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# Doppler shift and angle of incidence

The Doppler shift occurs when a source of wave is moving toward or away from a receiver (or when the receiver is moving toward or away from a wave source). When the distance between a wave source and the receiver is getting smaller, the observed frequency of the wave is greater than the source frequency. When the distance between a wave source and the receiver is getting larger, the observed frequency of the wave is less than the source frequency. How much of a change in observed frequency is related to the velocity of the receiver/source and the angle of incidence. For application in the anesthesiology world, the ultrasound that we are using is usually a TEE probe. The ultrasound beam hits moving red blood cells and reflects the beam back at a different frequencies and different angles, based on how the beam is positioned. This is called the Doppler shift frequency. This allows for us to measure the velocity of blood through a vessel, for which the equation is:

(see image)

Where:

• v=velocity of red blood cell targets
• f=Doppler shift frequency
• f0=transmitted ultrasound beam frequency
• θ=angle between the ultrasound beam and the vector of red blood cell flow
• c=velocity of ultrasound in blood (approximately 1570 m/sec)

As implied by the above equation, the impact of the angle on the Doppler shift will be greatest when the angle of incidence is 0 degrees (cos 0 degrees is 1) and least when the angle of incidence is 90 degrees (when the probe is exactly perpendicular to the source, the cos 90 degrees is 0).