Understanding Reflector Depth Calculation

Hi Learners, I'm from SonoNerds. This video is on Unit 7, Calculating Reflector Depth. Section 7.1 Creating the Image In Unit 4, we talked about how the machine sent a pulse out and then waited for that pulse to travel all the way to the max depth and return before it would send another pulse. That one pulse creates one scanline, and the next pulse creates the next scanline, and so on until a whole image is created. The amount of time it takes To create a whole image frame is based on the maximum imaging depth and the speed of sound. For each pulse that is sent out, the transducer will create the pulse and that will propagate into the body until it interacts with the reflector. Once it hits a reflector, some of that energy returns to the transducer and is processed for the image. Some of the energy is scattered or absorbed, and some of it continues going through the body. until it hits another reflector and the same thing happens. Some returns to the transducer, some is scattered or absorbed, and some of it keeps going. Now this is going to happen all the way through the body through all the reflectors and eventually that sound will attenuate to the point that the transducer no longer is collecting information from the reflections. If the sound weakens or attenuates before the max imaging depth is achieved, then what we typically have in our far field is just a bunch of blackness. The sound never got there. However, if the sound is strong enough, gets to the max imaging depth, the machine will stop listening at that point because once it gets there, it's ready to start the next pulse. Once a pulse enters the body, the first reflector that it interacts with is going to return an echo from that pulse. And in this example, we have the first echo coming back from a reflector that took 13 microseconds for time of flight into the body, to the reflector, and back to the transducer. That echo is going to be displayed at one centimeter into the image. Now this is going to keep happening for each reflector that the sound interacts with. In my image I have that we have echo number two coming back after 39 microseconds and echo number three coming back after 52 microseconds. The machine is going to listen for up to 65 microseconds because that's how long it'll take for the pulse to travel to the max imaging depth and return to the transducer. This time from pulse creation waiting for echoes to return so another pulse can be sent is the PRP. It's pulse plus waiting time. So the machine then will take all the signals that came from this one pulse to create a scan line, and then another pulse is sent again to start the next scan line. So to look at it another way, a pulse is sent and then we have our waiting period. Echoes are coming back at certain times during that waiting period until the max depth waiting period is achieved. Again, that's the PRP, the on time and the off time. to the start of the next pulse. This one pulse and these echoes are going to create one scan line as long as it's a one pulse scan line. We'll learn in a subsequent unit how some scan lines need more than one pulse to be created. In reality, the machine is like a big stopwatch that uses sound and echoes to map the body. Section 7.2 PRP and PRF again. Recall that the time it took to make the pulse plus the waiting for the pulse to return is the pulse repetition period. It's on and off time. And the amount of times a pulse could be sent per second was the pulse repetition frequency. Remember that both pulse repetition frequency and pulse repetition period were highly dependent on the depth of the image. So the shallow imaging meant that there was less off time or less waiting. And with that we saw short pulse repetition periods, higher PRFs, and high duty factors compared to deep imaging which has more waiting time before the next pulse can be sent, resulted in longer pulse repetition periods, lower pulse repetition frequencies, and low duty factor. We also learned that PRP and PRF are reciprocals of each other, which gave us a very basic formula of PRP multiplied by PRF equals 1. From there we can derive that PRF is going to be equal to 1 divided by PRP and PRP is equal to 1 divided by PRF. So when we are given a graphical representation of a pulse in one second, it was actually pretty easy to calculate the PRF and PRP. We just counted the number of pulses within the second to get our pulse repetition frequency in hertz, and then we just needed our knowledge of reciprocals to calculate the pulse repetition period. But what if I asked you to calculate the pulse repetition from an image like this? We're not given the graphical representation to figure out the pulse repetition frequency, and we have no time frame to figure out the pulse repetition period. We only know what the maximum depth is. So how are we supposed to figure out the amount of time that it takes for the pulse to travel to the maximum depth and then back, which is our pulse repetition period? Well remember that sound can only travel as fast as the medium allows it to, and since propagation speed is constant at 1.54 millimeters per microsecond, we can actually calculate and know how long it takes for the sound pulse to travel from the transducer phase to the maximum depth and back, regardless of any other factors. Let's take a look at an example. Say we have a very special car. Doesn't matter the color, doesn't matter the model. This car can only go 10 miles per hour. No more, no less. And if that's the case, you should be able to calculate exactly how long it'll take you to get anywhere. So let's say you need to go to the store. And you know the store is 10 miles away. In your 10 miles per hour car, you know it'll take you one hour to get there. What if you have to come back? Well, you know it's going to be another hour back. So in this example, in our 10 mile per hour car, we know that going one way 10 miles will take you one hour. If you do a round trip, you know it'll be 20 miles of driving and it'll take you two hours. If the math isn't immediately obvious to you, here we've got how we calculated that. Just like any other formula that we use, we can rearrange the variables. to solve for the one that we don't have. So speed multiplied by time will give us a distance. We can rearrange to say that time is equal to distance divided by speed, or that speed is distance divided by time. In our example, we didn't know how long the time would be, so we took our distance of 10 miles, divided it by our speed, and calculated the time it would take to go 10 miles to be one hour. And just like we knew that our car could only go 10 miles per hour, we know that pulses in soft tissue can only go 1.54 millimeters per microsecond. So now we're looking at how long will it take for that pulse to get to the max image depth. And we know that max image depth, so let's say that it's 10 centimeters in our example. Using math, using calculations, we now know that it will take 65 microseconds to get there. and 65 microseconds to come back. So one way is a distance of 10 centimeters in 65 microseconds. Round trip would be 20 centimeters in 130 microseconds. That round trip time is the pulse repetition period. No matter the frequency, no matter the transducer, if your maximum imaging depth is set at 10 centimeters, it is going to take 130 microseconds for the pulse to leave the transducer, travel to the max imaging depth, and return to the transducer. Again, if the math wasn't super obvious on that one, let's take a look. This time we knew that the distance traveled into the body one way was 10 centimeters. I converted that to millimeters so it would match up with our speed. So we have 100 