Transcript for:
Ultrasound Parameters Overview

hi learners it's m from sound on nerds this video is going to be on unit 4 the five parameters of pulsed sound up until this point we've really just been talking about sound kind of in the abstract we know it's a thing you can hear my voice there's sound in the air we know we're using ultrasound with our machines but we might not know is that there is something called a continuous wave and a pulsed wave and ultrasound actually uses both it just is a matter of having a high enough frequency to be considered ultrasound so in this image here we have a continuous wave on top you can see that it is just one ongoing wave that is how most sound waves occur but then we also have pulse wave which is on the bottom and you can see that there is a transmit time where the wave is present and then there's an off time where you don't see a wave occurring in this unit we are going to cover a little bit more about what pulse waves are and what the on and off time all of that means but it's important to remember that those seven parameters of sound frequency period propagation speed wavelength amplitude power and intensity all can describe continuous waves and pulse waves but this chapter is going to focus on just pulsed waves now the important part about pulse waves and why we use them in ultrasound is because pulse waves are the only way an image can be created i mentioned earlier about the transmit time and the receive time we can refer to that as on time and off time or talking time and listening time but it's because of that off time that the machine has a moment to process the information coming back from the echoes and create the image information so take a look at this image on the top it says continuous wave ultrasound is kind of like writing in cursive without any spaces or periods it's all connected and there isn't a way for the brain to read the picture without time to figure out each word now compare that to the bottom which says pulse wave ultrasound sends sound energy out in verse just like each of these words you can understand each quote-unquote pulse because there is a clear beginning and end while this might not be the most clear-cut example about continuous wave versus pulse wave what i like about it is that it shows you that continuous wave the top word block is not super easy to clearly see the words it's not super easy to see the picture you can't really parse what it is saying without the breaks in the words like the bottom one so in the bottom one we see letters that are grouped together just like our cycles are grouped together to create a pulse and then there's a break in between so our brains can actually read the words and the letters as they are put together and make sense of them so again continuous waves do not create pictures we can get ultrasound information back from them we can get data back from it but at no point will a continuous wave create a 2d picture like we commonly see with diagnostic medical ultrasound so by having that received time the machine can process the information from the pulse and create an image and just like the words are made up of letters each pulse is made up of cycles but the cycles are going to work as a unit and travel together now this is why a lot of the books use trains as an example for pulses the idea behind the train analogy is to think of the train as consisting of a bunch of cars or cycles but the train travels together as one unit just like the cycles in a pulse travel together as one unit so we had our seven parameters that describe continuous and pulse wave to sound we now have five new parameters that we can use to define parts of the pulsed wave and these are going to include pulse duration spatial pulse length pulse repetition period pulse repetition frequency and duty factor and again for each of these new parameters we're going to focus on the definition synonyms units symbol or really more of the common abbreviation for these uh formulas and relationships and how the scenographer can impact each parameter before we get into the parameters though i think it's important that we spend some time learning how to identify a pulse and what it'll look like in our studies so we know that this is one cycle we've got the beginning to the peak to the trough back to the beginning again and when we put a non-ending string of cycles together what we're looking at is a continuous wave it just keeps going when we see an image that includes multiple cycles grouped together with a clear break in between we are looking at the graphical representation of pulses with an on time where the cycles are and the off time where there is a break in between the cycles puzzles can have many cycles or they can have very few cycles they can have long wavelengths or they can have short wavelengths the most important part though is that there is a start to the pulse and an end to the pulse and time in between for receiving now the receive time is super important for creating our images because we need time to process the echoes that are returning from the pulses being sent out but the puzzles themselves are actually really important to the process as well the number of cycles within the pulse plays a big role in the accuracy of the ultrasound image when we are using b mode or gray scale in clinical ultrasound imaging most machines are going to emit a pulse that has around two to four cycles in it the shorter pulses are going to create more accurate images compare that then to doppler ultrasound which is going to require more cycles per pulse to get more accurate information so ultimately as sonographers we are trying to create the most accurate ultrasound image that we can and to do so we need to know what creates accurate images and so when we look at pulse waves we know that short pulses are going to create a more accurate ultrasound image especially in b mode imaging short pulses are going to be made up of fewer cycles shorter wavelengths short periods and high frequencies i know we've discussed in earlier units that the use of a high frequency transducer is better because it gives us more detail well this list actually just kind of proves our point even further those high frequencies result in short wavelengths short wavelengths are going to make for shorter pulses and shorter pulses are going to improve our axial resolution which means we get more detail so i don't expect you four units into this course that you already know all of this but i want to provide this list for you because we're going to keep building on it as we move through the units i want you to have that information in the back of your mind so you start thinking and putting those pieces together why am i choosing this frequency or why am i setting the machine up this way compared to another way what am i improving when i do this and what physics am i paying attention to now another way that we can improve ultrasound images is by having short receive time and this is especially true for those of you who are going to be working with moving objects specifically the heart so adult pediatric fetal echoes take a look at the moving heart we want to be able to see the heart moving in as close to real time as possible and to do that we need to make sure that we are again setting up the machine appropriately to achieve that real time imaging now we're going to discuss this quite a bit more when we get to our frame rate unit i believe it's unit 10. but in the meantime especially for our five parameters the biggest thing that you need to know and then one of the biggest impacts that you'll have on your receive time as a sonographer is that you should always use the least amount of imaging depth as possible by reducing the imaging depth you shorten the receive time which means that the ultrasound machine can send out more pulses and get more samples of the anatomy as it's moving i just want to remind you that this is kind of an introduction we're going to keep building on these concepts talking about why we make the decisions that we do but these are the things that are really going to relate to the parameters in this chapter and some choices that you're going to start making as a sonographer be it as a student or a seasoned stenographer you're going to start to understand why you make the choices that you do so let's go ahead and get into our five parameters we're going to start with pulse duration now the definition of pulse duration is the time it takes to complete one pulse so pulse duration is going to be the amount of time it takes to just transmit the pulse it's the on time and because this is a time