Transcription
In our previous talk, we looked at a tissue-specific property known as acoustic impedance. And we said that the acoustic impedance of a tissue is the product of the density of that tissue and the speed at which sound travels through that tissue. And because of that relationship to the speed of sound in that tissue, we said that the acoustic impedance is largely determined by the bulk modulus of that tissue, the stiffness or the resistance to compression in that tissue. And I said it's the difference between acoustic impedance values of different tissues that determines how much of our incident ultrasound beam is reflected back towards our ultrasound machine and how much is transmitted through a tissue boundary.
Now, that type of tissue interaction, where we get some echoes going back towards our ultrasound machine and some being transmitted through that tissue boundary, is what's known as reflection, which we're going to be looking at today. Now, we can break down reflection into three main categories. We can talk about perpendicular reflection, specular reflection, or non-specular reflection.
Now, perpendicular reflection occurs where an incident ultrasound beam comes into contact with a tissue boundary that is perpendicular to that incident ultrasound beam. And that tissue boundary needs to be large and smooth. So, here we have a large, smooth boundary, let's say the capsule of our kidney, and that capsule is perpendicular to our ultrasound beam. Now, the fat around that kidney and the kidney soft tissue itself will have different acoustic impedance values. And depending on the difference in those values, we will get some ultrasound returning back towards our machine in the form of an echo, and some being transmitted through into the kidney.
Now, if all of that ultrasound is echoed backwards, this is called complete reflection. And we'll see now that this happens when there is a large difference in acoustic impedance values. So, this is the reason why we can't actually image into the lungs of our patient, because air has such a low acoustic impedance value, and our soft tissue before it has a much higher acoustic impedance value. That difference is so large that we get barely any transmission of this incident ultrasound beam.
Now, what happens if that beam comes in at an angle to that large, flat surface? This is what's known as specular reflection. Now, this angle here, from the perpendicular line to our reflector and the incident ultrasound beam, is what's known as our incidence angle. Now, if this surface is large and flat, that reflection angle, this angle here, will be equal to our incidence angle. Now, this reflected echo here won't head back towards our ultrasound machine. When we send pulses into the body, the ultrasound machine, in that receive time, in that listening time, when it's waiting for echoes to come back, only picks up echoes that come back to that real estate on the ultrasound machine. And if we are getting this echo reflecting off at an angle from a specular reflector, that echo is not going to head back towards our machine.
Now, luckily, most of the large, smooth surfaces within our body aren't true specular reflectors. They're what is known as non-specular reflectors, where our incident ultrasound beam comes into contact with a tissue boundary that is not perfectly smooth, and that beam is reflected off in multiple different directions. Now, the way I like to think of these is, think of this as a mirror. A flat mirror that, if we want to look at ourselves, we need to be perpendicular to that mirror to see ourselves. If we were to tilt the mirror, we would no longer see ourselves. We would be getting light signal from somewhere else in the room.
Now, if I was to drop that mirror onto the ground and then sweep the pieces up, so all the pieces were together, but the surface was all rough, and then I was to look down on those pieces of mirror, I would still kind of see my reflection back. I would see the movement as I go over those pieces, but I wouldn't get a crisp, perfect image of myself, because a lot of that signal is coming from other places in the room. There's non-specular reflection of the light signal coming onto that mirror. The same thing is happening with our ultrasound pulse. Some of these reflections will come back towards our detector, but it won't provide us with that crisp, strong echo signal like our perpendicular reflectors will.
Now, I've mentioned it's the difference in acoustic impedance that determines how much of that signal is transmitted through the tissue boundary and how much is reflected back. And we can think about this as a spectrum. Those acoustic impedances that are identical will have all of that incident ultrasound energy being transmitted through the surface. As that difference in acoustic impedance gets larger and larger and larger, we get more and more of that sound being reflected back towards our ultrasound probe.
Now, we can use a formula to determine how much of that incident ultrasound beam will be reflected back, and this is our reflectance or our echo value. Now, in order to calculate this value, we take the difference in our second acoustic impedance and our first acoustic impedance here. So, we take the acoustic impedance of this tissue and we take away the value of the acoustic impedance of that incident tissue. We then take the sum of those acoustic impedances, so we add these two values together, and we multiply this by itself. We times it to the power of two. This will give us a percentage value for how much will be reflected back.
Now, we can see that this value will never reach more than one. The difference between the two values can never be more than the sum of those two values. Now, if we can calculate how much will be reflected, we know how much will be transmitted through that surface, because energy in a system has to be conserved. So, the difference between one and our reflection value will give us how much is being transmitted through the tissue.
Now, this is a common question that comes up in exams. So, we can go through an example ourselves. An incident ultrasound beam reaches a tissue boundary between muscle and bone. Now, we know from this table, our acoustic impedance value is 1.71 MRayls for muscle and 7.8 MRayls for bone. So, we can then use this formula here to calculate how much echo will be reflected back towards our ultrasound transducer. Most importantly, these equations here only work for perpendicular reflection, those large, smooth tissue boundaries that are perpendicular to our ultrasound probe.
So, now that we have these values, we can plug them into this formula. So, we've got the acoustic impedance of bone minus that of muscle, and then the sum of the two acoustic impedances for these tissues. This gives us 6.09 MRayls over 9.51 MRayls. And when we square that value, we get 0.41. 41% of this incident ultrasound energy will be reflected back towards our ultrasound probe. And we've seen that if we take one and take away our R value, we get our transmission value. Now, this makes sense, because if 41% of that incident ultrasound energy is being reflected back towards our ultrasound transducer, then 59% must be transmitted through that tissue boundary.
Now, you may be looking at this value and wondering, I can't believe that 59% of this energy actually makes it through into bone. Because whenever I've scanned an ultrasound machine, say, over the ribs, I get no ultrasound pulse coming back. And if they are transmitted waves coming back, surely some of those then will provide echoes and give me detail in our image below the bone. And this is an interesting observation here. Although more than 50% of that ultrasound energy is being transmitted through this tissue boundary, bone itself is highly attenuating to ultrasound waves. So, it's not only reflection that's causing that loss of signal, but also attenuation through scattering and through heat production in the underlying bone. And it's that bone stiffness and density that is causing that high attenuation.
When we're looking at a tissue-air interface, we also get a large reflection back, much like we're getting here with bone. And that's because air's acoustic impedance value is extremely low. If we were to have a look at this table here, it's incredibly low MRayls here. Where, so most of that ultrasound will be reflected back. Our reflection value will be in the high 99s. It's not that air is highly attenuating to those transmitted ultrasound waves, it's that most of it is reflected at a tissue-air boundary. So, we can see that although bone casts a shadow and air casts a shadow, it's largely due to those differences in acoustic impedances, but it's also due to that high attenuation property of bone.
So, now we've had a look at reflection. We've seen perpendicular reflection, specular reflection, and non-specular diffuse reflection. And we've looked at how the differences in acoustic impedance values can help us determine how much of that ultrasound wave is returned back to us and how much is transmitted through in a perpendicular reflector. In our next talk, we're going to be looking at the concept of refraction of ultrasound waves, where we're getting an incident ultrasound wave hitting a tissue boundary at an angle, and because of the differences in speed between those two tissues, we will get that wave changing direction slightly, a transmission angle, as that wave heads through into the second tissue. So, join me in that next talk where we will look at the concept of refraction. And until then, goodbye everybody.