millimeters divided by 1.54 millimeters per microsecond. The millimeters cancel each other out. 100 divided by 1.54 equals 65 and we have our leftover microsecond unit. So for a sound pulse to travel one way into the body 100 millimeters, which is the same as 10 centimeters, it will take 65 microseconds. So if we look at the bigger picture of this, it takes 65 microseconds to travel one way into the body to 10 centimeters. It's going to take another 65 microseconds to travel back to the transducer. So the round trip of this pulse is 130 microseconds. Well if it takes 130 microseconds to go 10 centimeters, we can reduce that fraction and see that it'll take 13 microseconds to go 1 centimeter. And this is how we are going to calculate our pulse repetition period. If we take 13 microseconds, multiply it by the max imaging depth we calculate. our pulse repetition period. And again this applies to any transducer. Your 5 megahertz linear transducer set to 3 centimeters is going to be 13 times 3 for 39 microseconds pulse repetition period. That's because we have a constant speed of sound in which the pulse can only travel so fast. Continuing with the one centimeter, we have calculated then that the pulse repetition period of a sound wave in soft tissue to be 13 microseconds traveling one centimeter into the body. That is the maximum imaging depth. To figure out pulse repetition frequency for this maximum imaging depth, all we need to do is take the reciprocal of the pulse repetition period. So we move 13 into the denominator position under a 1 and we will see that PRF is going to be equal to 1 13th megahertz. Now 1 13th megahertz translates into 0.077 megahertz, but we don't typically represent pulse repetition frequency in the megahertz unit. We prefer to use kilohertz which would be 77 kilohertz and ideally to set up our formula we're going to convert all the way down to 77,000 hertz. So now for a depth set at one centimeter we know the PRF is 77,000 hertz. So we can use that knowledge to create our formula and we can say that PRF in hertz is going to be equal to 77,000 centimeters per second divided by the max imaging depth. And again, no matter the transducer that you're using, you are going to look at your maximum imaging depth and you're going to divide 77,000 centimeters by it. So if our max imaging depth is set at 7 centimeters, 77,000 divided by 7 is 11,000 hertz. That is your PRF. And again, since PRP and PRF have no relationship to frequency and really are bound more by propagation speed and the max imaging depth, any transducers PRP and PRF can be calculated based on our new formulas. So I hope you're getting into the swing of things. Every time we learn a new formula, I like to go and try to practice some examples regarding that formula. Go ahead and pause the video while you fill in the highlighted purple spaces in the practice chart. You have two of them in your practice section. The top chart you're going to be given a max imaging depth and you're going to calculate the pulse repetition period and the pulse repetition frequency. You can do one of two things. Use either formula to calculate the PRP and the PRF or practice calculating one of them and using the reciprocal of it to calculate the other. Now in the bonus practice, if you're up for the challenge, you're going to be given the frequency of the transducer, the maximum imaging depth, and the cycles per pulse. you're going to need to fill in or calculate the period, propagation speed, wavelength, PRF, PRP, pulsation, spatial pulsing, and the duty factor. So when you're ready, go ahead and resume the video to check out the answers. And here are the answers to our practice. So you will see that by just having knowledge of the new pulse repetition period formula, you should be able to take your max imaging depth and multiply it by 13 to calculate the PRP in microseconds. From that point on you can either take the reciprocal of the PRP to calculate the PRF or you can use the PRF formula 77000 divided by the max imaging depth to calculate your PRF. I did include it in both hertz and kilohertz as we do typically like to use kilohertz as our preferred unit of pulse repetition frequency. Now there's a little bonus question underneath that chart that asks us what happens to PRP and PRF if the sonographer changes to a three megahertz transducer. Well the answer is absolutely nothing. It only changes if we change the maximum imaging depth. Let's jump down to looking at the bonus practice. If you went ahead and went through all those, check out your values in the highlighted purple area. If all your answers are correct and you understand the math behind all this and have found all the formulas that you need to fill in these blanks, that is fantastic. Feel free to jump ahead, but we are going to head over to the board to check out the math behind both of these charts to work the math out together. Welcome to the board. We are going to look through the math on that first chart. So the question asks us, what are the PRP and PRFs for a 5 megahertz ultrasound beam in soft tissue set to the imaging depths below? Now I added some extra information in this question. It shouldn't happen too often on your tests or on your boards, but it does happen as a way to understand if you know how things are related. So that little bit of extra fluff information is at 5 megahertz. It doesn't matter what frequency we are operating at. because sound is bound by the medium that it is traveling in. So that 5 megahertz is kind of fluff information. What we are mostly focused on that we are in soft tissue and that we have different maximum imaging depths. The two formulas that we are going to focus then on are the PRP and PRF formulas. So PRP is going to be equal to 13 microseconds multiplied by the max imaging depth in centimeters. PRF then is going to be equal to 77,000 centimeters per second divided by the max imaging depth, also in centimeters. So these are the two formulas that we need to calculate all the blanks in this chart. Let's go ahead and start with the PRP column. All we need to do then is multiply 13 by whatever value is in the max imaging column. So we'll multiply 13 by 5 centimeters, by 8, by 13, and by 20 centimeters. Doing so with pen and paper or with your calculator then, 13 multiplied by 5 is 65 microseconds. 8 multiplied by 13 is 104 microseconds. 13 multiplied by 13 is 169 microseconds. And then lastly, 20 centimeters multiplied by 13 microseconds gives us a total of 230 microseconds. Now we could take the reciprocal of any of the pulse repetition period values to calculate the PRF. So if we look at the first one, we would take 1 divided by 65 microseconds, and that would actually give us 0.0154 megahertz. And that's not really a unit. that we want for ultrasound purposes. Now we could go from here and convert these down into into more usable units like 15.4 kilohertz or 15,400 hertz. But that's just a lot of extra steps, especially when we have a wonderful new formula that we just learned. To get rid of all this other stuff, we can just take a look then at our new formula, our PRF. formula tells us that we can take 77,000 centimeters per second and then again divide it by whatever is in our max depth column. So we're going to take 77,000 and divide by 5, by 8, 13, and 20. And when we do so, we are going to come up with a PRF in hertz. So make sure that you are remembering that the 77,000 centimeters per second over depth in centimeters is going to give us a hertz unit for our PRF. Watch the answers that you're given. You might be shown answers in hertz or you might be shown answers in kilohertz. Both are valid units when expressing pulse repetition frequency. On the answers page, I did give you both answers in hertz and kilohertz, but for the sake of the math here, I am just going to write down our hertz values. So 77,000 divided by 5 is equal to 15,400 hertz. And that's it. And I already showed you with this depth that by using the reciprocal of 65 microseconds, we are given that 0.0154 megahertz and that converts down to the same value 15,400 hertz. Moving down then we have 77,000 divided by 8 and that is going to give us a rounded 9,625 hertz. 