Transcript for:
Ultrasound Beam Anatomy

hi learners it's m from sano nerds and this video is going to be on beam anatomy unit 9 beam anatomy just as we discuss the anatomy of the transducer using a simple single element we'll use the single element transducer to discuss how an ultrasound beam looks in space note that this is going to be overly simplified for our initial discussion we'll add some more things to consider in regards to more modern transducers at the end of the unit for the time being though the following diagrams are all referring it to a single element transducer that is operating as a continuous wave a single element transducer is going to create a beam that changes shape as it moves away from the transducer it'll begin as the same size of the element and then start to converge to a natural focus and then in the far field it'll begin to diverge diverge means to widen which it'll do so indefinitely until it attenuates completely as we learn about the sound beam anatomy focus pun definitely intended on these few things we're going to look at the names of the areas that are within a sound beam so i want you to know any alternative names that come up with it and how all of these areas relate to one another you should also be able to describe the width of the beam at certain areas and then lastly we're going to really focus on relationships between diameter and divergence frequency and divergence diameter and focal depth and frequency and focal depth section 9.1 sound beam regions there are five regions that we're going to take a closer look at for the sound beam anatomy first we have our near zone that's going to be the part of the beam that's closest to the transducer before the focus our far zone then starts with the focus and extends away from the transducer and the focus is going to be where the beam is narrowest we also have the focal zone which extends equidistance into the near zone and into the far zone and then we'll also talk about the focal length which is the distance from the transducer to the focus let's go ahead and take a closer look at all five of these areas in a little bit more detail and talk about how they're all related to one another let's start with the near zone so the near zone is the very top of the beam the spot that is closest to the transducer and ends at the focus it has three names the near zone the near field and the fresnel zone so it is going to be this area starting from the transducer ending at the focal point where the beam becomes narrowest so the near zone is the near field and it's the area between the transducer and the focus the widest the near field will ever get is going to be equal to the diameter of the element now another term for diameter of the element is going to be the aperture and that often is abbreviated as d for diameter of the transducer so for example if you're given that the diameter of the element is five millimeters or the aperture is five millimeters then the widest that your zone is going to start it is five millimeters it cannot start any wider than what the crystal size is looking at these names as well near zone and near field are relatively common sense it's the part that's closest to the transducer fresnel zone might be a completely new and off-the-wall term for you just as a little preview to the far zone we are going to have another term similar to fresno zone farzone is the fraunhofer zone so for fresno zone i think of fresh that's the new this is the newest part of the beam the part that's coming directly out of the transducer that might help you to remember fresnel goes with near zone another thing you can try is the n e in fresno matches up with the n e in near next we're going to talk about the near zone length so we know that the near zone is this whole area from transducer to the focal point we also have an idea that there is a length in here too we want to know how far is it from the transducer to the focal point so the near zone length has three names as well focal length near zone length and focal depth so that should help to remind you that these are all length ideas millimeters centimeters some sort of length unit to describe where the focus is in comparison to the transducer face we consider this beam to be what we would call unfocus and that means that the element isn't curved there's no lens and there's no electronic pattern choosing where that focus is but because of physics the beam itself will naturally start to converge and get to a thinnest point and that thinnest point is our focus so again the near zone length or focal depth is the distance from the transducer face to the focal point or the narrowest part of the beam the near zone length can actually be calculated when we are working in soft tissue we know that the near zone length is going to be based on frequency and the transducer diameter if either diameter or frequency increase then what we are going to see is that near zone length is going to be deeper or is also going to increase in value and that is because of this formula so we have the near zone length in millimeters is equal to the diameter squared multiplied by the frequency in megahertz all divided by six and again this only works for soft tissue but the biggest thing that you need to take from this is that diameter and frequency are both directly related to the near zone length we're actually going to cover this in quite a bit detail in a couple sections moving forward then we have the focus so the focus has a bunch of names as