonable degree of accuracy, such as in peripheral vascular flow. In other physiologic applications, the cross-sectional area of flow may not be readily or accurately obtained. The power-weighted sum of velocities (PWS) is proposed as a means of volume flow ratio estimation that does not involve considerations of flow cross-sectional area. The PWS is the sum of each individual velocity component of the Doppler signal multiplied by its respective power, without subsequent division by total power. The signal PWS does not estimate absolute flow volumes but may be helpful in determining ratios that are clinically important, such as regurgitant fractions. If the signal power of each velocity component is proportional to the volume of blood flow traveling at that velocity, then the PWS will be proportional to the volume flow passing through the sample volume. The time integral of the PWS will then reflect the flow volume during the time interval studied. The pitfall of this approach is that the
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Figure 1 Pulsatile flow system.
magnitude of the returning Doppler signal is affected by a combination of factors including the transmit power, receiver gain, and tissue attenuation. If these factors are held constant between the sampling of both reverse and forward flows (i.e., if both flows are sampled from the same site), the PWS may yield an accurate estimation of the reverse to forward flow ratio, or regurgitant fraction. In principle, the PWS may be useful for prediction of the regurgitant fraction because PWS measurements do not rely on knowledge of flow area. This study addressed the hypothesis that PWS can be used to predict accurately regurgitant fraction in aortic regurgitation by estimating the PWS of forward and reverse flow at the same site in the proximal ascending aorta. To test this hypothesis, we chose an in vitro model that allows precise control of regurgitant flow volume, accurate measurement of regurgitant fractions, and consistent ultrasound signals to be readily obtained. This model overcomes the technical difficulties of measuring regurgitant fraction in a clinical setting and provides a robust reference standard for comparison.
METHODS Definitions For the purposes of this report, the following definitions will apply. Power-weighted and amplitude-weighted mean velocity. The PWMV is the sum of individual velocities multiplied by their respective power fractions (the power of that signal divided by the total instantaneous power). Analogously, the amplitude-weighted mean velocity (AWMV)
is the sum of the individual velocities of the Doppler signal multiplied by their respective amplitude fractions. Because the PWMV and AWMV are velocities multiplied by a dimensionless fraction, the resultant number is in velocity units. Power-weighted and amplitude-weighted sum of velocities. The PWS is the sum of each individual velocity component of the Doppler signal multiplied by its respective power, without subsequent division by total power. Similarly, the amplitude-weighted sum of velocities (AWS) is the sum of each individual velocity component of the Doppler signal multiplied by its respective amplitude. The resultant quantities therefore have units of (velocity 3 power) or (velocity 3 amplitude) for PWS and AWS, respectively. In Vitro Model Aortic regurgitation was simulated in a closed pulsatile flow system using a 27 mm Hancock valve in the aortic position. The pulse simulator consisted of the following components (Figure 1). (1) An atrial reservoir for control of left ventricular filling pressure. (2) A left ventricular pumping chamber consisting of a compressible bulb: Ventricular contraction was accomplished by compression of the bulb with an external air source. Solenoid valves under computer control opened and closed the inlet and exhaust ports of the ventricular chamber. The timing of the solenoid valves was computer-controlled such that the pulse rate and systolic time interval could be independently set. (3) An aortic flow chamber in which the Hancock tissue valve was mounted: Pressure was monitored 5 cm distal to the valve with a fluid-filled catheter connected to a pressure transducer (Abbott Critical Care Systems, Salt
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Lake City, Utah). Flow was measured 9 cm distal to the valve with an electromagnetic flowmeter and an 80 mm cannulating-type flow probe (model FM501 and model EP680, Carolina Medical Electronics, Inc., King, N.C.). (4) An ascending aorta consisting of 25.4 mm (inner diameter) semi-rigid Tygon tubing: This tube was submerged in ultrasonic gel distal to the electromagnetic flow probe to allow for ultrasound interrogation of flow. (5) An aortic compliance chamber consisting of an elastic tubing within a sealed pressure chamber. (6) A systemic resistance chamber, consisting of two narrowly spaced plates with adjustable separation. The pulse simulator was filled with a blood analogue fluid (30% glycerin by volume) prepared with water that had been degassed by boiling. The solution was prepared as a 2% (by weight) cornstarch particle suspension to provide ultrasound reflection characteristics (particle concentration was held constant within each study). The electromagnetic flow probe (EMF) was calibrated using a timed collection with automatic calculation of volume flow by the computer using the blood analogue fluid. The flow volume as measured by the EMF was found to be within 3% of actual volume within the range of flows used in this investigation. The pressure transducer and the EMF were interfaced with an IBM-compatible 386 computer through a 12-bit analog-to-digital converter using the ASYST software package (ASYST Software Technologies, Inc., Rochester, N.Y.). This system allowed simultaneous acquisition and display of the data. The pressure and flow waveforms were each sampled at 10 msec intervals, digitized, displayed in real time, and stored for subsequent analysis. In addition, the minimum, maximum, and mean values for the pressure and flow for each pulse were automatically calculated and displayed in real time. Doppler Examination Pulsed Doppler recordings of flow velocities in the ascending aorta were obtained simultaneously with EMF measurements of volumetric flow. The Doppler examinations of aortic flow were performed with a phased array ultrasound system (Acuson, Mountain View, Calif.) equipped with a 2.0 MHz, 128element transducer. The transducer was immersed in the ultrasonic gel 12 cm distal to the aortic valve and clamped in a fixed position (Figure 1). With the use of Doppler color flow mapping techniques, the transducer was positioned to image the entire diameter of the ascending aorta at a constant angle. This transducer position resulted in pulsed Doppler recordings obtained at an intercept angle of 60 degrees for all measurements. The sample gate was set at 3 cm to include the entire diameter of the tubing. The depth of the pulsed Doppler sample center was 32 mm. Doppler flow tracings for both forward and reverse flows were collected at the same site in the ascending aorta. The Doppler examinations were performed at log compression settings of 20 to 25 dB and at the lowest available