77,000 divided by 13 gives us a rounded 5,923 hertz. And then lastly, taking 77,000 and dividing it by 20 gives us a pulse repetition frequency of 3,850 hertz. Now on the bottom question here, I did ask you what happens to PRP and PRF if we change transducers. I started out the board telling you that I gave you information you didn't need about the transducer frequency. So it doesn't matter if we change the transducer frequency, PRP and PRF are not related to it. Another thing that we can view from this chart is to remind us again that as we increase our maximum imaging depth, our pulse repetition period gets longer and we cannot send out as many pulses per second, therefore our pulse repetition frequency decreases with more depth. Jumping down then to the bonus practice, if you want to go through the math on this one, please stick around. We'll quickly go through each blank on the chart. So we are told that we are imaging at a maximum depth of 9 centimeters with a transducer producing a 12 megahertz pulsed wave. And in those pulses, we have three cycles per pulse. Let's go ahead and start with period. Period we know is the reciprocal of frequency, so period is going to be calculated by taking 1 and dividing it by 12. the frequency that we are given. 1 divided by 12 gives us 0.083 microsecond period for our 12 megahertz wave. Next down we have the speed in soft tissue. So we should all have this value memorized at this point 1.54 millimeters per microsecond or 1540 meters per second. Wavelength then can be calculated based on the speed in soft tissue and the frequency. So that is calculated by taking the speed divided by the frequency in megahertz. 1.54 divided by 12 gives us a wavelength of 0.1283 millimeters. We already filled in the number of cycles per pulse. That was part of our equation. We need to know that for calculating our pulse parameters. Let's go down to PRF then. And we're going to use our new formulas for this one. So PRF, remember, was 77,000 divided by the max imaging depth, which is 9 centimeters. 77,000 divided by 9 rounds to 8,556 hertz. Next blank down we have pulse repetition period. Now we can either take the reciprocal of PRF which would be 1 over 8556 or we can use our new formula which would be 13 microseconds multiplied by the max imaging depth, which is 9. Either one is just fine, you'll get the same answer, and in this case we get 117 microseconds. Next down we have pulse duration, which can be calculated again two ways. We can take the number of cycles in a pulse and multiply it by the period of the wave, which is 0.83, or we can take the number of cycles in the pulse and divide it by the frequency. No matter which way you choose, you should get an answer of 0.25 microseconds. Next up we have spatial pulse length, which is going to be the number of cycles multiplied by the wavelength. And we already calculated that to be 0.1283. Multiply that out and we will get 0.3849 millimeters. And then lastly we have duty factor. And remember that duty factor is the pulse duration divided by the pulse repetition period. So we have pulse duration at 0.25 microseconds divided by the pulse repetition period, which we've already calculated to be 117 microseconds. Now kind of unlike the other examples that we had, we had to do some conversions. so we matched up our units. We already have them already matching so that's really awesome. We can take that and then we need to multiply that value by 100 to get the percent. So after we calculate all that we'll get a value of 0.21 percent. Next up we have section 7.3, the 13 microsecond rule. Our new pulse repetition period and pulse repetition frequency formulas are going to help the machine to know when echoes have reached the max imaging depth, and returned so it can send out a new pulse. But this unit is called calculating reflector depth, so let's get into that a little bit more. Remember that the machine is running a stopwatch during that off time. It knows exactly when it sent the pulse and it's waiting for those echoes to return from the reflectors that that pulse interacts with. As each echo returns, it's going to record the time that has gone by. So by taking the speed, which is our 1.54 millimeters per microsecond, and the time that that echo and pulse were gone, it can calculate a distance. But we need to be careful about how we are defining time. Are we speaking in terms of one-way time or are we talking about in terms of round trip time? Let's go back to our example of our 10 mile per hour cars. You and three of your friends moved into a new house in the middle of bizarro land. You have no internet. and you only have these 10 mile per hour cars. So you make the deal with each other that you're all going to drive down one road and as soon as one of you sees an interesting landmark, you're going to turn around and head back to the house recording the total time that you had been driving. Now as a group you decide that you're not going to drive any more than three hours total, so the maximum anybody is going to drive is one and a half hours one direction, and then they're going to return. So you all hop in your cars and start driving. Now your first friend tells everybody that I drove for a total of half an hour and in my half hour trip I saw a park. The second friend says well I drove for an hour and I saw a store. The third friend says I drove for a total of two hours and I saw a hospital. And you tell everybody well I drove for two and a half hours and saw a school. So total round trip time for the park was 30 minutes, for the store was an hour, two hours for the hospital, and two and a half hours for the school. Now remember you had no other knowledge than the time you left your house, saw something interesting, and returned back to the house. In this experiment, the only information that you had is the speed at which your car can travel and the time that you were gone from house to location back to house. So you have calculated your round trip time. Another way we can look at this is saying that the total time traveled by each driver from home to location and back is the time of flight or the go return time. Again, that's how long it took to complete the round trip. So later that night, You're all home. And one of your friends says, well, it'd be really nice if we had a map telling us how far away these locations were from our house. Did anybody look at their odometer to see how far they drove in their round trip? And everybody's like, no, I completely forgot. I was only focused on the time. And because you've been through physics class, you're like, no, we can figure this out because we know that speed multiplied by time will give us a distance. So everybody gets out their pen and paper and they take their 10 miles per hour, multiply it by their goal return time or the total time that they were driving and calculate the total distance that they drove. So that total distance is going to be the mileage from home to the location and back home. And as everyone's looking at the data that they just calculated out, someone's like, well if we make a map of these mileage that's not going to be right. We want the one-way distance. So here's what we need to do. We need to take the speed multiplied by the round