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 Table of Contents  
REVISITING THE FUNDAMENTALS
Year : 2021  |  Volume : 5  |  Issue : 1  |  Page : 31-39

Proximal Isovelocity Surface Area Method for Assessment of Mitral Regurgitation Severity: Principles, Pitfalls, and Future Directions


Department of Cardiology, Christian Medical College, Vellore, Tamil Nadu, India

Date of Submission15-Mar-2021
Date of Acceptance17-Mar-2021
Date of Web Publication21-Apr-2021

Correspondence Address:
Jesu Krupa
Department of Cardiology, Christian Medical College, Vellore, Tamil Nadu
India
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/jiae.jiae_8_21

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  Abstract 

Quantification of mitral regurgitation (MR) is important in clinical practice. As fluid approaches a finite circular orifice, concentric hemispherical shells are formed with gradually decreasing surface area and increasing velocity. Severity of MR by the proximal isovelocity surface area (PISA) can be quantified using this principle. Careful attention to detail needs to be paid in the acquisition and measurement to ensure accuracy and reproducibility of the PISA method. The pitfalls of this method are related to geometric assumptions, the limitations of ultrasound, and the shape of the orifice. Some of these can be overcome with a good understanding of the principles and limitations of PISA and also newer three-dimensional techniques for quantification.

Keywords: Flow rate, geometric assumptions, mitral regurgitation, proximal isovelocity surface area


How to cite this article:
Krupa J. Proximal Isovelocity Surface Area Method for Assessment of Mitral Regurgitation Severity: Principles, Pitfalls, and Future Directions. J Indian Acad Echocardiogr Cardiovasc Imaging 2021;5:31-9

How to cite this URL:
Krupa J. Proximal Isovelocity Surface Area Method for Assessment of Mitral Regurgitation Severity: Principles, Pitfalls, and Future Directions. J Indian Acad Echocardiogr Cardiovasc Imaging [serial online] 2021 [cited 2021 Jul 23];5:31-9. Available from: https://www.jiaecho.org/text.asp?2021/5/1/31/314190


  Introduction Top


Assessment of the severity of mitral regurgitation (MR) is very important for both the diagnosis of the severity of MR and determination of optimal timing of surgery. Severity is usually quantified using the proximal isovelocity surface area (PISA) method based on which the effective regurgitation orifice area (EROA) and regurgitation volume (RVol) are calculated. With improvement in mitral valve repair techniques, earlier surgery in these patients even before the appearance of symptoms reinforces the need for accurate assessment of the severity of MR.[1],[2]

The purpose of this article is to relook at the principles and pitfalls of the PISA method for the assessment of MR, some recent knowledge about PISA and potential directions for the future.


  Principles Top


As fluid approaches a finite circular orifice, concentric hemispherical shells are formed with gradually decreasing surface area and increasing velocity. The velocity on the surface of any such shell is same at every point and hence the term “isovelocity.”[3] [Figure 1] illustrates the PISA principle.[4]
Figure 1: Principle of proximal isovelocity surface area method. Streamlines of increasing velocity (solid lines) and tangential isovelocity lines (dotted lines) proximal to the orifice. If a proximal isovelocity surface area can be identified and quantified, then the volume flow rate can be calculated as proximal isovelocity surface area x isovelocity. Right panel, Color Doppler flow recording with identification of proximal isovelocity surface areas. The isovelocity line at 27 cm/s can be identified as the first blue-red velocity interface, and the isovelocity line at 54 cm/s can be identified as the second blue-red interface. Reproduced with permission from Utsunomiya T, et al. J Am Coll Cardiol 1993;22:277-82

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This principle can be applied to the echocardiographic evaluation of MR where the hemispherical shells form on the left ventricular (LV) aspect, proximal to the regurgitant orifice which is at the level of the mitral valve.[5],[6],[7],[8]

According to the law of conservation of mass, the flow rate at any of these hemispherical shells would be equal to the flow rate at the regurgitant orifice.

