1. Modified Bernoulli Equation

The Bernoulli equation describes how velocity and pressure are related as fluid flows through an orifice, such as a valve. The pressure gradient can be calculated using this formula:

Pressure Gradient = 4(V₁² - V₀²)

• V₀: Flow velocity before the valve

• V₁: Peak velocity through the valve

In most cases, V₁ >>> V₀, and when V₀ < 1.0 m/s, the term for V₀ can be ignored. This simplifies the equation to:

Pressure Gradient = 4V₁²

Example Calculation:

• If the peak velocity through the valve (V₁) is 3 m/s, the pressure gradient is:

• Pressure Gradient = 4 × (3²) = 4 × 9 = 36 mmHg

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2. Continuity Equation

The continuity equation is commonly used to calculate the aortic valve area in aortic stenosis. It can also be used for a number of other valve and flow calculations. It works on the principle of conservation of mass: the flow before an orifice must equal the flow at the orifice (assuming no shunt). Flow is calculated as the area multiplied by the velocity-time integral (VTI).

For the aortic valve:

• Area (LVOT) × VTI (LVOT) = Area (AV) × VTI (AV)

• To calculate the aortic valve area (AV):

• Area (AV) = (Area (LVOT) × VTI (LVOT)) ÷ VTI (AV)

• Simplified formula:

• Area (AV) = 0.785 × (LVOT Diameter)² × VTI (LVOT) ÷ VTI (AV)

Example Calculation:

• LVOT diameter = 2 cm

• VTI (LVOT) = 20 cm

• VTI (AV) = 40 cm

Area (AV) = 0.785 × (2²) × 20 ÷ 40 = 0.785 × 4 × 20 ÷ 40 = 1.57 cm²

An aortic valve  calculator is found on this site here. 

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3. Proximal Isovelocity Surface Area (PISA)

PISA is primarily used to measure the regurgitant orifice area in valvular lesions, such as mitral regurgitation. This method leverages flow convergence at an orifice, forming hemispheres of equal velocity.

• EROA = [2π × (PISA radius)² × Aliasing Velocity] ÷ Peak MR Velocity

Example Calculation:

• PISA radius = 1 cm

• Aliasing velocity = 40 cm/s

• Peak MR velocity = 500 cm/s

EROA = [2π × (1²) × 40] ÷ 500 = [2 × 3.14 × 1 × 40] ÷ 500 = 251.2 ÷ 500 = 0.50 cm²

An EROA calculator can be found on this site here. 

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4. Mitral Valve Area by Pressure Half-Time

This formula calculates the mitral valve area, primarily for rheumatic mitral valve disease:

MVA (cm²) = 220 ÷ Pressure Half-Time
OR
MVA (cm²) = 750 ÷ Deceleration Time

Example Calculation:

• If the pressure half-time is 110 ms:

• MVA = 220 ÷ 110 = 2.0 cm²

Alternatively, if the deceleration time is 300 ms:

MVA = 750 ÷ 300 = 2.5 cm²