parameter we are going to use a time unit typically we are going to use microseconds because microseconds is derived from the period of the frequency and the frequency is usually a megahertz so we want to again make sure that we are using complementary units the average value for pulse duration in ultrasound is 0.3 to 2 microseconds now there really isn't a symbol for pulse duration but you'll see it commonly abbreviated down to p d and in our formula for pulse duration we can see that pulse duration is equal to the number of cycles in a pulse multiplied by the period or we can calculate it as the number of cycles divided by the frequency so when we look at our formulas in the way that they are set up we can establish the relationships pulse ration is going to be directly related to the number of cycles in a pulse and to the time or the period of the wave so if there are more cycles our pulseration time is going to be longer if there's less cycles passeration time is shorter if the period is long then the pulse duration is long if the period is short then the pulse duration is also going to be short now we also can see that pulse duration is inversely related to frequency as frequency is the and the denominator and the quotient are inversely related so if frequency is low that means that the pulse duration is going to be longer or take up more time and if the frequency is high then the pulseration is going to take less time again if we have high frequencies we have shorter periods shorter periods mean shorter pulse durations now as a sonographer you're not really going to have any impact on the pulse duration because it is related to frequency and period we can't change frequency or period we can't change pulse duration either because of it and it will not be adjustable by you as the sonographer pulseration is going to answer the question how long does it take for one pulse to occur now this might sound really similar to period but it is not the period of the wave it is the period of the wave multiplied by the number of cycles or it's the number of cycles divided by the frequency so they're all related to one another but this is not the period of the wave it is the duration or the time it takes for the one pulse to occur so using our two new formulas that we have for pulse duration let's go ahead and look at an example over on the board and work through some of the math on it let's explore the two formulas that we just learned about pulse duration here we have a graph showing three pulses with three cycles each our two formulas our pulse duration in microseconds is equal to the number of cycles divided by the frequency and we also have that pulseration is equal to the number of cycles multiplied by the period taking a look at this wave and knowing that it's a 5 megahertz frequency let's go ahead and figure out pulse duration using frequency first so we're going to look at this formula we have the number of cycles divided by frequency when we are given a picture graph all we need to do is count the cycles we have 1 2 and three so three cycles and our formula says to divide it by the frequency in megahertz the pulse duration for this graph is three cycles divided by five which gives us 0.6 micro seconds if we were to take out a stopwatch and watch this pulse go by it would take 0.6 microseconds to do so using the same graphical representation of the wave and knowing that it's a five megahertz wave we can use the period-based formula to calculate pulse duration but this time we actually have to do a little bit of extra work first we have to calculate the period we're told that the frequency is five megahertz and we know that frequency multiplied by time equals one and that they are reciprocals so with the five megahertz frequency to figure out period all we really need to do is move the 5 into the denominator position underneath the 1. so period will be 1 divided by 5 which actually equals 0.2 microseconds now we can take our period and multiply it by the number of cycles in the pulse according to this formula and when we do that we also get 0.6 microseconds per pulse so again it's the time of the pulse that is the pulse duration we're looking for a time unit to match up with it so it works out either way we can use period multiplied by the number of cycles or we can use number of cycles divided by frequency and we will still get the correct pulse duration no matter how you do it but up next we do have our answer to our pulse duration practice in the pulse duration practice you're going to get an opportunity to fill in some charts that are missing either frequency or period and then you need to calculate what the pulse duration is based on the number of cycles provided so here we have the answers to our pulse duration practice how did you do well remember to check all the areas that are highlighted in green those are the areas that you needed to fill out if you feel good about all this and are ready to skip forward go ahead and head to the next section if you want to see this math worked out though hang out we're going to head back to the board we're going to take a look through our pulse duration practice questions in these questions you are responsible for filling out the highlighted green areas based on the pulse duration formulas that we just learned you have a chart with the number of cycles frequency period and pulse duration to fill in with certain elements of the graphs completed our first graph offers us that there are six cycles per pulse in a wave that has a frequency of two megahertz we need to figure out the period and the pulse duration to figure out the period we need to take the reciprocal of the frequency and that will give us a period so 1 divided by 2 megahertz gives us a period of 0.5 microseconds so we can put in 0.5 microseconds in our period column next we are going to use either the frequency or the period to figure out pulse duration because we had to calculate period i'm going to use the period method so we stay consistent throughout the rest of the charts to calculate pulse duration then we need to take the period of the wave and multiply it by the number of cycles which was six 0.5 times six equals three microseconds so our pulse duration for a six cycle pulse with two megahertz frequency is going to be three micro seconds let's look down then at the next example this time we have three cycles per pulse with the two megahertz frequency we already calculated our period at half of a microsecond so now we need to figure out the pulse duration by taking the half a microsecond multiplying it by three the number of pulses in the cycle and that will give us 1.5 microseconds so we can fill that part of our column in as well the final question and kind of the crux of the whole reason that we're doing these practices is to understand the relationships it's asking us what happened to pulse duration when the number of cycles decreased so when we went from 6 down to three our cycles decreased note that our frequency stayed the same our period stayed the same but our pulse duration decreased and that's because there are less pulses per cycle the next chart tells us that both of the waves that we are going to be comparing both have five cycles per pulse we need to calculate the frequency we're given the periods and then we need to calculate the pulse duration let's look at the top one we're given 0.1 microseconds as our period we know that that frequency has to be the reciprocal of that so we're going to do 1 divided by 0.1 and 1 divided by 0.1 equals 10 megahertz the frequency that complements 0.1 microseconds is 10 megahertz now we're going to switch over to calculating pulse duration and this time i'm going to use pulse duration being equal to the number of cycles divided by the frequency so we're told that our number of cycles is 5 we're going to divide that by the 10 megahertz 5 divided by ten equals one half so our pulse duration is half of a microsecond in a wave that has five cycles per pulse at a ten megahertz frequency let's switch to the bottom one again we're told that we have five cycles in this pulse we're told that the period then is 0.3 microseconds again we just need to take the reciprocal of 0.3 to calculate the frequency 1 divided by 0.3 is about 3 megahertz we're going to round so we can put 3 megahertz into our column now again we're going to use our number of cycles divided by the frequency to calculate the pulse duration so we have 5 divided by 3 and that is going to equal 1.6 so our pulse duration on a frequency of 3 megahertz with 5 pulses with five cycles per pulse gives us a pulse duration of 1.6 microseconds and