# Effect of Dynamic Flow Rate and Orifice Area on Mitral Regurgitant Stroke Volume Quantification Using the Proximal Isovelocity Surface Area Method

## Author + information

- Received February 26, 2008
- Revision received May 6, 2008
- Accepted May 21, 2008
- Published online August 26, 2008.

## Author Information

- Thomas Buck, MD, FACC, FESC
^{⁎},^{⁎}(thomas.buck{at}uk-essen.de), - Björn Plicht, MD
^{⁎}, - Philipp Kahlert, MD
^{⁎}, - Ingmar M. Schenk, MD
^{⁎}, - Peter Hunold, MD† and
- Raimund Erbel, MD, FACC, FESC
^{⁎}

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

Dr. Thomas Buck, West German Heart Center Essen, Department of Cardiology, University Essen, Hufelandstrasse 55, 45122 Essen, Germany.

Effect of Dynamic Flow Rate and Orifice Area on Mitral Regurgitant Stroke Volume Quantification Using the Proximal Isovelocity Surface Area Method

Thomas Buck, Björn Plicht, Philipp Kahlert, Ingmar M. Schenk, Peter Hunold, Raimund Erbel

Accurate evaluation of severity of mitral regurgitation (MR) is difficult because the proximal isovelocity surface area (PISA) method provides only mitral regurgitant flow rate (MRFR), whereas calculation of the clinically more important mitral regurgitant stroke volume (MRSV) is challenging because of dynamic variations of MRFR. We therefore clinically validated accuracy and feasibility of single-point versus time-integral PISA methods for quantification of MRSV in 73 patients with MR of different mechanisms using magnetic resonance imaging for reference. For single-point PISA methods, we found significantly greater underestimation of MRSV, particularly in functional MR compared with time-integral PISA, thus revealing an important dependency of MRSV calculation from the underlying mechanisms of MR.

## Abstract

**Objectives** This study sought to determine the effect of dynamic variations of mitral regurgitant flow rate (MRFR) and effective regurgitant orifice area (EROA) on mitral regurgitant stroke volume (MRSV) quantification using 4 different single-point and time-integral proximal isovelocity surface area (PISA) methods using magnetic resonance imaging (MRI) for reference.

**Background** Using PISA provides measures of MRFR, but calculating MRSV is challenging because of dynamic variations in the flow profile dependent on the underlying mechanism of mitral regurgitation (MR). Although various single-point and time-integral approaches have been described to overcome this limitation, uncertainty exists about the accuracy and feasibility of these methods in routine clinical practice.

**Methods** In 73 patients with MR of different etiologies, MRSV was calculated from an apical 4-chamber view using the following 4 hemispheric PISA methods: 1) PISA-velocity–time integral (VTI) = midsystolic MRFR by PISA × regurgitant flow VTI/peak velocity; 2) simplified PISA = midsystolic MRFR/3.25; 3) serial PISA *=*sum of instantaneous MRFRs over serial 2-dimensional frames; and 4) M-mode PISA = time-integral of MRFRs from color M-mode. The MRSV by MRI was calculated from mitral inflow minus aortic outflow.

**Results** Single-point PISA methods yielded greater underestimation of MRSV (mean error: −13.3 ± 10.2 ml [PISA-VTI]; −13.5 ± 10.3 ml [simplified PISA]), particularly in functional MR, compared with time-integral PISA methods accounting for variations of MRFR and EROA over time (mean error: −8.0 ± 6.4 ml [M-mode PISA]; −8.7 ± 7.4 ml [serial PISA]).

**Conclusions** Depending on the underlying mechanism of MR, dynamic variations of MRFR and EROA revealed important limitations of MRSV calculation using single-point and time-integral PISA methods.

- echocardiography
- mitral regurgitation
- dynamic variation
- proximal isovelocity surface area
- effective regurgitant orifice area

