Direct Measurement of Threedimensionally Reconstructed Flow Convergence Surface Area and Regurgitant Flow in Aortic Regurgitation
In Vitro and Chronic Animal Model Studies
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Abstract
Background Evaluation of flow convergence (FC) with twodimensional (2D) imaging systems may not be sufficiently accurate to characterize these often asymmetric, complex phenomena. The aim of this study was to validate a threedimensional (3D) method for determining the severity of aortic regurgitation (AR) in an experimental animal model.
Methods and Results In six sheep with surgically induced chronic AR, 20 hemodynamically different states were studied. Instantaneous regurgitant flow rates were obtained by aortic and pulmonary electromagnetic flow meters. Video composite data of color Doppler flow mapping images were transferred into a TomTec computer after computercontrolled 180° rotational acquisition. Direct measurement of the 3D reconstructed FC surface areas as well as measurements of FC areas estimated with 2D methods with hemispherical and hemielliptical assumptions were performed, and values were multiplied by the aliasing velocity to obtain peak regurgitant flow rates. There was better agreement between 3D and electromagnetically derived flow rates than there was between the 2D and the reference values (r=.94, y=1.0x−0.16, difference=0.02 L/min for the 3D method; r=.80, y=1.6x−0.3, difference=1.2 L/min for the 2D hemispherical method; r=.75, y=0.90x+0.2, difference=−0.20 L/min for the 2D hemielliptical method).
Conclusions Without any geometrical assumption, the 3D method provided better delineation of the FC zones and direct measurements of FC surface areas, permitting more accurate quantification of the severity of AR than the 2D methods.
A number of noninvasive methods have been reported to be useful for evaluating the severity of aortic regurgitation.^{1} ^{2} ^{3} ^{4} ^{5} ^{6} ^{7} ^{8} ^{9} ^{10} ^{11} ^{12} However, most echoDoppler methods such as color Doppler jet area planimetry, regurgitant flow velocity continuouswave (CW) pressure halftime, and retrograde flow signal in the descending aorta are influenced by many instrument as well as physiological factors.^{2} ^{3} ^{5} ^{9} Additionally, these methods are not truly quantitative.
Laminar acceleration phenomena for flows toward aortic and mitral orifices imaged by magnetic resonance imaging and color Doppler flow mapping have been studied experimentally and clinically regarding their use for quantifying regurgitant and stenotic flow rates.^{13} ^{14} ^{15} ^{16} ^{17} ^{18} ^{19} ^{20} ^{21} ^{22} ^{23} ^{24} ^{25} With the flow convergence methods, the flow rate through regurgitant or stenotic orifices is calculated as the product of the isovelocity surface area and its corresponding velocity based on the continuity concept.^{13} ^{14} ^{15} ^{16} ^{17} ^{18} ^{21} ^{22} ^{23} ^{24} ^{25}
To accomplish this, it is essential to obtain accurate isovelocity surface areas for estimating the flow rates. Considering the threedimensional nature of flow convergence phenomena, hemispherical or even hemielliptical assumptions of the geometry of the isovelocity surface used for previously reported flow convergence studies using twodimensional imaging systems may be overly simplified. The shapes of the isovelocity surfaces can be quite variable, depending on the aliasing velocities selected and the surrounding geometry, as has been pointed out in the study by Schwammenthal et al^{25} and in our own earlier studies.^{17} Twodimensional imaging methods require mental reconstruction and assumptions about shapes for the flow convergence isovelocity surface that can be problematic for flows associated with complex orifice geometry. In contrast, direct measurement of threedimensionally reconstructed flow convergence surface areas does not require any geometrical assumption or mental reconstruction of the flow convergence and thus should be more widely applied clinically and provide better quantification of the regurgitant flow in vivo compared with twodimensional flow convergence methods.