in this one we're asking what happened to pulse duration when the period increased so we're looking at our period went from 0.1 microseconds increasing to 0.3 microseconds by increasing the period we lowered the frequency because those are opposite they're inversely related and we see that with pulse duration the longer period created a longer pulse duration so we had five cycles for both if the period for the top one is shorter than the period for the bottom one then it stands to reason that the pulse duration is going to be longer when there is a longer period we can say that when period increases pulse duration increases they are directly related let's take a look at the last chart in this one we have cycles for pulse and frequency given to us we are again going to calculate the period and the pulse duration so we need to calculate the period by taking the inverse or the reciprocal of frequency for the top one we will move 10 into the denominator position underneath the 1 and we will see that 1 divided by 10 equals 0.1 seconds and we can fill in our column with that time we're then going to use the period base pulse duration formula to calculate pulse duration so we have 0.1 multiplied by two cycles in the pulse 0.1 multiplied by 2 gives us 0.2 microseconds let's take a look at the bottom one we now have 7 megahertz we'll move the 7 into the denominator position 1 divided by 7 equals 0.14 microseconds so the period for a 7 megahertz wave is going to be 0.14 microseconds we will take that 0.14 multiply it again by the number of cycles in our pulse for the chart it is 2 2 times 0.14 equals 0.28 microseconds and underneath we're asking what happened to the pulse duration when the frequency decreased so we went from 10 megahertz down to seven megahertz and when the frequency decreased we see the period increase and then we also see the pulse duration increase so if the time the period increases we're going to see the time of the pulseration also increase section 4.3 spatial pulse length is going to be our next parameter that we're going to learn about the definition of spatial pulse length is the distance that a pulse takes up in space so very similar to wavelength spatial pulse length are distance measurements now again if we had a ruler we could go and measure the length of the pulse but again there are formulas so we are able to actually calculate the spatial pulse length based on certain parameters because facial pulse length is a distance we are going to use any distance or length unit in ultrasound we typically use millimeters and in clinical ultrasound we will see that spatial pulse length is usually between 0.1 and 1 millimeter in soft tissue and yes we are highlighting soft tissue again because as you'll see in a second spatial pulse length is related to wavelength wavelength was related to the medium and therefore spatial pulse length is as well now we don't have really a symbol for spatial pulse length rather a common abbreviation you'll often see it as spl and we will see that spl is equal to the number of cycles multiplied by the wavelength so from this formula we can see that spatial pulse length is going to be directly related to the number of cycles in a pulse and directly related to the wavelength of the cycles if there are more cycles the spl will get longer if there are less cycles it'll get shorter and if the wavelength is longer then the spl will get longer and if the wavelength is shorter the spl also gets shorter now because facial pulse length is so closely related to wavelength and wavelength is determined by the machine and the medium so is spatial pulse length an important feature that i've kind of already introduced you to is the fact that spatial pulse length is going to have a major effect on axial resolution the shorter the spl usually means the better the axial resolution and the better the axial resolution means better the detail so again this just further illustrates why we really want the highest frequency possible because high frequencies are going to have shorter wavelengths shorter wavelengths are going to produce shorter spls and shorter spls improve our resolution so spatial pulse length is going to answer the question how much space does one pulse take up we're going to head back over the board to use our new formulas that we learned and see some mathy examples on them now that we've learned a new equation for spatial pulse length let's take a look at an example again using that new knowledge this graph probably looks pretty familiar to the graph that we use for pulse duration and in fact it is it's another five megahertz frequency traveling in soft tissue three cycles per pulse this time though we are going to calculate the distance of each pulse so using our spl formula we see that it is number of cycles multiplied by the wavelength of the frequency because we have a picture to take a look at all we simply need to do for this one is to count the number of cycles we can count one two and three so the number of our cycles for this image is going to be three cycles the next thing that we need to do is calculate the wavelength if you recall back to our unit 3 formulas we know that wavelength then is equal to propagation speed divided by frequency and because this is in soft tissue we can expand that to be wavelength equal to 1.54 millimeters per microsecond divided by the frequency in megahertz and in our example we're told that it's five megahertz if we do the math then 1.54 divided by 5 we see that wavelength is going to be equal to 0.31 millimeters we're going to take 0.31 plug it into our spl formula and what we end up getting is 3 multiplied by 0.31 equals 0.93 millimeters so if we could get just a tiny little ruler out and measure our spatial pulse length it wouldn't even be quite a millimeter given these frequencies and pulse parameters and now that we're back we're going to head into the practice for spatial pulse length in the practice you will be filling out a chart again filling in the missing spatial pulse link and then determining how some parameters will react based on the answers that you have found go ahead and pause and when you're ready on pause to see the answers and here we are with our answers again everything highlighted in green was your responsibility to fill out and how did it go if you understood the math behind spatial pulse length please feel free to jump forward to our next chapter otherwise hang around because we're going to head back to the board and go over these examples to complete the spatial pulse length practice we have again been given two charts to fill in with missing information the first chart gives us the number of cycles per pulse a frequency and we have to calculate the spatial pulse length remember that spatial pulse length is equal to the number of cycles multiplied by the wavelength so in both of these scenarios we need to calculate the wavelength based on the frequency both of our examples give us a two megahertz frequency so we're going to take wavelength being equal to 1.54 millimeters per micro second divided by two the frequency in megahertz 1.54 divided by two gives us 0.77 millimeters for the wavelength to calculate the spatial pulse length of the top row we are going to take the number of cycles which is 6 and multiply it by our wavelength 6 times 0.77 equals 4.6 millimeters so we can put that into our chart 4.6 millimeters now the next one tells us that we have three cycles in our pulse multiply that by the wavelength that we calculated and 3 multiplied by 0.77 equals 2.3 millimeters so let's go ahead and fill our chart in with that information now the question asks us what happened to the spatial pulse length when the number of cycles decreased so we started at six and we decreased to three so the number of cycles decreases we see that the spatial pulse length will also decrease this tells us that the number of cycles and spatial pulse length are directly related and that when there are fewer cycles and a pulse we are going to have a shorter spatial pulse length the second chart in the practice tells us that we have five cycles per pulse and this time we have two different frequencies a 12 megahertz and a 6 megahertz and we need to calculate the spatial pulse length again the spatial pulse length is equal to the number of cycles in the pulse multiplied by the wavelength so we're first going to figure out the wavelength for each of these frequencies 1.54 millimeters per microsecond divided by 12 megahertz 1.54 millimeters per microsecond divided by the 12 megahertz equals 0.1283 and 0.1283 multiplied by the number of cycles in our pulse equals 0.64 