  1. Flow rate at the hemispherical, isovelocity shell = 2 πr2 × Aliasing velocity


  2. Where “r” is the radius of the hemisphere and 2 πr2 is the area of the surface of the hemisphere. The aliasing velocity (Va) is the velocity at the isovelocity shell which shows change in color from blue to yellow in case of transthoracic echo (TTE) and yellow to blue in case of transesophageal echo (TEE). To optimally measure “r,” the baseline of the Nyquist limit should be shifted in the direction of the regurgitation to 30–45 cm/s. This velocity range provides the optimal balance between maintaining the shape of the hemisphere and the resolution of the shell which can be appreciated distinctly. A very low Nyquist limit will cause elongation of the shell and hence falsely high “r.” Conversely, a very high Nyquist limit will cause flattening of the shell and hence falsely low “r.”

  3. Flow rate at the regurgitant orifice = Effective regurgitant Orifice Area (EROA) × Peak MR velocity


  4. Where peak MR velocity (VMR) is obtained by continuous wave (CW) Doppler.

    Hence,

  5. EROA = 2 πr2 x Aliasing velocity (Va)/Peak MR velocity (VMR)


  6. Since, this EROA by the PISA method is obtained at the peak MR velocity, it is the maximum instantaneous EROA which means that it is calculated at that “instant” or point in time. As a rule, the radius of the hemisphere 'r' should be measured at the same time as when the peak MR jet velocity is measured. Hence, the timing of the peak of the MR jet velocity can be noted on the electrocardiogram trace and then “r” can be measured at the same point by freezing and scrolling frame by frame in the color Doppler clip which has been optimized for PISA.

    Regurgitant volume (RVol) is calculated by multiplying the EROA with the velocity time integral (VTI) of the MR jet.

  7. RVol = EROA x VTI (MR jet)


Regurgitant fraction (RF) is the ratio of RVol to the stroke volume. LV stroke volume is calculated as end-diastolic volume − end-systolic volume using the Biplane Simpson's method.[4],[5],[9],[10],[11],[12]

The proximal isovelocity surface area method

Careful attention to detail needs to be paid in the acquisition and measurement to ensure accuracy and reproducibility of the PISA method. The apical four chamber (A4C) or the long-axis views are generally chosen and a zoomed view of the mitral valve with color Doppler is acquired. The image should be optimized for depth, sector size, focus, color Doppler sector, and gain. This view should clearly show the regurgitant jet with the area of proximal flow convergence (PFC) and vena contracta. Then the baseline of the Nyquist limit is shifted to 30–45 cm/s in the direction of the regurgitant jet towards the left atrium (downward in TTE and upward in TEE) while observing the shape of the PFC to ensure that it is a hemisphere. For best measurements, color variance is turned off. [Figure 2] shows the PISA method.[1]
Figure 2: Schematic representation of the flow convergence method (proximal isovelocity surface area). The example on the right shows the measurement of the proximal isovelocity surface area radius after shifting the colour baseline in the direction of regurgitation and the timing of the selection of the color frame for measurement (solid yellow arrow), corresponding to the maximal jet velocity by continuous wave Doppler (dashed arrow). Reproduced with permission from Zoghbi WA, et al. J Am Soc Echocardiogr 2017;30:303-71. EROA: Effective regurgitant orifice area, PKV: Peak velocity of regurgitant flow by continuous wave Doppler, R Vol: Regurgitant volume, Reg: Regurgitation, Va: Aliasing velocity, VTI: Velocity time integral of the regurgitant jet by continuous wave Doppler

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Adjust the baseline if there is any constraint to the PFC by the ventricular wall. Magnify the image so that the PFC is clearly visualized and that a significant proportion of the ultrasound sector is filled with the PFC. The PFC shows a dark zone after the baseline of the Nyquist limit has been lowered indicating horizontal flow perpendicular to the ultrasound beam at the level of the regurgitant orifice. The PISA radius, “r” can be measured from this level after ensuring that the direction of flow is as parallel to the ultrasound beam as possible. If this level is not obvious, then we can use simultaneous color compare to visualize the valve and the regurgitant orifice. Measurement of “r” should be avoided from the sides of the PFC because flow in these areas are perpendicular to the ultrasound beam and hence the velocities are underestimated causing drop out on the color display of these velocities. In the case of multiple jets, PISA can be applied to each orifice with the flows and EROA added together. [Figure 3] and [Figure 4] demonstrate these concepts.[13],[14]
Figure 3: The proximal isovelocity surface area region is optimally measured where the region is hemispherical. Flows farthest away from the orifice assume an elongated or oval contour, overestimating flows, whereas flows closest to the orifice assume a flat contour, underestimating flows. Measurement of the radius should be avoided along the sides of the proximal isovelocity surface area region, because flow here is perpendicular to the ultrasound beam, resulting in underestimation of the velocity component with drop out of flow display at angles perpendicular to flow. Reproduced with permission from Judy Hung, Francesca Nesta Delling, Romain Capoulade. Mitral Regurgitation: Valve Anatomy, Regurgitant Severity, and Timing of Intervention. In: Otto C, editor. Practice of Clinical Echocardiography. 2018. p. 322–42

