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 not unspecular reflection now perpendicular reflection occurs where now incident ultrasound beam comes into contact with a tissue boundary that is perpendicular to that incident ultrasound B 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 are 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 Ultimate Sound 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 has 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 exam 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 rails for muscle and 7.8 rails for bone so we can then use this formula here to calculate how much Echo will be reflected back towards our ultrasound transducer now 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 rails over 9.51 rails 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 Transmissions 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 percent 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 as that bone stiffness and density that is causing that high attenuation now 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 rails here where so most of that ultrasound will be reflected back our reflection value will be in the high 99 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