wall filter settings. Ultrasound machine settings were optimized and then held constant as each dataset was acquired. The PWS was calculated by the ultrasound system as the sum of the individual velocities of the frequency bins multiplied by the respective signal power. In terms specific to the ultrasound system used: PWS 5
(U U 128
Yn
2
Vn
n51
where Yn 5 the amplitude of the nth frequency bin (there are a total of 128 frequency bins for each unit of time analyzed) and Vn 5 the velocity corresponding to the nth frequency bin. The ultrasound machine software automatically calculated and displayed the average instantaneous PWS when a time interval on the Doppler signal output is selected with electronic calipers. To obtain a PWS time integral, the average instantaneous PWS was multiplied by the time interval of flow selected. The PWS time integral for forward and reverse flows was obtained for each beat by first individually selecting the systolic and diastolic time intervals, respectively, then multiplying the average PWS value displayed by the appropriate time interval (Figure 2). Experimental Protocol Aortic flow was evaluated with an intact valve, a valve with regurgitant orifice size 4.9 mm2, and a valve with regurgitant orifice size of 9.8 mm2. The regurgitant orifices were created by punching a circular orifice of 2.5 mm diameter into one of the valve leaflets, corresponding to a crosssectional area of 4.9 mm2. A regurgitant orifice crosssectional area of 9.8 mm2 was made by the addition of a second circular hole with a 2.5 mm diameter. The ascending aortic flow was evaluated for each valve over a range of 12 hemodynamic conditions that were obtained by varying the following parameters: the cardiac output was set at 1.0, 2.0, 4.0, and 6.0 L/min, and the mean arterial blood pressure was set at 60, 80, and 100 mm Hg. The pulse rate was held constant at 60 beats/min. This resulted in a range of regurgitant fractions between 10% and 66% for the valves with regurgitant orifices. Net forward flow in the intact valve was analyzed using the average of four beats and comparing the PWS time integral for systolic flow with the forward flow measurement by the EMF. For each regurgitant orifice size, data were collected for the same hemodynamic conditions as the intact valve. Each period of forward flow and reverse flow was analyzed separately to calculate forward-flow PWS time integral and reverse-flow PWS time integral. The PWSderived regurgitant fraction was calculated as the ratio of the reverse-flow to forward-flow PWS time integrals. For each flow condition, the average of three PWS-derived regurgitant fractions was used in subsequent analysis. Data Analysis Because PWS values alone cannot predict the flow volume (and are only useful in predicting flow ratios), the accuracy of
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Figure 2 Spectral Doppler tracing demonstrating technique used to obtain power-weighted sum of velocities for forward and reverse flow.
this method cannot be tested for forward flow alone. The correlation between PWS time integral for forward flow and the forward flow volume measured with the EMF was assessed with linear regression analysis. The correlation between PWS time integral for reverse flow and the reverse flow volume measured by the EMF was assessed with linear regression analysis to illustrate this correlation for low flow volume. The regurgitant fractions calculated from the PWS data were compared with the regurgitant fractions calculated from the forward and reverse flow volumes measured by the EMF, using linear regression analysis to assess the correlation between two methods. In addition, the agreement between actual regurgitant fraction and PWS regurgitant fraction was assessed by calculating error magnitude of the prediction. Error bias was assessed as well by comparing the absolute error magnitude of the prediction. Error bias was assessed as well by comparing the absolute error magnitude of the PWS regurgitant fraction with the net forward flow derived by the EMF.
The graph of the PWS-derived regurgitant faction versus the regurgitant fraction measured by EMF is shown in Figure 5. Linear regression analysis demonstrated a fair correlation, with an r value of 0.59. The line of regression differed significantly from the line of unity ( p , 0.001). The mean error in PWS-derived regurgitant fraction was 44% 6 24.2% (range 2.7% to 96.6%). For most cases there was underestimation of regurgitant fraction with analysis of PWS values. The error magnitude of the predicted regurgitant fraction was compared with the forward flow measured by the EMF to determine whether flow volume affects the accuracy of the PWS prediction of flow ratios. A trend of higher errors at low cardiac output is observed (Figure 6).
DISCUSSION RESULTS Figure 3 demonstrates the relation between forwardflow PWS and the EMF-measured forward flow. For each valve there is a linear relation between the PWS and the forward flow volume, with an excellent correlation (r 5 0.98 for each valve). The correlation between EMF-measured flow and PWS flow for reverse diastolic flow volume (0.0 to 1.5 L/min) is illustrated in Figure 4. There is a fair correlation observed (r 5 0.69); however, wide variability in the data is observed when the flow volume is low.
This study was performed to evaluate whether PWS can be used to predict accurately regurgitant fraction in aortic regurgitation. To address this hypothesis, we first evaluated the relation between EMF-measured forward flow and the PWS time integral for forward flow. To assess the reliability of this method for conditions of mild to moderate aortic regurgitation, the relation between PWS and flow for low flow values was also assessed by comparing the regurgitant flow volume measured by the EMF with the PWS for regurgitant flow. The accuracy of PWS prediction of regurgitant fraction was then investigated. With the
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Figure 3 Relation between the Doppler-derived power-weighted sum of velocities (PWS) and the forward flow measured by the electromagnetic flow probe for each valve. For each valve, the machine settings and particle concentration were held constant. An excellent correlation is shown for each valve. However, the slopes between the three valves are different because of changes in these conditions between valves. This illustrates the fact that the relation between PWS and flow is variable and that comparisons between flow can only be made when factors affecting signal power are held constant.