Accurate determination of mitral regurgitant stroke volume (MRSV) as a measure of left ventricular volume overload is important in patients with mitral regurgitation (MR), especially because optimal timing of valve repair demands accurate assessment of the severity of MR (1–4). The proximal isovelocity surface area (PISA) method, although primarily intended for measurement of mitral regurgitant flow rate (MRFR) (5–7), has been shown to provide measures of effective regurgitant orifice area (EROA) and MRSV (8–12). However, until now, clinical application of the PISA method has been limited for 2 main reasons: 1) in most cases MR is dynamic throughout systole depending on the etiology (13–15), but the PISA method determines MRFR and EROA only at a single time point, causing uncertainty over what MRFR or EROA to use for calculation of MRSV; and 2) because the assumption of a hemispheric PISA only holds for circular orifices, uncertainty exists in cases in which regurgitant orifices are noncircular or slit-like, most common in functional MR (13,16,17). Although Yosefy et al. (16) recently validated clinical application of a hemielliptic PISA formula for quantification of EROA taking into account that the majority of regurgitant orifices were noncircular, the importance of dynamic variations of MRFR and EROA on quantification of MRSV using the PISA method has not yet been further explored in clinical validation studies. Chen et al. (18) first showed improved accuracy of mean flow rate calculated using the M-mode PISA method compared with peak flow rate by standard PISA application indicating relevant variation of MRFR and EROA during systole. Investigating the dynamic pattern of MR in different etiologies using M-mode recording of PISA, Schwammenthal et al. (13) and Hung et al. (19) found characteristic variations of MRFR and EROA throughout systole depending on the mechanism of MR. Importantly, in patients with typical functional MR, they described a characteristic flow pattern with peak flow rate in early and late systole and midsystolic trough caused by improved leaflet coaptation as a cause of peak midsystolic closure pressure. This dynamic pattern, however, is most challenging the PISA principle because commonly the largest PISA in midsystole is used for calculation of MRFR, EROA, and MRSV, whereas in functional MR midsystolic PISA is smallest.

We therefore hypothesized that routine clinical estimation of MRSV using a standard single-point PISA method should produce significant error in the presence of dynamic functional MR. Although prior investigators using either single-point or time-integral PISA methods found significant inaccuracy—mainly overestimation—of MRSV, especially when PISA calculation was based on maximum single-point MRFR (15,20,21), the error of single-point or time-integral PISA methods related to different patterns of dynamic MR has not yet been investigated against an independent reference method. We therefore compared the following 4 previously described PISA approaches based on single-point PISA measurements or integration of PISA over time in 3 distinct MR patient groups with different etiologies against magnetic resonance imaging (MRI) used as an independent reference: 1) standard PISA approach multiplying single-point MRFR times the ratio of velocity–time integral (VTI) and peak velocity of MR flow; 2) a simplified PISA formula multiplying single-point MRFR by an empirical factor of 3.25; 3) time-integral PISA by the sum of serial PISA MRFR; and 4) time-integral PISA from color M-mode recording.

## Methods

The study was performed prospectively in 87 consecutive patients referred for routine echocardiography who showed significant MR in color Doppler mode, and 73 patients (84%) (age 58.4 ± 17.1 years, 41 male, 32 female) had suitable image and color Doppler quality for this study. The leading etiology was functional MR in 37, degenerative or rheumatic in 21, and prolapse in 15 patients. Etiology was classified as functional MR based on the characteristic finding of leaflet tethering and incomplete mitral leaflet closure in the presence of left ventricular dilatation or remodeling, but with normal mitral valve anatomy (22,23). Degenerative or rheumatic MR was considered the underlying cause in patients with leaflet thickening and sclerosis or immobility without leaflet tenting or MVP (24). An MVP was considered in cases with systolic mitral leaflet motion of 2 mm or more beyond the mitral annulus of at least 1 segment of the anterior and posterior leaflet with or without flail leaflet (25,26). Eccentric MR jets were present in 8 of 37 patients with functional MR, 6 of 21 patients with degenerative or rheumatic MR, and 12 of 15 patients with prolapse. According to standard semiquantitative grading of MR based on color Doppler jet size, vena contracta width, and left atrial dilation, 12 patients had mild-to-moderate MR, 28 had moderate MR, and 33 had severe MR (1). Patients with implanted pace makers and defibrillators were excluded because of incompatibility with MRI. Echocardiographic studies were performed on a standard cardiac ultrasound system (Sonos 7500 and IE33, Philips Medical Systems, Andover, Massachusetts). The study was approved by the institutional committee on human research, and written informed consent was obtained from all patients who agreed to participate in the study.

### PISA method

The PISA method is based on the concept of measuring regurgitant flow within the proximal flow convergence zone instead of measuring it at the level of the small and irregularly shaped regurgitant orifice. Within ideal conditions, the proximal flow field consists of concentric hemispheric shells of isovelocities. According to the principle of conservation of mass, flow through any of the hemispheric proximal isovelocity surface areas (PISA) equals the flow through the regurgitant orifice. For practical application, PISA can be visualized by color Doppler aliasing at the Nyquist velocity limit. Instantaneous MRFR can be calculated by entering the PISA radius (r) into the hemisphere formula 2π × r^{2}× the Nyquist velocity v(Ny), with the radius measured from the zenith of the PISA surface to the regurgitant orifice, usually when the PISA radius is largest during systole.