well we can call it the focus or the focal point it is also known as the end of the near zone remember that was transducer to focus was near zone it's the beginning of the far zone and then we'll also see that it's the middle of the focal zone so not only can the focus be described as the thinnest part of the beam but we can describe it as the end of the near zone beginning of the far zone or the very middle of the focal zone so in regards to the focus we will see that the focus is where the beam is narrowest and we're also going to see that the focus is equal to half of the diameter so remember our crystal diameter was d half of the diameter is where that focus is at so again let's say that we had a 10 millimeter transducer diameter the beam coming out of that will at its narrowest become five millimeters because it is half of the diameter of the transducer crystal next up then we have the far zone so the far zone is going to start at the focus up until this point the beam has been converging it is going to get its smallest at the focus and it's going to start to diverge in the far field as you can see the far field also has three names so we have the far zone far field and fraunhofer zone so just like fresno we have kind of that interesting name the fraunhofer zone i've always thought of like off off in the distance so that makes me think of into the far field we also have the fra mix that up you can get far so fra far kind of go together as well so you'll want to know all of these other names for this portion of the beam so the narrowest that the far field will ever get is the focus it's going to start to diverge which means to widen out as it leaves the transducer further and further and we'll see that far field continue to diverge pretty consistently until it widens to the point that it's no longer useful for ultrasound or it will attenuate until it's no longer useful for ultrasound as far as measurements go in relation to the far field we know that at two near zone lengths the beam is going to diverge back to the size of the diameter of the element so remember we started out with d for diameter that is how big the transducer crystal is the beam comes out converges naturally to that half diameter and when we get to the focus that's our near zone length so transducer face to where it's half of the size of the diameter that's our near zone length once we go through another near zone length the beam will have diverged back to the same size as when it left the transducer then after this point it's just going to keep getting bigger and bigger and bigger so let's do another little example say we have a diameter of 12 millimeters and a near zone length of 5 millimeters so our diameter is 12 that means our focus is 6 and after we've gone five millimeters plus another five millimeters we will see that the beam again will have widened back up to that 12 millimeters so it goes from 12 converges to 6 diverges back to 12 and then continues beyond that 12 for the rest of the far zone near zone length will be equal on either side of the focus to tell us where that far field will meet up again with the diameter width now the amount of divergence that continues after this point is also dependent on the transducer diameter and the transducer frequency and we have another formula that goes along with that this one's a little bit more involved but we have the sine of the divergence angle is going to be equal to 1.85 divided by diameter multiplied by frequency so this formula is why we know that the diameter of the crystal and the frequency are going to be responsible for determining how much divergence occurs after the two near zone lengths so we will talk a little bit more about the relationship of how much divergence occurs in a couple sections so we're going to put this formula in our back pocket for the time being just remember that the far zone starts at the focus widens or diverges to the crystal diameter two near zone lengths into the beam and then after that it just keeps diverging our last section then is the focal zone so the focal zone is the area of the beam that is mostly narrow we can see that as the beam comes out of the transducer we're kind of wide up here starts to converge we're getting into a relatively narrow spot we get to our focus and it starts to diverge but we're still relatively narrow and it'll get to a point where it's just quite a bit wider so that focal zone again is where the beam is relatively narrow the focus is in the very very middle of it and the focal zone is going to extend equally into the near zone and into the far zone so say this is our focal point and the whole focal zone is four centimeters we're gonna see two centimeters into the near zone and two centimeters into the far zone because it is equidistance into either side of the focus clinically the focal zone is very important because this is where we're going to get some of our best detail resolution from our transducer anywhere that the beam is narrow is going to prove better for our lateral resolution so understanding that we have a relatively narrow area of the beam around the focus is important for where we decide to place our focus next up we have two practice problems in the workbook we have a 12 megahertz transducer that's eight millimeters wide and we have a six megahertz transducer that is also eight millimeters wide we're going to use the element width and the frequency to kind of discover a little bit more about the diameter the near zone length the