## JACC: Cardiovascular Imaging

# An Alternative Isovelocity Surface Model for Quantitation of Effective Regurgitant Orifice Area in Mitral Regurgitation With an Elongated OrificeApplication to Functional Mitral Regurgitation

### This article has a correction. Please see:

## Author + information

- Received April 14, 2010
- Revision received July 22, 2010
- Accepted August 9, 2010
- Published online November 1, 2010.

## Author Information

- Robert D. Rifkin, MD
^{⁎}(rrifkin{at}dom.wustl.edu) and - Shivak Sharma, MD

- ↵⁎
**Reprint requests and correspondence:**

Dr. Robert D. Rifkin, Division of Cardiology, Washington University School of Medicine, Campus Box 8086, 660 South Euclid Avenue, St. Louis, Missouri 63110

## Abstract

**Objectives** The purpose of this study was to develop and test a simple, clinically practical alternative isovelocity surface (ISVS) model for calculating effective regurgitant orifice area (EROA) in mitral regurgitation (MR) when the regurgitant orifice is elongated, such as in functional MR.

**Background** Clinical experience and 3-dimensional imaging suggest that the traditional hemispheric ISVS model used in the conventional proximal isovelocity surface area (PISA) calculation is invalid in certain MR cases and can cause erroneous EROA values.

**Methods** Our ISVS model consisted of 3 sections of equal radius (R): a cylindrical midsection of length (L) positioned between 2 hemispheroidal end sections. Total ISVS area (T_{S}) is equal to 2πR^{2} + πLR and EROA is equal to (V_{N/}V_{CW})T_{S}, where V_{N} is the flow velocity crossing perpendicular to the ISVS, and V_{CW} is the peak MR jet velocity by continuous-wave Doppler. This EROA was corrected for any obtuse angle, θ formed by tented leaflets, by multiplying T_{S} by a planar factor, (θ/180) or a combination of this planar factor for the cylindrical midsection and the solid-angle factor, 1−cos(θ/2), for the 2 spheroidal end sections. In 24 cases of severe or 3+ functional MR, we calculated EROA using 3 traditional hemispheric surfaces and 3 alternative ISVS models that differed in the leaflet angle correction applied. Results were compared with continuity-based EROA using the standard mitral valve − aortic valve stroke volume method and with predictions based upon theoretical geometric considerations.

**Results** The mean differences between continuity EROA and ISVS area–based EROA for no angle correction, planar correction, or combined angle correction were, respectively, 0.38, 0.32, and 0.28 cm^{2} for the 3 spherical surface models and 0.17, 0.018, and −0.012 cm^{2} for the 3 alternative 3-section ISVS models. The empiric EROA results with both the traditional spherical and alternative ISVS models agreed well with theoretical geometric predictions.

**Conclusions** The traditional spherical PISA model underestimates EROA in functional MR. For elongated MR orifices, an ISVS model that mirrors orifice shape yields more accurate EROA values. Correction to the ISVS area for obtuse leaflet angulation improves accuracy of EROA estimation.

Echocardiography is the primary clinical method for assessing severity of mitral regurgitation (1). The proximal isovelocity surface area (PISA) technique for quantifying the effective regurgitant orifice area (EROA) is a widely accepted echocardiographic approach and has performed well in routine clinical use (1). However, it has recently been recognized that the accuracy of the EROA approach is unsatisfactory in some conditions, particularly functional mitral regurgitation (MR). Three-dimensional (3D) echocardiography suggests that the assumption of spherical isovelocity surface (ISVS) geometry, the conceptual basis of the traditional PISA calculation, may be invalid in these cases (2–4). Although 3D echocardiography may prove superior to 2-dimensional (2D) for EROA, 3D is unlikely to attain general use. Therefore, we propose a simple, modified ISVS model that better reflects the geometry of functional MR and incorporates features neglected in the current approach, yet is feasible with conventional 2D imaging systems. The proposed model comprises a cylindrical middle section mirroring the orifice elongation in functional MR and 2 hemispheric end sections. Additionally, our model includes correction for the effect on isovelocity surface area (ISVSA) of the obtuse angle typically formed by leaflet tenting in functional MR.

