# Quantification of Mitral Regurgitation by the Proximal Convergence Method Using Transesophageal Echocardiography

## Clinical Validation of a Geometric Correction for Proximal Flow Constraint

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## Abstract

*Background *Proximal flow convergence is a promising method to quantify mitral regurgitation but may overestimate flow when the flow field is constrained. This has not been investigated clinically, nor has a correction factor been validated.

*Methods and Results *Eighty-five patients were studied intraoperatively with transesophageal echocardiography and divided into two groups: central convergence (no constraining wall) and eccentric convergence (at least one constraining wall). Regurgitant stroke volume (RSV) and orifice area (ROA) were calculated by ROA=2π r^{2} V_{a}/V_{p} and RSV=ROA×VTI_{cw}, where r and v_{a} are the radius and velocity of the aliasing contour and v_{p} and VTI_{cw} are the peak and integral of regurgitant velocity. In eccentric convergence patients, convergence angle (α) was measured from two-dimensional Doppler color flow maps, and ROA and RSV were corrected by multiplying by α/180. For reference, RSV was the difference between thermodilution and pulsed Doppler stroke volumes. In central convergence patients (n=45), RSV (*r*=.95, Δ=2.5±10.8 mL) and ROA (*r*=.96, Δ=0.02±0.08 cm^{2}) were accurately calculated, but significant overestimation was noted in the eccentric convergence patients (n=40, ΔRSV=63.9±38.0 mL, ΔROA=0.54±0.31 cm^{2}), 68% of whom had leaflet prolapse or flail. ΔRSV was correlated with α (*r*=–.69, *P*<.001). After correction by α/180, overestimation was largely eliminated (ΔRSV=15.5±19.3 mL and ΔROA=0.14±0.14 cm^{2}) with excellent correlation for the whole group (RSV, *r*=.91; ROA, *r*=.95).

*Conclusions *A simple geometric correction factor largely eliminates overestimation caused by flow constraint with the proximal convergence method and should extend the clinical utility of this technique.

Accurate quantification of mitral regurgitation is of primary importance for clinical decision making. Assessing a patient’s response to medical therapy, characterizing the time course of a destructive process such as endocarditis, and determining the optimal time for surgical intervention demand accurate assessment of regurgitant severity. Conventional color Doppler mapping of jet flow is a useful semiquantitative tool,^{1} ^{2} ^{3} but physical, geometric, and instrumentation factors preclude more quantitative use.^{4} ^{5} ^{6} Recently, analysis of flow convergence proximal to the regurgitant orifice was proposed as an alternative quantitative method because flow in this zone is laminar and easily interrogated by color Doppler echocardiography. Initial computational, in vitro, and clinical studies demonstrated that proximal flow contours have an approximately hemispherical shape for round orifices in a planar surface,^{7} ^{8} ^{9} ^{10} particularly when the contour velocity is between 5% and 10% of the orifice velocity^{11} ^{12} and accurate flow quantification has been achieved in these circumstances. In a subgroup of clinical studies, however, gross overestimation of mitral regurgitant flow rate by the proximal flow convergence method has been reported,^{8} ^{13} especially in patients with the most severe degree of regurgitation. Previous computational and in vitro work from our laboratory suggested that this overestimation results from proximal constraint of the flow field, precluding full hemispheric spread of the isovelocity contours.^{14} ^{15} Such constraint arises clinically, eg, in the case of flail posterior leaflet, where the proximal convergence zone is constrained by the posterior left ventricular wall.

However, this hypothesis has not been systematically tested in a large number of patients, nor has any possible correction factor been validated to address this problem. This encouraged us to undertake a prospective investigation to determine the overall clinical applicability of the proximal flow convergence method in a large number of patients undergoing heart surgery, characterize the impact that proximal flow constraint has on overestimation of flow, and validate the clinical applicability of a simple correction factor for this flow constraint based on visual assessment of the proximal geometry.

## Methods

### Patient Selection

All patients were derived from clinical transesophageal echocardiographic cases performed in the operating rooms of the Cleveland Clinic Foundation from September 1, 1993, through November 20, 1994. To validate our reference standard for mitral regurgitation (specifically, to affirm our ability to quantify flow through the mitral annulus echocardiographically), we selected 30 patients on the basis of the following criteria: morphologically normal mitral valve, no more than trace mitral regurgitation by color Doppler imaging, sinus rhythm, and no more than mild tricuspid regurgitation.