millimeters so we can take that value and place it in our chart let's do the same thing for the six megahertz frequency we'll take 1.54 millimeters per micro second and divide it all by the six megahertz now when we do that equals 0.256 millimeters and we'll multiply that by the number of cycles in our pulse and that will give us a total of 1.28 millimeters so we can add that value to our chart and now we can look at the question what happened to spl when the frequency decreased so we see that the frequency got lower and when we lower our frequency we see that our wavelengths get longer so we have a higher wavelength with a lower frequency and because we have that longer wavelength we then see that our spl also increased by showing this math we are seeing that when we decrease the frequency we increase the wavelength and by increasing wavelength we get longer spatial pulse links so to review up until this point we had pulse duration which is machine controlled and cannot be adjusted and we have spatial pulse length which is machine controlled and medium dependent and also cannot be adjusted but now we have three parameters that are very dependent on depth and because depth can be adjusted by you as a sonographer you actually have a lot of control over these three parameters so the depth dependent parameters include pulse repetition period plus repetition frequency and duty factor i want to highlight very very important pulse repetition period and pulse repetition frequency have nothing to do with the wave period and the wave frequency so prp and prf have nothing to do with period or frequency of a wave so when we look at a picture of a pulse wave like the one that you see on your screen if we are looking at this in a unit of time then we are able to determine what the pulse duration is and recall that it is determined by the source if we look at this in the unit of distance then we can define what the spatial pulse length is and recall again this is by source and medium so remember neither of these parameters are something you can adjust as a stenographer what you can change as a sonographer are the depth dependent parameters so when you change the maximum depth of the image that you are creating you are going to change the receive time or the off time and therefore pulse repetition period pulse repetition frequency and duty factor will all change along the side of an image is a scale and the scale is going to tell us the depth of the image we typically see it represented as centimeters and the maximum imaging depth is the bottom of the field of view to change the maximum depth there is a knob or toggle on the machine that will adjust the depth in this image here we see that the maximum depth is set at 3 centimeters in this example we can see that it goes all the way down to five centimeters and in this example we can see that the max imaging depth is more to about 16 centimeters so when you increase or decrease the depth you are going to change the prp prf and duty factor without getting too far into the physics or the at least the heavy duty part of the physics quite yet when an image is created what typically happens is that a sound pulse is sent into the body and that sound pulse is going to travel through the soft tissue sending back echoes about the reflectors that it interacts with and the machine is going to wait to get all the echoes back from at least to the distance of where we have our maximum depth set so if we have a three centimeter depth image it's going to wait until the echoes from three centimeters make it back to the transducer so one pulse one waiting period is going to create one scan line and that one scan line is just one tiny little bit of the image once the information comes back from that first pulse from the maximum imaging depth then another pulse can be sent and processed so we have to have a pulse weight weight process and display pulse weight process pulse wait for it to travel process display the scan line pulse wait get all those echoes back display the scan line so this is happening incredibly incredibly incredibly fast much faster than we can clearly process with our own minds because it looks like to us that the image is just always there but again the machine is sending a pulse waiting for those echoes to come back so it can process it and display each scan line until we make a full frame and when we make the full frame it starts all over again with the process and sweeps across creating those scan lines to make the next frame so the whole reason that prp prf and duty factor all related to depth is because of that waiting period the more depth there is the longer the machine has to wait for those echoes to return before it can scan the next scan line or send the next pulse so take a look at these two pictures we're just going to wait watch a few scan lines go through watch a few images being made notice on the top one that we are scanning to a maximum depth of 15 centimeters in the bottom picture we're only scanning to a maximum depth of seven centimeters and so when we reduce the depth we reduce the waiting time and therefore can produce more images so if you watch long enough you'll see that the seven centimeter depth is creating more images than the 15 centimeter depth because there is less waiting time for that pulse to travel to seven centimeters and come back this waiting time is the whole reason why we want to use the least amount of depth as possible especially for those of you that are imaging moving structures we want as many refreshes as we can of our frame so we can get a very realistic representation of how the body is moving so let's go take a look at our parameters we're going to start with pulse repetition period pulse repetition period is the time from the start of one pulse to the start of the next pulse so remember that pulse duration was only the actual time of the pulse pulse repetition period is going to be the pulse duration or the on time plus the off time or receive time remember pulse repetition period has nothing to do with the period of the wave it is 100 the time it takes to transmit the pulse and receive the echoes because this is a time parameter we are going to be measuring this in microseconds or any other unit of time as far as an average pulse repetition period it is actually kind of difficult to say exactly what the average is because we can change the depth for whatever you need so the time can actually vary quite a bit based on the depth that you have chosen to image at however it is usually somewhere between 13 microseconds if our maximum depth is set at one centimeter to about 260 microseconds if we have our depth set up to 20 centimeters again pulse repetition period is not really represented by a symbol but rather a common abbreviation prp and we see in our formula that prp multiplied by prf equals one so prp and prf are reciprocals but we also have another formula down there prp multiplied by 13 microseconds is going to be equal to the depth in centimeters we are going to focus mostly on the reciprocal relationship between prp and prf for this unit but when we get to unit 7 we're going to explore that other formula in a lot more detail i did include it in this lecture so you have it and you can put it on your formula sheet if you want to keep everything together but again we're going to cover that much more in a future unit so from these formulas i kind of already gave it away pulse repetition period is a reciprocal of pulse repetition frequency if prf is getting lower then we're going to see that prp is getting longer so if that doesn't immediately sound like inverse relationship remember if prf gets lower that means that the value numerical value of prf is going down or the numerical value of prp is increasing the bottom formula then shows us that pulse repetition period is directly related to depth that is why this is considered a depth dependent parameter if the maximum imaging depth is deeper then our pulse repetition period is going to be longer there's more weighting if the maximum imaging depth is shallow then our prp is going to be short because there's less weighting as a sonographer you're going to have a huge impact on pulse repetition period and you do this by changing the maximum imaging depth of the image shallow depths are going to reduce the prp or deeper depths are going to increase it as a sniper you should always make sure that you are using appropriate imaging depth that means to not have it too shallow where you're cutting important anatomy off or have it so deep that we're practically imaging into the table balancing your depth is going to be