Tools for Echocardiographic Calculations

Muhamed Saric, MD, PhD
New York University


Pressure Recovery

Theoretical Background

bulletA moving fluid has 3 types of energy: kinetic (velocity, V), potential (pressure, P), and thermal (heat loss due to friction, T).
bulletThe sum of all energies is constant; an increase in one form of energy can come only at the expense of other two forms:

E = V + P + T = constant
bulletAn increase in fluid velocity leads to a drop in local pressure. This is the basis of Venturi effect and the lift of an airplane.
bulletAs fluid velocity slows down, local pressure increases; i.e. there is pressure recovery.
bulletIf decrease in fluid velocity is accompanied by an increase in turbulent flow, there will be an increase in heat loss at the expense of pressure recovery.

Flow From LVOT to Aortic Valve to Ascending Aorta

bulletLVOT: Pressure is high (P1); velocity is low (V1)
bulletAORTIC VALVE AREA (AVA):  Pressure is low (P2); velocity (V2) is increased.
bulletASCENDING AORTA (AscA): Velocity (V3) decreases rapidly. The kinetic energy is dissipated into pressure (P3) or thermal loss (T).

Normally, as the blood enters from AVA into AscA, turbulence leading to heat loss prevents significant pressure recovery.

When AVA is moderately stenotic and the diameter of the receiving AA is small (< 2.0 cm), little turbulence & heat loss occur. Thus the kinetic energy is converted primarily into pressure;  i.e. a significant pressure recovery occurs.

Technical Hints

bulletP1 - P2 = Peak instantaneous pressure gradient by Doppler
bulletP1 - P3 = Peak-to-peak gradient by cardiac cath
bulletP3 - P2 = Pressure recovery

The larger the pressure recovery, the lower the peak-to-peak gradient will be for any given peak instantaneous gradient. In other words, the more pressure recovery there is, the more overestimation of aortic stenosis by Doppler will occur compared to cardiac cath.


Peak velocity (Vmax) across aortic valve by continuous Doppler


Aortic valve area (AVA, by continuity equation):


Diameter of ascending aorta (AscA)




Peak instantaneous aortic gradient (P1-P2)

 mm Hg

Cross-sectional area of ascending aorta (AscAA)


Pressure recovery  (P3-P2)

 mm Hg

Expected peak-to-peak cath gradient (P1-P3)

 mm Hg

Overestimation of peak gradient by Doppler compared to cath

 mm Hg


P3 - P2 = 4 * Vmax2 * C

C = 2 * (AVA / AscAA) * (1- AVA / AscAA)


Niederberger J, Schima H, Maurer G, Baumgartner H. Importance of pressure recovery for the assessment of aortic stenosis by Doppler ultrasound. Role of aortic size, aortic valve area, and direction of the stenotic jet in vitro. Circulation. 1996 Oct 15;94(8):1934-40.