The study population then consisted of 85 patients with 1 to 4+ mitral regurgitation defined by routine color Doppler or angiography; sinus rhythm; no severe mitral annular calcification; no more than mild tricuspid regurgitation; complete biplane or multiplane transesophageal 2D images and pulsed, continuous-wave, and color Doppler data of adequate quality to permit Doppler quantification of cardiac mitral inflow, regurgitant flow spectra, and the proximal flow convergence zone; and satisfactory thermodilution cardiac output data. Table 1⇓ lists the clinical characteristics of these patients.

### Echocardiographic Data

All patients underwent biplanar (n=15) or multiplanar (n=70) transesophageal echocardiographic interrogation (Sonos 1500, Hewlett Packard, or Acuson 128 XP). To obtain forward flow through the mitral annulus, careful 2D interrogation of the annulus was performed in the four-chamber (transverse or 0° plane) and two-chamber (longitudinal or 90° plane) projections with pulsed Doppler velocity measured at the center of the annulus. The proximal flow convergence zone was interrogated with 2D color flow mapping using both biplane (or continuous multiplane) views and a color flow imaging sector as small as possible to maximize frame rate. Color flow gain was adjusted to a level just before artifactual color was observed. Medium color packet size and minimal wall filter were used, yielding a frame rate of 18 to 22 per second; baseline shifting was used to adjust the aliasing velocity between 34 to 69 cm/s. Continuous-wave regurgitant velocity profiles were recorded at a sweep speed of 100 mm/s. All data were stored on -in videotape and, where possible (Sonos 1500), were stored digitally onto a 650-megabyte magneto-optic disk.

### Thermodilution Data

A Swan-Ganz catheter was inserted into the pulmonary artery as part of the routine intraoperative monitoring for all patients. Cardiac output was obtained by thermodilution simultaneous with the acquisition of the echocardiographic data. Cardiac output was obtained from the average of at least three consecutive thermodilution measurements, with SV calculated by dividing cardiac output by heart rate.

### Data Analysis

#### Mitral Inflow

The diameter of the mitral annulus was measured at the base of the mitral leaflets at the time of maximal valvular opening from both the transverse (four-chamber) and longitudinal (two-chamber) views. Assuming an elliptical shape, we calculated the cross-sectional annular area (A_{ma}) as πab, where a and b are the half-diameters of the annulus in the transverse and longitudinal projections, respectively. Pulsed Doppler recordings of flow were obtained in the mitral annular level, and the velocity-time integral (VTI_{ma}) was calculated for three to five consecutive beats and averaged. Mitral annular SV (SV_{ma}) was calculated as A_{ma}×VTI_{ma}. RSVRSV_{td} was given by the difference between the mitral annular SV and thermodilution SV (SV_{td}): RSV_{td}=SV_{ma}−SV_{td}. The ROA_{td}, a fundamental measure of valvular incompetence analogous to the stenotic orifice area, was calculated by dividing RSV_{td} by the velocity-time integral of continuous-wave mitral regurgitant velocity: ROA_{td}=RSV_{td}/VTI_{cw}. The mitral inflow measurements were performed by an investigator blinded to the thermodilution measurements.

#### Proximal Convergence

The appearance of the proximal convergence field was optimized by baseline shifting of the color Doppler aliasing velocity to between 34 and 69 cm/s (mean, 52.6±5.6 cm/s, 11.5±2.2% of peak mitral regurgitant velocity). The radial distance (r) between the first aliasing contour (red/blue interface) and the center of the regurgitant orifice was measured at the time of the largest convergence image. For patients with nonflail mitral leaflets, the orifice was assumed to be at the plane passing through the tips of the mitral leaflets; for flail mitral leaflets, the orifice was assumed to lie in the plane of the nonflail leaflet, as illustrated in Fig 1B⇓.

