Ultrasound Nyquist limit conundrum

[HeartEcho]

Hi all,
I work as a cardiac sonographer. I've been struggling to understand a concept as dictated in ultrasound textbooks and it regards the Nyquist limit.

During my work I observed that when I increased my ultrasound transducer frequency (e.g. from 1.7 MHz to 3.0 MHz) when using pulsed wave Doppler at a given depth, the maximal detectable velocity (i.e. Doppler shift) decreased; and vice versa.

The textbooks state that the maximal Doppler shift that can accurately be determined is based on the Nyquist limit (i.e. half the sample rate of a discrete signal processing system). I understand this concept. What I do not understand is why, in the case of pulse wave Doppler ultrasound, the Nyquist limit is determined by the PRF (pulsed repetition frequency): the Nyquist limit is half the PRF.

Why can't the ultrasound machine simply generate an initial pulse, followed by a time delay to estimate depth, and then very rapidly sample the returning pulse (i.e. pizoelectric crystal voltage changes). Would this not be independent of the pulse transmit/recieve frequency (i.e. PRF). Can some one please highlight what I am missing here? Any help would be greatly appreciated. thanks

 

[scottdave]

I'm not able to look up reference for you, at the moment, so this is just off what I remember. If I am remembering correctly, the pulse width helps determine the resolution - difference in distances between 2 objects which are reflecting the signal.

 

[HeartEcho]

That's right, a higher frequency (i.e. smaller wave length) will give better axial resolution. However, it doesn't answer my question. Hope my question wasn't too confusing

 

[CWatters]

Why can't the ultrasound machine simply generate an initial pulse, followed by a time delay to estimate depth, and then very rapidly sample the returning pulse (i.e. pizoelectric crystal voltage changes). Would this not be independent of the pulse transmit/recieve frequency (i.e. PRF).

As I understand it, the time delay isn't to measure the depth it's to separate out multiple reflections from objects at different depths. If you have a fixed time delay you can only measure at one depth.

I assume you mean why can't you measure the doppler shift multiple times during one burst and look for changes. The result would be a short burst of samples with gaps between due to the PFR. If the signal changes faster than the PRF you still don't have information to "fill in the gaps". It would be like getting a bank statement every day for one week then not getting any statements for say 3-6 months, then another week of daily statements. Would you be able to see the monthly pay cycle?

 

[tech99]

I presume that a pulse consisting of a number of waves at 1.7MHz is transmitted, and in a fixed time window the returning pulse is analysed. The received pulse consists of a number of cycles near 1.7MHz, but in addition to the Doppler shift, the receiver must have sufficient bandwidth to accommodate the duration of the pulse. In other words, because the waves are received in a burst, the bandwidth is increased (as you explain).
If the frequency is raised, the Doppler shift will increase. This means that a greater bandwidth is needed for the detector.
If the equipment does not increase the bandwidth when raising the frequency from 1.7MHz to 3.0MHz, the returned pulse will not rise to its full height.On the other hand, if the bandwidth is increased to accommodate the increased Doppler shift, the noise power will increase pro-rata.
The increased Doppler shift at 3.0MHz has the potential to provide more resolution of velocity, but to do that may require several pulses to be integrated so that the effective noise bandwidth can be reduced whilst at the same time allowing the pulse energy to accumulate. It is possible that the system under analysis, the cardiac system, is not sufficiently time stable to allow integration over a period of time like this.

 

[sophiecentaur]

As I understand it, the time delay isn't to measure the depth it's to separate out multiple reflections from objects at different depths.

A single burst pulse will produce many reflections, corresponding to different depths, I think the time delay between transmitted pulse bursts is to ensure that the last reflections of one pulse (greatest range) will have had a chance to return to the transducer before the firstl reflections (smallest range) can arrive. An overlap of reflection patterns could be interpreted as extra short range reflections (uncertainty as to which transmitted pulse they are from). The shorter the range of interest, the faster can be the transmitted pulse rate. The different transmission delays for the peaks of the reflections indicate the path lengths to the various objects along the path.

I've been struggling to understand a concept as dictated in ultrasound textbooks

It's a difficult subject and the books may be just giving you a rule of thumb, rather than actually explaining it. Here is my stab at it, as a result of skimming a few Google hits.
The Frequency of the carrier during the reflected bursts is what is changed by the movement of the blood. For non moving tissue there will be no frequency change so you have to measure the frequency change by beating the return signal with the reference transmitted carrier. The pulses for which there is a frequency shift can be gated out on the basis of a Non DC value which doesn't vary appreciably over each pulse period. You effectively have a string of samples at the PRF so Nyquist applies. Your string of samples will lie on a sine wave at the (Δf) low beat frequency. If the beat frequency is greater than half the PRF, you will get aliasing and a high velocity can be interpreted as a low velocity. The resulting distortion of the time profile of blood velocity could produce harmonics of the pulse rate. The low speeds are recorded correctly but then the higher speeds will appear to go back to zero and work upwards again.

I had a problem about the actual frequencies involved. I was picturing bursts of a high Δf at the PRF but, of course, the blood velocity is low enough that the Δf will actually be quite a small fraction of the carrier frequency - small enough to allow a low enough PRF to allow some reasonable distance measuring range. If the blood speed were much higher, the PRF would have to be inconveniently high. A good old engineering compromise with a workable system in the middle.