Figure 4 Relation between the Doppler-derived power-weighted sum of velocities (PWS) and flow measured by the electromagnetic flow probe for very low flow volumes during valve regurgitation.
use of an in vitro model of the left heart with varying degrees of aortic regurgitation, an excellent correlation between forward flow and the Doppler-derived PWS was demonstrated (Figure 3). For very low flow conditions (i.e., between 0 and 1.5 L/min), this correlation weakened. (Figure 4). When PWS-derived regurgitant fraction was compared with the regurgitant fraction for the same cycle measured by EMF, a fair correlation was found, with an r value of 0.59 (Figure 5). However, there was a high magnitude of the error of the predicted PWS (44% 6 24%). The reasons for this inaccurate prediction of regurgi-
tant fraction may be found in the relation between Doppler-derived PWS estimation of forward flow and forward flow measured by EMF (Figure 3). The line of regression for each valve did not pass through the origin, suggesting that either the relation between flow measured by the EMF and PWS forward flow values is nonlinear at low flow volume or there is a consistent underestimation of flow by PWS, resulting in a negative y-intercept. A potential explanation for this finding may be loss of low amplitude signals incurred by eliminating background noise or loss of low velocity information caused by wall filters.7,8 Wall
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Figure 5 Relation between power-weighted sum of velocities (PWS)-derived regurgitant fraction and the regurgitant fraction measured by the electromagnetic flow probe (EMF).
Figure 6 Relation between percent error of power-weighted sum of velocities (PWS)-predicted regurgitant fraction and flow volume.
filters eliminate the very high amplitude, low velocity signals originating from movement of cardiac structures (such as the ventricular walls); however, filtering of these signals also results in a loss of low velocity information. This loss of low velocity information may result in an error of relatively fixed and equal magnitude for both forward and reverse flow calculations with the use of the PWS. Because the regurgitant flow in our study was characterized by low velocity signals (because it was measured above the aortic valve), the impact of the wall filter on the regurgitant flow signal
would be greater than the impact of the wall filter on the forward-flow Doppler signal. This may explain the lower correlation between EMF and PWS measurements for low flow volume (Figure 4). Because of the impact of the wall filter on the low velocity Doppler signals, the measurement of the regurgitant fraction will be significantly altered when the Doppler PWS is used. Furthermore, when the net flow volume is low, a significant proportion of the signal from both forward and reverse flow may be filtered. This may explain the trend of higher error magnitude at lower flow volumes observed in this study (Figure 5).
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Previous Studies Several clinical studies have investigated the utility of assessing the amplitude of the backscattered signal as a means of determining volume flow ratios.9-12 Each of these studies reports a satisfactory correlation between AWS-derived flow ratios and those determined by a variety of standard techniques. These results contrast markedly with the results of this investigation. How did these clinical studies with less reliable reference standards yield such good results when the present study resulted in inaccurate prediction of flow ratios? Review of these clinical investigations is warranted to answer this question. Specifically: (1) how were the Doppler signal power data analyzed and (2) what different methods were used in data collection? Doppler signal power data analysis. Previous clinical studies have used signal amplitude instead of power in the assessment of flow ratios.9-12 The use of received signal amplitude instead of power is based on the assumption that in a system of interacting scatterers, the amplitude of the Doppler signal, not the power, is proportional to volume flow.9-11 This assumption is not supported by the literature. Investigations have examined the properties of the backscattering coefficient under laminar and turbulent flow conditions for a range of blood hematocrits to determine the effects of flow state and of particle interaction on the backscattered Doppler signal.13-18 These studies determined that the backscatter coefficient remains constant over a range of flows in a laminar system for all hematocrits tested and is not constant in a system of turbulent flow.14 Thus in a fluid of interacting particles in laminar flow conditions, any changes in the backscattered power of the received Doppler signal should be a result of changes in flow volume and not artifactual increases in the backscattered coefficient. In turbulent flow, this relation between flow volume and backscattered power is not present. Review of the algorithm used in these clinical investigations indicates that an amplitude-weighted sum was performed and was plotted as a line superimposed on the Doppler spectral output.9-12 The signal gain was then lowered until the line representing the amplitude-weighted sum of velocities approximated the Doppler peak flow velocity. By performing this adjustment, these investigators scaled the result to produce a result with a magnitude proportional to the peak velocity and lost the unique information in the signal intensity that has a magnitude proportional to volume flow. We propose that these adjustments result in an approximation of a velocity time integral, which has previously been shown to yield approximate flow ratios for shunt lesions. In addition, if the gain adjustment was inconsistent (because the different transducer windows would pro-
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duce different effects from tissue attenuation on overall signal gain), it is difficult to know how the signal intensities compare after these adjustments. Data collection techniques. In clinical investigations assessing backscattered signal intensity, continuous wave (CW) Doppler echocardiography has been applied to intracardiac flow.9-12,19 However, the CW Doppler samples flow along the entire length of the Doppler beam and is not specific to interrogation of flow across a valve annulus. CW Doppler was used in the published theoretical literature on backscattered signal power. These idealized in vitro studies were able to overcome the limitations of CW Doppler by interrogating flow through tubes at an angle.1,2,13-16 In this manner, the CW beam insonated the cross-sectional area of flow at one site in the tube only. However, when CW Doppler is applied to intracardiac flow to assess flow volume from signal power analysis, the lack of range resolution is theoretically a significant limitation.20 For example, if the CW Doppler beam is placed in the mitral annulus from the apical window to evaluate mitral inflow, one would be gathering information about pulmonary venous inflow as well as flow within the left ventricle during diastole. Not only is flow sampled at multiple sites simultaneously, but the same volume of blood will be insonated more than