Maximal instantaneous regurgitant flow (Q_{max}) was calculated as Q_{max}=2πr^{2}v_{a}, where r is the maximal distance to the contour of velocity v_{a} with a hemispheric contour assumed. The regurgitant orifice area was obtained by dividing maximal flow by the peak regurgitant velocity (v_{p}) obtained by continuous-wave Doppler: ROA_{pfc}=Q_{max}/v_{p}. RSV_{pfc} was obtained by multiplying ROA_{pfc} by the velocity-time integral of continuous-wave regurgitant velocity (VTI_{cw}): RSV_{pfc}=ROA_{pfc}×VTI_{cw} or 2π r^{2}v_{a}×VTI_{cw}/v_{p}.

### Convergence Morphology

The proximal flow fields were classified into two types, central and eccentric, on the basis of their spatial velocity distributions within the left ventricle (Fig 1⇑). cPFC required that all the displayed proximal flow convergence surface by color Doppler mapping be intact without any contact with or visible distortion by the left ventricular walls on any transesophageal imaging plane (Fig 1A⇑). ePFC was defined as one in which the proximal convergence field was constrained by an adjacent ventricular wall in one or more transesophageal views (Fig 1B⇑). Operationally, this distinction was made by comparing the radius (r) of the particular isovelocity contour chosen with the distance (d) from the regurgitant orifice to the nearest ventricular wall: if d<r, then the convergence was judged constrained; if d>r, it was considered unconstrained. Thus, a particular convergence zone might be considered unconstrained at a high-velocity aliasing contour and constrained at a lower-velocity (larger r) contour. This classification was based solely on analysis of the proximal convergence morphology without consideration of the jet direction within the left atrium.

#### Convergence Angle

The geometric convergence angle (α) was determined to be the minimum angle between the two sides of the proximal flow field obtained from two or more transesophageal projections (Fig 1B⇑ and 1C⇑), while the constraining angle was defined as 180−α. For cPFC, the converging angle was assumed to be 180° because there was no left ventricular constraint (Fig 1A⇑). For ePFC, α was obtained by identifying the height of the velocity contour of interest within the proximal flow field and projecting this distance onto the constraining wall. The constrained proximal flow field typically was skewed toward the constraining wall (Fig 1B⇑), so that the high point of the contour was adjacent to the wall. Mathematically, this definition of α was equivalent to using r and d as follows:

On-line, however, α was measured most easily with a small protractor.

#### Geometric Correction of Flow Constraint

Based on the observed α, a corrected RSV (cRSV_{pfc}) was calculated from a formula previously validated in vitro^{15} : cRSV_{pfc}=RSV_{pfc}×α/180. Similarly, ROA was corrected as cROA_{pfc}=ROA_{pfc}×α/180. This formula assumes implicitly that the constraint is primarily a one-dimensional (like the wedges of an orange) rather than an axisymmetric (funnel-like) constraint, which would adjust RSV and ROA by the proportion [1−cos(α/2)].^{16} ^{17} This approach also was chosen specifically because it was easy to apply on-line in the clinical situation.

### Statistical Analysis

All values are expressed as mean±SD. For the validation cases (without mitral regurgitation), SV by thermodilution and pulsed Doppler measurements were compared by linear regression and analysis of agreement.^{18} For the mitral regurgitant patients, proximal flow convergence and pulsed Doppler–thermodilution measurements of RSV and ROA were compared by linear regression and analysis of agreement. The data were analyzed as a whole and then divided into cPFC and ePFC patients. The error in RSV and ROA estimation by proximal flow convergence was compared between the cPFC and ePFC patients by unpaired *t* testing. The degree of overestimation in RSV (ΔRSV) was assessed as a function of constraint angle (180–α) by linear regression. After geometric correction of RSV and ROA, the degree of overestimation (ΔRSV and ΔROA) was compared with the uncorrected values by paired *t* testing, with linear regression and analysis of agreement used to judge the overall correction achieved by this approach.

### Interobserver and Intraobserver Variability

In 20 (10 cPFC and 10 ePFC) randomly selected cases, the proximal flow convergence and mitral inflow measurements were obtained independently by two observers. Intraobserver variability was also calculated by repeating measurements 1 month after the initial measurement.

## Results

### Accuracy of Mitral Inflow Measurements

In the 30 patients without mitral regurgitation selected to validate the Doppler transesophageal measurement of mitral inflow, thermodilution SV ranged from 36 to 104 mL per beat. There was close agreement between thermodilution (x) and pulsed Doppler (y) measurements of mitral inflow SV: y=0.92x+6.43, *r*=.94, *P*<.001; ΔSV(y–x)=1.78±5.90 mL. The use of biplanar measurements to calculate mitral annular area appeared to be critical to this accuracy; the biplanar measurements were superior to SV data using either transverse (*r*=.86) or longitudinal (*r*=.79) annular measurements alone.

