EROA Calculator for Mitral Regurgitation (PISA method, regurgitant volume)

Understanding the EROA calculator for mitral regurgitation (PISA method) — concept and principle

This calculator estimates the effective regurgitant orifice area (EROA) and regurgitant volume of a leaking mitral valve using the proximal isovelocity surface area (PISA) method on echocardiography. Cardiologists and sonographers use it to grade the severity of mitral regurgitation (MR).

Hemisphere flow → hole size: with the default inputs the result is 48 mL (0.32 × 150 VTI per beat).

How it is calculated

Regurgitant flow rate (mL/s) = 2π × r² × Va

EROA (cm²) = flow rate ÷ peak MR velocity

Regurgitant volume (mL/beat) = EROA × MR jet VTI

r is the PISA radius in cm, from the valve opening to the first colour aliasing line.
Va is the aliasing (Nyquist) velocity of the colour scale in cm/s, usually shifted toward the jet.
Peak MR velocity and VTI come from the continuous-wave Doppler trace; enter velocity in cm/s (5 m/s = 500 cm/s).

The principle

As blood speeds up toward a small hole, it forms shells of equal velocity shaped like hemispheres. On the shell where colour aliases, every point moves at Va. The flow through that shell equals its area (2πr²) times Va. The same flow must pass through the orifice at the peak jet velocity, so dividing flow by that velocity gives the orifice area. Multiplying by the jet VTI turns area into volume per beat.

Worked example

Default inputs: r 0.8 cm, Va 40 cm/s, peak velocity 500 cm/s, VTI 150 cm.

Flow = 2π × 0.64 × 40 = 160.8 → 161 mL/s.
EROA = 160.85 ÷ 500 = 0.322 → 0.32 cm² → Moderate–severe (0.30–0.39).
Regurgitant volume = 0.3217 × 150 = 48.3 → 48 mL → Moderate–severe (45–59 mL).

Each point is the calculator re-run with only “PISA radius r (cm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

PISA radius r (cm)	EROA (cm²)
0.2	0.02
0.4	0.08
0.6	0.18
0.8	0.32
1	0.5
1.2	0.72
1.6	1.29

How to read the result

Where does your result fall?

For chronic primary MR: EROA under 0.20 cm² mild, 0.20–0.29 mild–moderate, 0.30–0.39 moderate–severe, 0.40 or more severe; regurgitant volume under 30, 30–44, 45–59 and 60 mL or more. Secondary (functional) MR is judged with other thresholds, and the grade should agree with other signs such as vena contracta and chamber size.

Common mistakes

Measuring r at the wrong frame. Use mid-systole, when the PISA is largest and stable.
Entering velocity in m/s instead of cm/s.
Using the method for eccentric jets or non-circular orifices, where the hemisphere assumption fails.

Keep in mind: This is a measurement aid for trained echocardiographers, not a diagnosis. The grade must be combined with the full echo study and clinical findings.

Frequently asked questions

Why does a small error in r matter so much?

The radius is squared, so a 10% error in r changes flow and EROA by about 21%.

Should the colour baseline be shifted?

Shifting it toward the jet lowers Va and enlarges the PISA, which makes r easier to measure.

Does PISA work for other valves?

It is also used for tricuspid and aortic regurgitation and mitral stenosis, with different thresholds.

Sources: Zoghbi WA, Adams D, Bonow RO, et al., "Recommendations for noninvasive evaluation of native valvular regurgitation", J Am Soc Echocardiogr 2017;30:303–371 · Zoghbi WA et al., "Recommendations for evaluation of the severity of native valvular regurgitation with two-dimensional and Doppler echocardiography", J Am Soc Echocardiogr 2003;16:777–802

Checked 9 Nov 2026. Zoghbi WA, Adams D, Bonow RO, et al., “Recommendations for noninvasive evaluation of native valvular regurgitation”, J Am Soc Echocardiogr 2017;30:303–371 (PISA: flow = 2πr² × Va, EROA = flow ÷ peak velocity, RVol = EROA × VTI); severity cut-offs from Zoghbi WA et al., ASE “Recommendations for evaluation of the severity of native valvular regurgitation with two-dimensional and Doppler echocardiography”, J Am Soc Echocardiogr 2003;16:777–802, Table 1.

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