Few studies of threedimensional reconstructions of flow convergence have been undertaken with color Doppler echocardiography.^{26} Quantitative methods derived from threedimensionally imaged flow convergence zones have not yet been described in clinical or in vivo settings, although the importance of the threedimensional visualization of the flow convergence zone has been appreciated.^{26}
In the present study, using a chronic animal model with strictly quantified aortic regurgitation and a pulsatile in vitro flow model, we investigated the feasibility and value of direct measurements of threedimensionally imaged flow convergence zones for determining the severity of aortic regurgitation.
Methods
Longterm Animal Study
For this study, we created aortic regurgitation in six juvenile sheep weighing 31 to 59 kg (mean, 42±16 kg). Six to 15 months (mean, 10±3 months) before the hemodynamic and ultrasonic studies that constitute the experimental setting for the study, the sheep had undergone thoracotomy and open heart surgery. At that time, the free edge of right coronary cusp (n=1) or the noncoronary cusp (n=5) of the aortic valve was severed with a radial incision. Subsequent aortic dilatation and/or leaflet retraction resulted in anatomic leaflet defects and failure of coaptation. All operative and animal management procedures were approved by the Animal Care and Use Committee of the NHLBI. Preoperative, intraoperative, and postoperative animal management and husbandry methods are described in detail elsewhere.^{27} ^{28} During recovery, the sheep were maintained on digoxin and furosemide.
Electromagnetic Flow Probe and Meter Methods
During the experimental session, the sheep underwent repeat thoracotomy under general anesthesia using 2% isoflurane with oxygen. An electromagnetic flow probe (model EP455, Carolina Medical Electronics, Inc) was placed snugly around the pulmonary artery just above the pulmonary valve sinuses. Another electromagnetic flow probe (model EP455, Carolina Medical Electronics) was placed around the skeletonized ascending aorta distal to the coronary ostia. Both flow probes were connected to flow meters (model FM501, Carolina Medical Electronics), and these were connected to a physiological recorder (ES 2000, Gould Inc) used for hemodynamic pressure recordings. Aortic and left ventricular pressures were obtained from intracavity manometertipped catheters (model SPC350, Millar Instruments, Inc) positioned transmurally. All hemodynamic data were recorded at paper speeds of 250 mm/s. Four consecutive cardiac cycles were analyzed for each hemodynamic determination.
The problem of the zero baseline drift was managed as previously reported^{20} so that the baseline for the aortic flow recording was adjusted until the forward minus the backward aortic flow volume equaled the pulmonary forward flow volume. Coronary arterial blood flow during ventricular diastole was measured in three sheep in a preliminary study. The coronary flow rate was small (0.13 to 0.23 L/min). As in other studies of aortic regurgitation, these values were considered to be negligible compared with the regurgitant volumes delineated in this study.^{8} The correlation coefficient for the regression of pulmonary forward flow versus aortic forward minus aortic regurgitant flow was 0.99 (SEE=0.02 L/min).
Once the curves for pulmonary and aortic flow were properly adjusted, instantaneous regurgitant flow rates could be determined, and the aortic regurgitant volumes, the integrals of instantaneous retrograde flows over diastole, were determined by planimetry of the flow signal recordings. Regurgitant fraction was calculated as retrograde aortic flow volume per minute divided by forward aortic flow volume per minute.
After baseline measurements, varying degrees of severity of aortic regurgitation were produced by altering preload and/or afterload using blood transfusion and angiotensin II (Peptide Institute Inc, provided by Tanabe Seiyaku Co). The calibrations of the flow probes were readjusted according to the manufacture’s specification before each individual hemodynamic steady state, compensating for any changes in hematocrit produced by insensible fluid losses, blood loss, and/or the alteration of preload by blood transfusion. Insensible fluid loss and associated electrolyte disturbances exacerbated by the open thoracotomy were monitored by frequent (before each individual hemodynamic study) determinations of serum electrolytes and hematocrit; aberrations were avoided by continuous infusions of lactated Ringer’s solution and 5% dextrose in water supplemented with potassium and calcium as necessary. Threedimensional reconstruction study was attempted during a total of 22 steady hemodynamic states (2 to 5 per sheep).
