Fig. 10. Pulsed-wave Doppler interrogation at the level of the aortic valve.

pulses of ultrasound to be emitted and returned to the transducer. The rate at which these pulses are emitted is the PRF. It is important to understand the difference between the PRF and the frequency of the ultrasound wave itself. The ultrasound frequency is equivalent to the pitch of a note played on a piano, whereas the PRF represents the rate at which the note is repeated. Because pulses emitted from a transducer return to the transducer at the same rate at which they were emitted, the PRF essentially represents the sampling rate of the Doppler acquisition.

A cardinal principle of digital sampling in general states that the sampling rate must always be at least double the frequency of the waveform being sampled. This is true for digital audio recording as well as for ultrasound acquisition. For example, because humans can hear sounds up to 20,000 Hz, compact discs are recorded using a sampling rate of 44.1 kHz, ensuring the sampling of all frequencies. In Doppler ultrasound, we are sampling the frequency, not of the ultrasound itself, but of the Doppler shift, i.e., the frequency difference between the emitted and the received waveforms. This frequency, as previously discussed, is directly related to the velocity of blood flow. Hence, the sampling rate (or PRF) is a major determinant of the maximal Doppler shift that the ultrasound machine can accurately sample, and thus a major determinant of the maximal velocity that can be assessed (see Understanding Aliasing in Doppler; Figs. 12 and 13).

The point at which a waveform cannot be sampled unambiguously happens at a sampling rate of twice the highest frequency that needs to be sampled. This point is called the Nyquist limit, and is one-half the PRF. When the frequency of the Doppler shift (and hence the velocity of blood flow) is greater than twice the PRF, the waveform cannot be accurately sampled, and the velocity cannot be accurately assessed. The resultant image will demonstrate "aliasing." Aliasing occurs because the machine cannot figure out accurately the velocity or the direction of flow when the velocity exceeds the Nyquist limit. It is important to remember that the effective sampling rate is dependent on the PRF. What, then, limits the PRF? Because ultrasonic pulses must leave the transducer, reflect off moving blood cells, and return to the transducer, the PRF cannot be higher than the amount of time it takes for the ultrasound to make this round-trip. Thus, because the speed of sound is constant, the PRF is dependent on the depth of the region being interrogated. When using PW Doppler, we have the ability to select a particular

Fig. 12. Understanding aliasing: aliasing can best be understand by this simple example from sampling theory, the so-called "wagon-wheel" example, named after the wagon wheel illusion in old western motion pictures. Consider a rotating clock hand. In the top panel, the hand is rotating at one revolution per minute. If we were to "sample" the clock every 15 s (four times per minute) by snapping a picture, we would easily be able to "capture" the motion of the clock, we would see that the hand is rotating clockwise and would be able to discern the rate of rotation. If, however, we increased the rotational speed to two revolutions per minute, and maintained the same sampling rate, we would only "capture" the hand at the 12 o'clock and 6 o'clock positions. We could tell the rate of rotation, but would not be able to discern the direction. Finally, in the bottom panel, if the velocity of revolution increased to three revolutions per minute (still in the clockwise direction), with the same sampling rate, the perceived direction, based on the sampling, would be counterclockwise, and the perceived rate of rotation would be one revolution per minute.

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