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Figure 4: Illustration of a two-dimensional color Doppler acquisition used for a (a) representation of the proximal isovelocity surface area radius (r), (b) representation of the proximal isovelocity surface area width (w) in the case of functional mitral regurgitation where the hemi ellipsoid formula may be applied, and (c) representation of the two radii (r1, r2) measured in the case of a multiple-jet mitral regurgitation. Also note the dark line (orange-colored arrows in a and b) which indicates the level at which flow is horizontal to the orifice and from which proximal isovelocity surface area radius should be measured. Reproduced with permission from Papolla C, et al. J Am Soc Echocardiogr 2020;33:838-847.e1

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The PISA method is simple conceptually, but there are a few core principles to be adhered to for maintaining quality control.

Timing of measurements

MR is dynamic in systole which implies that the regurgitation orifice and hence EROA is not constant. Hence, the flow and velocity should be measured at the same moment of the regurgitation phase in systole, for example, a late systolic MR PISA radius should not be combined with a mid-systolic peak MR velocity. A PISA radius which is representative of the average size of PISA rather than the maximum could be chosen for quantification.[10],[15]

Duration of regurgitation

Not all MR is holosystolic and hence maximum EROA may over-estimate the severity of MR. In these situations, calculating RVol by tracing the densest part of the MR jet by CW Doppler (CWD) which is the actual regurgitation without extrapolating to what we think might be the whole jet would give a better indication of MR severity than EROA. Patients with mitral valve prolapse generally have late systolic MR due to the prolapse happening late in systole. These patients may hence have the maximum EROA in late systole. Functional MR is typically a bimodal with least flow in mid-systole. In rheumatic MR, the flow rate is constant throughout systole.[1],[13],[16] [Figure 5] shows the importance of duration and timing of MR.[17]
Figure 5: Non-holosystolic mitral regurgitation with variation in effective regurgitant orifice area shown in the top panel in a patient with P2 segment prolapse. Note the gradually increasing size of the proximal flow convergence to a maximum at end-systole. The lower panel shows the same on continuous-wave Doppler and colour M-mode

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Shape of proximal isovelocity surface area

The assumption for the standard PISA method is that the plane of the mitral valve is flat or planar (180°). However, this is not always true, and the plane may be conical in cases of tenting of the valve. This angle should hence be accounted for in the quantification of EROA. This is also important in situations like a flail mitral leaflet which often causes over estimation of the PISA radius 'r' due to constraint of the LV wall causing distortion of the PFC. To overcome this, an angle correction factor can be used by multiplying the EROA by α/180, where α is the angle between the mitral leaflet and the end of the PISA region constrained by the LV wall. [Figure 6] shows how to measure α in a nonplanar orifice.[18]
Figure 6: Representative images showing how to measure the radius and angle of the proximal flow convergence region. The eccentric mitral regurgitation flow was observed in two-chamber view (shown in a). In the magnified view of color Doppler flow mapping, chordae rupture was well demonstrated after removing Doppler signal (arrow in b) and the centre of proximal flow convergence could be easily determined using this two dimensonal image. Measurement of the radius and angle can be more easily done by using side-by-side demonstration of both two dimensional and color Doppler images (c and d). Reproduced with permission from Lee K, et al. J Am Soc Echocardiogr 2020;33:64–71. LA: Left atrium, LV: Left ventricle

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Furthermore, the shape of the PISA may not always be a hemisphere and the aliasing velocity (Va) should be adjusted such that the optimal shape is obtained.[3],[19]

Shape of the regurgitant orifice

In general, for organic mitral valve disease, the orifice is roughly circular. Hence, the standard PISA formula can be applied and the calculated EROA is more likely to reflect severity as comparted to functional MR where the orifice is elliptical, and hence, MR severity is likely to be underestimated by the formula for a hemisphere. However, computational fluid dynamics simulations have shown that the flow contours become hemispherical rapidly as we move away from the orifice depending on the extent of ellipticity. For very elliptical and crescentic orifices as in functional MR, three-dimensional (3D) PISA may offer a solution or the formula for a hemiellipse may be applied.[8],[20],[21],[22],[23],[24]


