##### Doppler Shift

Austrian Physicist Christian Doppler in 1842 put forth the idea that when sound waves are reflected off a moving object there is a change in the frequency that returns which is dependent on:

1) the velocity (speed and direction) of the moving object

2) the initial frequency of the sound waves

3) the angle at which the waves hit the moving object.

In the case of echocardiography, the ultrasound probe emits a particular frequency, and the moving object is the heart, red blood cells and tissues. Reflected ultrasound waves from red blood cells return to the probe with a Doppler shift that is translated by a computer into a velocity.

These elements are represented in the Doppler equation shown below: where:

V is the velocity of the moving blood, in the picture shown across the aortic valve

c is the speed of ultrasound sound in the body, which is known

Ft is the ultrasound frequency the transducer emits

Fs is the backscattered frequency that returns to the transducer

θ is the "insonification angle" or the angle between the ultrasound beam and the direction of blood flow. Ideally this angle, θ, should be zero meaning the ultrasound beam lines up perfectly in parallel with blood flow of interest (cos 0 = 1) . However often one is  off by a small angle as shown in the figure above.

Unfortunately the ultrasound machine doesn't take into account θ; it just generates velocities. When θ is above 30 degrees, then significant error (over 12%) starts to be introduced and the machine will underestimate the true velocity.

By corollary when θ is 90 (cos θ = 0) and the ultrasound beam is perpendicular to the direction of blood flow, it cannot be used to measured velocity. The amount of error in velocity measurement introduced is shown in the table below. For example, when θ is 10 degrees the value computed is 98.5% of the true velocity. Some machines do allow for an angle correction with the spectral Doppler, but this should be used with caution. The Doppler equation forms the basis of spectral Doppler, which incorporates both "pulsed wave" Doppler and "continuous wave" Doppler which we use to measure blood flow.