### Calculation of MRSV

Extending the basic PISA method, MRSV can be estimated in 2 ways: 1) by mean EROA × VTI of MR flow, with estimation of mean EROA from single-point MRFR; or 2) by integration of MRFR over the period of regurgitation. In the present study we compared 2 single-point PISA methods and 2 time-integral methods, all based on hemispheric PISA calculation from single-plane 2-dimensional color Doppler data obtained in apical 4-chamber view. An apical 4-chamber view was preferred over a parasternal long-axis view to ensure parallel orientation of the sound waves to regurgitant flow to reduce the Doppler angle error (27). All patients were studied in the left lateral supine position with the baseline shift of the Nyquist level optimized to achieve a hemicircular PISA cross section (27). The wall filter was kept at the factory default setting “high,” which was tested to provide the best color Doppler PISA representation with the least suppression and least oversaturation of color Doppler. For each method, the average time for acquisition and offline analysis was documented to assess clinical feasibility. All 4 PISA methods were performed subsequently within the same echocardiographic study and within 1 h from MRI. No method required special software, and therefore could be readily applied with standard measurement tools onboard the ultrasound system. Practical application and calculation of MRSV by the 4 different PISA approaches was as follows.

#### PISA-VTI

The PISA-VTI approach describes the standard PISA approach multiplying single-point MRFR times the ratio of VTI and peak velocity of MR flow (3,8,11,12). First, peak MRFR is obtained by using the hemispheric PISA formula 2π × r^{2}× v(Ny) as described earlier (Fig. 1A).Then, assuming the maximal PISA radius occurred simultaneously with midsystolic peak regurgitant velocity v_{max}from continuous-wave Doppler recording, EROA was derived as MRFR_{peak}/v_{max}. Assuming that the calculated single-point EROA represents mean EROA, MRSV was calculated as EROA_{mean}× VTI of MR flow from continuous-wave Doppler or

In cases of functional MR in which midsystolic PISA was too small because of midsystolic mitral leaflet closure (13), we selected the first PISA radius before midsystole that was large enough to be measured accurately.

#### Simplified PISA

Based on the PISA-VTI method, prior studies empirically determined a relatively constant ratio between regurgitant flow v_{max}and VTI of 3.25 ± 0.47 (28). Therefore, a simplified PISA approach, in which continuous-wave Doppler measurements could be avoided, was used as follows to obtain MRSV:

As an advantage of the simplification, only midsystolic single-point PISA radius was required for calculation of MRSV.

#### Serial PISA

To account for the dynamic variation of the PISA radius and MRFR throughout the period of regurgitation (Fig. 1B), MRSV was calculated as the sum of single-frame regurgitant flow volumes derived from single-frame MRFRs times color Doppler frame duration (14) or:

#### M-Mode PISA

Color Doppler M-mode acquisition of PISA was used before to calculate MRSV either: 1) by multiplying mean MRFR by the time of regurgitation, in which mean MRFR was calculated by integrating instantaneous MRFRs over the period of regurgitation using custom software (13); or 2) based on the mean radius derived from the PISA M-mode area divided by its width (18). However, MRFR is only proportional to the mean of squared radii (r^{2}_{mean}) but not to the mean radius squared (r_{mean})^{2}, which are different: as a simple example, r^{2}_{mean}of r_{1}= 2 cm, r_{2}= 3 cm, r_{3}= 4 cm equals 9.7 cm^{2}whereas (r_{mean})^{2}equals 9 cm^{2}. To account for this, we applied a practical approach that simply derives r^{2}_{mean}from a PISA M-mode volume instead of (r_{mean})^{2}derived from a PISA M-mode area using standard measurement tools onboard routinely used ultrasound systems. Although the following M-mode PISA approach is subject to the basic principle of temporal integration of instantaneous flow rates, we provided a brief description of the practical application for clarification of the assumptions we applied. First, we traced the aliasing border of the color Doppler PISA M-mode signal (Fig. 1C). Because in most cases the leaflets were not traced during color Doppler PISA M-mode registration as the scan line lies within the orifice, correspondence of the lower border of the M-mode PISA signal and the leaflet level was confirmed by slightly tilting the scan line off the axis toward the leaflet border. Although the unit of the horizontal axis of the M-mode signal is time, we assumed the resulting area to be the long-axis cross-sectional area of a volume [Vol (M-mode PISA)] in a Cartesian space; the volume was determined using the disc method with a horizontal long axis as given by the following formula (Fig. 1C):^{2}_{mean}:

Note that by using the M-mode PISA volume, this algorithm allowed calculation of the true mean of squared radii (r^{2}_{mean}), in which r^{2}_{mean}can virtually be derived from an infinite number of instantaneous r^{2}because it is derived from a PISA M-mode volume divided by the length of the volume. By using the vertical pixel calibration, which is the M-mode spatial dimension for the pixel calibration of the horizontal axis, which normally is time, this method simply overcomes the limitation that onboard conventional ultrasound systems no software for integration of individual disks described by 1/4 π r^{2}over time exists. In our approach the dimension of the horizontal axis cancels out when computing r^{2}_{mean}, so it is unimportant whether it is time or spatial dimension. Entering r^{2}_{mean}into the PISA formula, we obtained mean MRFR, which, multiplied by the time interval (t) of the PISA M-mode signal, provided MRSV:

By replacing r^{2}_{mean}we derived the following formula, consisting of parameters simple to measure:

Using this formula, MR volume calculation only required measurement of volume, length, and duration of the PISA M-mode signal.

#### Definition and Determination of Dynamic Variation of MRFR and EROA

To determine the effect of dynamic MR on the calculation of MRSV, we differentiated 3 patterns of dynamic variations based on color Doppler M-mode recording of PISA as previously described (13): 1) a convex pattern with a midsystolic maximum of the PISA radius typically found in degenerative MR, flail leaflet, or prolapse; 2) a pattern of nearly constant PISA radius throughout systole common in rheumatic and degenerative MR; and 3) a concave pattern with an early and end systolic maximum of the PISA radius and a midsystolic trough as typically found in functional or ischemic MR. For further analysis, patients were divided into 3 groups according to the 3 different patterns of MRFR dynamics primarily based on visual assessment of the M-mode PISA shape, assuming a ratio of midsystolic to mean MRFR (MRFR_{mid/mean}) >1 to indicate convex variation of MRFR, a ratio of 1 indicating constant MRFR and a ratio <1 indicating concave variation of MRFR.

Because MRSV is determined by the product of mean EROA ×VTI, in which VTI is an unambiguous parameter in each patient, effects of dynamic variations of MRFR and EROA on the accuracy of the 4 PISA approaches should be directly detected by the error of calculated mean EROA compared with true mean EROA. Thus, values of calculated mean EROAs for each method were obtained from dividing calculated MRSV by VTI, VTI being the same for all 4 PISA methods in each individual patient. Reference values of instantaneous EROAs were derived from superposition of M-mode PISA and continuous-wave Doppler signals and dividing instantaneous MRFR by the simultaneous continuous-wave Doppler velocity. From this reference PISA approach, mean EROA reference was then determined as the mean of instantaneous EROAs.

### MRI

The MRSV was obtained by MRI as mitral inflow minus aortic outflow from phase-velocity maps using a standard 1.5-T cardiac MRI system (Magnetom Sonata, Siemens Medical Systems, Erlangen, Germany). Phase-contrast cine acquisitions were obtained in planes aligned with the mitral annulus and orthogonal to the mid-ascending aorta (29). An electrocardiogram-triggered free-breathing through-plane phase-contrast sequence (repetition time 25 ms; echo time 4.8 ms; flip angle 15°; matrix 129 × 256; 4 averages) was used. A square field of view of 400 mm rendered a voxel size of 2.5 × 1.6 × 5.0 mm^{3}. The velocity-encoded value was set at 150 cm/s for mitral inflow and 250 cm/s for aortic flow. By manually drawing regions of interest over the appropriate flow areas, phase-contrast velocity maps were acquired, integrated over time, and subtracted using built-in software (Argus, Siemens).

### Statistical analysis

The MRSV values measured by the 4 different approaches were indicated as mean values ± SD and compared with MRI reference values using linear regression analysis. Agreement was assessed by plotting differences against the mean of calculated and reference values (30), comparing mean differences to 0 by *t*test using a 5% significance level. Interobserver variability of MRSV measurements of all 4 PISA methods was determined by the mean difference and SD of the differences from 2 independent measurements performed by 2 observers as well as correlation coefficients from linear regression analysis, respectively. Statistical significance of mean interobserver differences was tested versus 0 by the *t*test.