Echocardiography and Data Acquisition
The flow convergence toward the aortic regurgitant orifice was imaged by use of a 5MHz transducer placed directly on the heart near the apex with an aliasing velocity of 64 cm/s with an Interspec ultrasound system (Apogee RX 400) (Fig 1⇓). Guided by the twodimensional and color Doppler imaging of the regurgitant jet and the valve, CW Doppler recordings of the regurgitant flow velocity parallel to the direction of the aortic regurgitant jet were performed. This CW velocity profile was integrated over time to determine regurgitant volumes per beat.
In our previous in vitro steady flow studies,^{29} we had observed the influences of instrument settings for color Doppler flow mapping on transferring the color flow mapping data into a blackandwhite video composite data milieu for threedimensional reconstruction. After trying several different color Doppler flow mapping settings for threedimensional reconstruction, we determined that a red to yellow to blue aliased velocity and nonvariance color encoding produced the most clearly defined surface zones of color Doppler flow convergence (Fig 1⇑). The echocardiographic probe was mounted on a holding gantry that positioned the probe on the apex of the heart in a prototype stepper motor system that was controlled by a dedicated threedimensional image processing computer (TomTec Imaging System). The stepper motor, which was driven by a steering logic in the TomTec computer, allowed rotation of the probe at any desired increment between 0° to 180° while the probe was scanning the heart. With 1° increments of probe rotation, 180 slices of the flow convergence region were obtained over the entire scan arc (180°) for each hemodynamic condition and transferred during acquisition into the TomTec computer as previously reported.^{26} The scanning and acquisition of the color Doppler flow mapping data were gated to the ECG at heart rates of 91 to 136 bpm and to the respiratory cycles. An ECG gating interval of <20% of the RR interval (less than ±40 ms) and respiratory gating within limits between inspiratory and expiratory phase were predetermined before image acquisition using the “observe” function of the instrument. When the ECG and respiratory gating met the predetermined limits, video composite images were acquired at each 33ms interval (30 frames per second) after the Rwave signal. Time resolution (frame rate) of the threedimensionally reconstructed images was not limited by the TomTec system or the threedimensional method but was, in fact, limited to 12 to 17 frames per second, which were the original color Doppler acquisition frame rates. Image acquisition took a mean of 112±56 seconds to accomplish. Once the scanning sequence was completed, the digital images were stored for postprocessing.
In Vitro Study
To study central regurgitant flow and to minimize the effects of flow confinement in determining accelerating flow geometry proximal to the regurgitant orifice, we also performed an in vitro pulsatile flow study. Because the mean aortic diameter in the animal study was 1.8 cm and thus may have created more constraint of the convergence flow than might be clinically encountered in an enlarged aortic root, we designed a model with a plastic cylinder with a diameter of 3.3 cm around a regurgitant orifice, mimicking the size of an adult aorta. We created a circular central orifice (area=0.24 cm^{2}) in a plastic disk that had three leaflets, mimicking an aortic regurgitant orifice not closely bounded by the aortic wall or sinuses. In this flow model, which has been described previously,^{29} pulsatile flows were generated into the inlet chamber using a pulsatile pump (Harvard piston pump, model 1423). Flow passed through the regurgitant orifice into the outlet chamber and returned to the reservoir.^{29} Because the maximal regurgitant flow rate was 5.6 L/min in the animal study, a wider range of peak regurgitant flow rates (from 3.2 to 15.2 L/min) was generated in this in vitro pulsatile flow study, investigating the applicability of the threedimensional method for greater ranges of severity of aortic regurgitation. Actual regurgitant flow rates were obtained by a ultrasonic flow probe (model 16NB272, Transonic Systems Inc) and meter (model T106X, Transonic Systems Inc) that were connected to the flow model. We used the same ultrasound system with a 50MHz transducer and the TomTec system as the animal study. An aliasing velocity of 28 cm/s was selected for imaging flow convergence regions. An electromagnetic device was attached to this pulsatile pump to provide an “ECG” signal into the TomTec system for gating the acquisition and the transfer of the color Doppler twodimensional images.