trip time and divide it by two so we can get the one way distance. Everybody goes through their calculations again, divides them by two. So now the house friends can make a map knowing that the park was two and a half miles away, the store was five miles away, the hospital 10, and the school 12 and a half miles away. All calculated based on the speed that they were traveling and the round trip time divided by two. So remember, if we just leave it at 10 miles per hour times our round trip time, we are going to be calculating round trip distance. We divide it by two to calculate the one-way distance the way that most maps work. And just like our four friends mapping the town using go return time and their constant speed and dividing everything by two, the ultrasound machine can map the body using similar data points. It's important to remember that one pulse is going to create the information for one scan line. Now the machine is going to record the go return time from the start of a pulse to the return of each individual echo as the pulse interacts with reflectors in its path. The machine will stop listening for returning echoes once the pulse and echoes should have returned from the max imaging depth set by the sonographer. Remember that's the PRP. The machine then will calculate the depth of the reflectors based on the go return times of the echoes they created. The machine will then display the echoes on our image corresponding with the depth that goes along with its go return time and the brightness is typically determined by the strength of the echo that returned. To calculate the depth of a reflector then, the machine is going to use this formula. Depth in millimeters is going to be equal to the speed multiplied by the go return time divided by 2. Just like our friends did. They used their speed of the car, multiplied it by the time it took them to drive to a location and back, and divided everything by 2. If we do not divide by 2, then we are calculating the total distance traveled, not just the depth of the reflector. Let's say this is the max depth of an image and that it's set at 5 centimeters. So the machine is going to create a pulse and the longest it's going to listen is 65 microseconds. That is the longest it should take. for any pulses to travel to the max step and return echoes. Once that 65 microseconds has elapsed, it's going to send a new pulse to create a new scanline. From that original pulse then, the sound travels into the body and after 13 microseconds have elapsed, echoes from a first reflector have returned back to the transducer. The machine will record that and wait for more echoes to return from this pulse. After 26 microseconds, a second echo returns to the transducer from a second reflector. After 39 microseconds, a third echo returns from a third reflector. And after 52 microseconds, a fourth echo returns from the fourth reflector. And at 65 microseconds, the machine has stopped listening. We're at the bottom of our image. For my example, I've chosen that my reflectors are at 1, 2, 3, 4 centimeters into the body because I want to see if you've noticed the pattern or can guess where we're headed with the 13 microsecond rule. The 13 microsecond rule tells us that a sound pulse entering the body returns from a depth of 1 centimeter for every 13 microseconds of go return time. Let's take a look at a couple of examples of the 13 microsecond rule in action. Let's say we have a reflector in the body. The machine sends a pulse and it's going to wait. And it's going to wait for echoes to return that have been created by that pulse. So now it is timing from when that pulse was created to when it receives. an echo. And for our first reflector, let's say that it took 156 microseconds for that pulse to be created and an echo to return. That's a go return time. The machine will know then that this reflector is 12 centimeters into the body and then will display it on the image at the depth that is represented by 12 centimeters. The machine knows this because it can take the time it took 156 microseconds, the go return time, and divide it by 13 microseconds to give us a 12 centimeter depth. And that's the 13 microsecond rule. Let's take a look at another one. We have a reflector. The pulse is created. Timer starts. It waits for echoes to return, and in this case, it gets an echo back from that reflector at 78 microseconds. The machine then can take 78 microseconds, divide it by 13, and knows whatever echo is returned from that reflector should be displayed at 6 centimeters into the image because it's 6 centimeters into the body. The calculation for that again is 78 divided by 13 to give us that 6 centimeter depth. Now the 13 microsecond rule is based on the original formula that the depth of a reflector is the propagation speed in soft tissue multiplied by the go return time all divided by 2. It's important to remember that the 13 microsecond rule has already taken the division by 2 into account. And we can see that if we plug 13 microseconds into our go return time spot, multiply it by 1.5 for millimeters, divide it by 2, we get 10 millimeters or 1 centimeter. And that is how we come up with the rule. For every 1 centimeter, a reflector is into the body, It'll take 13 microseconds for the round trip time. Remember that using the 13 microsecond rule will tell us the depth of the reflector, and if we double the depth, we will be able to calculate the total distance the pulse and echo traveled, meaning into the body and back to the transducer. Now for this lesson, we've used very simple numbers using whole centimeter values, where in reality the machine is going to be calculating infinitely small minute values. it might get echoes back at 17.3, 17.6, and like 18.1 microseconds. And that would require displaying reflectors at 1.33 centimeters, 1.35 centimeters, and 1.39 centimeters respectively. But this is so beyond the scope of what we need to know or what we need to calculate. So when focusing on the 13 microsecond rule, make sure that you know the values for whole centimeter values. One centimeter reflector depth, should equal 13 microseconds. Two centimeter reflector depth equals 26 microseconds. Three is 39, four is 52, and so on. The other thing that you need to remember, because this might come up in your questions, is knowing the difference between a depth of a reflector and the total distance traveled. Again, if we have a one centimeter deep reflector, the sound time is 13 microseconds, but the total distance that the pulse and the echo have traveled is actually two centimeters. One centimeter into the body to the depth of the reflector and one centimeter back to the transducer. In questions then that ask you about the 13 microsecond rule or the depth of a reflector, make sure to watch for terms that ask you for depth of reflector or total distance traveled by the pulse. To finish up this unit then, make sure you head back to your workbook and work through your activities. It's a very short one this time because we are using rather straightforward formulas and we got a chance to practice them during the lecture. Remember that PRP is equal to 13 microseconds multiplied by the maximum imaging depth in centimeters. PRF is equal to 77,000 centimeters per second divided by your maximum imaging depth in centimeters. And to calculate the distance a reflector is into the body, all we need to do is take the go return time and divide it by 13 microseconds. So your activity section will have a few charts in it where you can practice these formulas. Lastly, then go through your NERD check and make sure that you are able to answer those open-ended questions. to evaluate your basic knowledge of the material in this unit.