## Methods

### Population

We screened the Barnes-Jewish Hospital Echocardiographic database from January 25, 2006, to September 15, 2009 for routinely acquired transthoracic studies with severe MR and severe left ventricular (LV) dysfunction, excluding cases with: 1) irregular rhythm; 2) more than mild aortic regurgitation; 3) intrinsic mitral valve (MV) leaflet or annular disease; or 4) inadequate image quality. This study was approved by the Washington University institutional review board.

### Ultrasound equipment

A full description of the ultrasound equipment is available in the Online Appendix.

### PISA radius

The ISVS radius (R) was measured in magnified apical 4-chamber MV images with color baseline shifted to Nyquist velocity 30 to 45 cm/s. Digital loops comprising 1 to 3 R-R intervals were manually cycled through systole to identify the frame with optimal timing and image quality, excluding the initial and final 2 systolic frames. Radius was measured from the color-aliasing boundary on the beam axis to the regurgitant orifice. The orifice position was identified by 2 criteria: 1) the thin neck of the color globe at the leaflet coaptation; and 2) the orifice is not posterior to the leaflet tips because flow must converge along the LV surface of the leaflets. In many cases, simultaneously acquired side-by-side magnified color and 2D MV loops (Fig. 1B) facilitated accurate orifice position identification.

### Leaflet angle

The obtuse angle between the tented leaflets (arc on ventricular side of leaflets) was measured by protractor to the nearest 20° in the frame that the PISA R was measured or the adjacent simultaneous 2D noncolor frame (Fig. 1B) when available.

### MR jet parameters

Continuous-wave (CW) Doppler MR jet flow profiles were planimetered for time velocity integral and peak MR velocity, V_{CW} and MR jet area (mosaic high-velocity portions only) was planimetered in the view and frame in which it was maximum, with Nyquist limits 50 to 60 cm/s.

### Continuity EROA

Continuity EROA was assumed to be the gold standard for EROA (1). Details of our technique are available in the Online Appendix.

### Alternative ISVS model

The 4-chamber view transects the MV commissures (leaflet edges) perpendicularly, whereas the 2-chamber view is nearly parallel to the commissures (Fig. 2, top). With tented leaflets, the commissures fail to coapt, leading to a narrow, elongated gap that forms the regurgitant orifice (Figs. 2A to 2C). We hypothesized that the ISVS in such cases differs from the traditional hemispheric model in 2 respects: 1) there is a cylindrical section lying between 2 partial spheroids that form the ends of the ISVS; and 2) flow can converge toward the orifice over the entire obtuse angle (>180°) formed by the tented leaflets; hence, the ISVS extends below the plane of the orifice until it intersects the leaflet surface.

### EROA calculation

Half-pipe and hemisphere surface areas are πLR and 2πR^{2}, respectively (L is the cylindrical section length). We tested 2 correction factors for the increased ISVSA owing to obtuse leaflet angle, θ (Fig. 2A): 1) planar angle correction = (ISVSA)(θ/180) (wedge leaflet configuration); and 2) solid angle correction = (ISVSA)[1−cos(θ/180)] (conical leaflet configuration) (5). In contrast to acute angles (<180°), the solid angle correction factor is always greater than the planar factor for obtuse angles (Fig. 3).

We applied the planar correction factor to the cylindrical midsection of our model. We evaluated the use of both factors for the model's spheroidal ends. Thus, the total ISVSA had 2 components: 1) the sum of the 2 spheroidal ends, S_{S}; and 2) the cylindrical midsection, S_{C}. Our formulas for total ISVSA, S_{T}, of the alternative ISVS models are:

Model 1: no angle correction: S_{T} = S_{S} + S_{C} = 2πR^{2} + πLR

Model 2: planar (linear) angle correction of both sections: S_{T} = S_{S} + S_{C} = (2πR^{2} + πLR)(θ/180)

Model 3: planar angle correction in cylindrical section and solid angle correction in spherical end sections: S_{T} = S_{S} + S_{C} = (2πR^{2})[1−cos(θ/2)] + (πLR)(θ/180)