very important for improving temporal resolution let's jump over then to pulse repetition frequency pulse repetition frequency is the number of pulses per second a system can send so pulse repetition frequency is going to tell us how many times a pulse can be sent into the body per second remember back to the image where we were sending a pulse and then waiting for that pulse to travel to the maximum imaging depth and then we could display our scan line well if we can send pulses quickly that means that we can display those scan lines very quickly and therefore create a full image very quickly but when we increase the maximum depth and make it really really deep we're going to make that waiting period longer and therefore we can't send as many pulses and it's going to take a lot longer to create the full image now pulse repetition frequency is not the frequency of the wave but it does share the similar definition and that we were talking about in events per second and because of that we do see that pulse repetition frequency is measured in a derivative of hertz typically kilohertz in ultrasound in clinical imaging then the average prf is about 1 to 10 kilohertz just like everything else there's more of a common abbreviation it's prf and so then we see that prp and prf multiplied together are going to equal 1 and prf is going to be equal to 1 divided by prp again just expressing that they are indeed reciprocals of one another and then just like prp i do have that other kind of fancy formula where prf is going to be equal to 77 000 centimeters per second divided by depth and again we are going to cover that a little bit more in unit 7 in much more detail and talk about why that is the formula that we have focusing on prp and prf being reciprocals we see again that if the prp gets longer we will have a lower prf if the prp gets shorter then we should have a higher prf we can send more pulses out we also see then too that prf is inversely related to depth increase your maximum imaging depth we're going to have a lower prf if you decrease your maximum imaging depth make it shallow we're going to have a higher prf and again just like pulse repetition period you have an immense impact on pulse repetition frequency all by changing the maximum imaging depth the shallower the depth the image is set to will increase our prf which means we can create more frames per second because we are sending out more pulses per second if we increase our depth we're going to start to see a worsening of our temporal resolution because we cannot make as many frames because we cannot send out as many pulses per second let's take a little bit closer look at prp and prf and their relationship to one another i've already mentioned that they are reciprocals so essentially if one increases the other must decrease and vice versa and we know that if we have five representing the value for prf then prp is going to be 1 over 5. we're going to move that 5 into the denominator position under a 1 to create the reciprocal so that is very similar to period and frequency but they are not the period and frequency of the wave they represent the time for on and off pulses and the amount of pulses we can send per second remember that pulse duration is part of the prp so paul it is pulse duration the on time plus the off time but pulseration is what it is it cannot be changed it's going to be set by the machine based on the transducer that we select and when we change depth it is actually changing the listening time it doesn't change the pulse duration it doesn't change the spatial pulse length doesn't change frequency or wavelength or any of that the only thing that changes the depth changes is it changing the listening time so let's take a look example at how prp and prf are related to one another and how they react to different depths let's say that these transducers are the exact same transducer in the green situation we have the transducer set to a 16 centimeter max depth and in the yellow situation the very same transducer has been reduced to an eight centimeter max depth so remember these are the same exact transducers so that means that the pulse duration the frequency the period the propagation speed the spl the wavelength all of it all of that's the same because these are the same transducers the only thing that's different between them is that one is imaging to 16 centimeters the other is imaging to eight so in the green transducer it has to image to a deeper maximum depth increase in depth we're going to see an increase in prp and a decrease in prf so it's going to have more depth more listening time less pulses per second and we can see that visually comparing that to the yellow one which is only imaging to eight centimeters that pulse is sent out much more quickly compared to the 16 centimeter pulse so in the yellow transducer we see that the depth is reduced which means that the pulse repetition period is reduced there's less listening time which means we can send out more pulses per second so of course now that we have some new formulas we are going to head over to the board to look at some of the math behind the formulas and to look at the example in the workbook just as we've been doing with all of the other new formulas that we are learning we should go ahead and practice our new prp and prf formulas for this unit i've decided that i want you to focus more on the pulse repetition period multiplied by the pulse repetition frequency equals one and if we manipulate this and transpose it to solve for prf and prp we will see that prf is equal to one over prp and prp is equal to 1 over prf and that is all because of their special reciprocal relationship so these three formulas are really going to help us for these two examples the first example shows us a picture of a pulsed wave traveling in soft tissue it is a five megahertz wave and if we look at the graphical representation we can see that there are two cycles per pulse the question then is what is the pulse repetition period and the pulse repetition frequency when presented with a picture like this one to figure out the pulse repetition frequency it is simple enough as just counting the number of pulses that occur in one millisecond so we have one two and three pulses within a millisecond using the millisecond time knowing how to convert numbers we can say that this is 3000 pulses per second or if we want to use values that are more applicable to pulse repetition frequency it would be more appropriate to say that this is a three kilohertz prf to calculate prp then we're just going to use the magic of reciprocal flip-flop so we need to move the 3 down into the denominator position under 1 1 divided by 3 equals 0.33 milliseconds for prp note that we are using complementary units for milliseconds and kilohertz for the prp and the prf now let's take a look at an example that increases the number of pulses per millisecond this time we have five pulses one two three four five so our pulses per second is five thousand or five kilohertz to calculate prp then we are going to divide one by five and that is going to give us 0.2 milliseconds for the p in the bottom part of our paragraph i actually was able to take it a little bit further with you so if you want to follow along for the math stick around for this part we had those other two formulas we had prp in microseconds being equal to 13 microseconds multiplied by the depth in centimeters and then we also know that prf in hertz is going to be equal to 77 000 centimeters per second divided by the depth in centimeters and the depth that we are talking about is the maximum imaging depth so i'll show you an example in each of them how i was able to calculate that on the top one let's use the prp formula now it's important that we have prp in microseconds but we calculated this to be 0.33 milliseconds so we need to convert that to microseconds first so 0.33 milliseconds is 330 microseconds to get depth by itself we need to divide by 13 on both sides so we're going to take our 330 divide it by 13 microseconds and that will equal our depth 330 divided by 13 equals about 25 centimeters of depth let's go ahead and calculate the depth of the second one using the prf formula so in the last one we calculated prf to be 5 kilohertz well 5 kilohertz does not match up with what we need for hertz so again we need to convert into the proper unit 5000 kilohertz is the same as 5 000 hertz and to solve for depth we are going to need to manipulate the formula again to isolate it on one side of the equal sign by itself so if i multiply both sides by depth that cancels that out and then i can divide this