focus the far field diameter and what happens in the far fart field make sure you try to work through your practice problems when you're ready come on back we'll go through the numbers and then also head to the board to do some of that math if you haven't already please make sure to go back and work through all these problems see if you can work through them before we go through the answers if you are ready to go though i will get to those answers so our first practice problem says that we have a beam that is created by a 12 megahertz transducer that has an eight millimeter wide element and we need to answer the following so the first question asks us what is the width of the beam as it exits the transducer so it wants to know what is d what is the near zone with right as it comes out of the transducer well that's eight millimeters because it equals the element diameter the next question asks us at what depth is the focus we are going to use our formula down here to determine that so diameter squared is 64 multiplied by the frequency of 12 all divided by 6 and we will see that the depth of the focus is going to be at 128 millimeters or 12.8 centimeters next question says how wide is the beam at the focus our answer is four millimeters because it is half of the diameter so if we started at eight up here half of the diameter is four millimeters next question asks us at what depth in the far field does the beam diameter equal eight millimeters well eight millimeters was our diameter and we know that if we get to two near zone links we should return to that eight millimeter width we already calculated that one near zone length was 128 millimeters because that is the depth that the focus is at so 128 plus 128 is 256. so the beam will return to 8 millimeters in width at 256 millimeters or 25.6 centimeters into the travel now this next question might be a little bit tricky so you might want to stick around for the math on this one but the focal zone starts at 9.8 centimeters into the beam where does it end we know that the focal zone is right centered around the focus so we should have equal distance into near zone and into the far zone so 9.8 centimeters is three centimeters into the near zone so that means it has to go three centimeters into the far zone if we started at 12.8 centimeters for the focus we just need to add three to that and we will get 15.8 centimeters into the far zone so the near zone starts at 9.8 and we'll end at 15.8 our last question then is what diameter is the beam at 30 centimeters this one might have thrown you off a little bit because there honestly isn't a good answer other than that it's just greater than eight millimeters we know at 25.6 centimeters we are back to eight millimeters the only thing we really know back here and the only thing you really need to know back here is that it's going to widen more than the diameter of the transducer after this point had this been a multiple choice and i gave you the options of six seven eight or nine the correct answer would have been nine because you just needed a number that's greater than the diameter or greater than eight millimeters in this case i'll go ahead and show you the answers then for our second one all the same questions just different numbers and really the only different numbers that we've dropped to a six megahertz transducer so same idea we've got the eight millimeter diameter plugging our numbers into our formula this time though we get a 64 millimeter near zone length or a depth of 64 millimeters or 6.4 centimeters of the focus the beam width is still four millimeters at this point the depth at which we get back to the eight millimeters is two near zone lengths so that's 64 multiplied by two which gives us 128 millimeters or 12.8 centimeters and same idea with the focal zone we are equal distance into near zone and far zone so if we start at 3.4 centimeters that means that we are three centimeters into the near zone so we need to go three centimeters into the far zone so our focal zone is going to end at 9.4 centimeters and then lastly same idea of the last question and the last slide asking what the diameter of the beam is at 15 centimeters that is beyond our 12.8 centimeters and so all we know is that it is going to be greater than 8 millimeters so i know i walked through that pretty quickly if you want to hang around and see the math of it we're going to go over to the board and go over how to calculate i'll draw a little bit more out for you so you can see the process and figuring all of these out if all the math makes sense to you please feel free to jump forward to section 9.2 all right welcome to the board we are going to walk through these practice examples with a little bit more drawing a little bit more math being shown out instead of just walking you through it verbally so our question here says a beam is created by a 12 megahertz transducer that has an 8 millimeter wide element so our transducer is 12 megahertz and our element is eight millimeters so d is going to be equal to that eight millimeters because the element width is the diameter that we're interested in and our first question says what is the width of the beam as it exits the transducer so this is a concept of the near zone that you just need to know you need to know that the widest the near zone will be is the diameter or the aperture of the element we were told that it's eight millimeters wide so that is the widest that this beam can be as it leaves the transducer so the correct answer