We also calculated S_{T} using the same R value but omitting the cylindrical section in 3 additional cases that represent traditional spherical ISVS models, with and without leaflet angle correction:

Model 4: no angle correction (traditional model): S_{T} = S_{S} = 2πR^{2}

Model 5: planar angle correction (wedge-shaped leaflet configuration): S_{T} = S_{S} = 2πR^{2}(θ/180)

Model 6: solid angle correction (conical leaflet configuration): S_{T} = S_{S} = 2πR^{2}[1−cos(θ/2)]

For each model, we calculated MR EROA as:

Equation 1: MR EROA = S_{T}(V_{N}/V_{CW})

V_{N}, the flow velocity crossing perpendicular to the ISVS, is equal to the baseline-shifted color Doppler aliasing velocity (Nyquist limit) in the direction of flow. V_{CW} is the peak MR jet velocity by CW Doppler. S_{T} is given by models 1 to 6. Therefore, we had a total of 6 ISVS EROAs to compare with the continuity EROA.

### Cylindrical section length

In MR with tented leaflets, a broad sheet of color regurgitation is observed in the apical 2-chamber view (Fig. 1C) emerging from the posterior leaflet border along the orifice length. We measured L immediately behind the leaflets (Figs. 1C and 1D, solid black double-headed arrows), tabulating 2 values of L for each case: 1) average width in mid-systolic frames; and 2) maximum mid-systolic width.

We calculated the EROAs for models 1 to 3 using both average and maximum values of L.

### Theoretical effect of cylindrical section on observed R for a given MR EROA

To determine the effect of elongated ISVS shape and obtuse leaflet angle on the aliasing R that will be observed, we used model 3's ISVSA formula for S_{T} with Equation 1:_{obs}:

_{obs}, for an assumed EROA = 0.5 cm^{2} for values of L and θ varying, respectively, between 0 to 2 cm and 180° to 270°. We assumed V_{N} and V_{CW} such that 2π(V_{N}/V_{CW}) = 1/2, enabling the shortcut formula, EROA = (R_{obs}^{2})/2, for calculating traditional PISA EROA (model 4). We graphed these apparent EROAs over the same values of L and θ used to graph R_{obs} to determine the theoretical error caused by use of the traditional model. All measurements were made by the authors before these theoretical results, and observers were therefore blinded to the theoretical predictions.

### Control cases

We calculated the EROA by traditional spherical PISA formula (model 4) and by continuity in 12 patients with the following features: 1) echo diagnosis of severe MR; 2) absent leaflet tenting; 3) ISVS zones deeper than they were wide; 4) isovelocity zone shape similar in both 4- and 2-chamber views; 5) well-defined vena contractas (VCs) of similar size in 4- and 2-chamber views; and 6) mild or less aortic regurgitation.

### Statistical analysis

We tested the mean differences between continuity and model EROA across the 6 models for significance by repeated-measures analysis of variance (ANOVA) using SPSS software (SPSS, Inc., Chicago, Illinois). We used *t* tests to test each of the 6 mean values against zero. We employed analysis of paired differences (6,7) for method comparison between each model's EROAs and the continuity EROAs, plotting the mean and limits of agreement (±1.96 SD) and a regression line for the difference between model and continuity EROA versus their mean values in each case for each model. We tested the significance of the means, correlation coefficients, and slopes versus zero (H_{o} = 0) by *t* tests (means and slopes) and *T* statistic for sample correlation coefficient and Fisher *Z* transformation (correlation coefficients). Sample size calculations and SPSS ANOVA output are available online (Online Appendix).

## Results

### Population composition and mean model values

There were 17 men and 7 women, with a mean age of 65 years. Fourteen had nonischemic and 10 had ischemic cardiomyopathy. The mean LV ejection fraction was 22%. Other important mean values related to the ISVS models and image acquisition settings are shown in Table 1. It is noteworthy that the mean cylindrical section ISVSA (2.65 cm^{2}, row 11) was approximately 56% of the mean total ISVSA (2.65/[2.65+2.05], row 9).

