Transcription
Hello and welcome back. In the next few talks, we're going to be looking at ultrasound resolution. We'll start by looking at axial resolution, then move on to lateral and elevational resolution, and finally round things off by looking at temporal resolution in our ultrasound images.
So, what exactly is axial resolution? Well, axial resolution is the ability to differentiate two objects of varying depths. There will be a point where those two objects are close enough that the ultrasound machine can't tell that there's a gap between those two objects. Once that happens, we have reached our axial resolution limit.
Now, in order to understand axial resolution, we need to understand the concept of spatial pulse length. Now, if you cast your mind back to the pulse echo ultrasonography talk, we looked at the pulse echo wave as it heads into tissue. We saw there's a transmit time and a receive time. And in the transmit time is when we are generating ultrasound pulses that are going to head into the tissues. And it's this pulse that travels through the tissues and heads back during the receive time before the next pulse is then released. The pulse that heads into the tissue, as it comes into boundaries of tissues that have differing acoustic impedances, will rescind reflections or echoes back to our ultrasound machine. It's those reflections, those echoes, that provide us with the data that we use to create the ultrasound image. So, it's this spatial pulse length, it's this pulse here, that interacts with the tissues and creates our echoes.
So, what exactly is a spatial pulse length? Well, the spatial pulse length is the distance, the total distance of a single pulse that we send into tissues. The time that this pulse takes is what's known as our pulse duration. So, our spatial pulse length is a distance measurement. And if we take the number of cycles within our pulse, in here, we've got two cycles, and we times it by the wavelength, two times by the length of a single wave here, we will get our spatial pulse line. And our spatial pulse length is what determines our axial resolution in tissues. It travels in the longitudinal plane, and our echoes returning back are also in that longitudinal plane. It gives us that resolution in the depth plane of our image.
So, let's look at an example. We have an ultrasound transducer here, and we want to see whether this transducer can differentiate these two different tissue boundaries. Now, the distance between these two tissue boundaries is equal to the spatial pulse length in this example. So, we've got the number of cycles within our pulse times by the wavelength of that pulse will give us our spatial pulse length. So, let's send out a pulse into the tissue. And first, that pulse will come into interaction with the first tissue boundary. Now, when that pulse gets half a pulse length deep into the tissue boundary, half of that pulse has traveled past this tissue boundary, has been transmitted through the first tissue boundary. That first half of the pulse will have sent back a corresponding echo. So, this orange echo now is heading back towards our ultrasound machine. As the blue pulse travels further into the tissue, it will reach the second tissue boundary here. By this stage, the entire pulse echo has been returned back from this orange tissue boundary. So, we've got this orange echo returning to our ultrasound machine and this blue transmitted pulse heading into the tissue. As that blue transmitted pulse heads further into the tissue, another wavelength into the tissue, we get a second echo returning from this green tissue interface. This blue pulse is still being transmitted through the tissue at the same rate. Our first echo is busy returning back to our ultrasound machine again. As that pulse heads further into the tissue, our full pulse of a green echo is now heading back towards our ultrasound machine as well as our initial echo from our first tissue boundary. You can see that these echoes returning back to the ultrasound machine have a space between them. The machine will know that that represents two separate tissue boundaries and it will plot those A-mode signals as brightness levels at two distinct depths. Remember, in pulse echo ultrasonography, the time taken for the initial pulse to head into the tissues and return back to the ultrasound machine will determine the distance that the ultrasound machine plots the various different tissue boundaries. So, here, when two objects are a spatial pulse length apart, the ultrasound machine will be able to resolve those two discrete tissue boundaries.
Now, let's take a second example where our tissue boundaries are half a spatial pulse length apart. Again, we send a pulse into the tissue. And once that pulse interacts with the first tissue boundary, it will start sending back an echo. The blue pulse is still heading into the tissue. Our orange pulse is now heading back to the ultrasound machine, showing that there is a tissue boundary. The blue transmitted pulse continues to head into the tissue and is now interacting with the red tissue interface. Our entire blue pulse has interacted with this first tissue interface and given back our orange echo. Here, we've now started to generate our red echo that corresponds to the second tissue boundary. The blue pulse continues heading into the tissue and the red echo is now returning towards our ultrasound machine. We can see here what is going to happen. As that blue pulse now heads further into the tissue, our echoes are unresolved. There is no space between the first echo and the second echo. When this information heads back towards our ultrasound transducer, the transducer itself will not be able to differentiate the first pulse echo from the second pulse echo, and it will plot this information as one solid line. The ultrasound machine is unable to resolve these two tissue boundaries because they are too close together, and our image will show one line at this tissue boundary and not two distinct lines.