Threedimensional Reconstruction
After image alignment, a process of feature extraction and interpolation by the TomTec computer filled in the gaps between slices to obtain the reconstruction and surface rendering of the flow convergence zones. For most hemodynamic conditions, only the aliased boundaries were transferred into the TomTec system for threedimensional reconstruction. This was accomplished by use of relatively low color Doppler gains and high wall filters to emphasize the brightness of the boundary of the alias. When this could not be satisfactorily accomplished, unaliased accelerating flow proximal to the flow convergence boundary as well as the aliased flow convergence boundary were transferred, as shown in Fig 1⇑. However, under these conditions, the brightest boundary surface that corresponded to the aliasing velocity could be selected later using the TomTec’s “threshold” function before reconstruction so that the flow convergence surface could be reliably reconstructed. The resulting threedimensionally reconstructed images could be inspected from any desired viewing perspectives, although the aliasing velocity could not be changed in the TomTec system (Fig 2⇓). Gray scale, surface rendering, and image resolution provided by the TomTec computer were optimized to obtain clearly defined isovelocity surfaces, which were recognized as the brightest demarcated surfaces proximal to the aortic regurgitant orifices. After determining the exact spatial locations and temporal changes of the flow convergence zones, we selected and magnified the maximal flow convergence zone, which was usually observed in early to mid diastole, for later analyses. The timing for measuring the maximal flow convergence was also selected using the ECG as well as the flow image on the monitor screen of the TomTec system.
Estimation of the Severity of Aortic Regurgitation
Direct Measurement of the Maximal Surface Area of the Flow Convergence Zones Without Geometric Assumption in the Chronic Animal Study
The maximal flow convergence zones were cut in parallel sections at 0.3 to 1.0mm intervals using the software of the TomTec computer (Fig 3⇓). By use of the computer trackball, the arc length of the flow convergence boundary in each sectioned plane (bold boundary arc lines in the right of Fig 3⇓) was measured as shown in Fig 3⇓. The boundary arc lengths of each parallel slice of the flow convergence were multiplied by the slice thickness; then these values were sequentially added, resulting in the entire surface area of the maximal flow convergence zone (S). Peak aortic regurgitant flow rates were calculated based on the continuity concept (Q=S · V, where V is aliasing velocity).
Conventional Twodimensional Flow Convergence Methods
To compare the threedimensional method with the conventional twodimensional color Doppler flow convergence methods for evaluating the severity of the aortic regurgitation, twodimensional color Doppler images recorded on super VHS videotapes during probe rotation also were analyzed. From these videotape records, we selected and measured the maximal axial distance from the orifice to the clearly imaged isovelocity surface (r) at the same aliasing velocity (V) as was used for threedimensional imaging. The regurgitant orifice position was defined as the smallest connection between the flow convergence and the regurgitant jet. Peak regurgitant flow rates were calculated by use of a simple hemispherical model (Q=2πr^{2} · V).
We also measured three orthogonal axes of the flow convergence region in two orthogonal planes (a=major axis, b=minor axis, and c=height) using the videotapes of the twodimensional images obtained during the probe rotation for the threedimensional data acquisition. Using the following equation,^{13} we calculated the maximal surface area of the flow convergence region: when Regurgitant flow rates were then calculated on the basis of the continuity concept (Q=S · V, V=aliasing velocity).
Calculated peak regurgitant flow rates using the threedimensional and twodimensional methods were compared with electromagnetically obtained peak regurgitant flow rates. Among the indexes of aortic regurgitant severity, only the peak regurgitant flow rate was directly related to the maximal flow convergence surface area. Because one of our previous studies revealed little dynamic change in aortic regurgitant orifice area during diastole,^{30} regurgitant volume per beat was also obtained noninvasively as the product of the calculated peak regurgitant flow rate and the ratio of the velocitytime integral to the CW peak velocity through the regurgitant orifice; these values were compared with those obtained from the electromagnetic flow meters.