side by prf divide this side by prf and now i have that depth is equal to our 77 000 centimeters per second divided by the prf so after our manipulation of prf into hertz we have 5000 hertz all we need to do is take that prf and divide 77 000 by it 77 000 divided by 5000 equals about 15 centimeters of depth so our top waveform shows us that we are imaging to a maximum depth of 25 centimeters we can see long wait times that match up with the idea deeper depths equal longer pulse repetition periods which decrease the pulse repetition frequency fact checking the bottom one then we can see that our depth has decreased so it makes sense that we are able to have a higher pulse repetition frequency and shorter prps the very last bonus question on this page then asks us can we figure out what the pulse duration is for these waves remember that pulse duration is equal to the number of cycles divided by frequency or the number of cycles multiplied by period and we're told in the problem that the frequency is five megahertz so we can count our cycles which is two and divide it by five which was our frequency in megahertz two divided by five equals zero point four we're talking about pulse duration so we are going to label this microseconds so 0.4 microseconds of pulse duration is the same for both of these waveforms that is not going to change that is a constant based on the frequency or the period of the wave has nothing to do with the depth and the prp and the prf so we're going to keep this value in our back pocket because we're going to need it for when we figure out the duty factor we do need to finish up our depth dependent parameters and our last one is duty factor now duty factor is the percentage of time that the machine is transmitting remember that in pulse wave ultrasound there's an on time and an off time so duty factor is going to be the fraction of the on time divided by the on and off time put together so it's the pulse duration divided by the pulse repetition period pulse duration is just the on time pulse repetition period is the on time and the off time what this ends up doing is helps to quantify the amount of time that a patient is actually being exposed to ultrasound energy so really only getting it during the pulse which is a very very small fraction of time but the duty factor tells us what that fraction or percentage is way back in unit 1 we talked about units and we said that every numerical value that we have should have a unit associated with it millimeters centimeters whatever well we've just come across our first parameter that we're okay saying that this is a percentage now a percentage is not technically a unit but it does fill the role of describing the number because it's telling us how much of a whole this number is when we're imaging with b mode or grayscale the average value of duty factor is going to be less than one percent so that means it's just just this little and then the rest of the time it's just listening and it's listening for those echoes to come back and then another quick little pulse and then it waits so it's talking far far less than it is actually listening for echoes to return when we turn on different parameters in the machine like using doppler it actually has to talk a little bit more to get a little bit more information and it also uses longer pulse durations or longer spatial pulse links and because of that that's going to increase the amount of talking time compared to listening so we'll see an increase from about one to ten percent when we turn on doppler continuous wave ultrasound is talking constantly and continuous wave ultrasound then has a duty factor of 100 percent because it never stops to listen it's always talking and that's why it can't create an image like our others we have common abbreviation for duty factor you'll often see it as df and in our formula we can see that duty factor represented as a percentage is equal to the pulse duration divided by the pulse repetition period to turn it into a percentage we do need to multiply it by 100 it is also appropriate to leave duty factor as a decimal if you wish the other big part of the formula that i want to point out is that you see pulse duration and pulse repetition period are using the same unit you must have the same unit in those value places so that the units cancel each other out and we get an actual percentage and the formula again will give rise to the relationships that we see so we have duty factor being directly related to pulse duration if we have a long pulse duration that means more talking time we'll see that the duty factor increases if the pulse ration is shorter then we'll see that the duty factor decreases duty factor that is inversely related to pulse repetition period when there is more listening time with the pulse repetition period we'll see that the duty factor decreases which makes sense if we're just getting a small little blip and then lots of listening time the percentage or fraction that the machine is talking is very low when the prp is long however if we have a very long pulse or a lot of talking and just a little bit of listening time we're going to see that that duty factor starts to increase it's taking up more of that time increasing the percentage that it's on unlike prp and prf duty factor does have some relationship with pulse duration and pulseration is determined by the machine so technically due to factor is also determined by the machine but we can change the duty factor by changing the depth and that is because of its relationship to pulse repetition period so of course we've learned yet another equation so we are going to head over to the board to discuss the example that's in your workbook and work through some of the math all right we made it to our last parameter example and we've been using the same example kind of building on it so we saw with prf and prp how to calculate both of those values based on the information that we have from these images and we have already calculated those and i've included that on the side here but this example is going to take a look at how to calculate duty factor i have provided the duty factor formula in the corner here for us we're going to use that in a minute to calculate the duty factor of either of these waves we first need to know what the pulse duration is and then we can divide it by the pulse repetition period because this is the same example that we use for prp and prf we've already calculated pulse repetition period the top waveform has a pulse repetition period of 0.33 microseconds and the bottom one has a prp of 0.2 microseconds the piece of information that we're missing though is the pulse duration so we need to calculate the pulse duration if you stuck around from the last example we calculated pulse duration using this formula number of cycles divided by the frequency we can count the number of cycles in each pulse to be 2 and we're told that the frequency is 5 megahertz 2 divided by 5 equals 0.4 microseconds but there's a really big red flag that we need to take care of we do not have matching units for these values we either need to convert pulse duration to milliseconds or we need to convert false repetition period to microseconds instead of converting both of the prps which are separate values into microseconds i'm going to convert the pulse duration into milliseconds because it is the same value for both of the waves 0.4 microseconds into milliseconds equals 0 0.0004 milliseconds now we can divide that by 0.33 milliseconds and .004 milliseconds divided by 0.033 milliseconds and gives us a value of 0.0012 and we can stop here if we wanted to it is okay to express duty factor as a unitless decimal but it's more accurate you'll see it more commonly in your books and in your tests to present it as a percentage so to finish this off we do need to multiply this by 100 and the final duty factor percentage of the top pulse is 0.1 percent we can do the exact same thing for the bottom pulse convert 0.4 microseconds into .0004 milliseconds divided all by 0.2 milliseconds and we get a value with that one of .002 again we can leave it as a decimal if we want but to convert it to a percentage we need to multiply by 100 and when we do so the duty factor of the bottom wave is 0.2 percent to finish up this unit then we are going to go over a summary of everything that we've talked about and i do have some practice problems that will include a bunch of the new formulas that we just learned and kind of put it all together with the last unit so here i have an example of a pulse wave and we're going to say everything that we describe on the top is time and