once, depending on how long the sample remains within the Doppler beam. The essential properties of backscattered signal intensity should be equally applicable to pulsed Doppler ultrasound, which can be thought of simply as a sampled version of the CW signal from a selected region of blood.1 For the reasons stated above, the pulsed wave Doppler should provide a more accurate estimation of volume flow ratios with PWS than CW Doppler because its interrogation is site-specific.1 For these reasons, we elected to use pulsed wave Doppler. Flow ranges. In each of the clinical studies in the literature, the regurgitant fraction was calculated from aortic and pulmonary Doppler tracings with a subtraction method.9-12,19 Because the flow was interrogated at two sites with relatively high velocities without interrogation of any low velocity flow, the effect of the wall filter was minimized. In the present study, low velocity signals represented by the reverse diastolic flow in the ascending aorta were sampled. Our results indicate that the PWS correlation with flow is less reliable in the setting of low flow and low velocity. Potential Sources of Error Incomplete flow profile insonation. Ultrasound transducers typically used in clinical applications transmit a relatively narrow beam width in comparison to the cross-sectional area of flow under evaluation
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when intracardiac flow is being assessed. If the flow profile is flat, the flow ratio calculated from a portion of flow should be representative of the flow ratio across the entire cross-sectional area of flow. In complex flow profiles, a significant amount of error in the Doppler frequency profile and power spectrum will be incurred by this nonuniform insonation of flow.8 If unknown or complex flow profiles are to be evaluated by the PWS method, complete and uniform insonation by the Doppler beam probably would be necessary.1,7,8,20 In this study, the entire diameter of the flow profile was sampled but the total cross-sectional area of flow was not. If the flow profile is axisymmetric, this insonation would have been an adequate and representative sample for flow ratio determination. However, the PWS method did not provide an accurate estimation of flow ratios using the in vitro system with rigorous reference standards. This error may be due in part to a nonaxisymmetric flow profile. This speculation is supported by an investigation that demonstrated that the forward flow velocity distribution in the aorta is slightly skewed, with the highest velocities toward the septum in normal subjects.21 Measurement site. The Doppler measurements were performed 12 cm above the aortic valve and 3 cm distal to the EMF. These rather distal measurement sites were believed to be within reason because the tubing between the aortic valve and measurement sites was rigid. Thus any changes occurring at or above the valve were assumed to be reflected at the site of measurement. If any significant compliance were present in the system between the regurgitant valve and the ultrasound transducer, error may have resulted.
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Conclusions In summary, the Doppler PWS is proportional to volume flow. The regurgitant fraction was not accurately predicted from the ratio of forward to reverse PWS in our in vitro system. We hypothesize that the source of this error lies in the loss of low velocity and low amplitude information caused by filters. We conclude that further experiments assessing the impact of filter settings and Doppler beam geometry are indicated. Studies investigating PWS assessment of regurgitant fraction in the clinical setting9-12 should be interpreted with caution because the results reported cannot be extrapolated with confidence to other patient populations.
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REFERENCES 1. Brody WR. Theoretical analysis of the ultrasonic blood flowmeter. Stanford Electronic Laboratories. Palo Alto: Stanford University, 1971. 2. Brody W, Meindl J. Theoretical analysis of the CW Doppler
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ultrasound flowmeter. IEEE Trans Biomed Eng 1974;21: 183-92. Reid J, Sigelman R, Nasser M, Baker D. The scattering of ultrasound by human blood. Proc. 8th International Conference Medical and Biological Engineering; 1969; Chicago, Ill. Sigelman R, Reid J. Analysis and measurement of ultrasound backscattering from an ensemble of scatterers excited by sinewave bursts. J Acoust Soc Am 1973;53:1351. Flax S, Webster J, Updike J. Theoretical and experimental evaluation of Doppler blood flow. Proc. 8th International Conference Medical and Biological Engineering; 1969; Chicago, Ill. Minich L, Snider A, Meliones J, Yanock C. In vitro evaluation of volumetric flow from Doppler power-weighted and amplitude-weighted mean velocities. J Am Soc Echocardiogr 1993; 6:227-36. Wells P, Skidmore R. Doppler developments in the last quinquennium. Ultrasound Med Biol 1985;11:613-23. Bascom P, Cobbold R. Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum: a theoretical study. Ultrasound Med Biol 1990;16:279-95. Hoppeler H, Jenni R, Ritter M, Krayenbuhl H. Quantification of aortic regurgitation with amplitude-weighted mean flow velocity from continuous wave Doppler spectra. J Am Coll Cardiol 1990;15:1305-9. Jenni R, Ritter M, Vieli A, et al. Determination of the ratio of pulmonary blood flow to systemic blood flow by derivation of amplitude-weighted mean velocity from continuous wave Doppler spectra. Br Heart J 1989;61:167-71. Jenni R, Ritter M, Eberli F, Grimm J, Krayenbuhl H. Quantification of mitral regurgitation with amplitude-weighted mean velocity from continuous wave Doppler spectra. Circulation 1989;79:1294-9. Enriquez-Sarano M, Kaneshige A, Tajik A, Bailey K, Seward J. Amplitude-weighted mean velocity: clinical utilization for quantification of mitral regurgitation. J Am Coll Cardiol 1993;22:1684-90. Shung K, Sigelman R, Reid J. Scattering of ultrasound by blood. IEEE Trans Biomed Eng 1976;23:460-7. Shung K, Yuan Y, Fei D, Tarbell J. Effect of flow disturbance on ultrasonic backscatter from blood. J Acoust Soc Am 1984; 75:1265-72. Mo L, Cobbold R. A unified approach to modeling the backscattered Doppler ultrasound from blood. IEEE Trans Biomed Eng 1992;39:450-61. Shung K, Cloutier G, Lim C. The effects of hematocrit, shear rate and turbulence on the ultrasonic Doppler spectrum from blood. IEEE Trans Biomed Eng 1992;39:462-9. Angelsen B. A theoretical study of the scattering of ultrasound from blood. IEEE Trans Biomed Eng 1980;27:61-7. Mo L, Cobbold R. Theoretical models of ultrasonic scattering in blood. In: Shung K, Thieme G, eds. Ultrasonic Scattering in Biological Tissues. Boca Raton: CRC Press, 1993:125-67. MacIsaac A, McDonald I, Kirsner R, Graham S, Gill R. Quantification of mitral regurgitation by integrated Doppler backscatter power. J Am Coll Cardiol 1994;24:690-5. Tacy T, Cape E. Use of backscattered Doppler signal intensity in estimation of volume flow ratios [letter]. J Am Coll Cardiol 1995;25:1474-5. Rossvoll O, Samstad S, Torp H, et al. The velocity distribution in the aortic annulus in normal subjects: a quantitative analysis of two-dimensional Doppler flow maps. J Am Soc Echocardiogr 1991;4:367-78.