In Vitro Study
After the reconstruction of the flow convergence zones (Fig 4⇓), direct measurements of the maximal flow convergence zones were performed as described for the animal study. Twodimensional methods using the hemispherical and hemielliptical models were also performed as in the animal study to estimate the maximal flow convergence surface areas. Then peak flow rates were calculated as the products of the surface areas and the aliasing velocities used. Threedimensionally and twodimensionally calculated peak flow rates were compared with those obtained by the ultrasonic flow meter.
Interobserver Variability
To evaluate the effect of observational variability on the measurement of volumes of the maximal flow convergence zones and peak regurgitant flow rates, 10 randomly selected flow conditions were analyzed at different times with the same computer by two independent observers, each without knowledge of the results obtained by the other or the actual flow data.
Statistical Analysis
Data are presented as mean±SD for descriptive statistics. Because multiple points were used in the same sheep in the animal study, the relationship between the twodimensional methods and the threedimensional method of flow determination versus the electromagnetic flow meter method was analyzed by use of a univariate ANCOVA. One ANCOVA model was fitted for each of the three calculation methods versus the electromagnetic flow meter method to give the estimates of the regression coefficients (ie, the intercepts and slopes). Each of these ANCOVAs included sheep as a factor with dummy variable coding to control for sheep to sheep differences.^{31} The estimates for these ANCOVAs were presented as follows: y=(common slope)x+(averaged intercept for all sheep), where y is the two or threedimensionally obtained value, x is the value obtained by the electromagnetic flow meters, and common slope refers to the slope of the regression common to all sheep. To compare the twodimensional methods with the threedimensional method, a combined ANCOVA model that included both the method of flow determination and sheep (again with dummy variable coding) as factors was used. Because the interest here is to compare the performance of the twodimensional methods with the threedimensional method, the comparisons of intercepts and slopes in this ANCOVA were as follows: the twodimensional hemispherical method versus the threedimensional method and the twodimensional hemielliptical method versus the threedimensional method (ie, these were the contrasts used in the model).
To assess agreement and predictability between the actual flow rates and threedimensional and twodimensional image–based calculated flow rates, the method of Bland and Altman^{32} was used. Statistical analyses were performed by use of the statistical package SPLUS (SPLUS for Windows, version 3.2 supplement, StatSci Division of Mathsoft, Inc, 1994). Statistical significance was defined as a value of P<.05.
Results
Longterm Animal Study
For all 22 hemodynamic conditions except 2, video composite data of color Doppler flow mapping images of the flow convergence were transferred successfully into the TomTec computer, and diastolic frames with the largest flow convergence zones could be selected from the reconstructed threedimensional image loops. The mean reconstruction time was 15 minutes for highestresolution threedimensional images, including the time for the initial lowresolution reconstructions.
Severity of Aortic Regurgitation
Aortic regurgitant volumes and regurgitant fractions for the remaining 20 hemodynamic conditions were within clinically relevant ranges of mild to moderate aortic regurgitation from 1.0 mL/beat to 23 mL/beat (average 11±6.3 mL/beat) and from 3% to 42% (average 24±12%), respectively. Peak and mean regurgitant flow rates were also within clinically relevant ranges from 1.2 to 5.6 L/min (average 2.9±1.4 L/min) and from 0.1 to 2.3 L/min (average 1.1±0.7 L/min), respectively.
