Page 34 - Libro vascular I

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DOPPLER ULTRASOUND
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Table 3.1 Variation of the cos term of the Doppler equation with the angle of insonation
(°) cos
01 30 0.87 45 0.71 60 0.5 75 0.26 90 0
Transmitting element Tissue Gel
Receiving element
Blood flow
θ, angle of insonation
Figure 3.2 Simple Doppler ultrasound instruments
use transducers consisting of two piezoelectric elements, one to transmit ultrasound and the other to receive
the returning echoes back-scattered from the moving blood cells.
between the transmitted frequency, ft, and received frequency, fr) is given by:
(3.1)
where v is the velocity of the blood, is the angle between the ultrasound beam and the direction of blood flow (also known as the angle of insonation) and c is the speed of sound in tissue. The factor of 2 is present in the Doppler equation as the Doppler effect has occurred twice, as explained above.
Consider, for example, a 5 MHz transducer used to interrogate a blood vessel with a flow velocity of 50cm/s using an angle of insonation of 60°. Taking the speed of sound in tissue to be 1540m/s, the Doppler equation can be used to estimate that the Doppler shift frequency produced will be 1.6 kHz. In fact, it is a useful coincidence that the typical values of blood velocity found in the body and the transmitted frequencies used in medical ultrasound result in Doppler shift frequen- cies that are in the audible range (from 20 Hz to 20 kHz). The simplest Doppler systems can extract the Doppler shift frequency and output it to a loudspeaker, enabling the operator to listen to the Doppler shifts produced from the blood flow.
The Doppler equation shows that the detected Doppler shift depends on the angle of insonation,
Blood flow
The detected Doppler shift frequency changes as the angle of insonation changes.
fd fr ft 2vft cosu c
Figure 3.3
, through the term ‘cos ’. Table 3.1 shows how the cos term varies between 0 and 1 as the angle changes from 0° to 90°. When the angle of inso- nation is 90°, the cos term is 0, so virtually no Doppler shift is detected. When the angle of inso- nation is 0° (i.e., the Doppler beam is parallel to the direction of flow), the cos term is 1, giving the maximum detectable Doppler shift frequency for a given velocity of blood and transmitted fre- quency. Figure 3.3 shows how the detected Doppler shift frequencies change as the Doppler angle changes. When the transducer is pointing toward the flow, a positive frequency shift is seen, but once the transducer is pointing away from the direction of flow, a negative frequency shift is seen. The smaller the angle of insonation, the larger the fre- quency shift detected, but as the angle of insonation approaches a right angle, very small frequency shifts are detected.