So we've spent some time now looking at Doppler imaging and one of the things that keeps coming up is this concept of aliasing where the velocities that we have calculated from the Doppler shifts that we've measured with the ultrasound transducer is higher than our scale on the Doppler machine and this peak systolic velocity has wrapped around and is being displayed incorrectly on our velocity scale. we are no longer able to accurately measure this peak systolic velocity because the frequencies returning are higher than we are able to sample. Now I want to show you why aliasing occurs and how we can go about reducing aliasing within these spectral Doppler images. Now let's start with two examples. First we are measuring the velocity of blood flow within a vessel here and we've got this velocity scale on the right hand side on our yaxis of the spectral doppler here. Now, what happens if the velocity in this vessel were to increase and we were to not change any settings on our machine? Well, that increase in velocity would result in an increase in Doppler shift. That increase in Doppler shift that we measure will then be converted into a velocity value that is higher than the scale on our machine. The second scenario that we could have is we're imaging a vessel again with the same Doppler settings, but this time we slide our transducer to the left on our image here. And we see that this vessel is getting deeper and deeper. Now, as we slide our transducer to the left, the depth that we are sampling increases. When we increase that depth that we're sampling, our pulse repetition period needs to increase. The total return time of that echo gets longer. We need a longer receive time here. So as the depth increases, our pulse repetition period increases and our pulse repetition frequency decreases. The number of times that we can sample per second decreases. And as a result, our scale on the right hand side changes. The velocity of this blood hasn't changed, but now our scale has changed because of this increasing depth. So what exactly has happened in these two scenarios? Well, the first scenario, the blood is going faster in the vessel and the Doppler shift has increased and we are no longer able to sample that Doppler shift quick enough in order to accurately calculate the velocities from that Doppler shift. In the second example, we have reduced our sampling rate. We've reduced the pulse repetition frequency. Nothing has changed about the Doppler shift or the velocity within the vessel. Our sampling rate has decreased to a level where we can no longer accurately calculate the velocities. And this is what's known as the Nyquis limit. Either the Doppler shift is getting too high or the pulse repetition frequency has gotten too low. Now, what exactly is the Nyquis limit? Well, the best way I like to think about the Nyquis limit is to think about a wheel turning on a car. Now, often you'll see in a video when there's a video of a car, the wheels almost look like they're going backwards, but the car is going forward. What's happened here is the frequency that that wheel is turning forward is more than half the frame rate of the video. Now, we've seen that a video is separate frames overlaid over one another in quick succession. And our eye can't tell that difference. Now, each separate frame can be seen as a sample of where that wheel is at a given point in time. Now depending on how quickly that wheel is turning, the frame rate will determine our ability to pick up the direction that that wheel is traveling as well as the frequency that that wheel is turning. So let's have a look at an example here. We have a wheel with a spoke facing at 12:00 on the clock face. As that wheel rotates in a clockwise direction, as it's rotating round, we can see that spoke turning round. So from here it turns 90° 90° 90° and then turns back to normal. Now I've drawn these dotted lines to represent one full turn of the wheel. That can be seen as one wavelength of that wheel. Now each snapshot here represents a sampling period. Now think of this as our pulse repetition frequency. How often are we checking what the Doppler shift is? Well the time that we check what the Doppler shift has been is that pulse that we are sending in. So for each pulse that we send in we are getting data back as that pulse returns as an echo and that one pulse is giving us one data point. Now the number of times that we sample per second is the pulse repetition frequency. So if we take this wheel for example we are sampling this entire wavelength four times and if we sampled four times we would see that in fact the wheel is moving in a clockwise fashion and we will be able to determine the rate at which that wheel is moving. Now, what if we reduce the sampling rate? What if we only had three samples per cycle here? Well, we can see that the distance between this spoke and this spoke is shortest still in the clockwise position. We would still guess that this wheel is turning in a clockwise manner. So, we've got the direction of the wheel and we will be able to