### RSV and ROA Calculations

Table 1⇑ lists the clinical characteristics of the patients with central and eccentric flow convergence; Table 2⇓ gives RSV and ROA (from Doppler-themodilution measurements) for each angiographic grade of severity in those patients with adequate angiographic data. Because many of the patients were young, not all underwent left ventriculography.

For the 45 patients with cPFC, there was close concordance between thermodilution (x) and proximal flow convergence (y) measurements of both RSV (y=0.98x+3.52 mL, *r*=.95, *P*<.0001; ΔRSV=2.51±10.8 mL; Fig 2A⇓) and ROA (y=1.05x+0.004 cm^{2}, *r*=.96, *P*<.0001; ΔROA=0.02±0.08 cm^{2}; Fig 2B⇓). Although some data scatter was seen, systematic overestimation of RSV and ROA by the proximal flow convergence method was not shown in the cPFC group.

For the ePFC patients, however, both RSV and ROA were significantly overestimated compared with thermodilution measurements (RSV: y=1.23x+48.9, *r*=.78, *P*<.001; ΔRSV=63.9±38.0 mL; Fig 3A⇓; ROA: y=1.41x+0.30 cm^{2}, *r*=.87, *P*<.001; ΔROA=0.54±0.31 cm^{2}; Fig 3B⇓). The overestimation was significantly greater for ePFC than for cPFC patients (*P*<.0001 for both RSV and ROA).

From Doppler-thermodilution measurements, both RSV (70.3±38.4 versus 43.6±34.2 mL, *P*<.01) and ROA (0.58±0.35 versus 0.32±0.31 cm^{2}, *P*<.01) were significantly larger for the ePFC patients, reflecting the higher prevalence of severe leaflet disruption in these patients. However, it should be recognized from Fig 2⇑ that some cases of severe mitral regurgitation were accurately estimated, provided that the flow convergence zone was unconstrained. Thus, for the cPFC patients, the proximal convergence method yielded accurate estimates of RSV and ROA for a wide range of regurgitant severity.

#### Relation Between Proximal Constraint and Jet Direction

In general, there was concordance between the nature of the proximal convergence zone and the jet direction within the left atrium (see Table 1⇑). Posterior mitral valve prolapse or flail was more common in ePFC patients (n=27, 68%) than cPFC patients(n=9, 20%; *P*<.01). For the cPFC patients, there was no statistically significant difference between the patients with central and eccentric distal jets for ΔRSV (1.3±10.2 versus 6.7±16.1 mL, respectively; *P*>.05) and ΔROA (0.01±0.07 versus 0.05±0.11 cm^{2}, respectively; *P*>.05). Thus, flow overestimation by the proximal flow convergence method was determined primarily by the nature of the convergence zone rather than the jet direction within the left atrium.

#### Relation of Regurgitant Overestimation to Flow Constraint

Based on the minimal angle of the global geometry surrounding the regurgitant orifice, α ranged from 92° to 153° (119±17°); thus, the constraint angle (180–α) ranged from 27° to 88° (61±17°). As Fig 4⇓ shows, there was a significant linear correlation between the amount of constraint (180–α) and the amount of RSV overestimation.

### Correction for Flow Constraint

Fig 5⇓ demonstrates the impact that geometric correction of the proximal flow constraint has on the accuracy of RSV (Fig 5A⇓) and ROA (Fig 5B⇓). For both parameters, there was significant improvement in the correlation and reduction in the overestimation. Mean RSV and ROA were still somewhat higher, but there was significantly less overestimation than without the correction (ΔRSV=15.5±19.3 versus 63.9±38.0 mL and ΔROA=0.14±0.14 versus 0.54±0.31 cm^{2}, *P*<.001, compared with the uncorrected data for each). Combining the central data with the corrected eccentric data demonstrated excellent overall agreement for RSV (y=0.93x+12.7, *r*=.91, *P*<.001; ΔRSV=8.9±17.5 mL; Fig 6A⇓) and ROA (y=1.05x+0.06, *r*=.95, *P*<.001; ΔROA=0.08±0.13 cm^{2}; Fig 6B⇓).

