PISA Calculator
Calculate PISA Calculator quickly with our cardiovascular system tool. Get results based on evidence-based formulas with clear explanations.
Reviewed for accuracy by Rahul Singh, Health & Wellness Specialist
Medical disclaimer: This calculator is provided for educational and informational purposes only and does not constitute medical advice, diagnosis, or treatment. Results are general estimates and may not reflect your individual circumstances. Always consult a qualified healthcare professional before making decisions about your health.
PISA Calculator
Calculator
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Formula: Q = 2 x pi x r^2 x Va x (alpha/180); ERO = Q / Vmax; RVol = ERO x VTI
Worked example — Flow rate: 193.4 mL/s | ERO: 0.387 cm^2 | Regurgitant Volume: 50.3 mL | Severity: Moderate
Formula
Q = 2 x pi x r^2 x Va x (alpha/180); ERO = Q / Vmax; RVol = ERO x VTI
Q is the flow rate through the proximal hemispheric shell in mL/s, r is the PISA radius in cm (measured from the color aliasing boundary to the orifice), Va is the color Doppler aliasing velocity in cm/s, and alpha is the angle in degrees subtended by the structures bounding the convergence zone (180 degrees for a flat wall, giving a correction factor of 1.0). Dividing the flow rate by Vmax, the peak regurgitant velocity in cm/s measured by continuous wave Doppler, gives the effective regurgitant orifice area ERO in cm^2. Multiplying ERO by the regurgitant jet velocity time integral VTI in cm gives the regurgitant volume RVol in mL.
Worked Examples
Example 1: Hemispheric PISA in Mitral Regurgitation
Problem:A patient with mitral regurgitation has a PISA radius of 9 mm at an aliasing velocity of 38 cm/s. Continuous wave Doppler shows a peak regurgitant velocity of 500 cm/s and a regurgitant jet VTI of 130 cm. The orifice lies in a flat plane, so the convergence angle is 180 degrees. Calculate the flow rate, effective regurgitant orifice area and regurgitant volume.
Solution:Convert the radius: r = 9 mm = 0.9 cm Angle factor = 180 / 180 = 1.00 (full hemisphere) Flow rate Q = 2 x pi x r^2 x Va x 1.00 = 2 x 3.14159 x (0.9 cm)^2 x 38 cm/s = 6.28319 x 0.81 cm^2 x 38 cm/s = 5.08938 cm^2 x 38 cm/s = 193.40 mL/s ERO = Q / Vmax = 193.40 mL/s / 500 cm/s = 0.387 cm^2 (units: (cm^3/s) / (cm/s) = cm^2) Regurgitant Volume = ERO x VTI = 0.387 cm^2 x 130 cm = 50.3 mL Peak gradient = 4 x (5.00 m/s)^2 = 4 x 25.0 = 100 mmHg Severity: ERO 0.387 cm^2 falls in the 0.20-0.39 cm^2 band and RVol 50.3 mL falls in the 30-59 mL band, so both indices agree on moderate mitral regurgitation.
Result:Flow rate: 193.4 mL/s | ERO: 0.387 cm^2 | Regurgitant Volume: 50.3 mL | Severity: Moderate
Example 2: Angle-Corrected PISA in Severe Mitral Regurgitation
Problem:A patient with a tethered posterior leaflet has a PISA radius of 11 mm at an aliasing velocity of 40 cm/s. The leaflets form a funnel subtending 160 degrees rather than a flat 180 degrees. Peak regurgitant velocity is 550 cm/s and the regurgitant VTI is 150 cm. Apply angle correction and grade the severity.
Solution:Convert the radius: r = 11 mm = 1.1 cm Angle factor = 160 / 180 = 0.8889 Flow rate Q = 2 x pi x r^2 x Va x (alpha/180) = 2 x 3.14159 x (1.1 cm)^2 x 40 cm/s x 0.8889 = 6.28319 x 1.21 cm^2 x 40 cm/s x 0.8889 = 7.60265 cm^2 x 40 cm/s x 0.8889 = 304.11 mL/s x 0.8889 = 270.32 mL/s ERO = Q / Vmax = 270.32 mL/s / 550 cm/s = 0.491 cm^2 Regurgitant Volume = ERO x VTI = 0.491 cm^2 x 150 cm = 73.7 mL Peak gradient = 4 x (5.50 m/s)^2 = 4 x 30.25 = 121 mmHg Note the effect of the correction: without it the flow rate would be 304.11 mL/s and the ERO 0.553 cm^2, an overestimate of 12.5 percent. Severity: ERO 0.491 cm^2 exceeds the 0.40 cm^2 threshold and RVol 73.7 mL exceeds the 60 mL threshold, so this is severe mitral regurgitation.