So, we can see here that the limit of axial resolution is actually half of the spatial pulse length. And we can create this formula here. Our axial resolution limit is equal to half of the spatial pulse length. If any two objects are closer than half a spatial pulse length apart within the axial plane of our ultrasound beam, we will be unable to differentiate those two objects.
Now, our spatial pulse length, we've seen, is determined by the number of cycles within the pulse as well as the wavelength of that pulse. Now, there are various factors that we can change which will change our spatial pulse length and ultimately will change the axial resolution.
Now, the first thing that we can do is change the number of cycles within the ultrasound pulse. You'll remember when we looked at creating an ultrasound pulse, we looked at what is known as dampening. If we were to fire a piezoelectric crystal and let that crystal resonate at a set frequency, like hitting a cymbal on a drum set, that crystal will ring for a long time, letting out ultrasound pulses into the tissue. If we place a damping block behind that piezoelectric material, it will prevent that crystal from resonating for a long time. It's much like putting a wet rag on top of a cymbal. If we were to hit a cymbal on a drum set and that cymbal had a wet rag on top, the cymbal wouldn't ring at a frequency for a long period of time. It will have a wide bandwidth, many frequencies within that note, as well as very few cycles within the pulse. So, if we increase the dampening behind our piezoelectric material, we reduce the number of cycles released in our pulse, we reduce the spatial pulse length, and increase our axial resolution. The shorter this pulse length, the better our axial resolution, as we've looked at in those two examples. We've got a lower quality factor pulse heading out into the tissues. There's a greater range of frequencies within this pulse, but the pulse length has reduced, and we've improved our axial resolution.
The second thing that we can do, we've reduced the number of cycles. We can also reduce our wavelength. Making our wavelength shorter will reduce our spatial pulse length and ultimately improve our axial resolution. Now, our wavelength is related to the thickness of the piezoelectric material. We had the example of a guitar string. The length of that guitar string was half the wavelength of the wave. If we pluck that guitar string, the same thing happens with a piezoelectric material. The thinner the piezoelectric material, the shorter the wavelength. And we saw that the thickness of the piezoelectric material was half the wavelength of the wave it produces. So, we can see here that a thin piezoelectric material will result in shorter wavelengths and subsequently higher frequencies. We've seen that in a specific tissue, wavelength and frequency are inversely proportional. As we reduce our wavelength by reducing the thickness of our piezoelectric material, we increase our frequency. A thicker piezoelectric material will give rise to a longer wavelength and subsequently a lower frequency wave. So, we can see now that higher frequency waves give better axial resolution. So, the higher our frequency of the ultrasound transducer, the better axial resolution we get. Now, that comes at a trade-off, because high frequency ultrasound probes get attenuated quickly. So, perhaps we don't get as much depth in our image, but we get better axial resolution.
Now, importantly, axial resolution, as we go into the depth of our ultrasound image, it doesn't change. Our axial resolution remains the same despite the depth of the ultrasound beam. We don't lose frequency as the ultrasound pulse is traveling through tissues. We're losing intensity of that pulse, but the spatial pulse length doesn't change as it heads into tissues. So, it's important to note that axial resolution doesn't change with depth in our ultrasound image. And the only thing that changes our axial resolution is our spatial pulse length. And the spatial pulse length is related to the quality factor of our beam, how much dampening we have in our beam, the number of cycles that are released in that spatial pulse length, as well as the wavelength of our ultrasound beam, or another way to think about it is the frequency of our ultrasound beam. The higher the frequency, the better the axial resolution.
So, now we've looked at axial resolution in the longitudinal plane, the depth plane of our ultrasound beam. Next, we're going to be looking at lateral resolution and elevational resolution. How can we differentiate objects that are at the same depth within our tissues but at different regions within the lateral portions of our ultrasound beam and within the elevational portions of the ultrasound beam?
Now, knowing resolution, knowing what affects resolution, and knowing how resolution changes within depth in the tissue is extremely important if you are studying for a radiology physics exam or an ultrasound physics exam. And if you are someone who is studying for an exam, I've linked a curated question bank in the first line in the description below, which you can go and check out if you want. Otherwise, I'll see you all in the next talk where we're going to look at lateral and elevational resolution. Until then, goodbye everybody.