  Pitfalls and Sources of Error Top


  1. Central jets allow better alignment of the ultrasound beam with the centerline of the flow convergence.[21],[25] However, eccentric jets pose a challenge both for PISA radius measurement and CWD recording due to angulation and hence inability to record the maximum velocity of the MR jet. This will lead to falsely high EROA. Similarly, an inaccurate measurement of the PISA radius will cause the error in EROA to be squared since


  2. EROA = 2 πr2 × Aliasing velocity/Peak MR velocity

  3. As mentioned earlier, the EROA is likely to over-estimate the severity of MR in nonholosystolic MR. To an extent, this over-estimation can be offset by accurately tracing the actual MR VTI which will give RVol which is a better reflector of true severity
  4. In functional MR, the regurgitant orifice is noncircular, and hence, the EROA estimated by the formula for a hemisphere which works for a circular orifice is likely to under-estimate the true severity of MR[22],[23],[25]
  5. In a study of 33 patients with eccentric MR due to prolapse or flail, it was found that the conventional PISA method tended to overestimate the RVol as compared to that estimated by cardiac magnetic resonance (CMR) Imaging as the gold standard. However, the accuracy improved from 57.6% to 84.8% with the use of angle correction.[26]


Furthermore, in a study of 166 patients with degenerative MR and chordae rupture, RVol was measured using both PISA and 2D volumetric methods. The volumetric method calculated RVol as the difference between the total stroke volume calculate by the biplane Simpson's method and the forward stroke volume at the left ventricular outflow tract (LVOT) by pulsed wave Doppler. There was a discrepancy noted in 41% of patients. On multivariate analysis, the best predictors of discordance in values were small LV end-diastolic volume (LVEDV) and narrow PISA angle with cut off values of 173 ml and 103°, respectively. The likelihood of 2-year surgery-free survival was higher in the discordant group. Thus, an additional quantitative method on echocardiography or CMR is necessary in those with a small LVEDV and a narrow PISA angle.[18]


  Discussion Top


Despite its limitations, the PISA method by means of visual estimation of the size of the PFC and full calculation still provides the most used method for quantitation of MR.

A study of 25 consecutive patients from 5 tertiary French hospitals by Coisne et al. to assess the reproducibility in parameters of MR severity independently by 16 junior and senior cardiologists specialized in echocardiography concluded that even in 2019, quantification of MR by echocardiography was challenging. The interobserver agreement for EROA by the PISA method was moderate (0.61, 95% confidence interval [CI] 0.43–0.76 for primary MR and 0.46, 95% CI 0.15–0.79 for secondary MR) among senior cardiologists. The agreement was lower among junior cardiologists. A senior cardiologist was one who had specialized in cardiac imaging and graduated at least 2 years earlier. A junior cardiologist was a final-stage cardiology resident. Agreement for RVol by PISA method was generally lower than for EROA, and it was the least among junior cardiologists assessing functional MR (0.05, 95% CI 0.00–0.83). This highlights the fact that assessment of MR severity by PISA method is a function of the amount of the echocardiographer's experience. [Figure 7] shows the same.[17]
Figure 7: Distribution of interobserver agreement for grading mitral regurgitation severity using the multiparametric approach according to the experience of the reader. Based on data from Coisne A, et al. Arch Cardiovasc Dis. 2020;113:599–606

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Even as late as 2017, a study of 145 patients describes a score called the ROSE-index which was calculated by evaluating five parameters namely valve morphology, jet characteristics, vena contracta, systolic reversal, and LV dimensions. Each parameter was assigned a score of 0 or 1 depending on whether it corresponded to severe MR based on pre-specified criteria. The total score was then calculated using the formula: ROSE-index score = (valve morphology * 1) + (jet characteristics * 2) + (venacontracta * 2) + (systolic reversal * 2) + (LV dimensions * 1). The maximum score was 8 based on these parameters. It is interesting to note that the calculation of quantitative parameters like EROA and RVol by PISA method is still being considered as a research tool, and hence, the development of a score which does not include EROA and RVol. Nevertheless, in this study, a cutoff score (≥4) had a sensitivity 0.84 and specificity 0.83 to diagnose severe MR. Negative predictive value was 100% for score 0 and 1; score 6–8 showed a 100% positive predictive value. Inter- and intra-observer agreements were excellent (K >0.80). This study in a way highlights the practical difficulty of taking reliable PISA measurements.[27]

It is because of its limitations in quantification and the lack of any single parameter reflecting MR severity that the American Society of Echocardiography (ASE) 2017 guidelines for valvular regurgitation recommend an integrated approach to assessment of MR severity and decision making for timing of surgery.