That one pulse creates one scanline, and the next pulse creates the next scanline, and so on until a whole image is created. The amount of time it takes To create a whole image frame is based on the maximum imaging depth and the speed of sound. For each pulse that is sent out, the transducer will create the pulse and that will propagate into the body until it interacts with the reflector. Once it hits a reflector, some of that energy returns to the transducer and is processed for the image. Some of the energy is scattered or absorbed, and some of it continues going through the body.

until it hits another reflector and the same thing happens. Some returns to the transducer, some is scattered or absorbed, and some of it keeps going. Now this is going to happen all the way through the body through all the reflectors and eventually that sound will attenuate to the point that the transducer no longer is collecting information from the reflections.

If the sound weakens or attenuates before the max imaging depth is achieved, then what we typically have in our far field is just a bunch of blackness. The sound never got there. However, if the sound is strong enough, gets to the max imaging depth, the machine will stop listening at that point because once it gets there, it's ready to start the next pulse. Once a pulse enters the body, the first reflector that it interacts with is going to return an echo from that pulse.

And in this example, we have the first echo coming back from a reflector that took 13 microseconds for time of flight into the body, to the reflector, and back to the transducer. That echo is going to be displayed at one centimeter into the image. Now this is going to keep happening for each reflector that the sound interacts with.

In my image I have that we have echo number two coming back after 39 microseconds and echo number three coming back after 52 microseconds. The machine is going to listen for up to 65 microseconds because that's how long it'll take for the pulse to travel to the max imaging depth and return to the transducer. This time from pulse creation waiting for echoes to return so another pulse can be sent is the PRP. It's pulse plus waiting time. So the machine then will take all the signals that came from this one pulse to create a scan line, and then another pulse is sent again to start the next scan line.

So to look at it another way, a pulse is sent and then we have our waiting period. Echoes are coming back at certain times during that waiting period until the max depth waiting period is achieved. Again, that's the PRP, the on time and the off time.

to the start of the next pulse. This one pulse and these echoes are going to create one scan line as long as it's a one pulse scan line. We'll learn in a subsequent unit how some scan lines need more than one pulse to be created.

In reality, the machine is like a big stopwatch that uses sound and echoes to map the body. Section 7.2 PRP and PRF again. Recall that the time it took to make the pulse plus the waiting for the pulse to return is the pulse repetition period.

It's on and off time. And the amount of times a pulse could be sent per second was the pulse repetition frequency. Remember that both pulse repetition frequency and pulse repetition period were highly dependent on the depth of the image. So the shallow imaging meant that there was less off time or less waiting. And with that we saw short pulse repetition periods, higher PRFs, and high duty factors compared to deep imaging which has more waiting time before the next pulse can be sent, resulted in longer pulse repetition periods, lower pulse repetition frequencies, and low duty factor.

We also learned that PRP and PRF are reciprocals of each other, which gave us a very basic formula of PRP multiplied by PRF equals 1. From there we can derive that PRF is going to be equal to 1 divided by PRP and PRP is equal to 1 divided by PRF. So when we are given a graphical representation of a pulse in one second, it was actually pretty easy to calculate the PRF and PRP. We just counted the number of pulses within the second to get our pulse repetition frequency in hertz, and then we just needed our knowledge of reciprocals to calculate the pulse repetition period. But what if I asked you to calculate the pulse repetition from an image like this?

We're not given the graphical representation to figure out the pulse repetition frequency, and we have no time frame to figure out the pulse repetition period. We only know what the maximum depth is. So how are we supposed to figure out the amount of time that it takes for the pulse to travel to the maximum depth and then back, which is our pulse repetition period? Well remember that sound can only travel as fast as the medium allows it to, and since propagation speed is constant at 1.54 millimeters per microsecond, we can actually calculate and know how long it takes for the sound pulse to travel from the transducer phase to the maximum depth and back, regardless of any other factors.

Let's take a look at an example. Say we have a very special car. Doesn't matter the color, doesn't matter the model. This car can only go 10 miles per hour. No more, no less.

And if that's the case, you should be able to calculate exactly how long it'll take you to get anywhere. So let's say you need to go to the store. And you know the store is 10 miles away.

In your 10 miles per hour car, you know it'll take you one hour to get there. What if you have to come back? Well, you know it's going to be another hour back.

So in this example, in our 10 mile per hour car, we know that going one way 10 miles will take you one hour. If you do a round trip, you know it'll be 20 miles of driving and it'll take you two hours. If the math isn't immediately obvious to you, here we've got how we calculated that.

Just like any other formula that we use, we can rearrange the variables. to solve for the one that we don't have. So speed multiplied by time will give us a distance. We can rearrange to say that time is equal to distance divided by speed, or that speed is distance divided by time.

In our example, we didn't know how long the time would be, so we took our distance of 10 miles, divided it by our speed, and calculated the time it would take to go 10 miles to be one hour. And just like we knew that our car could only go 10 miles per hour, we know that pulses in soft tissue can only go 1.54 millimeters per microsecond. So now we're looking at how long will it take for that pulse to get to the max image depth.

And we know that max image depth, so let's say that it's 10 centimeters in our example. Using math, using calculations, we now know that it will take 65 microseconds to get there. and 65 microseconds to come back. So one way is a distance of 10 centimeters in 65 microseconds.

Round trip would be 20 centimeters in 130 microseconds. That round trip time is the pulse repetition period. No matter the frequency, no matter the transducer, if your maximum imaging depth is set at 10 centimeters, it is going to take 130 microseconds for the pulse to leave the transducer, travel to the max imaging depth, and return to the transducer.

Again, if the math wasn't super obvious on that one, let's take a look. This time we knew that the distance traveled into the body one way was 10 centimeters. I converted that to millimeters so it would match up with our speed.

So we have 100 millimeters divided by 1.54 millimeters per microsecond. The millimeters cancel each other out. 100 divided by 1.54 equals 65 and we have our leftover microsecond unit.

So for a sound pulse to travel one way into the body 100 millimeters, which is the same as 10 centimeters, it will take 65 microseconds. So if we look at the bigger picture of this, it takes 65 microseconds to travel one way into the body to 10 centimeters. It's going to take another 65 microseconds to travel back to the transducer. So the round trip of this pulse is 130 microseconds.