### MR jet characteristics

Jet geometry measurements relevant to MR severity are shown in Table 1 (rows 2 and 3). Additional jet features are available in the Online Appendix.

### ISVS EROA versus continuity EROA

The 3 spherical models (models 4 to 6) produced the smallest EROAs in all cases (Table 2 and Fig. 4⇓, bars 1 to 3, each case) and the largest differences from continuity EROA (Table 2 and Figs. 5A and 5B, bars 1 to 3).

Mean EROA differences from the continuity EROA (Fig. 5C) among the 6 models were significant (p = 0.0016, ANOVA). Angle compensation alone did not adequately correct spherical model deviation from continuity EROA (Figs. 5A and 5B, bars 2 and 3 in each case; Fig. 5C, models 5 and 6 in bars 2 and 3). Smaller but persistent differences were noted for the new model without angle-correction (Fig. 5C, model 1, bar 4). However, when both L and the obtuse leaflet angle are accounted for, either using planar or combined angle correction (Fig. 5C, models 2 and 3, bars 5 and 6), the disparity with continuity EROA was small.

Use of the maximum, instead of the mean, 2-chamber jet width slightly worsened agreement with continuity EROA for models 2 and 3 (differences from continuity = −0.019 and −0.049 cm^{2} vs. +0.018 and −0.012 shown above bars 5 and 6, respectively; Fig. 5C). Model 1 improved, but only slightly (difference = 0.138 vs. 0.165 shown above bar 4; Fig. 5C).

The variation in the mean differences (continuity EROA − model EROA) across the 6 models was significant (p < 0.00001) by repeated-measures ANOVA under either Greenhouse-Geisser, Huynh-Feldt, or lower-bound corrections. Detailed ANOVA results are available in the Online Appendix.

Paired-difference analysis (Fig. 6) also showed that the mean difference between model and continuity EROA was significant for all traditional models (models 4 to 6; p ≤ 0.023) but not significant for the alternative models (models 1 to 3; p ≥ 0.15). Similarly, regression slopes differed significantly from zero for all 3 traditional models (p < 0.000001) but not for the alternative models, indicating the absence of influence of EROA magnitude on accuracy only for the alternative models, particularly models 2 and 3 that included angle correction. The correlation between model and continuity EROA for model 2 was 0.823 (Fig. 7).

### Qualitative severity classification

Traditional spherical PISA misclassified many cases as mild or moderate, despite leaflet angle correction (Table 3). The cylindrical model without angle correction moderately improved classification; however, with leaflet angle correction, classification accuracy almost matched classification of continuity EROA.

### Theoretical predictions

With either leaflet tenting or orifice elongation, theory predicts a reduction in R (Fig. 8A). For the case of a true orifice area of 0.5 cm^{2} (severe MR), for θ = 270°, and L = 0, R will be approximately 0.76 cm instead of 1 cm. With orifice elongation also present (L > 0), R falls further. For L = 1 cm and θ = 240°, R will be approximately 0.63 cm rather than 1 cm. This reduced R results in underestimation of the EROA to approximately 0.19 cm^{2} when it is used in spherical models to calculate EROA (Fig. 8B). Even when the ISVS is spherical (L = 0), the obtuse leaflet angle results in reduced R and EROA underestimation (y-axis intersections, Figs. 8A and 8B, respectively).

Figure 9 generalizes Figure 8, top, showing percent R changes for various orifice areas from 0.2 to 0.6 cm^{2}.

### Control cases

The EROAs by traditional spherical PISA, 0.61 cm^{2}, and Doppler continuity, 0.65 cm^{2}, agreed closely (Table 4, rows 1 and 2). Mean PISA R was 1.18 cm (Table 4, row 6). Other parameters support the presence of severe MR in these cases. The correlation between the LV stroke volume (SV) by Doppler continuity and the PISA MR was 0.73.