is eight millimeters the next question is asking at what depth is the focus so the focus is right where the beam is becoming narrowest and we know that that is at the end of the near zone it is a near zone length away it's beginning of the far zone we have a few ways that we can refer to the focus but this formula down here is the near zone length and if the near zone ends at the focus then it makes sense that the near zone length is equal to the focal depth so we are going to use this formula to also calculate focal depth and remember that was a synonym for our near zone length as well by plugging in the numbers we are going to get 8 squared multiplied by 12 the frequency of the transducer we're going to divide all of that by six so we have 64 times 12 divided by six and we will get 128 millimeters or if it's easier to think of we can think of it in centimeters which is 12.8 centimeters next question down says then how wide is the beam at the focus and this is another concept that you need to know if our diameter starts at eight millimeters the thinnest this type of beam is going to get is one half of the diameter so we need to take this eight millimeters and divide it by two eight divided by 2 equals 4. so the width of the beam at the focus is half of the diameter and in this example is 4 millimeters the next question down asks us at what depth in the far field does the beam diameter equal the eight millimeters so remember we have eight millimeter diameter coming out we traveled 128 millimeters to our focal point the beam is going to diverge at the same rate that it converged so if we travel another 128 millimeters or another near zone length we should reach a width that is equal to the diameter so two near zone lengths is going to be equal to the diameter of the element so 128 plus 128 or 128 times 2 gives us 256 millimeters or 25.6 centimeters now the next question is a little tricky and this one says if the focal zone starts at 9.8 centimeters into the beam where does it end this is going to come back to understanding what the focal zone is and how it relates to other structures in the beam so remember our focus is in the center here it is the end of the near zone it is the beginning of the far zone and it's the middle of the focal zone so the focal zone needs to extend equally into the near zone and equally into the far zone we calculated that the focus is at 12.8 centimeters and the beginning of the focal zone in the near zone started at 9.8 centimeters so we have a difference of three centimeters from the beginning of the focal zone to the focus a key concept of the focal zone is that it extends equally into the near zone as it does the far zone so we want to know where does the focal zone end well if we've got three centimeters into the near zone then we need to have three centimeters into the far zone so we can take three and add it to 12.8 to get 15.8 centimeters so our focus is 12.8 centimeters in and our focal zone expands from 9.8 centimeters to 15.8 centimeters for that focal zone so that is our answer for this one so for calculating the focal zone make sure that you are understanding that the focus is at the very center of it if you had to calculate it it'll either give you a value of one side or it might give you a value of both sides had we said the focal zone is six centimeters where does it start where does it end you'd subtract three to get the start and add three to get the end because it's going to be equal distance into both near and far zones our last question then asks us what is the diameter at 30 centimeters the last diameter that we figured out in the far zone had us at 25.6 centimeters here and so now it's wanting to know what where are we at at 30 centimeters and this is going to be more of a conceptual answer versus a concrete discrete value and really all that we need to know is that that beam is going to keep diverging as it leaves the transducer and so all we need to know is that anything past two near zone lengths is just going to be bigger than the diameter so we know that at 30 centimeters the beam is just going to be more than eight millimeters in width as i had mentioned when i was kind of walking you through everything if we were to do this as a test question maybe answer a would be ten millimeters seven millimeters and five millimeters by logical reasoning if we know that anything past two near zone lengths has to be more than the diameter then the only one that fits that is our 10 millimeter option so a would be the correct answer for that one so either greater than the diameter if we're more than two near zone lengths away or choose the answer the numerical value that it's over the diameter of the crystal working through the second practice problem will probably be a little bit easier because we've already calculated a lot of stuff and we talked about a lot of the concepts that we need to get the right answers the only thing we've changed this time is that we are now working with a six megahertz transducer we still have an eight millimeter diameter which means our focus is four millimeters two near zone lengths away is eight and anything past that is going to be greater than eight so that was all things that we can get from just knowing the diameter of the transducer or the diameter aperture of the crystal so our first question says what's the beam as it exits well we know that's eight millimeters so we can write that in now this is going to be a new one that we need to calculate because we've changed