Well if it takes 130 microseconds to go 10 centimeters, we can reduce that fraction and see that it'll take 13 microseconds to go 1 centimeter. And this is how we are going to calculate our pulse repetition period. If we take 13 microseconds, multiply it by the max imaging depth we calculate.

our pulse repetition period. And again this applies to any transducer. Your 5 megahertz linear transducer set to 3 centimeters is going to be 13 times 3 for 39 microseconds pulse repetition period. That's because we have a constant speed of sound in which the pulse can only travel so fast.

Continuing with the one centimeter, we have calculated then that the pulse repetition period of a sound wave in soft tissue to be 13 microseconds traveling one centimeter into the body. That is the maximum imaging depth. To figure out pulse repetition frequency for this maximum imaging depth, all we need to do is take the reciprocal of the pulse repetition period.

So we move 13 into the denominator position under a 1 and we will see that PRF is going to be equal to 1 13th megahertz. Now 1 13th megahertz translates into 0.077 megahertz, but we don't typically represent pulse repetition frequency in the megahertz unit. We prefer to use kilohertz which would be 77 kilohertz and ideally to set up our formula we're going to convert all the way down to 77,000 hertz. So now for a depth set at one centimeter we know the PRF is 77,000 hertz.

So we can use that knowledge to create our formula and we can say that PRF in hertz is going to be equal to 77,000 centimeters per second divided by the max imaging depth. And again, no matter the transducer that you're using, you are going to look at your maximum imaging depth and you're going to divide 77,000 centimeters by it. So if our max imaging depth is set at 7 centimeters, 77,000 divided by 7 is 11,000 hertz. That is your PRF. And again, since PRP and PRF have no relationship to frequency and really are bound more by propagation speed and the max imaging depth, any transducers PRP and PRF can be calculated based on our new formulas.

So I hope you're getting into the swing of things. Every time we learn a new formula, I like to go and try to practice some examples regarding that formula. Go ahead and pause the video while you fill in the highlighted purple spaces in the practice chart. You have two of them in your practice section. The top chart you're going to be given a max imaging depth and you're going to calculate the pulse repetition period and the pulse repetition frequency.

You can do one of two things. Use either formula to calculate the PRP and the PRF or practice calculating one of them and using the reciprocal of it to calculate the other. Now in the bonus practice, if you're up for the challenge, you're going to be given the frequency of the transducer, the maximum imaging depth, and the cycles per pulse. you're going to need to fill in or calculate the period, propagation speed, wavelength, PRF, PRP, pulsation, spatial pulsing, and the duty factor. So when you're ready, go ahead and resume the video to check out the answers.

And here are the answers to our practice. So you will see that by just having knowledge of the new pulse repetition period formula, you should be able to take your max imaging depth and multiply it by 13 to calculate the PRP in microseconds. From that point on you can either take the reciprocal of the PRP to calculate the PRF or you can use the PRF formula 77000 divided by the max imaging depth to calculate your PRF. I did include it in both hertz and kilohertz as we do typically like to use kilohertz as our preferred unit of pulse repetition frequency.

Now there's a little bonus question underneath that chart that asks us what happens to PRP and PRF if the sonographer changes to a three megahertz transducer. Well the answer is absolutely nothing. It only changes if we change the maximum imaging depth. Let's jump down to looking at the bonus practice. If you went ahead and went through all those, check out your values in the highlighted purple area.

If all your answers are correct and you understand the math behind all this and have found all the formulas that you need to fill in these blanks, that is fantastic. Feel free to jump ahead, but we are going to head over to the board to check out the math behind both of these charts to work the math out together. Welcome to the board. We are going to look through the math on that first chart. So the question asks us, what are the PRP and PRFs for a 5 megahertz ultrasound beam in soft tissue set to the imaging depths below?

Now I added some extra information in this question. It shouldn't happen too often on your tests or on your boards, but it does happen as a way to understand if you know how things are related. So that little bit of extra fluff information is at 5 megahertz. It doesn't matter what frequency we are operating at. because sound is bound by the medium that it is traveling in.

So that 5 megahertz is kind of fluff information. What we are mostly focused on that we are in soft tissue and that we have different maximum imaging depths. The two formulas that we are going to focus then on are the PRP and PRF formulas. So PRP is going to be equal to 13 microseconds multiplied by the max imaging depth in centimeters. PRF then is going to be equal to 77,000 centimeters per second divided by the max imaging depth, also in centimeters.

So these are the two formulas that we need to calculate all the blanks in this chart. Let's go ahead and start with the PRP column. All we need to do then is multiply 13 by whatever value is in the max imaging column. So we'll multiply 13 by 5 centimeters, by 8, by 13, and by 20 centimeters. Doing so with pen and paper or with your calculator then, 13 multiplied by 5 is 65 microseconds.

8 multiplied by 13 is 104 microseconds. 13 multiplied by 13 is 169 microseconds. And then lastly, 20 centimeters multiplied by 13 microseconds gives us a total of 230 microseconds.

Now we could take the reciprocal of any of the pulse repetition period values to calculate the PRF. So if we look at the first one, we would take 1 divided by 65 microseconds, and that would actually give us 0.0154 megahertz. And that's not really a unit.

that we want for ultrasound purposes. Now we could go from here and convert these down into into more usable units like 15.4 kilohertz or 15,400 hertz. But that's just a lot of extra steps, especially when we have a wonderful new formula that we just learned. To get rid of all this other stuff, we can just take a look then at our new formula, our PRF.

formula tells us that we can take 77,000 centimeters per second and then again divide it by whatever is in our max depth column. So we're going to take 77,000 and divide by 5, by 8, 13, and 20. And when we do so, we are going to come up with a PRF in hertz. So make sure that you are remembering that the 77,000 centimeters per second over depth in centimeters is going to give us a hertz unit for our PRF. Watch the answers that you're given. You might be shown answers in hertz or you might be shown answers in kilohertz.