## Results

In all patients, the 4 PISA approaches could be successfully applied. In the apical 4-chamber view, hemicircular PISA could be obtained in the proximal flow field in all patients, independent from jet eccentricity. Hemodynamic conditions measured by heart rate and blood pressure varied not significantly between the echocardiography study and MRI (83 ± 14/s vs. 87 ± 16/s; 127 ± 11/84 ± 6 mm Hg vs. 125 ± 12/83 ± 8 mm Hg). In each individual patient the same Nyquist limit was applied for all 4 PISA approaches; Nyquist velocities in all patients ranged between 12 and 61 cm/s (39.5 ± 13.6 cm/s). Average color Doppler frame rate during serial PISA recording was 15.9 ± 1.7 s^{−1}. For the ratio of peak regurgitant velocity over VTI used in the simplified PISA approach, we found a similar value of 3.16 ± 0.53 s^{−1}compared with 3.25 ± 47 s^{−1}determined by Rossi et al. (28).

Average acquisition and offline analysis time was shortest for the simplified PISA method (t = 92 ± 7 s), followed by PISA-VTI (t = 113 ± 15 s), serial PISA (t = 178 ± 40 s), and M-mode PISA (t = 244 ± 70 s). For serial PISA an average number of 7.6 ± 2.1 systolic frames with appropriate PISA representation could be analyzed. For MRI total acquisition time was 38 ± 9 min with an extra 14 ± 3 min for offline manual tracing and analysis.

Over all patients and mechanisms of MR, M-mode PISA correlated and agreed best with MRI with the smallest mean error (r = 0.88, SEE = 4.8 ml, mean error = −8.0 ± 6.4 ml) followed by serial PISA (r = 0.83, SEE = 5.9 ml, mean error = −8.7 ± 7.4 ml). For PISA-VTI (r = 0.64, SEE = 7.4 ml, mean error = −13.3 ± 10.2 ml) and simplified PISA (r = 0.63, SEE = 7.4 ml, mean error = −13.5 ± 10.3 ml) we found to have a poorer correlation with MRI with a larger mean error (Fig. 2).For all 4 PISA methods, we found significant systematic underestimation (p < 0.0001) of MRSV most likely because of underestimation of hemielliptic PISA surfaces by the hemispheric PISA formula. However, we observed significant differences in underestimation related to the pattern of dynamic MR, with significantly larger underestimation of MRSV by all 4 methods in patients with functional MR (Fig. 2).

Interobserver variability of MRSV measurements was satisfactory, with the mean difference not significant versus 0 by *t*test for all 4 PISA methods and good correlation coefficients (M-mode PISA: r = 0.91, mean difference = 1.0 ± 5.4 ml; serial PISA: r = 0.82, mean difference = −2.3 ± 6.9 ml; PISA-VTI: r = 0.83, mean difference = 1.1 ± 6.4 ml; simplified PISA: r = 0.89, mean difference = 2.5 ± 5.7 ml).

### Dynamic variation of MRFR and EROA

Based on the visual aspect of the dynamic variation from M-mode PISA registration as well as according to the ratio MRFR_{mid/mean}, 32 of 73 patients were found with a concave dynamic pattern (MRFR_{mid/mean}= 0.51 ± 1.8), 19 of 73 with a flat pattern (MRFR_{mid/mean}= 0.95 ± 1.5), and 22 of 73 with a convex pattern (MRFR_{mid/mean}= 1.4 ± 1.2). Importantly, all patients with a concave pattern had functional MR, patients with a convex pattern had predominantly degenerative or rheumatic MR (10 of 22) or prolapse (10 of 22) (only 2 of 22 had functional MR), and 11 of 19 patients with a flat pattern had degenerative or rheumatic MR, 5 of 19 had prolapse, and 3 of 19 had functional MR.