In a recent prospective multicenter study with 159 participants, it was found that there was limited concordance (6%) between the eight parameters that are generally studied for assessing MR severity namely PISA-derived EROA, PISA-derived RVol, vena contracta, color Doppler jet/left atrial area, left atrial volume index, LV end-diastolic volume index, peak E wave, and the presence of pulmonary vein systolic reversal. The concordance improved (68%) when only three quantitative parameters – vena contracta, PISA-derived EROA, and PISA-derived RVol were considered. This underlines the challenges in MR assessment and hence the need for an integrated approach.[28] [Figure 8] shows that that there was poorer concordance in moderate grades of MR as compared with the extremes of severity.[28]
Figure 8: Concordance score according to the severity of mitral regurgitation by the American Society of Echocardiography guidelines. Based on data from Uretsky S, et al. Circ Cardiovasc Imaging. 2020;13:1–10

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Earlier echocardiographic studies assessed MR severity against angiographic grade of MR as the gold standard which we know today is inaccurate. In the search for a gold standard, CMR appears to be most reliable for the quantification of MR severity based on the outcome data.

A prospective, multi-center study by Uretsky et al. included 103 patients who underwent assessment of MR severity by echocardiography and CMR. Thirty-eight of these patients underwent mitral valve surgery and there was poor agreement between the two imaging modalities (r = 0.4; P = 0.01) in this subset. There was a strong correlation between LV remodeling after surgery and MR severity as assessed by CMR (r = 0.85; P < 0.0001) and no correlation of the same with echocardiography (r = 0.32; P = 0.1). This is a pointer to the fact that CMR may be able to better assess the severity of MR and hence the timing of surgery. CMR measures total LV stroke volume using the steady state free precession sequence as the difference between end-diastolic and end-systolic volumes. Forward flow across the aortic valve is measured using phase contrast sequence. The difference between the LV stroke volume and the forward flow is quantified as the RVol.[29]

So how does echo compare with CMR which is the gold standard for the quantification of MR? In a recent systematic review and meta-analysis of 1187 patients with varying degrees of primary or secondary MR, there were seven studies which compared echocardiography (TTE or TEE) and CMR. In a total of 280 of these patients with severe MR, the severity was overestimated by echocardiography in 38% of patients. The agreement among echocardiographic methods and CMR was best with 3D PISA method (R = 0.84 [95% CI 0.78–0.89]) which allows orthogonal views thereby enabling the largest PFC to be visualized. A limitation of 3D as compared to two-dimensional (2D) method is the less availability of good acoustic window and poor resolution, especially with TTE which is most often used for MR assessment. Furthermore, various studies in this meta-analysis showed that the 2D PISA method either over or underestimated MR severity.[30]

Hence, while the PISA method for MR quantification is theoretically attractive, there are many practical issues relating to its accuracy in the real world.


  Future Directions Top


There is recent literature on research to overcome the limitations of the 2D PISA method and to quantify MR more accurately. The 3D PISA method which allows measurement of the PISA radius “r” in orthogonal planes as mentioned earlier still has geometric assumptions. If the radii are equal then the area of a hemisphere can be used whereas if they are unequal, then the area of a hemiellipse needs to be used. [Figure 9] illustrates the 3D PISA method.[31] Another potential way to measure the PISA could be by surface rendering similar to that of the mitral valve using software like Philips 3D MVQ.
Figure 9: Hemispheric and hemielliptical proximal isovelocity surface area (PISA) calculation acquired from a 3-dimensional, transesophageal echocardiographic (TEE), full-volume, colour-flow Doppler data set. Upper left, mid-esophageal five-chamber TEE view equivalent (green plane) demonstrating PISA radius (D1) and base width (D2). Upper right, mid-esophageal mid-commissural TEE view equivalent (i.e., red plane: orthogonal to the view in the upper left panel) demonstrating PISA base length (D3). Lower left, short-axis view (blue plane) of PISA base. Lower right, composite image of the 3 image planes identified in upper left, upper right, and lower left panels. Reproduced with permission from Buck T, Plicht B. Curr Cardiovasc Imaging Rep 2015;8:38. LVOT: Left ventricular outflow tract