our frequency and the near zone length is based on frequency and diameter so we're going to take our diameter again 8 squared multiplied by 6 our frequency and divide all of that by six eight squared is 64 multiplied by six and then divide by six is actually going to equal 64 millimeters or 6.4 centimeters so this distance is 64 millimeters and if that's linear zone length another near zone length distance then would be another 64 millimeter so we can label our diagram with that value now the next question down says how wide is the beam at the focus we already figured that out so we know that's four millimeters because it's half of the diameter next question at what depth in the far field does the beam diameter equal eight millimeters again so we know eight millimeters two near zone lengths so one two we should be back to our eight millimeters so to calculate that depth we need to multiply two times our near zone length and that is going to give us 128 millimeters so it's one near zone length plus another near zone length to get to where the beam depth is going to be equal to the diameter again next question down then says if the focal zone starts at 3.4 centimeters into the beam where does it end so again we know that the focus is at 6.4 centimeters into the body or 64 millimeters this is our focus we were told that the focal zone started at 3.4 and we know it should be equal into the far zone so if we are three centimeters this way then we need to go three centimeters the other way so we can take six point four plus three and that will give us the end of our focal zone at 9.4 centimeters in the far field so we're gonna see that focal zone being equal distance on either side of the focus three centimeters into the near zone three centimeters into the far zone and that will give us that 9.4 centimeters ending area and then our last question what diameter is the beam at 15 centimeters again we figured out that our near zone length is 128 millimeters or 12.8 centimeters into the body that was the last step that we were able to calculate the beam width for so now we know anything past 12.8 is just going to be greater than 8 millimeter section 9.2 focal depth in our 9.1 practice examples we had these two transducers we had 12 megahertz with eight millimeter diameter and we had a six megahertz with the eight millimeter diameter as well so the only things that are different between these two transducers are their frequencies when we plugged in our numbers to our near zone length formula to calculate the focal depth or the near zone length we got the 12 megahertz transducer showing a focal depth of 128 millimeters and the six megahertz transducer showing a focal depth of 64 millimeters so by using those numbers and using our formula we get to see one of our first relationships in action we can now see that frequency and focal depth are going to be directly related so in other words as frequency gets higher our focal depth gets deeper and if the frequency goes lower then our focal depth gets shallower and we know that again because of our formula we learned in our very first unit that when the numerator is compared to the quotient the numerator and the quotient are directly related and we can see that in our example as well our high frequency transducer has a deep focal depth the low frequency transducer has a shallow focal depth when this number increases this number should increase when this number decreases this number will decrease but frequency isn't the only thing on the numerator side we also have diameter so i bet you can already guess how diameter is related to near zone length as well but of course we're going to take a look at an example so i've got two new transducers here we've got a 10 megahertz nine millimeter diameter transducer and we have a 10 megahertz three millimeter diameter transducer so this time i've left the frequencies the same but the diameter of the crystals are different and just like when frequency increase near zone length increase we're going to see the same thing with diameter as diameter increases we will see the near zone length also increase so just by plugging in these numbers into our formula we'll see that the nine millimeter diameter calculates to a near zone length of 135 millimeters where the same frequency but three millimeter diameter calculates only to a 15 millimeter or 1.5 centimeter near zone length so from this example we can see again that diameter and focal depth are directly related again in other words if the diameter gets wider our focal depth will get deeper and if the diameter gets smaller then our focal depth gets shallower let's go back to that picture again real quick and we can see that nine millimeter diameter deep depth three millimeter diameter shallow depth diameter number value increases focal depth value increases diameter decreases focal depth value also should decrease i also want to point out because diameter squared is part of this relationship when the diameter changes the diameter is going to have a larger effect on the near zone length than just the frequency does on its own so our key takeaways from section 9.2 is that the focal depth is directly related to the frequency and the diameter of the transducer but that's not all that's related to the frequency in the diameter because now we have section 9.3 beam divergence remember back just a few slides ago when we were talking about the regions of the beam we were talking about the far zone i mentioned that in the far zone the beam