Both are valid units when expressing pulse repetition frequency. On the answers page, I did give you both answers in hertz and kilohertz, but for the sake of the math here, I am just going to write down our hertz values. So 77,000 divided by 5 is equal to 15,400 hertz.

And that's it. And I already showed you with this depth that by using the reciprocal of 65 microseconds, we are given that 0.0154 megahertz and that converts down to the same value 15,400 hertz. Moving down then we have 77,000 divided by 8 and that is going to give us a rounded 9,625 hertz.

77,000 divided by 13 gives us a rounded 5,923 hertz. And then lastly, taking 77,000 and dividing it by 20 gives us a pulse repetition frequency of 3,850 hertz. Now on the bottom question here, I did ask you what happens to PRP and PRF if we change transducers.

I started out the board telling you that I gave you information you didn't need about the transducer frequency. So it doesn't matter if we change the transducer frequency, PRP and PRF are not related to it. Another thing that we can view from this chart is to remind us again that as we increase our maximum imaging depth, our pulse repetition period gets longer and we cannot send out as many pulses per second, therefore our pulse repetition frequency decreases with more depth. Jumping down then to the bonus practice, if you want to go through the math on this one, please stick around. We'll quickly go through each blank on the chart.

So we are told that we are imaging at a maximum depth of 9 centimeters with a transducer producing a 12 megahertz pulsed wave. And in those pulses, we have three cycles per pulse. Let's go ahead and start with period.

Period we know is the reciprocal of frequency, so period is going to be calculated by taking 1 and dividing it by 12. the frequency that we are given. 1 divided by 12 gives us 0.083 microsecond period for our 12 megahertz wave. Next down we have the speed in soft tissue. So we should all have this value memorized at this point 1.54 millimeters per microsecond or 1540 meters per second. Wavelength then can be calculated based on the speed in soft tissue and the frequency.

So that is calculated by taking the speed divided by the frequency in megahertz. 1.54 divided by 12 gives us a wavelength of 0.1283 millimeters. We already filled in the number of cycles per pulse.

That was part of our equation. We need to know that for calculating our pulse parameters. Let's go down to PRF then. And we're going to use our new formulas for this one. So PRF, remember, was 77,000 divided by the max imaging depth, which is 9 centimeters.

77,000 divided by 9 rounds to 8,556 hertz. Next blank down we have pulse repetition period. Now we can either take the reciprocal of PRF which would be 1 over 8556 or we can use our new formula which would be 13 microseconds multiplied by the max imaging depth, which is 9. Either one is just fine, you'll get the same answer, and in this case we get 117 microseconds. Next down we have pulse duration, which can be calculated again two ways.

We can take the number of cycles in a pulse and multiply it by the period of the wave, which is 0.83, or we can take the number of cycles in the pulse and divide it by the frequency. No matter which way you choose, you should get an answer of 0.25 microseconds. Next up we have spatial pulse length, which is going to be the number of cycles multiplied by the wavelength.

And we already calculated that to be 0.1283. Multiply that out and we will get 0.3849 millimeters. And then lastly we have duty factor.

And remember that duty factor is the pulse duration divided by the pulse repetition period. So we have pulse duration at 0.25 microseconds divided by the pulse repetition period, which we've already calculated to be 117 microseconds. Now kind of unlike the other examples that we had, we had to do some conversions. so we matched up our units. We already have them already matching so that's really awesome.

We can take that and then we need to multiply that value by 100 to get the percent. So after we calculate all that we'll get a value of 0.21 percent. Next up we have section 7.3, the 13 microsecond rule.

Our new pulse repetition period and pulse repetition frequency formulas are going to help the machine to know when echoes have reached the max imaging depth, and returned so it can send out a new pulse. But this unit is called calculating reflector depth, so let's get into that a little bit more. Remember that the machine is running a stopwatch during that off time.

It knows exactly when it sent the pulse and it's waiting for those echoes to return from the reflectors that that pulse interacts with. As each echo returns, it's going to record the time that has gone by. So by taking the speed, which is our 1.54 millimeters per microsecond, and the time that that echo and pulse were gone, it can calculate a distance.

But we need to be careful about how we are defining time. Are we speaking in terms of one-way time or are we talking about in terms of round trip time? Let's go back to our example of our 10 mile per hour cars. You and three of your friends moved into a new house in the middle of bizarro land.

You have no internet. and you only have these 10 mile per hour cars. So you make the deal with each other that you're all going to drive down one road and as soon as one of you sees an interesting landmark, you're going to turn around and head back to the house recording the total time that you had been driving. Now as a group you decide that you're not going to drive any more than three hours total, so the maximum anybody is going to drive is one and a half hours one direction, and then they're going to return. So you all hop in your cars and start driving.

Now your first friend tells everybody that I drove for a total of half an hour and in my half hour trip I saw a park. The second friend says well I drove for an hour and I saw a store. The third friend says I drove for a total of two hours and I saw a hospital.

And you tell everybody well I drove for two and a half hours and saw a school. So total round trip time for the park was 30 minutes, for the store was an hour, two hours for the hospital, and two and a half hours for the school. Now remember you had no other knowledge than the time you left your house, saw something interesting, and returned back to the house.

In this experiment, the only information that you had is the speed at which your car can travel and the time that you were gone from house to location back to house. So you have calculated your round trip time. Another way we can look at this is saying that the total time traveled by each driver from home to location and back is the time of flight or the go return time. Again, that's how long it took to complete the round trip. So later that night, You're all home.

And one of your friends says, well, it'd be really nice if we had a map telling us how far away these locations were from our house. Did anybody look at their odometer to see how far they drove in their round trip? And everybody's like, no, I completely forgot.

I was only focused on the time. And because you've been through physics class, you're like, no, we can figure this out because we know that speed multiplied by time will give us a distance. So everybody gets out their pen and paper and they take their 10 miles per hour, multiply it by their goal return time or the total time that they were driving and calculate the total distance that they drove. So that total distance is going to be the mileage from home to the location and back home.

And as everyone's looking at the data that they just calculated out, someone's like, well if we make a map of these mileage that's not going to be right. We want the one-way distance. So here's what we need to do.