Evaluation of the Severity of Aortic Regurgitation
There were better agreements between the threedimensionally calculated peak flow rates and electromagnetically derived peak regurgitant flow rates than those between the twodimensionally calculated peak flow rates and the reference values (r=.94, difference=0.02±0.29 L/min for the threedimensional method; r=.80, difference=1.2±1.7 L/min for the twodimensional hemispherical model; r=.75, difference=−0.20±0.94 L/min for the twodimensional hemielliptical model, Fig 5⇓). ANCOVA was used to eliminate the effect of multiple points from the same sheep and showed that peak regurgitant flow rates obtained from the threedimensional method best agreed with those obtained electromagnetically (y=1.0x−0.16, Fig 5A⇓1). It revealed a significant difference in the slope of the regression between the twodimensional hemispherical method (y=1.6x −0.3, P<.001; Fig 5B⇓1) and the twodimensional hemielliptical method (y=0.90x+ 0.2, P<.002; Fig 5C⇓1) versus the threedimensional method (probability values are from comparisons to the slope of the regression between the threedimensional and the electromagnetically derived peak regurgitant flow rates). This showed that the twodimensional methods differ from the threedimensional method (with an estimated slope of 1) and are significantly different from a reference identity (a line with a theoretical slope of 1).
Regurgitant volumes calculated by the threedimensional method agreed better with those electromagnetically obtained measurements than did the twodimensional hemispherical and hemielliptical methods (r=.92, y=0.98x −0.3, difference=1.2±2.4 mL per beat for the threedimensional method; r=.81, y=1.6x−0.7 [P<.001], difference=7.7±7.8 mL per beat for the hemispherical model; r=.68, y=0.92x+2.3 [P<.05], difference=−3.2±6.5 mL per beat for the hemielliptical model) (both as compared to the slope of the regression between the threedimensional and the electromagnetically derived regurgitant volumes).
The conventional hemispherical twodimensional method substantially overestimated the peak regurgitant flow rates and regurgitant volumes.
In Vitro Study
As Fig 4⇑ shows, skewed hemielliptical shapes of the flow convergence zones were seen on the threedimensional reconstruction images. Fig 6⇓ shows an excellent agreement between the threedimensionally obtained peak flow rates and those obtained by the flow meter (r=.99, P<.0001, y=0.98x−0.2, SEE=0.06 L/min, mean difference=−0.16±0.20 L/min). As observed in the animal study, both twodimensional methods provided less agreement with reference peak regurgitant flow rates and greater data scatters (r=.94, P<.001, y=1.38x−1.6, SEE=1.4 L/min, mean difference=0.75±1.8 L/min for the hemispherical model; r=.90, P<.002, y=0.93x+ 0.12, SEE=1.7 L/min, mean difference=−0.77±1.6 for the hemielliptical model).
Interobserver Variability
There was a good agreement between the two independent observers’ measurements for threedimensionally calculated peak regurgitant flow rates for the animal study and the in vitro study (r=.89, mean difference=0.26±0.24 L/min; r=.96, mean difference=0.13±0.15 L/min, respectively).
Discussion
Previous Flow Convergence Studies
The flow convergence phenomenon has been used for quantifying aortic regurgitation, as well as mitral regurgitation, in in vitro and in vivo studies.^{11} ^{12} ^{13} ^{14} ^{15} ^{16} ^{17} ^{18} ^{19} ^{20} ^{21} ^{22} ^{23} ^{24} ^{25} ^{30} Previous reports attempting to quantify regurgitant flow rates and flow orifice areas with the flow convergence phenomenon assumed a simple or modified hemispherical or hemielliptical shape of the isovelocity surface using twodimensional imaging of the flow convergence.^{13} ^{14} ^{15} ^{16} ^{17} ^{18} ^{19} ^{20} ^{21} ^{22} ^{23} ^{24} ^{25} Based on the continuity concept, the regurgitant or forward flow rates in these articles were calculated as the product of the isovelocity surface area and the aliasing velocity used for imaging the flow convergence. Thus, accurate measurements of the isovelocity surface area are of primary importance for correctly estimating the flow rate. The geometry of the flow convergence isovelocity surface, however, depends on many factors, including regurgitant flow rate, the selected aliasing velocity, orifice geometry, surrounding, confining structures, and pathophysiological factors such as left ventricular compliance.^{13} ^{15} ^{16} ^{25} Even when the isovelocity shape appears to be a hemisphere in one plane in a typical view, such as an apical four chamber view, it may not actually be a hemisphere. The converse may also be true. Because of both the complex acceleration field geometry and because of the angle dependence of the color Doppler flow imaging, in our previously performed twodimensional flow convergence studies, we encountered difficulties in judging the geometry of the flow convergence isovelocity surface, often resulting in underestimation or overestimation of the electromagnetically obtained regurgitant flow rates.^{30} ^{33} However, in these experimental studies, the best aliasing velocity for the simple hemispherical assumption could be selected to determine the regurgitant flow rates to match those from the electromagnetic flow method after the direct transfer of the digital flow convergence velocity assignment into the microcomputer or by use of complicated selection formulas based on regurgitant flow rates and velocities.^{30} ^{33} These methods often are not practical in clinical settings.