is going to start to diverge after the focal point it'll just kind of keep diverging indefinitely but the rate at which it diverges or the angle that it diverges at is also dependent on the frequency and the diameter so here is our formula we see that the angle of divergence is going to be equal to 1.85 divided by diameter multiplied by frequency i'd be very surprised if you actually had to calculate the near zone length and i would be very very very surprised if you ever had to calculate the divergence angle it's just not going to happen so instead we are going to focus on the relationships that this formula tells us so we know from this formula that diameter and divergence are inversely related and that frequency and divergence are inversely related and we know that because of our formula we've got diameter and frequency both in the denominator position so they are going to be inversely related to our quotient the idea of beam divergence though is super important for the sonographer and that's because if we choose lower frequency transducers that's going to cause our beam to widen more in that far field and when we have a wider far field we are affecting our lateral resolution the beam width is going to have a direct relationship to the lateral resolution of the image now we're going to talk about lateral resolution in quite a bit more detail in the next unit but why lateral resolution is important and why we are concerned about how wide the beam gets is because first off we know that the focus in the focal zone should be placed just at the area of interest or just below it and that's because the beam is narrowest here that thin beam improves our lateral resolution a lot and that's really what we want we want good detail in our images the second problem though is that when we have that diverging far field it's going to diverge to a point where it's going to really affect our lateral resolution the beam is just going to be too wide to recognize small structures and image them appropriately so when we choose high frequency transducers we're going to have less divergence which means that that is going to give us better detail with that high frequency transducer going to a low frequency transducer we learned helps us with penetration the attenuation is much much less than a high frequency but then we have the trade-off of losing detail in our images in that far field i told you we wouldn't be doing any math with that formula i did all the math for you i just want to show you some examples plugging in some numbers and looking at some diagrams so now i've got two transducers they are both four millimeters in diameter we're going to look at the frequency change first so we have a five megahertz transducer and a one megahertz transducer i went through and calculated out the near zone lengths again just to kind of prove that our low frequency has a shallow near zone length high frequency has a deep near zone length but this time we really want to focus on what's happening in that far field how is the beam diverging so we see with our 5 megahertz transducer if we plug all our numbers in use our calculator use our charts we will see a 5 degree divergence that means that instead of continuing straight through here it angles out just at five degrees and will keep going in that direction so five degrees hardly anything look at our one megahertz though when we plug all those numbers in we're going to get a 27 degree divergence so instead of coming down and going straight which would be zero degrees it's taking a turn at 27 degrees and will continue expanding out at that 27 degree angle so the larger the angle the more divergence that is occurring so from these examples we can see that frequency and beam divergence are inversely related when the frequency gets higher there will be less divergence frequency gets lower there's going to be more divergence and in true fashion of course we got to flip it around because diameter is also related to divergence so we're going to take a look at these 2 megahertz transducers but change the diameters around so our first one is eight millimeter diameter a large wide aperture and then we have a two millimeter diameter or aperture now again i went through and calculated out our near zone lengths based on these diameters we can see that we have small diameter shallow near zone length large diameter deep near zone length but again we're focusing on our divergence this time so let's take a look at what it means for how the beam looks in the far field so now we see that our eight millimeter diameter has barely even expanded out because once we plug all those numbers in we'll see a six degree divergence angle compare that to our two millimeter diameter which also happens to produce a 27 degree angle of divergence so remember it's coming down here if there was zero divergence at this point the beam would just keep heading straight forward but at this point it turns at 27 degrees and keeps widening beyond that point so now from these examples we can see again that beam diameter and beam divergence are inversely related so as the beam diameter gets wider less diversions will occur if the diameter gets smaller then we're going to see more divergence section 9.4 let's go ahead and review these two concepts in conjunction with one another so remember first and foremost frequency and diameter are related to the focal depth and the beam divergence let's focus on our increased numbers so our up arrows our high frequencies and are wide