The power-weighted sum of velocities (PWS) is the sum of each velocity component of the Doppler signal multiplied by its power. The purpose of this study was to determine (1) whether PWS is linearly related to volume flow and (2) whether PWS can predict the regurgitant fraction in an in vitro pulsatile flow system simulating aortic regurgitation. Doppler analysis of aortic flow was performed with an intact valve and two regurgitant valves. For each valve a linear relation between the forward flow PWS and forward flow volume was demonstrated, with excel-
Ultrasound theory suggests that the volume flow through the ultrasound beam is proportional to the power of the received Doppler signal.1-5 The power is equivalent to the amplitude of the signal squared. Current ultrasound techniques process the received Doppler signal by fast Fourier transform analysis into a spectrum of frequencies that are displayed at their corresponding velocities. The power information of the returning signal is expressed on the Doppler display through the intensity of the gray scale corresponding to each velocity. Quantification of the power information currently encoded in the gray scale of the Doppler display may provide a means of volume flow estimation.1,2,5 Calculations of volume flow from Doppler echocardiography have usually involved determination of a velocity time integral multiplied by the flow cross-sectional area. If the velocity time integral is traced along its outermost edge, which is frequently recommended in clinical studies, its application to flow volume measurements may result in overestimation. The powerweighted mean velocity (PWMV) has been proposed as From Children’s Hospital of Pittsburgh, Division of Cardiology, University of Pittsburgh Medical Center, and C. S. Mott Children’s Hospital, Department of Pediatrics, University of Michigan Medical Center. Reprint requests: Theresa A. Tacy, MD, Division of Cardiology, Children’s Hospital of Pittsburgh, 3705 Fifth Ave., Pittsburgh, PA 15213. Copyright © 1998 by the American Society of Echocardiography. 0894-7317/98 $5.00 1 0 27/1/87809
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lent correlation (r 5 0.99). For the valves with regurgitant orifices, the values for the PWS-derived regurgitant fraction were compared with measured regurgitant fraction. A fair correlation was demonstrated (r 5 0.59), with low accuracy in prediction (error 44% 6 24%). The PWS was inaccurate in predicting flow ratios in our in vitro system despite the strong relation with forward flow volume. The error incurred may be due to effects of filters that remove low velocity and low amplitude information. (J Am Soc Echocardiogr 1998;11:266-73.)
a means for more accurate flow volume determination. The PWMV is the sum of individual velocities multiplied by their respective power fractions (the power of that signal divided by the total instantaneous power). The accuracy of this method in measuring volume flow in a laminar in vitro flow system has been reported.6 Both the power-weighted and amplitude-weighted mean velocities were accurate predictors of the volume flow for the flow conditions tested. Thus the PWMV estimation of flow volume is useful in applications wherein the cross-sectional area of flow can be measured with a reasonable degree of accuracy, such as in peripheral vascular flow. In other physiologic applications, the cross-sectional area of flow may not be readily or accurately obtained. The power-weighted sum of velocities (PWS) is proposed as a means of volume flow ratio estimation that does not involve considerations of flow cross-sectional area. The PWS is the sum of each individual velocity component of the Doppler signal multiplied by its respective power, without subsequent division by total power. The signal PWS does not estimate absolute flow volumes but may be helpful in determining ratios that are clinically important, such as regurgitant fractions. If the signal power of each velocity component is proportional to the volume of blood flow traveling at that velocity, then the PWS will be proportional to the volume flow passing through the sample volume. The time integral of the PWS will then reflect the flow volume during the time interval studied. The pitfall of this approach is that the
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Figure 1 Pulsatile flow system.
magnitude of the returning Doppler signal is affected by a combination of factors including the transmit power, receiver gain, and tissue attenuation. If these factors are held constant between the sampling of both reverse and forward flows (i.e., if both flows are sampled from the same site), the PWS may yield an accurate estimation of the reverse to forward flow ratio, or regurgitant fraction. In principle, the PWS may be useful for prediction of the regurgitant fraction because PWS measurements do not rely on knowledge of flow area. This study addressed the hypothesis that PWS can be used to predict accurately regurgitant fraction in aortic regurgitation by estimating the PWS of forward and reverse flow at the same site in the proximal ascending aorta. To test this hypothesis, we chose an in vitro model that allows precise control of regurgitant flow volume, accurate measurement of regurgitant fractions, and consistent ultrasound signals to be readily obtained. This model overcomes the technical difficulties of measuring regurgitant fraction in a clinical setting and provides a robust reference standard for comparison.