### PISA-VTI and simplified PISA

Based on the analysis of calculated mean EROA versus mean EROA reference for the 3 patterns of dynamic MR, when using single-point PISA methods we found significantly greater underestimation of mean EROA in cases with a flat (PISA-VTI: −0.06 ± 0.02 cm^{2}; simplified PISA: −0.06 ± 0.03 cm^{2}) or a concave pattern of dynamic MR (−0.07 ± 0.05 cm^{2}; −0.07 ± 0.06 cm^{2}) compared with a convex pattern (−0.02 ± 0.03 cm^{2}; −0.03 ± 0.04 cm^{2}) (Fig. 3).That was because dividing MRFR derived from midsystolic PISA by midsystolic peak regurgitant velocity in a flat pattern of M-mode PISA provided instantaneous EROA, which was smallest in midsystole and therefore underestimated the true mean EROA (Fig. 4A),that effect being even stronger in a concave pattern (Fig. 4C). As a consequence, a similar underestimation was found for values of calculated MRSV by PISA-VTI and simplified PISA, respectively (flat: −9.0 ± 2.7 ml, −9.1 ± 3.4 ml; concave: −10.8 ± 6.3 ml, −11.0 ± 6.8 ml; convex: −3.1 ± 4.6, −3.8 ± 5.3 ml) (Fig. 3). Importantly, in cases with a flat pattern of M-mode PISA underestimation of the mean EROA could be nearly eliminated by dividing midsystolic MRFR by mean regurgitant velocity (derived from VTI divided by MR duration) instead of peak velocity. By this approach, the error of mean EROA could be reduced to −0.02 ± 0.03 cm^{2}and the error of MRSV to −2.8 ± 2.5 ml, MRSV simply estimated as midsystolic MRFR × MR duration.

### M-mode PISA

For M-mode PISA we found only a slight underestimation of mean EROA that was similar for all 3 patterns (mean error: −0.02 ± 0.01 cm^{2}), the underestimation primarily caused by the mathematical difference between dividing calculated mean MRFR by mean regurgitant velocity (=time interval of regurgitation/VTI) to obtain mean EROA versus calculating mean EROA as the mean of instantaneous EROAs as done by the reference PISA method. Errors of MRSV by M-mode PISA were also small and not significantly different between the 3 patterns (concave: −2.0 ± 2.2 ml; convex: −2.3 ± 1.7 ml; flat: −2.3 ± 2.1 ml).

### Serial PISA

Although serial PISA calculation of instantaneous MRFRs, in principle, should agree with reference MRFRs, it was limited by the number of 2-dimensional PISA measurements (7.6 ± 2.1), causing an inaccurate representation of the dynamic variation of regurgitant flow (Figs. 4A to 4C), and thus larger variability of mean EROA and MRSV (Fig. 3). However, no significant differences between the 3 patterns of MR were found (mean errors, concave: −0.03 ± 0.03 cm^{2}, −3.8 ± 4.0 ml; convex: −0.01 ± 0.04 cm^{2}, −2.1 ± 4.6 ml; flat: −0.02 ± 0.02 cm^{2}, −3.8 ± 3.6 ml).

It must be noted that this analysis was not affected by the underestimation of MRSV resulting from hemispheric PISA assumption, because reference values of MRFR, EROA, and MRSV were derived from M-mode PISA signals using hemispheric PISA calculation as well. However, underestimation of hemiellipsoid proximal flow convergence zones by hemispheric PISA might significantly contribute to the underestimation of MRSV by M-mode PISA compared with independent reference values, particularly in patients with functional MR, in whom a concave dynamic MR pattern and nonhemispheric PISA is common (Fig. 2).

## Discussion

In the present study, we found underestimation of MRSV by all 4 PISA methods compared with MRI. This underestimation was more severe for the 2 single-point methods, PISA-VTI and simplified PISA, compared with the 2 time-integral methods. As an explanation for the observed differences of errors, we could show that for single-point methods underestimation of MRSV was critically dependent on dynamic variations of MRFR and EROA, and therefore on the single PISA frame selected for MRSV calculation. That is, because MRSV was directly related to mean EROA by VTI as a factor, therefore, underestimation of MRSV was a result of underestimation of mean EROA by single-frame EROA. As a consequence, for single-point methods, underestimation of MRSV was most severe in cases in which midsystolic EROA was small compared with larger EROA in early and late systole as typically found in functional MR with incomplete mitral leaflet closure (13,22). However, using the maximal PISA radius during systole and peak velocity when they do not occur at the same time will yield significant overestimation of mean EROA and MRSV in a concave dynamic MR pattern as present in functional MR (Fig. 4C). Thus, in cases with a concave dynamic pattern of M-mode PISA, single-point PISA approaches are in principle incapable of selecting the time point at which PISA MRFR divided by regurgitant flow velocity estimates mean EROA correctly, and therefore, MRSV calculation will be inaccurate. As shown, limitations of single-point PISA calculation could be overcome by the use of time-integral methods. Thus, MRSV calculation was most robust and accurate by a simplified M-mode PISA approach. This method was only limited by the mild systematic underestimation of mean EROA that occurs from the mathematical difference between dividing calculated mean MRFR by mean regurgitant velocity instead of calculating the mean of instantaneous EROAs as used by Schwammenthal et al. (13) and in our study for reference values of mean EROA. Another time-integral method, the serial PISA approach, calculating MRSV as the sum of serial MRFRs by 2-dimensional PISA, however, was limited by technically demanding serial PISA measurements and low color Doppler frame rate.

