Doppler equations (Doppler shift equation, Bernouilli equation, Nyquist principle, calculation of cardiac output)Table 4.4

Doppler shift equation

2FV Cosine 0

Frequency shift = C where

F = emitted frequency V = velocity of the reflecting target (blood cells) 0 = the angle between the ultrasound beam and the direction of blood flow C = is the velocity of sound in the body (1560 m/sec) Bernoullli equation (modified)

P = 4 x (V22 - V12)

where

P = the pressure gradient across the narrowing (e.g. valve or VSD) Vi = the initial velocity V2 = the maximum velocity in the narrowing Usually when Doppler measurements of velocity are made, velocity is high and V1 is negligible, so P can be approximated to = 4 x (V22)

Nyquist principle

Nyquist limit PRF/2

i.e. aliasing occurs when Doppler frequency > ½ pulse repetition frequency

Calculation of cardiac output

Stroke volume velocity time integral x internal area of vessel

(Velocity time integral (VTI) = area within envelope of spectral Doppler trace)

CO=stroke volume x heart rate