everything we describe on the bottom is going to be related to distance now remember we had those seven parameters that could describe both continuous and pulse waves so we have our wavelength which is equal to the propagation speed divided by frequency we have period which is 1 divided by frequency and then not shown on this graph we do have our frequency which is one divided by the period also not shown on this graph but related to the parameters that can describe continuous impulse wave then is propagation speed and we know that in soft tissue propagation speed equals 1.54 millimeters per microsecond also not shown on this graph are amplitude power and intensity but they can all describe continuous and pulsed waves this unit we learned about the five parameters that can only describe pulse waves and so that we have spatial pulse length which is the wavelength multiplied by the number of cycles we have the pulse repetition period which includes the on and off time and is the reciprocal of the pulse repetition frequency we have the pulse duration which is the period multiplied by the number of cycles and those two factors together are going to help us to calculate the duty factor of the pulse wave and then we know that how many pulses can be sent per second is the prf and we can calculate that as a reciprocal of prp remember that pulse duration is related to time of the pulse and we want shorter pulserations to create better images we're going to see that short pulserations come along with few cycles in the pulse or short periods where long pulsedurations are going to have many cycles in the pulse or longer periods facial pulse length describes a distance and we want short spatial pulse links to improve our images by having shorter spls we are going to see fewer cycles in the pulse or shorter wavelengths creating that pulse where longer spatial pulse links are going to have many cycles in the pulse or recreated from long wavelengths next we have how all of our depth dependent parameters are related to shallow imaging versus deep imaging so when we have a shallow maximum image depth we are going to see that we have less off time there's not going to be as much listening happening so because of that we're going to see short pulse repetition periods with short pulse repetition periods we are going to see high pulse repetition frequencies because there's more talking that means there's a higher duty factor compare that then to deep imaging but there's more off time so there's more time to listen we're going to get a longer pulse repetition period because of that and because we have more waiting time we can't send as many pulses so we have a low pulse repetition frequency and because there's not as much talking we end up lowering our duty factor and speaking of duty factor when the machine is off our duty factor is at zero percent there is no sound being transmitted there is no fraction of on time when we are in 2d imaging that means getting those grayscale images our duty factor is less than one percent it's doing much more listening than it is actually doing with talking when we start to turn on color or turn on our doppler imaging we are going to increase our duty factor because the spatial pulse lengths become longer there's more talking time to create doppler images so we up our duty factor to about one to ten percent lastly continuous wave ultrasound is going to have a duty factor of 100 and that's a really big one continuous wave ultrasound has a duty factor of 100 because it is always on there is at no point a time that it'll stop and listen and that's why continuous wave ultrasound cannot create images so one more final summary of all the five parameters of the pulse wave we have duty factor it is controlled by the machine and it's going to change when the depth changes also controlled by the machine are pulse repetition period and pulse repetition frequency they are reciprocals of one another and they are going to be greatly affected by the maximum imaging depth next we have pulse duration which is controlled by the machine and cannot be adjusted it is very innate to the transducer itself the machine decides how many pulses will be used and the pulse ration is going to be equal to the number of cycles multiplied by the period or the number of cycles divided by the frequency and lastly we have spatial pulse length much like wavelength spatial pulse length is also determined by both the machine and the medium in which the wave is traveling so up next we have the answer to practice number one from our summary practice problems now this practice number one is kind of a tricky one and that's because we are figuring out pulse duration prp prf frequency propagation speed we're going over all the concepts that we've talked about in the last couple units and kind of putting them all together based on knowing the frequency of the transducer and a picture of the pulse so see what you can get through on your own and then unpause the video and let's double check your answers and here are the answers to practice number one remember you're filling in all of the green areas and if you understand the math behind all of this please feel free to jump ahead to the takeaway portion for practice number one otherwise stick around and we're going to go through all the math of how we figured these out let's head over to the board so we can take a look at all those formulas and fill out that chart completely if you were able to calculate all of the practice number one pieces that we were missing congratulations that was a lot of work to go and find all those formulas and put them all together and make some sense of this very little information that i've given to you but the really cool part about this is that we can figure out so much based on just a few parameters so it's actually really neat that it all kind of works out and we can do the math for all of this and if you weren't able to figure it out that's okay we're going to go through it now and i want to show you how it all works together and you're going to have another opportunity in the activities section to try another one of these fill in the charts let's review really quick what we've been given we've given a picture of a wave and each of these represents a pulse so let's go ahead and count those right now we have one two three four five six seven eight we have eight pulses occurring over one microsecond we're also given a zoomed in view of one of the pulses and we can see in there that there is one two three four cycles within that pulse looking at the chart then we're told that we are imaging to a max depth of 10 centimeters and that the frequency of this wave is five micro hertz so we have to figure out all the rest of this stuff well just looking through some of these we can figure them out very quickly we're told that this is traveling in soft tissue so we know our number for soft tissue and we can fill in our constant speed of 1.54 millimeters per microsecond also glancing down the list here number of cycles per pulse we counted that earlier so we can fill that value in as well looking at some of the other factors that we can fill in we know that prf is the number of pulses per second and in this case we already counted that we got eight pulses per one micro second which is the same as eight kilohertz so that's probably about all we can fill out just by kind of looking at things and not doing too many calculations so let's go ahead and start with period and kind of work our way down with the calculations using the formulas that we've learned starting with period we know that the period is the reciprocal of the frequency if the frequency is 5 megahertz then we just need to take 1 divided by 5 and that will give us a period of 0.2 microseconds next down on the list we have wavelength and we are told that this is traveling in soft tissue we have the frequency and we know that wavelength is equal to the speed of sound divided by the frequency in megahertz 1.54 millimeters per microsecond divided by 5 is going to give us a value of 0.31 millimeters so again we've been we've been working with these formulas we know how to do this we just have to take the time to figure out the pieces and plug our numbers in our next value down is the prp can just use the reciprocal of the prf so one divided by the eight kilohertz prf gives me a pulse repetition period of 0.125 milliseconds next on our list then we have pulse duration now pulse duration had a couple formulas for it we could do number of cycles divided by the frequency of the wave or we could do number of cycles multiplied by the period of the wave and we