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Common Equations

1. Modified Bernoulli Equation

The Bernoulli equation is used to describe the relationship between velocity across an orifice such as a valve and the pressure gradient across the orifice. 


Pressure gradient = 4V1^2-4V0^2

Here V0 is the flow velocity proximal to the valve and V1 is the peak velocity through the valve. In most situations, V1>>>V0 and if V0 is <1.0 m/s, this term can be ignored and the modified Bernoulli equation can be used: 

Pressure gradient = 4V1^2

2. Continuity Equation

The continuity equation is most commonly employed to calculate the aortic valve area in aortic stenosis. However, theoretically it can be used to calculate any stenotic valve area. The continuity equation is based on the principle of conservation of mass - i.e. that flow proximal to an orifice must equal flow at the orifice in the absence of a shunt. Note that in echocardiography, we calculate flow by multiplying area by velocity time integral through that area.


For the aortic valve:

Area (LVOT) x VTI (LVOT) = Area (AV) x VTI (AV)

Area (AV) = Area (LVOT) x VTI(LVOT) / VTI (AV)


Area (AV) = 0.785 x LVOT Diameter Squared x VTI(LVOT) / VTI (AV)


3. Gorlin Equation

The Gorlin Equation is the "gold standard" for invasive assessment of aortic and mitral valve areas with cardiac catheterization. The complete Gorlin formula for aortic stenosis is:

Valve area (cm2) = Cardiac Output (ml/min) 
Heart Rate (beats/min) * Systolic Ejection Period (s) * 44.3 * square root(mean gradient)

However, the Hakki modification of the Gorlin formula allows for a rough and ready assessment of aortic valve area during a procedure. It is based on the observation that at most heart rates the product of HR x SEP x 44.3 is close to 1000. Thus, the equation becomes:

Aortic Valve area (cm2) ~ Cardiac Output (L/min)
square root (mean gradient) 

4. Proximal Isovelocity Surface Area (PISA)

PISA is used to most commonly used to calculate the regurgitant orifice area with regurgitant valvular lesions, typically mitral regurgitation. PISA takes advantage of flow convergence at an orifice with multiple hemispheres of color flow of equal velocity (isovelocity)


EROA = [2*Pi*(PISA radius)2 x aliasing velocity)/peak MR velocity

5. Mitral Valve Area by Pressure Half Time

MVA (cm2) = 220/pressure half time OR

MVA (cm2) = 750/deceleration time

Note this equation is only reasonable to consider for rheumatic mitral valve disease, not in mitral stenosis causes by degenerative calcification. 

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