Transcription
So we've looked now at some of the ultrasound probes that are available to us, as well as the various different transducer types. Now let's turn our attention to the ultrasound beam itself. We're going to look at the shape of the ultrasound beam and some of the properties that will change the ultrasound beam shape, as well as later on looking at the various parameters that we can change in order to manipulate that ultrasound beam shape, depending on the type of image we are trying to create.
Now I mentioned in our previous talk that we can broadly separate transducer types into single element transducers and multi-element transducer arrays. These transducer arrays have many discrete transducer elements that can be fired independently of one another.
Now when looking or learning about the ultrasound beam and the properties of the ultrasound beam, it's useful to look at a single element transducer. Now these principles, the principles that apply to a single element transducer, will also apply to these multi-element transducer arrays, and at the end of this talk, I'll show you how we go about doing that.
So let's look at an ultrasound beam here and assume that this transducer is a single element transducer array. We have our beam forming on the face of that transducer, and this width here, this diameter of our transducer, is the diameter of our ultrasound beam. Now that ultrasound beam will more naturally converge to a point known as our focal point, and that converging region is also known as our near field or our Fresnel Zone. This is a distance from our transducer to the narrowest part of our beam, and we saw that when we looked at intensity, our beam narrows down to a point, to the most intense point of our beam. It then diverges at a set angle known as the divergence angle, and this is what's known as our far field.
Now our far field is infinite. It goes until the ultrasound beam is fully attenuated. There's no end to this far field zone, it just diverges out as it hits into the tissue. Now the far field is also known as the Fraunhofer Zone. Now this distance from the transducer to our focal point is also known as the focal distance, and you may have seen on your ultrasound machines that you can manipulate that focal distance. And in our next talk, we're going to look at how we can go about manipulating this distance here.
Now the region slightly closer from the focal point to our transducer and slightly past that focal point is what's known as our focal zone, and you'll see that that focal zone is the region that has our best resolution within our image.
So why does the ultrasound beam converge like this to our focal point before diverging? Well, whenever we create a wave, we can use the principle known as Huygens' principle. Now in the single element transducer, we think of that as creating one solid wave that's heading into tissues. But Huygens' principle states that a wave can be separated into an infinite amount of small discrete wavelets, and these wavelets can act independently as small sources of wave energy. Now the outermost parts of our ultrasound beam here will constructively interfere with those innermost wavelets, and that interference continues until we reach our focal point, the end of our near field zone. And the geometry of that wave and the pattern of interference will then cause the beam to diverge into our far field.
Now when we look at the width of our ultrasound beam here, it should be the same width as our single element transducer. This width, or the diameter of our ultrasound beam, should be double that of the diameter at the end of our near field zone, at our focal point. So this width here is half of this width here.
Now when we are looking at the shape of an ultrasound beam, we are generally interested in the distance between the transducer and our focal point, or our near field distance, and we are interested in the amount of divergence that happens after that near field distance. Obviously, the more divergence that happens, the less information, or the less useful information, that comes back to our ultrasound probe. So we want to look at the factors that change that near field distance, as well as the factors that change that divergence, that divergence angle. And there are generally two factors that change this: the diameter of our ultrasound probe and the frequency of the wave that we are generating.
So let's start by having a look at our near field distance. Now again, our near field is the distance between our transducer and the focal point. We can calculate our near field by taking the diameter of our transducer element and squaring that value. We can then divide that value by four times the wavelength of the wave we are propagating through tissue. Now we looked at previously, wavelength is determined both by the frequency of the ultrasound probe and the tissue through which the wave is traveling through. That we can see that the wavelength is the speed of sound divided by the frequency. This is a formula that we've seen over and over again in these talks. So we can plug this back into our initial equation and see that the diameter times the frequency over four times the speed of sound in soft tissue will give us our near field distance. Another way to write this is the radius of our transducer element, half the diameter squared, over the wavelength of our wave. But I prefer to use this equation here because once we've substituted our speed of sound and our frequency into this equation, we can get this equation at the bottom here. Our near field distance in soft tissue is equal to our diameter in millimeters squared times our frequency in megahertz over four times the speed of sound in soft tissue. Now the speed of sound in soft tissue, I've written it as millimeters per second here, 1.54 millimeters per second, to ensure that all our units are the same.
Now I have very rarely seen this question asked where you actually asked to calculate specific values. What is important to understand here is what does changing the diameter of our transducer element do to our near field distance, and what does changing the frequency of our ultrasound probe do to our near field distance? You can see that as we increase the diameter of our transducer element, we increase that near field distance, the depth at which our focal point is within the tissues. The same, perhaps counter-intuitively, happens for frequency. The higher the frequency, the deeper our focal point will be. Now people often get this confused because we think of high frequency as attenuating early, and that's true. The higher the frequency of the ultrasound wave, the faster that wave attenuates. But that has nothing to do with the shape of the ultrasound beam heading into the tissue. The higher the frequency, the slower that convergence of the ultrasound beam, based on that interference of our wavelets in Huygens' principle, and the deeper our focal point will be. So the take-home point here is, as we increase the diameter of our transducer elements and as we increase the frequency of our wave, we increase the depth of our near field, the depth of our focal zone.