diameters high frequency and wide diameters are going to affect the focal depth and the beam divergence in the same way so high frequency wide diameter we're going to see deep focuses with that then we also see less divergence so increased frequency increased diameter means an increase in the focal depth and a decrease in the divergence let's take a look then at our smaller numbers our down arrows so if we have low frequencies or small diameter transducers we're going to see shallow focuses with more divergence so as we decrease the frequency decrease the diameter we're going to see a decreased value of our focus so shallow focus and then we're going to see more diversions or increase in the far field and this is the picture that you have in your workbook kind of showing you the relationships of all of them so if you're still looking at this and thinking i just need another way to think about this let me show you another thought that i had about this we know that diameter and frequency are both going to be determining factors of the near zone length and divergence now what i thought was kind of cool when i was going through all this and thinking it through i saw that near zone length and near zone length has diameter and frequency in the numerator position and we know from unit 1 that the numerator is going to be directly related to the quotient so near zone length numerator position directly related to the quotient so as diameter and frequency increase we'll see that near zone length also increase the other thing that i thought was kind of cool is that the near zone length sits above where we would look at divergence so the near zone is a kind of the numerator of the beam so it sits higher than the divergence but then the really cool thing was that divergence also kind of helped out in this too so we have divergence and denominator so now we move diameter and frequency into the denominator position when we're talking about divergence and we know that when we have denominator and quotient relationships that they are inversely related so if you can remember near zone numerator and then remember that giant rule that i taught you right in the beginning numerators and quotients are directly related that's all you need to know you really just need to know the relationships same idea with divergence if you can remember divergence denominator then you know that they are going to be inversely related to the divergence of the angle and that might help you to kind of work through the values and draw all the arrows out again should you be asked a question about these relationships so speaking of questions about those relationships that's going to be our practice we are going to pause here go through the practice part and try to figure out which transducer in the comparisons have more divergence less divergence deeper depth or shallow depth unpause and we'll go through those answers all right again just a reminder make sure that you've tried these practice examples but let's go ahead and go through those answers so the first question says which transducer will have a deeper focus we have two examples one with diameter comparison and one with frequency comparison so we'll just kind of go down through each one so which transducer has the deeper focus when we're looking at diameter we know that deep focus goes along with wide diameter big diameter deep focus so that is going to be our 19 millimeter transducer as far as frequency goes we know that increased frequency provides an increased or deeper focus so that's going to be our 12 megahertz transducer now the next question down says which transducer will have a shallower focal point so we're using some of our synonyms in here as well so focal point is the same as the focus we're also using aperture in this example as well remember diameter and aperture are the same thing so shallow focal points are going to go along with narrow or small apertures so our correct answer is our 13 millimeter transducer next one down is comparing a 1 megahertz or 4 megahertz low frequencies equal shallow focal points so you should have selected your one megahertz next question down asks us which transducer beam will diverge more so which will have more divergence and we know that frequency and diameter are inversely related to our divergences so when we have more divergence we're looking at lower values in our numbers so six millimeters versus three millimeters it should be our three millimeter low numerical value will have a high divergence value same idea with frequency low frequency value is going to result in a high divergence value or that divergence angle that we were talking about and then our last question which transducer beam will diverge less so again frequency and diameter are inversely related so we're looking for the numbers that are higher out of the pairs so the 33 millimeter diameter is going to diverge less than the 23 millimeter diameter because it is a higher value a higher number and the 17 megahertz transducer is also going to diverge less compared to the 10 megahertz transducer increase your frequency will decrease your divergence inversely related now this last question is probably something that's going to be more similar to what you might have on a test you might be given some frequencies of transducers and some different diameters and then this question asks us which transducer will have the best lateral resolution in the fraunhofer zone so we learned that the frownhoffer zone is the far field and then