Overall, although practical application of single-point PISA methods was easier and less time demanding, underestimation was significantly greater compared with time-integral methods, which are technically more demanding and time-consuming but more accurate because they account for the dynamic variations of MR.

As an important finding, all 4 PISA approaches yielded greater underestimation of MRSV reference values obtained by MRI than was expected from comparison with the PISA reference method. For example, M-mode PISA only mildly underestimated MRSV by the PISA reference method, whereas underestimation of MRSV by MRI was significant. Importantly, as shown in Figure 2, underestimation mainly affected patients with a concave MR pattern, all of whom had functional MR. We therefore explained the underestimation by the fact that all 4 PISA approaches as well as the PISA reference method were based on hemispheric PISA obtained in a single-plane apical 4-chamber view, which incompletely represented more hemielliptic PISA shapes, as typical in functional MR with noncircular or slit-like regurgitant orifices along the leaflet commissure (16,31). However, considering an ideal approach that accounts not only for dynamic variations in the vertical dimension of a hemispheric PISA as accomplished in our study but also for the horizontal width of a hemielliptic PISA in 2 orthogonal views by combining the M-mode PISA approach and the hemielliptic PISA formula could not be realized in the present study, because simultaneous biplanar or 3-dimensional acquisition of hemielliptic PISA dimensions and M-mode PISA acquisition was not possible.

### Prior work

Although quantification of MRFR and EROA using the PISA principle for the evaluation of MR severity has been the subject of a number of prior studies (5–7,9,10), only a few have investigated PISA for quantification of MRSV to date. Rivera et al. (32) first described the practical application of a standard single-point PISA method for calculation of MRSV in a way that the largest PISA radius during systole was determined under the assumption of its coincidence with peak regurgitant velocity at midsystole. Other investigators adopted this approach (3,11,12,21,28) despite the fact that because of a different dynamic pattern of MR the largest PISA radius does not coincide with midsystolic peak regurgitant velocity in all cases, as shown by Schwammenthal et al. (13) and confirmed by our study results. The assumption of coincidence of the largest PISA radius and peak regurgitant velocity was fundamentally violated in functional MR, in which the PISA radius is largest in early and late systole when regurgitant velocity is lowest, and the PISA radius is smallest when regurgitant velocity is highest in midsystole. In fact, when the PISA method was initially used for calculation of peak MRFR, it was more obvious to measure peak MRFR from the largest PISA radius during systole. However, for calculation of MRSV, the midsystolic PISA radius must be used regardless of whether it is largest or not, as shown by our study results.

In view of prior study results, clinical validation of quantification of MRSV by PISA was limited by the absence of an accurate and independent reference technique. Quantitative methods used for comparison, such as the quantitative Doppler method (11,13,18,28,32) or combined thermodilution and quantitative angiography (8,21), were limited by indirect measurements of regurgitant flow prone to error, whereas angiographic grading did not provide absolute values of MRSV (11,13,33). Compared with this, MRI provides accurate estimates of MRSV from direct measurements of mitral inflow and aortic outflow from integration of flow over flow cross-sectional area and time (29,34), which can be used for reference in clinical studies (35). Comparison of prior study results with current results obtained using MRI for reference revealed 2 important differences: 1) although in most prior studies agreement (11,28), mild overestimation (13,18), or mild underestimation (8,31) was found between MRSV by PISA and comparative methods, and significant overestimation was found in one study (21), we found significant underestimation for all 4 PISA methods, but of a different degree depending on the PISA method used and the mechanism of MR (Fig. 2); and 2) although patients with severe MR based on common clinical, angiographic, and color Doppler criteria were included in the present study, MRSV ranged only up to 64 ml, compared with ranges of up to 101 to 230 ml in previous studies (11,13,18,21,28). As shown in the present study, overestimation of MRSV by single-point PISA in prior studies could potentially be explained by the fact that the largest PISA radius during systole did not necessarily coincide with the midsystolic peak regurgitant velocity.