METHODS Definitions For the purposes of this report, the following definitions will apply. Power-weighted and amplitude-weighted mean velocity. The PWMV is the sum of individual velocities multiplied by their respective power fractions (the power of that signal divided by the total instantaneous power). Analogously, the amplitude-weighted mean velocity (AWMV)
is the sum of the individual velocities of the Doppler signal multiplied by their respective amplitude fractions. Because the PWMV and AWMV are velocities multiplied by a dimensionless fraction, the resultant number is in velocity units. Power-weighted and amplitude-weighted sum of velocities. The PWS is the sum of each individual velocity component of the Doppler signal multiplied by its respective power, without subsequent division by total power. Similarly, the amplitude-weighted sum of velocities (AWS) is the sum of each individual velocity component of the Doppler signal multiplied by its respective amplitude. The resultant quantities therefore have units of (velocity 3 power) or (velocity 3 amplitude) for PWS and AWS, respectively. In Vitro Model Aortic regurgitation was simulated in a closed pulsatile flow system using a 27 mm Hancock valve in the aortic position. The pulse simulator consisted of the following components (Figure 1). (1) An atrial reservoir for control of left ventricular filling pressure. (2) A left ventricular pumping chamber consisting of a compressible bulb: Ventricular contraction was accomplished by compression of the bulb with an external air source. Solenoid valves under computer control opened and closed the inlet and exhaust ports of the ventricular chamber. The timing of the solenoid valves was computer-controlled such that the pulse rate and systolic time interval could be independently set. (3) An aortic flow chamber in which the Hancock tissue valve was mounted: Pressure was monitored 5 cm distal to the valve with a fluid-filled catheter connected to a pressure transducer (Abbott Critical Care Systems, Salt
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Lake City, Utah). Flow was measured 9 cm distal to the valve with an electromagnetic flowmeter and an 80 mm cannulating-type flow probe (model FM501 and model EP680, Carolina Medical Electronics, Inc., King, N.C.). (4) An ascending aorta consisting of 25.4 mm (inner diameter) semi-rigid Tygon tubing: This tube was submerged in ultrasonic gel distal to the electromagnetic flow probe to allow for ultrasound interrogation of flow. (5) An aortic compliance chamber consisting of an elastic tubing within a sealed pressure chamber. (6) A systemic resistance chamber, consisting of two narrowly spaced plates with adjustable separation. The pulse simulator was filled with a blood analogue fluid (30% glycerin by volume) prepared with water that had been degassed by boiling. The solution was prepared as a 2% (by weight) cornstarch particle suspension to provide ultrasound reflection characteristics (particle concentration was held constant within each study). The electromagnetic flow probe (EMF) was calibrated using a timed collection with automatic calculation of volume flow by the computer using the blood analogue fluid. The flow volume as measured by the EMF was found to be within 3% of actual volume within the range of flows used in this investigation. The pressure transducer and the EMF were interfaced with an IBM-compatible 386 computer through a 12-bit analog-to-digital converter using the ASYST software package (ASYST Software Technologies, Inc., Rochester, N.Y.). This system allowed simultaneous acquisition and display of the data. The pressure and flow waveforms were each sampled at 10 msec intervals, digitized, displayed in real time, and stored for subsequent analysis. In addition, the minimum, maximum, and mean values for the pressure and flow for each pulse were automatically calculated and displayed in real time. Doppler Examination Pulsed Doppler recordings of flow velocities in the ascending aorta were obtained simultaneously with EMF measurements of volumetric flow. The Doppler examinations of aortic flow were performed with a phased array ultrasound system (Acuson, Mountain View, Calif.) equipped with a 2.0 MHz, 128element transducer. The transducer was immersed in the ultrasonic gel 12 cm distal to the aortic valve and clamped in a fixed position (Figure 1). With the use of Doppler color flow mapping techniques, the transducer was positioned to image the entire diameter of the ascending aorta at a constant angle. This transducer position resulted in pulsed Doppler recordings obtained at an intercept angle of 60 degrees for all measurements. The sample gate was set at 3 cm to include the entire diameter of the tubing. The depth of the pulsed Doppler sample center was 32 mm. Doppler flow tracings for both forward and reverse flows were collected at the same site in the ascending aorta. The Doppler examinations were performed at log compression settings of 20 to 25 dB and at the lowest available
wall filter settings. Ultrasound machine settings were optimized and then held constant as each dataset was acquired. The PWS was calculated by the ultrasound system as the sum of the individual velocities of the frequency bins multiplied by the respective signal power. In terms specific to the ultrasound system used: PWS 5
(U U 128
Yn
2
Vn
n51
where Yn 5 the amplitude of the nth frequency bin (there are a total of 128 frequency bins for each unit of time analyzed) and Vn 5 the velocity corresponding to the nth frequency bin. The ultrasound machine software automatically calculated and displayed the average instantaneous PWS when a time interval on the Doppler signal output is selected with electronic calipers. To obtain a PWS time integral, the average instantaneous PWS was multiplied by the time interval of flow selected. The PWS time integral for forward and reverse flows was obtained for each beat by first individually selecting the systolic and diastolic time intervals, respectively, then multiplying the average PWS value displayed by the appropriate time interval (Figure 2). Experimental Protocol Aortic flow was evaluated with an intact valve, a valve with regurgitant orifice size 4.9 mm2, and a valve with regurgitant orifice size of 9.8 mm2. The regurgitant orifices were created by punching a circular orifice of 2.5 mm diameter into one of the valve leaflets, corresponding to a crosssectional area of 4.9 mm2. A regurgitant orifice crosssectional area of 9.8 mm2 was made by the addition of a second circular hole with a 2.5 mm diameter. The ascending aortic flow was evaluated for each valve over a range of 12 hemodynamic conditions that were obtained by varying the following parameters: the cardiac output was set at 1.0, 2.0, 4.0, and 6.0 L/min, and the mean arterial blood pressure was set at 60, 80, and 100 mm Hg. The pulse rate was held constant at 60 beats/min. This resulted in a range of regurgitant fractions between 10% and 66% for the valves with regurgitant orifices. Net forward flow in the intact valve was analyzed using the average of four beats and comparing the PWS time integral for systolic flow with the forward flow measurement by the EMF. For each regurgitant orifice size, data were collected for the same hemodynamic conditions as the intact valve. Each period of forward flow and reverse flow was analyzed separately to calculate forward-flow PWS time integral and reverse-flow PWS time integral. The PWSderived regurgitant fraction was calculated as the ratio of the reverse-flow to forward-flow PWS time integrals. For each flow condition, the average of three PWS-derived regurgitant fractions was used in subsequent analysis. Data Analysis Because PWS values alone cannot predict the flow volume (and are only useful in predicting flow ratios), the accuracy of
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Figure 2 Spectral Doppler tracing demonstrating technique used to obtain power-weighted sum of velocities for forward and reverse flow.