## Discussion

### Main findings

Our principal findings were: 1) in functional MR, the traditional hemispheric ISVS model underestimated the true ISVSA, resulting in marked underestimation of the EROA; 2) an elongated ISVS model consisting of a simple cylinder flanked on both sides by spheroids having R identical to the cylinder improved EROA estimation; and 3) correction to the resulting combined ISVSA for the increased flow owing to the obtuse angle formed by tented leaflets in functional MR may be necessary to accurately estimate the EROA with either model.

### Accuracy of new model

Despite moderate case-to-case variation in quantitative accuracy of the new model (Figs. 5A and 5B), agreement of mean values with Doppler continuity was very good (Fig. 5C). Moreover, in the individual cases, the new model produced the closest quantitative estimates and best qualitative classification of severity compared with the Doppler continuity reference. This superiority obtained despite angle correction of spherical models (Fig. 5C, bars 2 and 3).

We also found good agreement between theoretical and measured values of ISVS L and R. Theory showed that for a given EROA, R falls substantially as the orifice lengthens and tenting worsens. This may explain why Grigioni et al. (8) reported that adverse event rates in functional MR begin to increase at EROA = 0.2 cm^{2} versus 0.4 cm^{2} in other forms of MR. The EROAs based on average 2-chamber apical view mid-systolic MR jet width agreed with continuity-EROAs slightly better than when the maximum width was used.

### MR jet area

The MR jet to left atrial (LA) area ratio performed as well in classification of MR severity as our new method (Table 3) and far superior to the traditional PISA model. This could be due partly to the use of consistent Nyquist limits and other machine settings in our lab for recording MR jets and partly to our highly selected study population.

### Angle correction factor

In contrast to mitral stenosis (5), angle correction has been neglected in the application of the PISA method for MR (9). However, computational and in vitro tank models have been used to analyze the effect of angulation on traditional PISA-based area estimates for regurgitation through circular orifices at the apex of inverted funnels (10,11). Cape et al. (10) used a tank model of MR with funnel-shaped obtuse inflow angles up to 270° and reported that, compared with a flat (180°) surface, PISA R decreased progressively as the obtuse inlet angle increased. The solid angle factor, 1−cos(θ/2), accurately corrected their ISVSAs. In contrast, using a similar tank model, Giesler et al. (11) found the empirically measured correction factor was less than 1−cos(θ/2). The reduction increased for small orifices and proximity to the orifice. For example, with a 7-mm diameter, 240° funnel orifice (area = 0.4 cm^{2} corresponding to 3+ MR), and at 10 to 12 mm from the orifice (typical color isovelocity shell R for this size orifice), the empiric correction factor was approximately 1.3 instead of 1.5 given by 1 − cos(θ/2). Thus, the solid angle factor could result in a 15% overestimation (1.5/1.3) of orifice area for a circular orifice.

### Previous alternative ISVS models

Matsumura et al. (4) developed customized software using 7 measurements of the 3D color MR Doppler field to reconstruct the ISVS as a collection of discrete triangular facets and numerically computed their area. Its shape tended to be hemiellipsoidal. This complex model required specialized hardware and software, yet only reduced the EROA underestimation from 49% in the traditional hemispheric model to 26% when compared with the Doppler continuity EROA.

The present study was motivated by an interest in developing a model that would be practical for routine clinical use on standard ultrasound equipment. Our parametric model meets this objective; in this initial investigation, its performance appears similar or superior to that of Matsumura et al. (4). It is unclear whether their program inherently corrected for obtuse leaflet angles; however, if not, this could explain our improved results. In this regard, it is of interest that when we omitted angle correction from our model (Fig. 5C, bar 4), mean underestimation of continuity EROA was 29.5% (0.165/0.56), a value similar to the 26% underestimation reported by Matsumura et al. (4), suggesting that their numeric method may not have corrected for leaflet angle.

### Basis for elongated ISVS model

The need for an axially asymmetric ISVS model relates to its proximity to the orifice. Were it sufficiently remote from the orifice, the ISVS would be spheroidal regardless of orifice shape. However, with lower Nyquist aliasing thresholds, an expanded ISVS would collide with tissue boundaries and overlap LV outflow, distorting its shape. Additionally, excessive low Nyquist color noise would obscure the isovelocity color boundary. Thus, at practical Nyquist thresholds, the ISVS model for an asymmetric orifice may need to mirror orifice shape more closely. This implies that the interpreter must assess from image features whether a cylindrical or spherical model should be used to compute the EROA. Our results imply that the ISVS with our alternative geometry is far enough from an elongated orifice that minor irregularities in orifice width along its length and its crescentric shape (Fig. 2, top) do not distort the ISVS shape significantly (Figs. 2A to 2C).