### Reproducibility

The intraobserver variability was 4.1±10.5% (mean difference±SD) for mitral inflow, 1.1±11% for radius measurements, and 6.7±17.9% for the convergence angle measurements. The interobserver variability was 4.3±10.7% (mean difference±SD) for mitral inflow, 3.2±9.0% for radius measurements, and 8.8±8.0% for the convergence angle measurements.

## Discussion

### Quantification of Mitral Regurgitation

A number of techniques are available for the characterization of mitral regurgitant severity in the clinical setting. The most commonly used are semiquantitative, such as contrast ventriculography^{19} and characterization of the size^{1} and morphology^{2} ^{3} of the regurgitant jet within the left atrium as visualized by color Doppler echocardiography. These semiquantitative approaches are valuable in their own right, allowing rapid differentiation among mild, moderate, and severe regurgitation. However, they are inappropriate for measuring the relatively subtle changes that may occur in regurgitant volume over time, either as a result of medical therapy or as the valvular apparatus deteriorates further.

For more precise quantification, a number of options are available, but none are ideally suited for routine use. Quantitative angiography has been validated by deriving the RSV from the difference between the net forward stroke volume (thermodilution) and the ventriculographic stroke volume (from biplanar angiography).^{20} ^{21} Such an approach is technically demanding, however, and is inappropriate for routine follow-up of patients with mitral regurgitation. Quantitative Doppler echocardiographic methods were proposed some years ago^{22} ^{23} ^{24} and have enjoyed a recent resurgence in interest.^{25} These methods, which use the difference in SV between a regurgitant and nonregurgitant valve (or ventricular SV from 2D imaging as the flow through the regurgitant valve), should be considered the current clinical gold standard. They are theoretically sound, and recent improvements in instrumentation have simplified their practical implementation. Nevertheless, these pulsed Doppler methods are technically demanding, with multiple measurements required from several echocardiographic windows; any errors in measurement are propagated and magnified through the remainder of the calculations, so extremely careful measurement of the fundamental data is necessary to assure accuracy in the final estimation.

#### Proximal Convergence Method

With the echocardiographic data acquisition limited to a single acoustic window, the proximal convergence method has been proposed as a simpler, more robust method for quantifying valvular regurgitation.^{7} ^{8} ^{9} Based on the physical principle of conservation of mass, this method assumes that all blood passing through an isovelocity contour surrounding a regurgitant orifice is ultimately destined to pass through the orifice itself. Furthermore, if these contours are assumed to be hemispheric, then flow rate can be calculated simply with knowledge of the radius (r) at which a contour of given velocity (v_{a}) occurs: Q=2πr^{2}v_{a}. Dividing this maximal flow rate by peak regurgitant velocity (obtained by continuous-wave Doppler) yields a very simple expression for the ROA, an important fundamental measurement of valve integrity.^{10} ^{26}

The general accuracy of the proximal convergence concept with its hemispheric assumption for contour shape has been validated in several in vitro and clinical studies.^{7} ^{8} ^{9} ^{10} In a number of clinical studies, however, overestimation of flow has been reported, particularly for severe mitral regurgitation. In the first clinical report of this method, Bargiggia et al^{8} reported one patient with a regurgitant flow rate as high as 1263 mL/s, which appears to be well outside a realistic clinical range. Furthermore, Chen et al^{13} reported consistent overestimation of RSV by the proximal convergence method whenever the regurgitant volume by pulsed Doppler methods exceeded 120 mL per beat. Recently, substantially high calculated regurgitant flow rates by the proximal convergence method (403 to 1155 mL/s) were reported in patients with flail mitral leaflet.^{27} Because of these anecdotal reports of flow overestimation by the proximal convergence method, we undertook this systematic study to determine the cause of the overestimation and to develop methodologies to correct it in the clinical setting.

### Geometric Aspects of Proximal Flow Convergence

The mathematical technique of potential field analysis has demonstrated that isovelocity contours should be hemispherical when an inviscid fluid is assumed to converge on a pointlike orifice in a planar surface.^{11} However, each assumption—inviscid fluid, pointlike orifice, and planar surroundings—must be tested for its impact on proximal convergence calculations in the clinical setting.