We need to take the speed multiplied by the round trip time and divide it by two so we can get the one way distance. Everybody goes through their calculations again, divides them by two. So now the house friends can make a map knowing that the park was two and a half miles away, the store was five miles away, the hospital 10, and the school 12 and a half miles away.

All calculated based on the speed that they were traveling and the round trip time divided by two. So remember, if we just leave it at 10 miles per hour times our round trip time, we are going to be calculating round trip distance. We divide it by two to calculate the one-way distance the way that most maps work.

And just like our four friends mapping the town using go return time and their constant speed and dividing everything by two, the ultrasound machine can map the body using similar data points. It's important to remember that one pulse is going to create the information for one scan line. Now the machine is going to record the go return time from the start of a pulse to the return of each individual echo as the pulse interacts with reflectors in its path.

The machine will stop listening for returning echoes once the pulse and echoes should have returned from the max imaging depth set by the sonographer. Remember that's the PRP. The machine then will calculate the depth of the reflectors based on the go return times of the echoes they created. The machine will then display the echoes on our image corresponding with the depth that goes along with its go return time and the brightness is typically determined by the strength of the echo that returned. To calculate the depth of a reflector then, the machine is going to use this formula.

Depth in millimeters is going to be equal to the speed multiplied by the go return time divided by 2. Just like our friends did. They used their speed of the car, multiplied it by the time it took them to drive to a location and back, and divided everything by 2. If we do not divide by 2, then we are calculating the total distance traveled, not just the depth of the reflector. Let's say this is the max depth of an image and that it's set at 5 centimeters. So the machine is going to create a pulse and the longest it's going to listen is 65 microseconds. That is the longest it should take.

for any pulses to travel to the max step and return echoes. Once that 65 microseconds has elapsed, it's going to send a new pulse to create a new scanline. From that original pulse then, the sound travels into the body and after 13 microseconds have elapsed, echoes from a first reflector have returned back to the transducer.

The machine will record that and wait for more echoes to return from this pulse. After 26 microseconds, a second echo returns to the transducer from a second reflector. After 39 microseconds, a third echo returns from a third reflector. And after 52 microseconds, a fourth echo returns from the fourth reflector.

And at 65 microseconds, the machine has stopped listening. We're at the bottom of our image. For my example, I've chosen that my reflectors are at 1, 2, 3, 4 centimeters into the body because I want to see if you've noticed the pattern or can guess where we're headed with the 13 microsecond rule.

The 13 microsecond rule tells us that a sound pulse entering the body returns from a depth of 1 centimeter for every 13 microseconds of go return time. Let's take a look at a couple of examples of the 13 microsecond rule in action. Let's say we have a reflector in the body. The machine sends a pulse and it's going to wait. And it's going to wait for echoes to return that have been created by that pulse.

So now it is timing from when that pulse was created to when it receives. an echo. And for our first reflector, let's say that it took 156 microseconds for that pulse to be created and an echo to return. That's a go return time. The machine will know then that this reflector is 12 centimeters into the body and then will display it on the image at the depth that is represented by 12 centimeters.

The machine knows this because it can take the time it took 156 microseconds, the go return time, and divide it by 13 microseconds to give us a 12 centimeter depth. And that's the 13 microsecond rule. Let's take a look at another one. We have a reflector. The pulse is created.

Timer starts. It waits for echoes to return, and in this case, it gets an echo back from that reflector at 78 microseconds. The machine then can take 78 microseconds, divide it by 13, and knows whatever echo is returned from that reflector should be displayed at 6 centimeters into the image because it's 6 centimeters into the body. The calculation for that again is 78 divided by 13 to give us that 6 centimeter depth. Now the 13 microsecond rule is based on the original formula that the depth of a reflector is the propagation speed in soft tissue multiplied by the go return time all divided by 2. It's important to remember that the 13 microsecond rule has already taken the division by 2 into account.

And we can see that if we plug 13 microseconds into our go return time spot, multiply it by 1.5 for millimeters, divide it by 2, we get 10 millimeters or 1 centimeter. And that is how we come up with the rule. For every 1 centimeter, a reflector is into the body, It'll take 13 microseconds for the round trip time.

Remember that using the 13 microsecond rule will tell us the depth of the reflector, and if we double the depth, we will be able to calculate the total distance the pulse and echo traveled, meaning into the body and back to the transducer. Now for this lesson, we've used very simple numbers using whole centimeter values, where in reality the machine is going to be calculating infinitely small minute values. it might get echoes back at 17.3, 17.6, and like 18.1 microseconds. And that would require displaying reflectors at 1.33 centimeters, 1.35 centimeters, and 1.39 centimeters respectively. But this is so beyond the scope of what we need to know or what we need to calculate.

So when focusing on the 13 microsecond rule, make sure that you know the values for whole centimeter values. One centimeter reflector depth, should equal 13 microseconds. Two centimeter reflector depth equals 26 microseconds. Three is 39, four is 52, and so on. The other thing that you need to remember, because this might come up in your questions, is knowing the difference between a depth of a reflector and the total distance traveled.

Again, if we have a one centimeter deep reflector, the sound time is 13 microseconds, but the total distance that the pulse and the echo have traveled is actually two centimeters. One centimeter into the body to the depth of the reflector and one centimeter back to the transducer. In questions then that ask you about the 13 microsecond rule or the depth of a reflector, make sure to watch for terms that ask you for depth of reflector or total distance traveled by the pulse.

To finish up this unit then, make sure you head back to your workbook and work through your activities. It's a very short one this time because we are using rather straightforward formulas and we got a chance to practice them during the lecture. Remember that PRP is equal to 13 microseconds multiplied by the maximum imaging depth in centimeters.

PRF is equal to 77,000 centimeters per second divided by your maximum imaging depth in centimeters. And to calculate the distance a reflector is into the body, all we need to do is take the go return time and divide it by 13 microseconds. So your activity section will have a few charts in it where you can practice these formulas. Lastly, then go through your NERD check and make sure that you are able to answer those open-ended questions.

to evaluate your basic knowledge of the material in this unit.

Transcript for:Understanding Reflector Depth Calculation

Transcript for:
Understanding Reflector Depth Calculation