Result:Flow rate: 270.3 mL/s | ERO: 0.491 cm^2 | Regurgitant Volume: 73.7 mL | Severity: Severe
Frequently Asked Questions
What does PISA stand for and what physical principle is it based on?
PISA stands for Proximal Isovelocity Surface Area. It is a quantitative Doppler echocardiography method for measuring flow through a small orifice, most often a leaking (regurgitant) heart valve. The method rests on conservation of mass: blood approaching a narrow orifice accelerates and organises itself into concentric shells on which every particle has the same speed. Because flow must be continuous, the volume of blood crossing any one of those shells per second is identical to the volume crossing the orifice itself. If you can measure the surface area of one shell and the velocity on it, you have measured the flow rate through the orifice without ever imaging the orifice directly. Color Doppler makes one specific shell visible for free: where the flow speed crosses the aliasing velocity the color map abruptly reverses, and that color reversal boundary is a surface on which the velocity is known exactly. Which color sits on each side of the boundary depends on whether the accelerating flow is moving toward or away from the transducer, so it is the reversal itself, rather than any fixed red-to-blue order, that marks the shell.
How is the PISA radius measured correctly?
The PISA radius is the distance from the regurgitant orifice to the first color aliasing boundary, measured along the axis of flow convergence. Zoom in on the convergence zone, shift the color Doppler baseline toward the direction of the regurgitant jet so the aliasing velocity falls into the 30 to 40 cm/s range, and then scroll frame by frame to the moment in the cardiac cycle where the hemisphere is largest. For mitral regurgitation that is mid-systole; for aortic regurgitation it is early diastole. Place one caliper on the regurgitant orifice at the leaflet coaptation defect and the other on the color reversal boundary. The measurement should be made at the highest available frame rate and with the narrowest color sector, because a slow frame rate can simply miss the peak shell. Because effective orifice area depends on the radius squared, this single measurement dominates the accuracy of the entire calculation.
Why is the PISA shell treated as a hemisphere, and when does that assumption fail?
A hemisphere of radius r has a curved surface area of 2 x pi x r squared, which is where the factor of 2 in the flow equation comes from. The hemisphere is a good model when the orifice sits in a broad, flat surface so that flow can converge from every direction in the half-space above it. The assumption degrades in several common situations. If the leaflets form a narrow funnel above the orifice, the shell is a partial cone rather than a hemisphere and the true area is smaller, so uncorrected PISA overestimates flow. If the jet is eccentric and hugs an adjacent wall, the shell is constrained and distorted. Very close to the orifice the shells flatten out, and far from it they become elongated, so the hemispheric geometry holds best over a middle band of radii, roughly 0.5 to 1.0 cm in most reported series. That band is a practical rule of thumb drawn from the flow convergence literature rather than a guideline-defined validity window, so treat it as guidance on where the model is most trustworthy rather than as a hard cut-off. Recognising a non-hemispheric convergence zone is a reason to apply angle correction or to fall back on another quantitative method.
What is the angle correction factor in PISA, and when should it be applied?
The angle correction factor scales the shell area to account for a convergence zone that is not a full hemisphere. If the two structures bounding the flow (typically the valve leaflets) subtend an angle alpha measured in degrees, the shell is only alpha divided by 180 of a complete hemisphere, so the flow rate becomes 2 x pi x r squared x Va x (alpha / 180). When the orifice lies in a flat plane, alpha equals 180 degrees and the factor is 1.0, leaving the standard equation unchanged. Angle correction is most often required in aortic regurgitation, where the convergence zone is confined within the aortic cusps, in rheumatic mitral stenosis, where the funnel angle is often near 100 degrees, and in eccentric or tethered mitral regurgitation. Skipping the correction when the funnel is genuinely narrow inflates the calculated orifice area: at alpha equal to 120 degrees, the uncorrected result is 50 percent too high.
How is the PISA flow rate converted into an orifice area?
The proximal shell gives you an instantaneous flow rate in millilitres per second, but that is not yet an area. To convert it, apply the continuity principle a second time at the orifice: the same flow rate must equal the effective regurgitant orifice area multiplied by the velocity of blood passing through it. The velocity through the orifice is measured separately with continuous wave Doppler as the peak regurgitant velocity, typically 400 to 600 cm/s for mitral regurgitation because of the large pressure difference between ventricle and atrium. Dividing flow rate by peak velocity gives area, and the units confirm it: millilitres per second divided by centimetres per second yields square centimetres. Both the shell measurement and the peak velocity must be taken at the same point in the cardiac cycle for the ratio to be physiologically meaningful.