#### Local Geometric Effects

In the clinical situation, the regurgitant orifice is not pointlike but rather a finite orifice. Previous in vitro and numerical analyses have demonstrated that isovelocity contours lose their hemispheric shape and flatten out as they approach such a finite orifice.^{11} ^{12} ^{28} Therefore, simple application of the hemispheric convergence formula will underestimate the actual flow. Fortunately, this underestimation is approximately equal to the ratio of the contour velocity to orifice velocity; in left-sided regurgitant lesions, therefore, where the aliasing velocity (v_{a}) typically is between 5% and 10% of the orifice velocity (v_{o}), this underestimation has not been clinically significant.^{12} For tricuspid regurgitation, with its much lower orifice velocity, multiplying the calculated flow rate by the correction factor v_{0}/(v_{0}–v_{a}) was required to achieve maximal accuracy.^{29}

#### Impact of Viscous Flow

The primary effect of viscosity is to cause low-velocity boundary layers to form near the leaflet walls, forcing the isovelocity contours away from the orifice. However, because most of the proximal convergence zone is away from any stationary surface, the impact of viscosity is actually quite small. This is in keeping with the nature of converging orifice flow occurring in the presence of a favorable pressure gradient (∂p/∂s<0, where s is the distance along any streamline), which suppresses boundary layer formation and maintains laminar flow until very high Reynolds numbers are reached.^{30} Indeed, a numerical simulation with viscosity increased 100-fold above its physiological value demonstrated only a 1% change in localized velocities within the proximal convergence zone.^{11} Although these studies have not investigated the complex geometry of flail mitral leaflets, it is unlikely that viscosity by itself will significantly affect proximal convergence calculations.

#### Impact of Global Geometric Distortion

The final assumption to consider, and the primary focus of the current study, is the impact that a nonplanar surrounding geometry has on the proximal convergence field. Previous numerical work demonstrated that, to the extent that the global geometry surrounding an orifice is more constraining than a planar surface, the isovelocity contours are forced outward for a given flow rate.^{14} Indeed, because the effects of viscosity and the development of boundary layers are so negligible, for a given combination of contour radius and aliasing velocity, the actual flow rate is nearly proportional to the solid angle subtended by the global geometry. For a planar surface, the solid angle is that of a full hemisphere, or 2π steradians, which yields the constant of 2π in the proximal convergence formula. Two simple formulas were proposed to correct for the impact of global geometry on the proximal flow field. For geometries constrained in only one dimension (like the wedges of an orange), the true flow can be obtained by multiplying the hemispheric calculation by α/180, where α is the angle between the two walls of the surrounding geometry. This correction factor was validated in the clinical setting of mitral stenosis,^{16} where the flow rate had to be corrected by the angle between the anterior and posterior leaflets to yield accurate estimates of mitral valve area. A second correction factor was proposed for geometries that are more axisymmetric, like a funnel. If θ is the angle between the central axis and the surrounding wall, the appropriate constant in the proximal convergence field would be 2π(1−cos θ). This formula was validated in an in vitro model of prosthetic valve flow where flow could converge on the prosthetic valve over a larger area than that of a hemisphere, and a constant larger than 2π was necessary to yield accurate flow estimations.^{12} For clinical patients, when mitral regurgitation results from posterior mitral leaflet prolapse or flail, the regurgitant orifice is often very close to the posterolateral left ventricular wall. This global geometric effect of the left ventricular wall may significantly distort the proximal flow convergence field. The present work is the first clinical study of mitral regurgitation to examine the impact of global geometry on the accuracy of the proximal convergence formula and then to develop methodologies to correct for this effect.

### Results of the Present Study

In the present study, we examined 85 patients with mild to severe mitral regurgitation, dividing them into two populations according to convergence morphology: those whose convergence zones were remote from any ventricular walls (cPFC, Fig 1A⇑) and those whose convergence zones were eccentric, constrained by one of the ventricular walls (ePFC, Fig 1B⇑). In keeping with the predictions of potential field theory, the central convergence zones were accurately estimated by applying the simple hemispheric formula with only a slight, nonsignificant overestimation of RSV and ROA compared with the reference standard of pulsed Doppler transmitral flow and thermodilution SV. In contrast, the constrained convergence fields led systematically to significant overestimation of RSV and ROA, indicating that the isovelocity contours were displaced outward from the regurgitant orifice compared with the unconstrained situation, although the aliasing velocity in ePFC (54.0±4.9 cm/s) was not different from that in cPFC (51.3±5.9 cm/s). Our previous in vitro and initial clinical studies showed that an adjacent ventricular wall causes overestimation of regurgitation flow by the proximal convergence method in flail mitral valve,^{15} ^{31} ^{32} which is confirmed in this study. These results may explain the finding of previous studies that flow overestimation occurs in the setting of extremely high regurgitant flow rates.^{8} ^{13}