calculate the frequency that that wheel is turning because these are accurate representations of where that spoke actually is in time if it was moving in a clockwise position. Now, what if we reduce that sampling rate to two samples per cycle? Well, now what we've got is that spoke is going in 180° from itself. We have no longer got the ability to calculate which direction this wheel is turning. If these are the only snapshots that we see of this wheel due to our sampling rate, the spoke will just be turning on its axis. We don't know if this wheel is now turning anticlockwise or if it's turning clockwise. We can still calculate the frequency that this wheel is turning because these spokes accurately match up with the original frequency. But we've now lost direction. We've reached what is known as our Nyquis limit. The sampling rate is twice that of the frequency of the initial wheel. Now think of the frequency of this rotation here being the frequency of the Doppler shift coming back to our ultrasound machine. In order to accurately calculate that frequency returning, our sampling rate needs to be twice that of the Doppler shift frequency. So look now when we average 1 and a half samples per cycle here, we've got two samples in our first cycle, one sample in the second cycle. Now, what it looks like to our machine is that the wheel is turning in an anticlockwise position. It looks now that the spoke is turning 90° anticlockwise and at a much lower frequency. We've now lost direction of the wheel spinning and we've lost frequency. It looks now that this spoke has taken four times longer, four cycles to get back to its original position. When in fact, it has gone round four times in the clockwise direction during that period of time. We've lost direction data and we've lost frequency data. And that gets even worse when we sample only once per cycle. Now, it will look like that car wheel on our video is staying still in place. We are only sampling once per full rotation of this wheel. We've lost directional data here and we've lost frequency data. It looks like the wheel is standing still even though it is rotating in a clockwise direction. So the Nyquis limit states that once we sample two times or fewer per wavelength of a specific frequency, we can no longer detect the velocity or direction of that wave accurately. And that is what's happening when our pulse repetition frequency is not fast enough to detect the Doppler shift returning. So now let's have a look at the various formulas that describe this Nyquis limit. We've looked at all of these formulas within the preceding Doppler lectures. Now this equation in the middle here represents the Nyquis limit. The sampling frequency, the number of times we sample those returning echoes is the pulse repetition frequency. The maximum Doppler shift that we can then calculate accurately is half of that pulse repetition frequency. Remember the Doppler shift coming back is much lower than our transducer frequencies. It's coming back in the audible acoustic spectrum. So our pulse repetition frequency needs to be double that of the maximum Doppler shift. Otherwise, we're going to get aliasing artifact. Now, what affects our pulse repetition frequency? Well, the pulse repetition period is inversely proportional to the pulse repetition frequency. And that pulse repetition period is dependent on the depth in our tissues. That's why as the area that we are sampling gets deeper, the pulse repetition period gets longer, our pulse repetition frequency gets shorter. We are unable to sample as quickly. And then we can see that Doppler shift is determined by multiple different factors. And I'm going to show you these different factors and how we can adjust them to reduce aliasing within our image. So let's go to this first example where we've got increased depth within the tissue. Now the increased depth has resulted in that increase in pulse repetition period. The time it takes for that echo to return back to our transducer has increased because of that depth. And as a result, the number of times we can sample that tissue per second has decreased. The amount of Doppler shift that we can then calculate and subsequently convert into a velocity value has also decreased with this decreasing pulse repetition frequency. So what can we do in this example? Well, if this vessel has a region where there's a shallower depth, we can move our transducer to that shallower depth. And as a result, we can increase our pulse repetition frequency. We can increase that sampling rate because of the shallower depth and the shorter pulse repetition period. Now, what happens if at that depth the velocities are still higher than our scale on the Doppler machine? We may have used this Doppler probe previously to look at a vein with much lower velocities and we've changed the scale in order for those velocities to be accurately represented on our Doppler machine. So the scale here was still based on the vein when we were measuring low velocities and we had changed our pulse repetition period in order to change the