### Elliptic versus cylindrical ISVS shape

Unlike a sphere or cylinder, the surface area of a general ellipsoid cannot be expressed by an exact algebraic function (12). Thus, elliptic models may require numeric reconstruction of the ISVS, rendering them impractical for clinical use. By contrast, the simplicity of our model lends itself to a simple shortcut for EROA when the Nyquist limit (V_{N}) is approximately 40 cm/s and MR peak velocity (V_{CW}) is approximately 5 m/s:

EROA = (2πR^{2}+πRL)(V_{N}/V_{CW}) = πR(2R+L)×(V_{N}/V_{CW})∼R^{2}/2 + RL/4

Accordingly, addition of the term RL/4 provides the ISVSA of an elongated orifice for this special case of V_{N} and V_{CW}. The obtuse angle correction can then be applied for the final EROA estimate. Thus, for planar angle correction in all model sections:

EROA ∼ (R^{2}/2 + RL/4)(θ/180)

### Vena contracta

Our study suggests that the vena contracta (VC) measurement must be used cautiously for severity assessment in functional MR. With orifice elongation, a scan plane not precisely perpendicular to the orifice may produce a factitiously large VC. The true VC is seen only in the plane precisely perpendicular to the long axis of the orifice and may be misleadingly small (Fig. 2C). Geometric considerations using a rectangular or elliptic shape to model the elongated orifice show that for EROAs of 0.3 to 0.5 cm^{2} and L of 1.0 to 2 cm, the VC seen exactly end-on in the plane perpendicular to the long axis of the orifice (Fig. 2B) would measure between 75% and 25%, respectively, of that with a circular orifice of identical ERO. In our retrospective series, images were not optimized for VC. Therefore, we omitted this indicator of MR severity from the analysis.

### Pitfalls in use of the cylindrical model

Just as the spherical ISVS model may cause underestimation of EROA when applied to an elongated orifice, the cylindrical model can cause overestimation of EROA if applied to a circular orifice, the magnitude of which is approximately RL/4. Therefore it is important to recognize the presence of an elongated orifice and to avoid applying the cylindrical model when features of significant orifice elongation are absent. Potentially, this source of error could be removed by subtracting the 4-chamber view VC dimension from the 2-chamber broadside jet length and using this value for L in the cylindrical model, but we did not investigate this approach in the present study. However, correction for obtuse leaflet angle, if present, may still improve accuracy even in the setting of a circular or nearly circular orifice.

### Recognizing orifice elongation

Elongation is suggested in a 2-chamber view by a wide central band of free regurgitation perpendicular to the valve plane, appearing to originate along the posterior leaflet surface without a visible VC. A narrow band of color reversal parallel to the valve leaflet plane is seen on the LV side of the leaflet surface, similar in depth to the 4 chamber ISVS radius R (corrected for Nyquist differences) and length similar to the color MR jet width, L, on the LA side (Figs. 1C and 1D). This band represents the cylindrical ISVS seen broadside.

In a 4-chamber view, with a circular orifice and spherical ISVS, the color-aliased zone is as deep as, or deeper than, it is wide, and its width tapers near the orifice. By contrast, when the orifice is elongated, the aliased zone tends to be wider than it is deep owing to scan plane obliquity off the perpendicular with the commissure. This shape, and the relatively shallow size of the zone for the MR jet area, are often mistakenly attributed to technical factors, but they actually reflect the elongated ISVS shape. However, the width of the isovelocity zone will generally be smaller in the 4- than in the 2-chamber view, whereas the dimensions of the zones are similar in both views with a circular orifice and spheroidal zone. Finally, the 4-chamber VC, if carefully imaged, will be much narrower than the minimum width of the MR jet seen in the 2-chamber view at the leaflet.