To correct for this overestimation, we estimated the angle of constraint in each of the eccentric flow convergence situations. Because the constraint in general occurred on only one side, we applied the one-dimensional correction formula α/180 rather than the axisymmetric correction formula 2π(1–cos θ). An important issue to consider is precisely how the converging angle (α) is measured. Note in Fig 1⇑ that the constraining wall does not extend into the regurgitant orifice but rather runs parallel to the central axis of flow, displaced several millimeters from this axis. Therefore, for contours that are very close to the orifice (high-velocity contours), there is relatively little flow constraint, whereas more distant contours (low-velocity contours) are progressively more constrained, with a reduction in α. For operational purposes, we defined α on the basis of a chosen velocity contour as follows: From a frozen, color 2D image, the height of the isovelocity contour was noted, and a line was extended from this contour to the adjacent constraining wall; α was defined by connecting this point on the constraining wall to the center of the orifice and then extending the line parallel to the leaflet on the unconstrained side. Because the severity of flow constraint varied in different patients, two or more color Doppler 2D views should be used to obtain the minimal convergence angle.^{33} With α defined in this way, we achieved a very significant improvement in the accuracy of regurgitant flow estimation, though still with slight overestimation. The source of this overestimation probably is our assumption of a one-dimensional constraint rather than integrating constraint in all views to produce a three-dimensional correction angle. The potential importance of the three-dimensional nature of constraint may be seen in Fig 1B⇑. Although the primary effect we see is displacement of the yellow-cyan aliasing contour away from the regurgitant orifice, it should be recognized that the flow field is also displaced anteriorly (to the left in Fig 1B⇑), but much of this spread is not apparent because the streamlines of flow in this region are largely orthogonal to the interrogating ultrasound beam. Recent developments in three-dimensional echocardiography^{34} may make possible the full reconstruction of a single component of velocity or even the reconstruction of the full velocity vector field if multiple imaging windows are used, but even the simplified formula used here yielded significantly improved results across a wide range of flow constraint. It should be reiterated that the principal goal of this study was to validate a simple correction strategy that could be applied quickly and easily on-line in the clinical setting.

### Study Limitations

As in all clinical studies of mitral regurgitation, one limitation is the lack of a precise gold standard against which to compare our results. Because changing loading conditions can significantly affect regurgitant flow rate and orifice size,^{35} we thought it imperative that a reference measurement be made simultaneously with the proximal convergence imaging and thus chose the combined transmitral SV–thermodilution SV approach. Such an approach requires meticulous care in measuring the raw data and excluding patients with significant tricuspid regurgitation.^{36} A large number of patients were used in the learning phase of this technique before 30 consecutive patients who constituted the validation of this technique in our hands were selected. Others have shown that such a learning curve is critical for accurate flow calculations.^{13} ^{25} Atrial fibrillation can significantly affect the accuracy of this technique, so our study excluded patients with this arrhythmia. One might consider alternative validation methodologies, such as using transesophageal echocardiographic 2D volumes to define the transmitral SV. Unfortunately, prior studies demonstrated significant underestimation of left ventricular volume resulting in part from an inadequate display of the left ventricular long axis.^{37} ^{38}

For analysis of the proximal convergence zone, we used 2D imaging rather than color M-mode imaging. This has the advantage of yielding a 2D image of the entire flow field, which is critical for accurate measurement of the convergence angle but has a lower temporal resolution and thus may fail to detect dynamic changes in ROA.^{39} The accuracy of our RSV calculations in the central convergence patients, however, indicates that dramatic variation in ROA during systole was not prominent in this patient population. Concern might be raised, however, that the overestimation in the ePFC patients may have resulted in part from choosing a maximal aliasing contour that was not representative of the mean ROA. This might occur in mitral valve prolapse with predominant late systolic regurgitation; however, most of our ePFC patients had flail leaflets and exhibited pansystolic regurgitation. As a rule, the aliasing contour was measured from a frame in midsystole and thus would be unlikely to systematically overestimate mean ROA. In only 5 patients was prolapse identified with nonholosystolic regurgitation, and all had central convergence. Thus, it is unlikely that variability in ROA during systole significantly affected the study results.