scale here. Now what we can do is try and increase the scale on the Doppler machine by increasing the pulse repetition frequency. Perhaps this pulse repetition period was originally calculated not on this original depth here. So there's a dial on the machine that can change scale and if we are not past our Nyquis limit, we can change the scale on our yaxis here and accurately then see the spectral waveform on our Doppler machine. So one thing we can always try when we see aliasing within our Doppler spectral waveform is increase the pulse repetition frequency. We can increase that pulse repetition frequency, increase the amount of Doppler shift that we are able to recognize on our ultrasound transducer and hopefully then have the spectral waveform lie within the scale that we have now set. Now what happens if we can no longer reduce this pulse repetition period here, but we still have aliasing within our image? Well, then we can look at the Doppler equation where the maximum Doppler shift that we can detect is determined by the transducer frequency, the velocity of blood that we are sampling and the Doppler angle, the angle at which we are sampling this blood. The first thing we could do is reduce our transducer frequency, the actual pulses that we are sending into the tissues. If the frequency of those pulses is less, the amount of Doppler shift will be less and ultimately the more velocity we'll be able to measure with a set pulse repetition frequency. Now, this is often counterintuitive. You would think that a higher frequency would more accurately pick up the Doppler shift. Like when we looked at axial resolution, a higher frequency, a shorter spatial pulse length gave us better axial resolution. That's not the case here. What we're measuring is Doppler shift and the amount or the magnitude of Doppler shift is dependent on the transducer frequency. The lower that initial frequency, the lower the Doppler shift. The second thing we could do is change the Doppler angle. Now, we've seen that angle correction comes with faults. The higher our angle, the more likely we are to inaccurately measure the velocity of blood. But increasing this Doppler angle will reduce the amount of Doppler shift that is recognized by the ultrasound transducer and increase the velocities that we are able to accurately calculate. Now I wouldn't recommend going to changing the Doppler angle as your initial approach to reducing aliasing. First try and change the depth the pulse repetition frequency or the transducer frequency that you're using prior to changing Doppler angle. Now there are two other things that we can change that don't relate to this formula here. The first thing we can change is the actual baseline of the spectral waveform that is being displayed on our Doppler machine. If this wraparound or aliasing doesn't cross the baseline, what we can in fact do is just lower that baseline down in order to fit the spectral waveform on the scale that we have here on our machine. And that could be all that is needed to reduce the aliasing in our image. Now, this isn't always the case. You'll see that aliasing often crosses that baseline. And if we have optimized the depth, the pulse repetition frequency, and our transducer frequency as well as the Doppler angle, and we still have this wraparound that is crossing the baseline, we can't move that baseline to reduce aliasing. What we're left with now is no option but to convert to continuous wave Doppler ultrasound. The reason we are getting aliasing here is because we are sampling at set frequencies. The pulse repetition frequency continuous wave Doppler ultrasound gets continuous frequencies coming back. There's no receive time. There's no sampling period. We are continually sampling the velocities within the vessels here. Now if we switch to continuous wave Doppler ultrasound, we are sampling a larger area. So if there are other blood vessels in here, we may get some artifact there. Although we are sampling a larger area and we can't be as specific within our vessel, we can now sample much higher frequencies than we could with pulse wave Doppler with a pulse repetition frequency. Now obviously the velocities of blood within this vessel change because of that lamina flow in the vessel, but we can still accurately represent our peak systolic velocity as well as our end diastolic velocity and ultimately calculate the resistive index that we looked at in the previous talk. So there are six main factors that we can change in order to try and reduce aliasing within the image and you can go through all of these sequentially while trying to troubleshoot if you get aliasing in your pulse wave Doppler ultrasound imaging. So that brings us to the end of Doppler imaging. Now we're going to move on and look at harmonics within ultrasound imaging and then we're going to round off this ultrasound module by looking at some artifacts that you can see in beam mode imaging and looking at safety within ultrasound imaging. So, I'll see you all in the next talk where we're going to look at harmonic imaging.