### Study limitations

Systematic overestimation of the MV SV or underestimation of ISVS R could cause the traditional PISA method to appear to underestimate continuity-based MR EROA. Identifying orifice location is often challenging, allowing both underestimation and overestimation of ISVS R. However, because flow must converge along the leaflet's ventricular surface, the orifice cannot be behind this surface. Importantly, our theoretical predictions of expected ISVS R with elongation and leaflet tenting agreed closely with our empiric R measurements, and our control series PISA EROA agreed well with their corresponding continuity EROAs, validating our measurement technique and supporting the absence of systematic errors in our ISVS R measurements.

The major potential source of overestimation of MV SV is mitral annular diameter. Our mean diameter was 3.3 cm. Mihalatos et al. (13) reported that the MV orifice becomes circular and its diameter increases progressively with MR severity. They found mean end-systolic and end-diastolic diameters of 1.95 cm/m^{2} and 1.86 cm/m^{2}, respectively, in 19 severe MR cases. For an average adult body surface area of approximately 1.7 m^{2}, this equates to a diameter of approximately 3.23 cm (1.9 × 1.7), in close agreement with our measurements. Moreover, our mean Doppler continuity EROA, 0.55 cm^{2}, and regurgitant fraction, 61.5%, are not unusually large and are highly consistent with the mean jet to LA area ratio, 50.7%. These findings suggest that overestimation of continuity-based EROA by overmeasurement of MV orifice diameter was unlikely in our series.

Our study was retrospective with a small population size. Because we had theoretical model–predicted values that we generated after all measurements were made, we treated them as a proxy for image blinding and observer variability studies. The close agreement between our theoretical and empiric values strongly supports accuracy of our measurements for both continuity MR SV and ISVS R and mitigate these limitations. Accuracy of the new model in cases with more normal LV function and/or significantly less leaflet tenting and MR was not established in this study.

## Conclusions

Our findings add insight to the ISVS methodology in MR but also introduce additional complexity that will require greater attention in image acquisition and interpretation. The popular conception of the PISA method, based on a hemisphere, appears to be an oversimplification. It is necessary for the interpreter to assess image features and select the appropriate model to apply. Image acquisition protocols may need revision to bring out these features more clearly. In particular, magnified MV images should be obtained in 4- and 2-chamber views in color and 2D modes, with attention given to recording the shape of the flow convergence zones in both views.

When the ISVS R > 1 cm in any view (with Nyquist ∼40 cm/s and peak MR velocity ∼5 m/s), MR is likely to be severe. But when R < 1 cm, careful scrutiny of the orthogonal plane will be necessary to assess whether an elongated or spherical model is appropriate to calculate EROA. We note that that 10 of our 24 cases carried an ischemic cardiomyopathy diagnosis, suggesting that our model may be applicable in more than one etiology of MR. The alternative model clarifies the not uncommon cases in which the traditional PISA EROA calculation appears too small for the size of the color flow Doppler MR jet.

Finally, our data suggest that angle correction should be employed for final calculation of EROA regardless of which model is used. The simple planar correction appears satisfactory. However, more data are needed to verify the need for and especially the correct magnitude of angle correction given the differences reported in the literature cited.

## Appendix

For expanded Methods, Results, and Discussion sections, please see the online version of this article.

## Footnotes

The authors have reported that they have no relationships to disclose.

- Abbreviations and Acronyms
- CW
- continuous wave
- EROA
- effective regurgitant orifice area
- ISVSA
- isovelocity surface area
- L
- width of MR jet in apical 2-chamber view immediately behind leaflets
- PISA
- proximal isovelocity surface area
- R
- ISVS radius
- S
_{C} - surface area of cylindrical ISVS section
- S
_{S} - surface area of 2 spherical end sections
- S
_{T} - surface area of total ISVS area (S
_{S}+ S_{C}) - SV
- stroke volume
- VC
- vena contracta

- Received April 14, 2010.
- Revision received July 22, 2010.
- Accepted August 9, 2010.

- American College of Cardiology Foundation

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