Advantages of the Threedimensional Flow Convergence Method
With the threedimensional method, one does not need to assume any specific geometric configuration such as that of a hemisphere. Variations in confining structures surrounding aortic regurgitant orifices in patients and selected aliasing velocity can create important variations in the shape of, and skew of, the flow convergence and thus in the flow measurements. The threedimensional method should be less prone to error than twodimensional methods because the surface area of any flow convergence geometry can be determined by the threedimensional method used in the present study, eliminating the need for imaginative mental reconstruction or assumptions regarding its threedimensional geometry from twodimensional observations. Additionally, one can use a wider range of aliasing velocities permitting the flow convergence surface to be clearly imaged. This advantage may be of clinical importance since cumbersome efforts for selecting the optimal aliasing velocity for assuming a certain geometry of a flow convergence surface, such as a hemisphere, can be avoided.
Study Limitations
In this study, the echoDoppler imaging was performed with the transducer directly on the heart, somewhat reducing translational heart motion problems. Thus, the quality of the original twodimensional color Doppler imaging may have been better than that obtained in clinical settings.^{30} ^{33} However, because the threedimensional data sets were derived from the twodimensional imaging during the probe rotation, some of the heart motion artifacts may have degraded the threedimensional reconstruction images. The comparison between two and threedimensional images is thus somewhat biased in favor of the twodimensional data analyses by this limitation.
Limitations inherent to the color Doppler flow mapping for imaging the flow convergence, including instrument factors such as color gain, wall filter settings, and variability of aliasing velocities, are carried into the threedimensionally reconstructed flow convergence images. Low frame rates (12 to 17 frames per second) may cause underestimation of the maximal flow convergence size. However, this underestimation resulting from frame selection should be minimal because relatively constant aortic regurgitant flow and orifice area throughout diastole have been observed in our earlier studies.^{20} ^{30}
Especially important is the loss of velocity information for flows at the edges of the flow convergence region induced by the angle between Doppler interrogation and the actual direction of blood flow. Because of these problems, portions of the imaged flow convergence surface adjacent to the valves in this study do not correspond strictly to true isovelocity surfaces. Thus, this technique needs correction for flow constraint, competing flows, and Doppler angle dependency. Imaging from more than one site or compound image rasters recently reported for realtime volume imaging would be desirable.^{34} ^{35} Angleindependent methods, such as magnetic resonance imaging and digital particle tracking, should also provide insight into methods for correcting angle dependent color Doppler data.^{16}
In a recent in vitro study,^{29} probably because of the Doppler angle problems discussed above, we encountered significant underestimation using the three orthogonal measurements for threedimensional reconstruction of the flow convergence zones used to calculate steady flow rate through a restrictive orifice. However, in the present study, no such underestimation was observed in either the in vivo or in vitro study. Several factors may have been involved. Higher pulsatile regurgitant flows with the maximal flow rate of 5.6 L/min observed in the present in vivo study and 15.2 L/min in the in vitro pulsatile flow study as opposed to lower steady flow rates with the maximal flow rate of 2.4 L/min in the in vitro steady flow study may have lessened the underestimation. However, the range of the severity of regurgitation examined in the present animal and in vitro pulsatile flow studies was closer to clinical conditions in terms of volume and flow rate than that in