this method cannot be tested for forward flow alone. The correlation between PWS time integral for forward flow and the forward flow volume measured with the EMF was assessed with linear regression analysis. The correlation between PWS time integral for reverse flow and the reverse flow volume measured by the EMF was assessed with linear regression analysis to illustrate this correlation for low flow volume. The regurgitant fractions calculated from the PWS data were compared with the regurgitant fractions calculated from the forward and reverse flow volumes measured by the EMF, using linear regression analysis to assess the correlation between two methods. In addition, the agreement between actual regurgitant fraction and PWS regurgitant fraction was assessed by calculating error magnitude of the prediction. Error bias was assessed as well by comparing the absolute error magnitude of the prediction. Error bias was assessed as well by comparing the absolute error magnitude of the PWS regurgitant fraction with the net forward flow derived by the EMF.
The graph of the PWS-derived regurgitant faction versus the regurgitant fraction measured by EMF is shown in Figure 5. Linear regression analysis demonstrated a fair correlation, with an r value of 0.59. The line of regression differed significantly from the line of unity ( p , 0.001). The mean error in PWS-derived regurgitant fraction was 44% 6 24.2% (range 2.7% to 96.6%). For most cases there was underestimation of regurgitant fraction with analysis of PWS values. The error magnitude of the predicted regurgitant fraction was compared with the forward flow measured by the EMF to determine whether flow volume affects the accuracy of the PWS prediction of flow ratios. A trend of higher errors at low cardiac output is observed (Figure 6).
DISCUSSION RESULTS Figure 3 demonstrates the relation between forwardflow PWS and the EMF-measured forward flow. For each valve there is a linear relation between the PWS and the forward flow volume, with an excellent correlation (r 5 0.98 for each valve). The correlation between EMF-measured flow and PWS flow for reverse diastolic flow volume (0.0 to 1.5 L/min) is illustrated in Figure 4. There is a fair correlation observed (r 5 0.69); however, wide variability in the data is observed when the flow volume is low.
This study was performed to evaluate whether PWS can be used to predict accurately regurgitant fraction in aortic regurgitation. To address this hypothesis, we first evaluated the relation between EMF-measured forward flow and the PWS time integral for forward flow. To assess the reliability of this method for conditions of mild to moderate aortic regurgitation, the relation between PWS and flow for low flow values was also assessed by comparing the regurgitant flow volume measured by the EMF with the PWS for regurgitant flow. The accuracy of PWS prediction of regurgitant fraction was then investigated. With the
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Figure 3 Relation between the Doppler-derived power-weighted sum of velocities (PWS) and the forward flow measured by the electromagnetic flow probe for each valve. For each valve, the machine settings and particle concentration were held constant. An excellent correlation is shown for each valve. However, the slopes between the three valves are different because of changes in these conditions between valves. This illustrates the fact that the relation between PWS and flow is variable and that comparisons between flow can only be made when factors affecting signal power are held constant.
Figure 4 Relation between the Doppler-derived power-weighted sum of velocities (PWS) and flow measured by the electromagnetic flow probe for very low flow volumes during valve regurgitation.
use of an in vitro model of the left heart with varying degrees of aortic regurgitation, an excellent correlation between forward flow and the Doppler-derived PWS was demonstrated (Figure 3). For very low flow conditions (i.e., between 0 and 1.5 L/min), this correlation weakened. (Figure 4). When PWS-derived regurgitant fraction was compared with the regurgitant fraction for the same cycle measured by EMF, a fair correlation was found, with an r value of 0.59 (Figure 5). However, there was a high magnitude of the error of the predicted PWS (44% 6 24%). The reasons for this inaccurate prediction of regurgi-
tant fraction may be found in the relation between Doppler-derived PWS estimation of forward flow and forward flow measured by EMF (Figure 3). The line of regression for each valve did not pass through the origin, suggesting that either the relation between flow measured by the EMF and PWS forward flow values is nonlinear at low flow volume or there is a consistent underestimation of flow by PWS, resulting in a negative y-intercept. A potential explanation for this finding may be loss of low amplitude signals incurred by eliminating background noise or loss of low velocity information caused by wall filters.7,8 Wall
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Figure 5 Relation between power-weighted sum of velocities (PWS)-derived regurgitant fraction and the regurgitant fraction measured by the electromagnetic flow probe (EMF).
Figure 6 Relation between percent error of power-weighted sum of velocities (PWS)-predicted regurgitant fraction and flow volume.
filters eliminate the very high amplitude, low velocity signals originating from movement of cardiac structures (such as the ventricular walls); however, filtering of these signals also results in a loss of low velocity information. This loss of low velocity information may result in an error of relatively fixed and equal magnitude for both forward and reverse flow calculations with the use of the PWS. Because the regurgitant flow in our study was characterized by low velocity signals (because it was measured above the aortic valve), the impact of the wall filter on the regurgitant flow signal
would be greater than the impact of the wall filter on the forward-flow Doppler signal. This may explain the lower correlation between EMF and PWS measurements for low flow volume (Figure 4). Because of the impact of the wall filter on the low velocity Doppler signals, the measurement of the regurgitant fraction will be significantly altered when the Doppler PWS is used. Furthermore, when the net flow volume is low, a significant proportion of the signal from both forward and reverse flow may be filtered. This may explain the trend of higher error magnitude at lower flow volumes observed in this study (Figure 5).