Although the interobserver variability of the α measurements was relatively high at 8.8±8.0%, it may not significantly affect practical RSV and ROA calculations, given the wide range of regurgitation observed clinically. Because α was divided by 180°, a 10° measurement difference will yield only a 5.6% difference in RSV and ROA.

It should be noted that our study population contained a highly enriched proportion of patients with severe mitral regurgitation, particularly flail leaflet requiring mitral valve surgery. This was done by design to obtain maximal experience with the geometric correction factor proposed here and to validate it in a large number of patients in a clinical setting. In routine daily practice (such as our earlier series of ambulatory patients with mitral regurgitation in whom no cases of flail leaflet were noted),^{9} ^{10} such a correction factor might need to be applied only occasionally. Special care should be taken for patients with posterior mitral leaflet prolapse when the proximal flow convergence method is used to calculate RSV and ROA because proximal flow constraint is so common in this setting.

Furthermore, in patients with acute severe regurgitation, one might anticipate that the limited ventricular dilation would lead to prominent flow constraint. Unfortunately, the number of such patients in the present study was too small to allow meaningful analysis. A dedicated study of this issue would certainly be of value.

We^{12} and others^{40} previously described an automated algorithm that seeks simultaneously to define the location of the regurgitant orifice and to quantify the flow rate through it. Application of those algorithms to these patients was not a study goal but would represent an important future application. For this study, we defined the regurgitant orifice as lying in the plane of the tips of the mitral leaflet for the unconstrained situation and at the level of the plane of the nonflail leaflet for flail mitral leaflet; these localizations seemed to yield accurate flow estimates.

### Conclusions

In summary, using biplanar and multiplanar transesophageal echocardiography, we have demonstrated that calculation of RSV and ROA by the proximal convergence method is highly accurate, assuming hemispheric contour shape, when the proximal convergence zone is unconstrained by a surrounding ventricular wall. However, significant overestimation occurs when an adjacent left ventricular wall constrains the proximal flow field. Fortunately, however, a simple correction factor based on the observed geometry surrounding the regurgitant orifice yields nearly complete correction of the regurgitant volume estimate, even for significantly constrained convergence zones. Application of such a correction factor should have important practical results in improving the quantification of mitral regurgitation by the proximal convergence method in clinical practice.

## Selected Abbreviations and Acronyms

2D | = | two-dimensional |

cPFC | = | central proximal flow convergence |

ePFC | = | eccentric proximal flow convergence |

ROA | = | regurgitant orifice area |

RSV | = | regurgitant stroke volume |

SV | = | stroke volume |

## Acknowledgments

We acknowledge the important technical assistance provided by sonographers and clinical fellows in our laboratory in the collection of these data and the assistance of Suzan Zelko in preparation of the manuscript.

## Footnotes

Presented in part at the 66th Scientific Sessions of the American Heart Association, Atlanta, Ga, November 7-11, 1993.

- Received August 4, 1994.
- Revision received February 27, 1995.
- Accepted May 4, 1995.

- Copyright © 1995 by American Heart Association

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- Quantification of Mitral Regurgitation by the Proximal Convergence Method Using Transesophageal EchocardiographyMin Pu, Pieter M. Vandervoort, Brian P. Griffin, Dominic Y. Leung, William J. Stewart, Delos M. Cosgrove and James D. ThomasCirculation. 1995;92:2169-2177, published online before print October 15, 1995http://dx.doi.org/10.1161/01.CIR.92.8.2169
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- Quantification of Mitral Regurgitation by the Proximal Convergence Method Using Transesophageal EchocardiographyMin Pu, Pieter M. Vandervoort, Brian P. Griffin, Dominic Y. Leung, William J. Stewart, Delos M. Cosgrove and James D. ThomasCirculation. 1995;92:2169-2177, published online before print October 15, 1995http://dx.doi.org/10.1161/01.CIR.92.8.2169

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