Transcription
So the first interaction that we've looked at between ultrasound and matter is reflection. And we've seen that we can divide reflection into perpendicular reflection, specular reflection, and non-specular or diffuse reflection.
And we saw that in perpendicular reflection, we could use the differences in acoustic impedance values for different tissues to determine how much of that incident ultrasound pulse was reflected back towards our transducer and how much was transmitted through the tissue. We also saw that in specular reflection, when ultrasound came in at an angle to a large flat surface, we got a reflection of that ultrasound echo at an angle that was the same as the incidence angle.
Now when we combine specular reflection and transmittance, we get what's known as refraction. Now when we look at refraction, we can see that our incident ultrasound beam coming in at an angle to our tissue boundary results in reflection, specular reflection, and transmittance of an ultrasound pulse. Now this transmitted ultrasound pulse, you can see, is not parallel to the incident ultrasound pulse. We see there's been a change of angle. Either the angle gets smaller or the angle gets bigger here.
Now we can represent this without the waves. It's a bit easier to see. Our incidence angle equals our reflected angle. This tissue here is all the same. That's why these angles are the same. When this incident ultrasound pulse is transmitted into a different tissue, we can get what's known as the transmittance angle. Now this transmittance angle here is either smaller than our incidence angle or it's larger than our incidence angle.
Now when we looked at perpendicular reflection, we were calculating the energy or the amount that was transmitted from one tissue to another. Here, we're not calculating the amount of energy or the amount of wave that is passing through this angle. What we are calculating here is the angle change. Now the angle change is determined by the difference in the speed of sound from our first tissue to our second tissue. If our incident ultrasound pulse slows down as it heads into the next tissue, we get a reduction in our transmittance angle. And if it speeds up, we get an increase in this transmittance angle.
Now we can actually go about calculating these differences by using this formula here. We have speed of sound in our second tissue that is slower than speed of sound in our first tissue. We get a reduction in this angle. Our transmittance angle is smaller than our incidence angle. Here, the speed of sound is equal, and we get no change in the angle. We get no refraction here. That ultrasound pulse continues on as if nothing had happened. In this last example, the speed of sound in our transmitted ultrasound pulse is higher than the speed of sound of our incident ultrasound pulse. Our transmittance angle is greater than our incidence angle.
And we can use this formula here. If we take the sine theta of our transmittance angle and divide it by the sine theta of our incidence angle, we get the speed of sound in our second tissue over the speed of sound in our first tissue. The ratio between the speed of sounds is the same as the sine theta ratio between our transmitted and our incident angles.
Now this can be a little bit of a difficult concept to grasp. And there are two major takeaways that I want you to get. The first is that we are dealing with the speed of sound difference here, or the ratio between the speed of sound here. We are not dealing with the acoustic impedance values. Don't make the mistake of putting the acoustic impedance values here. It's the speed change that determines this angle change. The amount of energy that is transferred through is determined by the differences in our acoustic impedance values. That is something that we are not going to calculate in this ultrasound module, mainly because it doesn't actually have much value when it comes to creating our actual ultrasound image. These reflected ultrasound pulses aren't coming back towards our ultrasound transducer.
Now, a refraction only happens at an angle. If this incident ultrasound beam was perpendicular to the surface, it would travel straight through the tissue interface. And if you plotted an angle of zero into this equation here, you would see that there would be no change between our incident angle and our transmitted angle, despite the differences in speed here.
Now, one way I like to think about this when trying to remember, does the angle get smaller or does it get bigger, is to represent an ultrasound wave like this here. I've represented these lines as the periods of compression within our ultrasound wave. Now, we've got this wave coming into a tissue boundary at a set speed. Now, we know that frequency doesn't change as the ultrasound wave goes through tissues. The frequency stays the same. The wavelength changes to compensate for those changes in a speed of sound. So if the speed of sound is faster, our wavelength is longer. Our frequency has stayed the same. Our wavelength needs to increase in order to account for that increase in speed of sound. And we know the speed of sound is determined by our bulk modulus and our density of this tissue.
Now, if we were to then go into a tissue where the speed of sound was slower, our wavelength would decrease. We can see that our frequency has remained the same here. Our speed has decreased. Our wavelength then needs to compensate for that loss of speed. And we can see that as our wavelength gets shorter, that angle of the wave needs to change in order to compensate for that reduction in speed. Here is where this ultrasound pulse would first come into contact with this tissue boundary. And we can see that reduction in wavelength results in this angle change here.
So when you're thinking about, does this transmittance angle get smaller or does it get bigger, it helps me to think about how this would look from a, a bird's eye view. If I was looking at these regions of compression and I went into a slower tissue, our wavelength is getting smaller. How would that angle need to change in order for these wavelengths to match up at this tissue boundary? And you can see that if we were moving into a tissue that had a faster speed of sound, our wavelength would need to get bigger, and our transmittance angle would get bigger.
So we can use this formula here to calculate the change from incident angle to transmission angle. And once you've got your answer, you can look at that answer and say, okay, my transmittance angle is larger. Does that make sense when I think back to this diagram? Is the speed of sound getting faster? Yes. Is the wavelength then getting longer? Yes. Oh, my transmittance angle must be bigger than my incidence angle. So you can use this as a good mental model to check your answer when you have calculated the refraction angle using this formula here.
So now we've looked at reflection and we've looked at refraction of ultrasound waves as they come into tissue interfaces. Next, we're going to be looking at attenuation of sound. And remember, if you are studying for an ultrasound physics exam or a radiology physics exam, I've linked a question bank in the first line of description below that you can go and check out. Otherwise, I'll see you all in the next talk. Goodbye everybody.