### Study limitations

To determine the error of each PISA approach caused by dynamic variations of MR, we had to use an echocardiographic reference method for calculation of instantaneous MRFRs and EROAs because, currently, no independent technique exists that provides the dynamics of MRFR and EROA. On the other hand, because the PISA reference method was based on hemispheric PISA as well, it was ideally suited for determination of the error of the mean EROA of each PISA approach because the potential error from misrepresentation of nonhemispheric PISA was excluded. As stated in the introduction, it was not the purpose of this study to explore potential errors of the PISA approaches because of geometric assumptions of the PISA shape. Also, an ideal approach accounting for both aspects, dynamic variations of MR and shape of the PISA surface, currently does not exist, because biplane or real-time 3-dimensional acquisition does not provide determination of dynamic variations of MR with high temporal resolution.

We used MRI for reference because it is considered to be the most accurate independent reference method currently available. Other methods, such as angiography or thermodilution, are limited because of qualitative grading with high observer variability or inaccurate measurements of MRSV (21,33). However, only a few validation studies on MR flow measurement using MRI exist, mainly because of the unavailability of a reference method independent of MRI. Flow quantification of MR by MRI, although potentially limited by indirect measurement from mitral inflow minus aortic outflow, has previously been shown to provide satisfactory low scattering of differences between mitral inflow and aortic outflow (mean difference: −1 ± 3 ml) in patients without MR (34). However, because MRI has only been validated to provide measures of MRSV but not EROA, only absolute values of MRSV could be used for validation of the 4 PISA approaches, although EROA has recently been shown to be an important parameter for determination of the severity and prognosis of MR (3,4).

In the present study, the simplified M-mode PISA approach could only be performed offline, requiring 2-dimensional calibration of the M-mode image because the ultrasound system did not allow onscreen volume calculations using the disk method while in M-mode modus. This, however, could be readily implemented into existing ultrasound systems.

### Practical implications

According to our findings, accuracy of the different single-point and time-integral PISA approaches is critically dependent on the dynamics of MRFR and EROA in each individual patient. We therefore derive the following procedure for quantification of MRSV using the PISA method. Before the application of a PISA method, information on the dynamics of the PISA radius should be obtained either from cine 2-dimensional color Doppler imaging or, better yet, from M-mode PISA recording. Based on this, the following approaches are proposed: 1) given that the PISA radius is constant throughout the period of regurgitation, MRSV can be calculated by midsystolic single-point PISA using the mean regurgitant velocity (VTI/MR duration) instead of the peak regurgitant flow velocity; 2) given that dynamic variation of the PISA radius is convex (increasing–decreasing), midsystolic peak regurgitant velocity and simultaneous maximum PISA radius can be used for single-point estimation of mean EROA and MRSV; and 3) in cases with a concave (decreasing–increasing) PISA radius variation, no single-point PISA application can be recommended, therefore a time-integral method should be used. Note that the most accurate hemispheric PISA approach accounting best for dynamic variations would comprise the time integral of instantaneous products of EROA times velocity as performed to obtain PISA reference values in this study. Practical application of this approach, however, would require onboard software implementation including automated synchronization and superposition of M-mode PISA and continuous-wave Doppler MR flow velocity recordings.

## Conclusions

In our study, accuracy of the PISA method for estimation of MRSV was highly dependent on dynamic variation of MRFR and EROA and the underlying mechanism of MR. Inaccuracies caused by dynamic variations were most significant when commonly used single-point PISA methods were applied in patients with functional MR. However, effects of dynamic MR could be overcome by time-integral PISA approaches, which were shown to be significantly more accurate but technically demanding. Thus, because there is a need for accurate quantitative assessment of the severity of MR, application of the PISA method for quantification of MRSV should account for dynamic variations of MR that have been neglected in the past.

## Footnotes

Dr. Buck was supported in part by grant Bu1097/2-2, Deutsche Forschungsgemeinschaft, Bonn, Germany. Dr. Plicht was supported by a grant of the IFORES research program of University Clinic Essen.

- Abbreviations and Acronyms
- EROA
- effective regurgitant orifice area
- MR
- mitral regurgitation
- MRFR
- mitral regurgitant flow rate
- MRI
- magnetic resonance imaging
- MRSV
- mitral regurgitant stroke volume
- PISA
- proximal isovelocity surface area
- VTI
- velocity–time integral

- Received February 26, 2008.
- Revision received May 6, 2008.
- Accepted May 21, 2008.

- American College of Cardiology Foundation

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