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Previous Studies Several clinical studies have investigated the utility of assessing the amplitude of the backscattered signal as a means of determining volume flow ratios.9-12 Each of these studies reports a satisfactory correlation between AWS-derived flow ratios and those determined by a variety of standard techniques. These results contrast markedly with the results of this investigation. How did these clinical studies with less reliable reference standards yield such good results when the present study resulted in inaccurate prediction of flow ratios? Review of these clinical investigations is warranted to answer this question. Specifically: (1) how were the Doppler signal power data analyzed and (2) what different methods were used in data collection? Doppler signal power data analysis. Previous clinical studies have used signal amplitude instead of power in the assessment of flow ratios.9-12 The use of received signal amplitude instead of power is based on the assumption that in a system of interacting scatterers, the amplitude of the Doppler signal, not the power, is proportional to volume flow.9-11 This assumption is not supported by the literature. Investigations have examined the properties of the backscattering coefficient under laminar and turbulent flow conditions for a range of blood hematocrits to determine the effects of flow state and of particle interaction on the backscattered Doppler signal.13-18 These studies determined that the backscatter coefficient remains constant over a range of flows in a laminar system for all hematocrits tested and is not constant in a system of turbulent flow.14 Thus in a fluid of interacting particles in laminar flow conditions, any changes in the backscattered power of the received Doppler signal should be a result of changes in flow volume and not artifactual increases in the backscattered coefficient. In turbulent flow, this relation between flow volume and backscattered power is not present. Review of the algorithm used in these clinical investigations indicates that an amplitude-weighted sum was performed and was plotted as a line superimposed on the Doppler spectral output.9-12 The signal gain was then lowered until the line representing the amplitude-weighted sum of velocities approximated the Doppler peak flow velocity. By performing this adjustment, these investigators scaled the result to produce a result with a magnitude proportional to the peak velocity and lost the unique information in the signal intensity that has a magnitude proportional to volume flow. We propose that these adjustments result in an approximation of a velocity time integral, which has previously been shown to yield approximate flow ratios for shunt lesions. In addition, if the gain adjustment was inconsistent (because the different transducer windows would pro-
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duce different effects from tissue attenuation on overall signal gain), it is difficult to know how the signal intensities compare after these adjustments. Data collection techniques. In clinical investigations assessing backscattered signal intensity, continuous wave (CW) Doppler echocardiography has been applied to intracardiac flow.9-12,19 However, the CW Doppler samples flow along the entire length of the Doppler beam and is not specific to interrogation of flow across a valve annulus. CW Doppler was used in the published theoretical literature on backscattered signal power. These idealized in vitro studies were able to overcome the limitations of CW Doppler by interrogating flow through tubes at an angle.1,2,13-16 In this manner, the CW beam insonated the cross-sectional area of flow at one site in the tube only. However, when CW Doppler is applied to intracardiac flow to assess flow volume from signal power analysis, the lack of range resolution is theoretically a significant limitation.20 For example, if the CW Doppler beam is placed in the mitral annulus from the apical window to evaluate mitral inflow, one would be gathering information about pulmonary venous inflow as well as flow within the left ventricle during diastole. Not only is flow sampled at multiple sites simultaneously, but the same volume of blood will be insonated more than once, depending on how long the sample remains within the Doppler beam. The essential properties of backscattered signal intensity should be equally applicable to pulsed Doppler ultrasound, which can be thought of simply as a sampled version of the CW signal from a selected region of blood.1 For the reasons stated above, the pulsed wave Doppler should provide a more accurate estimation of volume flow ratios with PWS than CW Doppler because its interrogation is site-specific.1 For these reasons, we elected to use pulsed wave Doppler. Flow ranges. In each of the clinical studies in the literature, the regurgitant fraction was calculated from aortic and pulmonary Doppler tracings with a subtraction method.9-12,19 Because the flow was interrogated at two sites with relatively high velocities without interrogation of any low velocity flow, the effect of the wall filter was minimized. In the present study, low velocity signals represented by the reverse diastolic flow in the ascending aorta were sampled. Our results indicate that the PWS correlation with flow is less reliable in the setting of low flow and low velocity. Potential Sources of Error Incomplete flow profile insonation. Ultrasound transducers typically used in clinical applications transmit a relatively narrow beam width in comparison to the cross-sectional area of flow under evaluation
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when intracardiac flow is being assessed. If the flow profile is flat, the flow ratio calculated from a portion of flow should be representative of the flow ratio across the entire cross-sectional area of flow. In complex flow profiles, a significant amount of error in the Doppler frequency profile and power spectrum will be incurred by this nonuniform insonation of flow.8 If unknown or complex flow profiles are to be evaluated by the PWS method, complete and uniform insonation by the Doppler beam probably would be necessary.1,7,8,20 In this study, the entire diameter of the flow profile was sampled but the total cross-sectional area of flow was not. If the flow profile is axisymmetric, this insonation would have been an adequate and representative sample for flow ratio determination. However, the PWS method did not provide an accurate estimation of flow ratios using the in vitro system with rigorous reference standards. This error may be due in part to a nonaxisymmetric flow profile. This speculation is supported by an investigation that demonstrated that the forward flow velocity distribution in the aorta is slightly skewed, with the highest velocities toward the septum in normal subjects.21 Measurement site. The Doppler measurements were performed 12 cm above the aortic valve and 3 cm distal to the EMF. These rather distal measurement sites were believed to be within reason because the tubing between the aortic valve and measurement sites was rigid. Thus any changes occurring at or above the valve were assumed to be reflected at the site of measurement. If any significant compliance were present in the system between the regurgitant valve and the ultrasound transducer, error may have resulted.
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3.
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7. 8.
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13. 14.
Conclusions In summary, the Doppler PWS is proportional to volume flow. The regurgitant fraction was not accurately predicted from the ratio of forward to reverse PWS in our in vitro system. We hypothesize that the source of this error lies in the loss of low velocity and low amplitude information caused by filters. We conclude that further experiments assessing the impact of filter settings and Doppler beam geometry are indicated. Studies investigating PWS assessment of regurgitant fraction in the clinical setting9-12 should be interpreted with caution because the results reported cannot be extrapolated with confidence to other patient populations.
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