How is regurgitant volume derived from the PISA orifice area?
Effective regurgitant orifice area describes how big the leak is at one instant, while regurgitant volume describes how much blood actually goes backwards over an entire beat. To bridge the two, multiply the orifice area by the velocity time integral of the regurgitant jet, obtained by tracing the continuous wave Doppler envelope. The velocity time integral has units of centimetres and represents the distance a column of blood travels through the orifice during one beat, so area in square centimetres multiplied by that distance gives a volume in cubic centimetres, which equals millilitres. A typical mitral regurgitant velocity time integral is 120 to 160 cm. This step assumes the orifice area stays roughly constant through the ejection phase, and that assumption breaks down whenever the orifice is dynamic, which includes two of the commonest referrals. In secondary or functional mitral regurgitation the effective orifice varies through systole, typically in a biphasic pattern that peaks in early and late systole and falls in mid-systole, so a single mid-systolic shell underestimates the true regurgitant volume. In mitral valve prolapse the bias runs the other way, because the leak is often confined to late systole and a single largest shell applied across the whole ejection period overstates the average orifice. In both settings a measurement integrated across systole is more reliable than one instantaneous shell.
What orifice area thresholds does PISA use to grade severity?
The thresholds differ by valve because the haemodynamic consequences of the same orifice area differ. For mitral regurgitation, an effective regurgitant orifice area below 0.20 square centimetres is mild, 0.20 to 0.39 is moderate, and 0.40 or greater is severe. For aortic regurgitation the thresholds are lower, with below 0.10 square centimetres mild, 0.10 to 0.29 moderate, and 0.30 or greater severe. For tricuspid regurgitation, 0.40 square centimetres or greater indicates severe disease. Regurgitant volume thresholds run in parallel: for mitral regurgitation, below 30 mL is mild, 30 to 59 mL is moderate, and 60 mL or greater is severe, while severe tricuspid regurgitation is defined at 45 mL or greater. These cut points are decision aids rather than verdicts and should always be integrated with chamber sizes, vena contracta width, pulmonary vein flow patterns and the patient's symptoms.
How sensitive is the PISA result to an error in the radius measurement?
Very sensitive, and this is the single most important practical limitation of the method. Because flow rate is proportional to the square of the radius, any percentage error in the radius is roughly doubled in the final answer. A 10 percent overestimate of the radius produces an orifice area 21 percent too large, since 1.1 squared equals 1.21. A 20 percent overestimate produces a 44 percent error, since 1.2 squared equals 1.44. On a convergence zone with a true radius of 0.9 cm, mistaking the boundary by just 1 mm shifts the calculated orifice area by more than 20 percent, which is easily enough to move a patient across the moderate to severe boundary. This is why the radius should be measured on a zoomed image with an optimised baseline shift, why several cardiac cycles should be averaged, and why a borderline PISA result should never be the sole basis for an intervention decision.
Can the PISA method also be used for mitral stenosis?
Yes. The underlying conservation of mass argument does not care whether the orifice is leaking backwards or obstructing forward flow, so the same shell measurement can be used to calculate mitral valve area in rheumatic mitral stenosis. The convergence zone is imaged on the left atrial side of the valve during diastole, the flow rate is calculated the same way, and it is divided by the peak transmitral inflow velocity to give the valve area. Angle correction is essential in this setting because the rheumatic mitral funnel is distinctly cone shaped rather than flat, with the angle between the leaflets commonly measured near 100 degrees, and omitting the correction substantially overestimates the valve area. The flow convergence approach is valuable in mitral stenosis precisely because, unlike the pressure half-time method, it is not confounded by coexisting aortic regurgitation or by changes in left ventricular compliance.
When should PISA be replaced or supplemented by another quantitative method?
PISA should be supplemented whenever its geometric assumptions are visibly violated or when the result conflicts with the rest of the study. Multiple regurgitant jets cannot be summed reliably with a single hemisphere. Eccentric wall-hugging jets, funnel shaped or slit shaped orifices, and poor image quality that leaves the aliasing boundary indistinct all undermine the radius measurement. In mitral valve prolapse the orifice is dynamic and a single largest shell overstates the average leak, so an integrated approach across systole is preferable. The main alternatives are the volumetric method, which derives regurgitant volume as the difference between mitral inflow and left ventricular outflow stroke volumes, vena contracta width measured on a zoomed color image, and three dimensional color Doppler, which measures the vena contracta area directly and does not depend on any assumed shell shape. Cardiac magnetic resonance provides an independent reference standard when echocardiographic measures remain discordant.
References
Reviewed for accuracy by Rahul Singh, Health & Wellness Specialist · Editorial policy
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