ECHONOMY
Tools for Echocardiographic Calculations
Muhamed Saric, MD, PhD
New York University


Theoretical Background

 A moving fluid has 3 types of energy: kinetic (velocity, V), potential
(pressure, P), and thermal (heat loss due to friction, T).

 The 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

 An increase in fluid velocity leads to a drop in local pressure. This
is the basis of Venturi effect and the lift of an airplane.

 As fluid velocity slows down, local pressure increases; i.e. there is
pressure recovery.

 If 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

 LVOT:
Pressure is high (P1); velocity is low (V1)

 AORTIC VALVE
AREA (AVA): Pressure is low (P2); velocity (V2) is increased.

 ASCENDING
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

 P1  P2
= Peak instantaneous pressure gradient by Doppler

 P1  P3
= Peaktopeak gradient by cardiac cath

 P3  P2 =
Pressure recovery 
The larger the pressure recovery, the lower the peaktopeak 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.

Calculator

Peak velocity (Vmax) across aortic valve by continuous
Doppler 

m/sec 
Aortic valve area (AVA, by
continuity equation): 

cm^{2 } 
Diameter of ascending aorta (AscA) 

cm 


Answers

Peak instantaneous aortic gradient (P1P2) 

mm Hg 
Crosssectional area of ascending aorta (AscAA) 

cm^{2} 
Pressure recovery (P3P2) 

mm Hg 
Expected peaktopeak cath gradient (P1P3) 

mm Hg 
Overestimation of peak gradient by Doppler compared to
cath 

mm Hg 
Formulas
P3  P2 = 4 * Vmax^{2} *
C
C = 2 * (AVA / AscAA) * (1 AVA / AscAA)

Reference

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):193440.