already calculated both of them we have the five megahertz and we have the 0.2 microseconds for ease i'm just going to do the number of cycles divided by the frequency so we will get 4 number of cycles divided by 5 the frequency and that is going to give us a value of 0.8 microseconds next on our list we have the spatial pulse length the number of cycles multiplied by the wavelength and we've already calculated the wavelength out and we've counted our cycles so we can simply plug in our numbers 4 for the number of cycles multiplied by the wavelength and 4 times 0.31 gives us a value of 1.24 millimeters now we just have one last parameter to calculate and that is the duty factor and duty factor is equal to the pulse duration divided by the pulse repetition period multiplied by 100 so we can present it as a percentage so pulse duration has already been calculated we did that at 0.8 microseconds and we've already calculated the pulse repetition period to be 0.125 milliseconds but like our example earlier in the lecture we can't have microseconds and milliseconds we have to convert one of them this time i'm going to go ahead and convert my pulse repetition period from milliseconds into microseconds so 0.125 milliseconds into microseconds equals 125 microseconds now we can take 0.8 and divide it by 125 microseconds and that is going to equal 0.0064 multiply that by 100 so we can get our percentage and our duty factor is going to be 0.64 i hope you're able to follow along it is a lot of math but we got to use all those formulas that we've been learning and now we're going to compare 10 centimeters max depth to 5 centimeters max step and see what happens so i copied all of our values into the first part of the chart and now we're going to work on the second part of the chart now i'm going to give you a little secret here the only values that could change based on depth are prf prp and duty factor all the other values are going to be exactly the same because they have no relationship to the depth of the machine this really shows us that it's important to understand the relationships between the different parameters so you can discuss how if one thing changes another might change or it might not change let's go ahead and finish up the chart by calculating our prf prp and duty factor instead of going through the math on all of these i'm going to show you another shortcut to finish out this chart remember that when we decrease our depth we are going to see an increase in prf a decrease impulse repetition period and an increase in our duty factor we have gone from 10 to 5 centimeters so 10 divided by five equals two we are decreasing by a factor of two so if we decrease the depth by a factor of two that means that prf is going to increase by a factor of 2 prp will decrease by a factor of 2 and duty factor will increase by a factor of 2. so we can take the values that we've already calculated and apply our factors eight kilohertz times two is sixteen kilohertz we've increased it by a factor of two one pulse repetition period has its factor applied instead of divided by two so 0.125 divided by 2 makes our pulse repetition period 0.0625 milliseconds and lastly for depth decrease by a factor of 2 duty factor is going to increase by a factor of 2 and 0.6 percent multiplied by 2 is 1.2 percent now as i mentioned at the top of the practice this is most likely way more math than you are ever going to need to do and i know that i kind of keep bringing this up that we are really diving into the math but my goal is to show you how that math affects the basics of physics so in my experience a lot of students think that they don't know how to do math or think that they're not comfortable with the math part of it but then when i show them the math the physics makes more sense and so if you are the type that wants to memorize this is why we always come back to our takeaways if you want to memorize this information that is completely up to you but my ultimate goal is to make sure that you also understand which is why i really like to show you the math behind the physics as well so the takeaways that i want you to get from practice number one we have parameters that do not change with depth that was basically what was happening in that we had depth set at 10 centimeters and then we changed it to 5 centimeters and the goal was to see what did not change with depth and what did change with depth and then how did it change parameters that do not change with depth are going to be our frequency period propagation speed wavelength number of cycles per pulse pulse duration and spatial pulse length those are not depth dependent features the ones that do change with depth are going to be prf prp and duty factor the next step that you need to look at is what happened when we change the depth so in our example we went from 10 centimeters to 5 centimeters or we decreased up by a factor of 2. remember that decreasing by a factor of 2 means to divide by 2. so when we decreased depth by a factor of 2 we saw prf increase by a factor of two we saw pulse repetition period decreased by a factor of two and we saw a duty factor increase by a factor of two now we not only are able to represent the relationships that we see between depth but also express how they are proportionally related as well as an example test question here i have a sonographer's imaging at 10 centimeters and increases the depth to 20 centimeters what happened to the pulse repetition period so this question is asking you do you understand how imaging depth affects the image and specifically how does it affect pulse repetition period your choices are doubled have stayed the same or that depth is not related to pulse repetition period and in this case the correct answer is doubled the depth doubled increased 10 centimeters to 20 centimeters so it increased by a factor of two and because depth and prp are directly related and proportional to one another we'll see that the prp also doubles in that case so the correct answer is a i know practice one was a little beefy but we do have one more practice and this is going to focus mostly on duty factor there's just two waveforms and you'll need to determine the duty factor based on the graphical representation of each pulsed wave go ahead and unpause when you're ready for the answers and here they are we have two waves that are being represented on these graphs the graphs have dashes on them to represent an equal unit of time and you've been asked to figure out what the duty factor is well the first one has no off time so we should immediately know that when there is zero off time that that is a one hundred percent duty factor there is no listening the fraction is one hundred percent it's always on the bottom one however is a little bit tricky remember that duty factor is pulse duration divided by the pulse repetition period so that's on time divided by the on and off time so in this example we have the on time here off time off time and the start of another pulse and why this is a little bit trickier for a lot of people is they want to look at these spaces in between they want to say there's four of them and somehow say that this is 25 duty factor but that's not true because remember pulse duration is the on time impulse repetition period is one unit of time two three units of time start of one pulse to the start of the other pulse is the definition of the pulse repetition period so we actually just kind of want to cover this one up get rid of it that's not part of figuring out duty factor we're only looking at the pulse duration and the prp which is on time and off time to the next pulse so we take the pulse duration which is a unit of one and divide it by one two three and we'll see that the duty factor of this example is 33 percent and that'll bring us to the end of unit four so make sure that you're going through the activities in the workbook and take a look through the nerd check make sure that you are familiar with what the questions are asking make sure that you know how to define all the parameters that we've talked about the units that they are represented in common symbols or abbreviations that they use formulas that are related with the parameters the relationships that those formulas represent and then what your impact is on that parameter can you adjust it where is it created if you can't adjust it what else is affecting it is it the machine is it the medium what affects it there are plenty of charts in the workbook and in your readings i suggest that you take a look through those those might be really helpful to organize all this information in a very digestible way