the previously performed steady flow study. Postmortem inspection of the aortas and threedimensional reconstruction of the anatomic configuration of the aortic valve leaflets showed complicated, curved structures surrounding the regurgitant orifice, which may have caused confinement of convergent flow. As opposed to the flat orifice used in the previous in vitro steady flow study,^{29} the geometrically complicated, nonflat orifice and constraint of flow observed near the walls of the aorta in the present in vivo study would decrease the amount of flow perpendicular to and increase the flow parallel to the Doppler interrogation, lessening the Doppler angle effect. This effect may be exaggerated in the animal study because of small aortas (mean diameter=1.8 cm) compared with those of adult humans. Thus, in the in vitro pulsatile flow study, the simulated aorta was made larger than the animal aorta so that clinically relevant flow constraint could be studied. Not only in the animal study but also in the in vitro pulsatile study, very good agreement was present between values obtained by the reference flow meter methods and those by the threedimensional method. The present threedimensional method therefore appears to be valid for evaluating clinically encountered aortic regurgitation. Although probably of lesser importance, certain technical issues related to the data acquisition need to be considered. High color Doppler wall filters used for obtaining distinct isovelocity contours may result in overestimation. The center axis of probe rotation may change during data acquisition. In addition, averaging datafill algorithms for voxels may cause deterioration of lateral resolution and expand the spatial extent of the flow data set, resulting in overestimation of the lengths of the axes which are then multiplied.
The relatively high cost of the additional equipment, the time required to process the images, and the limitations of the measurement algorithms supported may hinder immediate clinical application of threedimensional flow computation methods. In the future, however, continuing development of computer technology and ultrasound equipment should provide direct transfer of colorencoded signals for threedimensional reconstruction of color Doppler flow images derived as realtime volume images to improve further visualization and quantification of cardiovascular flow phenomena.
Conclusions
In our study, direct measurements of threedimensionally reconstructed proximal isovelocity flow convergence surface areas provided more accurate regurgitant flows than conventional twodimensional color Doppler methods.
Acknowledgments
This study was supported in part by a grant (HL43287) from the National Heart, Lung, and Blood Institute. We acknowledge the assistance of the veterinary professional and technical staff of the Laboratory of Animal Medicine and Surgery, NHLBI, and the dedication of Michelle Ann Cheney for help with editing and preparing the manuscript.
Footnotes

Reprint requests to Dr Michael Jones, National Institutes of Health, NHLBI, 9000 Rockville Pike, Bldg 14E, Room 107A, Bethesda, MD 20892.
 Received October 3, 1996.
 Revision received June 17, 1997.
 Accepted June 26, 1997.
 Copyright © 1997 by American Heart Association
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 Direct Measurement of Threedimensionally Reconstructed Flow Convergence Surface Area and Regurgitant Flow in Aortic RegurgitationTakahiro Shiota, Michael Jones, Alain Delabays, Xiaokui Li, Izumi Yamada, Masahiro Ishii, Philippe Acar, Scott Holcomb, Natesa G. Pandian and David J. SahnCirculation. 1997;96:36873695, originally published November 18, 1997https://doi.org/10.1161/01.CIR.96.10.3687
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 Direct Measurement of Threedimensionally Reconstructed Flow Convergence Surface Area and Regurgitant Flow in Aortic RegurgitationTakahiro Shiota, Michael Jones, Alain Delabays, Xiaokui Li, Izumi Yamada, Masahiro Ishii, Philippe Acar, Scott Holcomb, Natesa G. Pandian and David J. SahnCirculation. 1997;96:36873695, originally published November 18, 1997https://doi.org/10.1161/01.CIR.96.10.3687Permalink: