Chapter 4

Christian Doppler, in his 1842 paper titled, “On the Coloured Light of the Binary Stars and Some Other Stars of the Heavens,” was the first to note that stars moving towards the earth emitted blue light while stars moving away from earth radiated red light. Thus, he postulated that the observed frequency of a wave depends on the relative speed of the source and the observer. Although Doppler himself never extended the principle to other natural phenomena, the common observation that the pitch of sound is different for a locomotive approaching the listener than one moving away led to a more widespread application of Doppler's initial observation.

In clinical echocardiography, the Doppler technique depends upon an analysis of the frequency and wavelength of an emitted ultrasound beam. Frequency is defined as the number of waves passing though a certain point in 1 second, and is a fundamental property of the sound waves. It is expressed in units of hertz (Hz) and determines the resolution and the depth of penetration of the medium. However, the Doppler assessment of ultrasound waves depends upon not just the absolute emitted frequency, but the relative change in frequency as the sound waves are reflected back (by red blood cells) towards the transducer. The frequency of the reflected sound waves increases when the red blood cells are moving towards the transducer and decreases when red blood cells are moving away from the transducer (Figure 4–1). This relative change in the frequency, known as the Doppler shift, enables the echocardiographer to assess the direction, speed, and turbulence of blood flow, which in turn helps to objectively quantify intracardiac pressures and the severity of valvular stenosis and regurgitation.

###### Figure 4-1.

Principle of Doppler shift. The frequency (cycles/second) of the reflected sound waves increases when the red blood cells are moving towards the transducer and decreases when red blood cells are moving away from the transducer.

The Doppler shift is defined as the change in frequency of the reflected ultrasound waves and is described by the following mathematical relationship1:

• Δf = 2ft × (v × Cosθ)/c
• Δf = Difference between the transmitted frequency (ft) and received frequency
• v = Velocity of red blood cells
• θ = Angle between the Doppler beam and the direction of blood flow
• c = Speed of ultrasound in blood (1540 m/s)

When the Doppler beam is parallel to the direction of blood flow, the cosine of θ is 1 and the Doppler shift is most accurately calculated, but with increases in θ there is a progressive decrease in the measured Doppler shift. This underestimation of Doppler shift remains clinically insignificant until θ exceeds 20° and the associated percentage error exceeds 7% (Figure 4–2).2 When the Doppler beam is perpendicular to the direction of ...

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