# Modified Bernoulli Equation Calculator

Determines the instantaneous pressure gradient by converting the velocity difference obtained by spectral Doppler.

Refer to the text below the tool for more information about the equation used and its variables.

The modified Bernoulli equation helps retrieve the instantaneous pressure gradient (ΔP) by converting the velocity difference obtained by spectral Doppler.

The modified equation is simplified by assuming that viscous losses and acceleration effects are negligible. Also, an approximation is used to account for the constant that relates to the mass density of blood.

`Δ`

*P* = 4 x [(*V*_{2})^{2}−(*V*_{1})^{2}]

Where:

- ΔP – Instantaneous pressure gradient
*V*_{1}– proximal velocity- V
_{2 }– distal velocity

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**Steps on how to print your input & results:**

1. Fill in the calculator/tool with your values and/or your answer choices and press Calculate.

2. Then you can click on the Print button to open a PDF in a separate window with the inputs and results. You can further save the PDF or print it.

Please note that once you have closed the PDF you need to click on the Calculate button before you try opening it again, otherwise the input and/or results may not appear in the pdf.

## Modified Bernoulli Equation Explained

The modified Bernoulli equation helps retrieve the instantaneous pressure gradient (ΔP) by converting the velocity difference obtained by spectral Doppler.

Continuous wave Doppler and pulsed wave Doppler measure erythrocyte velocity through the blood vessels, which is then used to estimate pressure gradient, for example across small openings, such as valves.

The modified equation is simplified by assuming that viscous losses and acceleration effects are negligible. Also, an approximation is used to account for the constant that relates to the mass density of blood.

`ΔP = 4 x [(V`

_{2})^{2}−(V_{1})^{2}]

Where:

- ΔP – Instantaneous pressure gradient
*V*_{1}– proximal velocity- V
_{2 }– distal velocity

Some consider that in the setting of valvular stenosis or regurgitation, when the proximal velocity is smaller than 1 m/s and significantly smaller than distal velocity, it may be ignored, thus the equation can become: Δ*P* = 4 x (*V*_{2})^{2}

The pressure gradient across a stenotic valve is directly related to the valve orifice area and the transvalvular flow

But when the proximal velocity is over 1.5m/s or the distal velocity is less than 3 m/s, the proximal velocity should be included.

The Bernoulli equation is dependent on the precision of the two Doppler measurements with the beam having to be parallel to the direction of the blood flow. Any angle error may result in an underestimation of the velocity.

## References

Baumgartner H, et al. Echocardiographic assessment of valve stenosis: EAE/ASE recommendations for clinical practice. J Am Soc Echocardiogr. 2009; 22(1):5.

Requarth JA, et al. In vitro verification of Doppler prediction of transvalve pressure gradient and orifice area in stenosis. Am J Cardiol 1984; 53(9):1369-73.

Specialty: Cardiology

System: Cardiovascular

Article By: Denise Nedea

Published On: July 15, 2020

Last Checked: July 15, 2020

Next Review: July 15, 2025