Now the second thing we look at when looking at the ultrasound beam geometry is the divergence angle, how much that beam diverges after it's reached the end of our near field. Now again, this far field has no set limit, it's continuous until that beam is completely attenuated. Now we can use this formula here: sine theta, theta being this angle here, equals 1.22 times the wavelength divided by the diameter of our transducer. Here again, we can substitute wavelength here for speed over frequency. Now speed in soft tissue is constant, 1514 meters per second, and this 1.22 is a constant. Here we see that our diameter and our frequency are now the denominator in this equation. As our diameter increases, this angle gets smaller. As our frequency increases, this angle gets smaller. So the wider the diameter of our transducer element, the less divergence there is, and the higher the frequency of our ultrasound probe, the less divergence there is. So increasing frequency and increasing diameter prevents that beam from diverging too much. We get more information coming back towards our ultrasound probe because those returning echoes are in line with the ultrasound probe. The lower the frequency or the smaller the diameter of our ultrasound transducer, the more divergence there is, the less information that we'll get back from our far field. Here again, this is something that we don't necessarily need to calculate, we more need to understand that the diameter and the frequency affect that far field geometry.
So we've looked at two things: our near field and our beam divergence, and we've seen how diameter and frequency affect both the distance of that near field, as well as the divergence of that far field beam. Now both of these factors refer to the primary ultrasound beam that is being propagated within tissues. There are two separate ultrasound phenomena that I want to touch on just so that you're aware of them. The first is what's known as side lobes. Here we can see our primary ultrasound beam here in blue, being propagated into tissues. We also get what is called a side lobe, where an ultrasound wave is propagated in the forward direction and can contribute to some of the signal that returns towards our transducer.
Now when we looked at the piezoelectric effect, we saw that the shape of the crystals change depending on the location of this Titanium or Zirconium atom. You can see that this change results in the crystal getting thinner, but not only does the crystal get thinner, it also gets taller. There are two dimensions that are changing here. I've represented this with these boxes here. We have our crystal changing from a cube into a rhomboid. We see the thickness of the crystal is changing, and as that thickness changes, that allows for propagation of our ultrasound wave in the primary beam. But a second thing is changing: the height of our crystals is also changing, and not only the height in the y-axis, but also the width in the z-axis is changing into the slide here. We are getting radial expansion of our ultrasound transducer elements. So not only is that thickness changing, but also the crystal is changing in diameter here. And it's this change, this changing height of our ultrasound crystals, that causes a separate wave or side lobe to be propagated into the tissue.
Now there are a couple of ways that we can reduce the amount of side lobe that is created in this tissue. Continuous ultrasound waves, high quality factor ultrasound waves, have greater side lobes. Waves with a low quality factor, a high dampened wave, will have less side lobes. So the more we dampen our transducer elements, the lower our quality factor, the less these side lobes will come into effect. We can also reduce the amplitude of the waves that we create on the peripheries of our transducer element. If this is a multi-element transducer array, we can decrease the intensity of the waves that we create on the edge here in order to prevent these side lobes from interfering with our primary image. And the last thing we can do is reduce the width of our individual transducer elements in our multi-element transducer array. We can reduce the width of those single transducer elements to less than half the wavelength of our ultrasound beam that we are propagating. And when that width is less than half, we get reduction in the amount of side lobe that is created. So to reduce the amount of side lobe produced by our ultrasound machine, we can firstly dampen our ultrasound wave, reduce the quality factor. We can narrow our transducer elements to less than half the wavelength of our ultrasound beam, and we can reduce the amplitude of these peripheral waves that we create here.
Now there's another type of wave that is produced or field from our ultrasound transducer, it interferes less with the image that we are creating, and this is what's known as the grating lobe. If we were to take a single element transducer, we would get very little grating lobes produced. It's called a grating lobe because if we were to place a grate in front of the single element transducer, we would get interference of those waves that would cause these grating lobes to be produced. Now effectively, what is happening here is we are creating a multi-element transducer array. So these grating lobes generally occur more in these transducer arrays, and this is again a function of Huygens' principle, where the points along a wave can be seen as single wavelets, and the interference of those waves will cause a grating lobe to be produced out the side.
So we've looked at the primary beam, the side lobes, as well as the grating lobes, and we've seen that changing the diameter of our transducer, as well as the frequency of the ultrasound wave, changes both the near field and the amount of divergence in that far field. Now when we were looking at this primary ultrasound beam, we were looking at a single element transducer. But we've seen that in our multi-element transducer arrays, we have small elements that can be fired off independent of the other elements. Now when calculating either our divergence angle or our near field distance and using this diameter and frequency, we can take the diameter of the transducers that we fire off when creating the wave. In a linear sequential transducer array, we fire off multiple elements at the same time. In this example, we are firing off three transducer elements. When calculating the diameter here, or when using the diameter to calculate our divergence and our near field distance, we take the diameter of the elements combined, the diameter of all three of these transducer elements.
Now that's the reason we use multiple transducer elements instead of one individually, allowing us to increase that near field distance enough that we can actually image tissues. If we were to fire off one of these elements at a time, our focal point would be far too shallow within our tissues. Firing multiple transducer elements at once allows us to increase the depth of our near field, as well as decreasing the amount of divergence within our beam. We can then shift that one transducer element at a time in order to keep our lateral resolution, which we're going to look at in a future talk.
The take-home point here is that as we increase our diameter and our frequency, we increase our near field distance, our focal point, as well as decreasing the amount of divergence within our wave. So we can see that changing that diameter and changing that frequency will change our focal point within our ultrasound beam. And we've seen that in a phased array, we can manipulate that ultrasound beam in order to steer that beam through tissues.
So in the next talk, we're going to look at the various mechanisms that allow us to change that focus, as well as steer that beam, as well as looking at spatial compounding, which allows us to get a crisper ultrasound image. After that, we can then go on to look at ultrasound resolution. Again, if you are studying for an exam, I have linked a question bank in the description below, curated multiple past paper questions and answered them in video format, and it's a great way to test your knowledge, see where your gaps are within your knowledge. So that's something you think you'd find helpful, go and check that link out. Otherwise, I'll see you in the next talk where we look at focusing, steering, and spatial compounding. Until then, goodbye everybody.