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In a recent study, 51 patients with varying degrees of MR severity due to various causes and mechanisms underwent TTE, TEE, and CMR for MR evaluation. A 3D enabled MR flow quantification in complex MR with multiple and eccentric jets showed better agreement with CMR than 2D PISA TTE or TEE. No geometric assumptions were made. From the 3D color Doppler data, first a 3D orifice was identified based on the largest jet. Then, a 3D surface rendered model of the valve surface was created following which the flow rate for each frame was obtained from the 3D modelled streamlines of flow. An integration of these flow rates over the entire duration of regurgitation then gave RVol. With improvement in technology and workflow, this could provide a clear advantage since there are no geometric assumptions. [Figure 10] illustrates this concept.[32]
Figure 10: From 3D color Doppler data, first a 3D orifice is detected at the largest jet, then a 3D surface-rendered model of the valve surface is created and optimized from these streamlines. Thereafter, for each frame the regurgitant flow rate is integrated from the velocities along the modeled 3D streamlines over the surface and over time. No geometric assumptions are made. Reproduced with permission from Militaru S, et al. J Am Soc Echocardiogr 2020;33:342-54. 3D: Three-dimensional, MR: Mitral regurgitation, Rvol: Regurgitant volume

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In another recent in vitro study, various MR shapes (central, oblong, and multiple jets) were mimicked in a left heart simulator. It was found that hemicylindrical and hemi ellipsoidal assumptions improved the quantification of MR as compared to the traditional PISA method which measures the radius and width of the PFC. In the case of a double-jet MR, measurement of both radii and PISA quantification using the hemispherical method is recommended. Validation of these findings in vivo compared with CMR and outcomes would provide a new way to quantify MR.[14]

Assessment of the severity of functional MR is difficult even among senior cardiologists and highly unreliable when assessed by less experienced persons. Whether the mitral valve requires intervention is an important decision. In a study by Namazi et al., in 359 patients with moderate-to-severe secondary MR, who were followed for a median duration of 51 months, RVol/EDV ratio <20% was independently associated with increased all-cause mortality (hazard ratio 1.465 [95% CI 1.030–2.086], P = 0.034). Hence, by taking account of the LV volume, RVol/EDV might aid the risk stratification of patients with functional MR disproportionate to LV dilatation.[33]


  Conclusion Top


The quantification of MR is a common clinical question with a huge bearing on management, especially the decision on timing of surgery. The 2D PISA method is still the most widely used for assessment of MR severity. Although the formula for the calculation of EROA and RVol is based on certain geometric assumptions like many other echocardiographic parameters, (e.g., 2D Biplane Simpson's method for LV volumes and EF, M-mode cubed formula for LV mass), it is the recommended method for quantification in the ASE 2017 valvular regurgitation guidelines. A good knowledge of the principles, pitfalls, and limitations of this method will enable us to use it appropriately. Newer methods based on 3D echocardiography are in the process of being developed and validated.


  Opinion Top


In the common Indian context, where cost-effectiveness needs to be balanced against available resources of time for each study, trained workforce and echocardiographic equipment, we feel that the integrated approach to assessment of MR severity as recommended by the ASE 2017 guideline is most suited and is likely to remain. The 2D PISA method for the determination of EROA, RVol with all its limitations in addition to other Doppler parameters and assessment of chamber dilatation will continue to remain vital. Hence, there is a need to educate physicians and cardiac sonographers on the correct use of the 2D PISA method and its pitfalls. Unless 3D echocardiography overall and specifically with respect to quantification of MR becomes easier, quicker, well validated, and cost-effective it is likely to remain a tool only in the hands of expert echocardiographers and a topic for academic discussion. Addition of extra steps in the quantification by PISA method and more numbers like α in case of nonplanar mitral valve leaflets or using the formula for a hemiellipse for functional MR adds to the complexity, scope for error and hence, would limit practical widespread utility.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.

 
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    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10]



 

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