we also learned that lateral resolution is best when the beam is narrow so we are looking for a combination of frequency and diameter that is going to give us the best chance of having the least amount of divergence in that far field and because we are inversely related we're looking for our biggest frequency and our biggest diameter to create the transducer that will have the best lateral resolution in the far own hopper or far field so in this example our 12 megahertz transducer at the 10 millimeter diameter is the best option it's got the highest frequency out of everything and it has the largest diameter section 9.5 clinical discussion so up until this point we really needed to simplify the beam shape to discuss some of the key features of the beam and learn how it acts in space but for our modern clinical ultrasound the physics is a lot more complex so i've created kind of a q a to think a little bit more about what's happening in space with our beam and kind of start thinking about how this clinically applies to what you're going to be doing day in and day out with your ultrasound machine i know when i was a student one of the things i was kind of confused about when we were learning about the beam shape and how everything looks is i was thinking well i have a knob on my machine that says focus and i can move that around and i can change where the focus is has that been what we're talking about well the answer for this one is actually no the beams that we've been talking about in this unit so far we consider to be unfocused meaning they don't have anything that's going to cause them to focus like a lens or curved elements or electronic focusing and i'm sure you're not surprised by any of this we're going to learn about those very soon but what we are talking about with these beams is that they do have a natural focus and that's because of two things first we're creating diffracted wavelets from the transducer and then hoijin's principle is at play as well so when the pzt crystal is created they can be made very very small or we might make them a little bit bigger but within that bigger pct crystal there are going to be very small sound producing points it's not that the whole crystal just creates a sound beam that there are these tiny little spaces within the pct crystal that are actually going to produce the sound beam or the pressure wave out of the pct crystal when sound comes out of a very very tiny area it takes on more of a v-shaped wave so we have this example here we can see the pressure you know pressure changes are happening on the pct crystal this tiny little crystal is creating this v-shaped wave so these are v-shaped waves also known as poisons wavelets and this v shape that we get out of here is the diffraction so if you know we have this pressure kind of coming through as a wide point once it hits this very small structure it diffracts and creates these tiny little wavelets so we are either creating tiny little wavelets out of single small pct crystals or we're creating lots of little points of sound in a larger crystal and what ends up happening is those tiny little wavelets are all going to come out and they're all going to interfere with one another and that's where huejian's principle comes in huygens principle tells us that as these waves interact they're going to interfere both constructively and destructively and what's going to result is that natural focus or hourglass shape to the beam so a completely unfocused pct crystal will have a natural focus the problem is is that that focus isn't always where we want it so we have discovered if we introduce lenses curved elements or electronic focusing we have more control of where that focus is another thing that may have crossed your mind while we were talking about frequencies and focal depth and divergence is that high frequencies have those deep focal depths and you might be thinking to yourself but we use high frequency transducers to image shallow so shouldn't they have a shallow depth and yeah that might be what you would think at first but we learned in this unit that the physics tells us that that higher frequency has a deeper focal point and less divergence but we also learned that those high frequency transducers are going to attenuate really quickly too so a lot of times they're going to attenuate before we get any meaningful information from their deep focal points but on top of that there's more physics that tells us that that small diameter is going to have a bigger effect on that near zone length than the frequency will so if we can make high frequency crystals that are very tiny that's going to bring that focus up and make it more shallow so knowing this when manufacturers make the transducers those high frequency transducers are going to be made with tinier crystals to bring that focus up to a more useful depth so just as an example one of our highest frequencies that we use in medical ultrasound is 17 megahertz if we had a transducer with an eight millimeter aperture on that it would have a focal depth of 18 centimeters that 17 megahertz transducer is going to be gone long before 18 centimeters so instead we can turn that around and make it a 17 megahertz transducer with a one millimeter aperture now we're looking at a transducer that only has a 2.8 centimeter focal deck and that is going to be more conducive to using that high frequency for those superficial shallow structures at the beginning of the lecture i mentioned that we're going to look at diagrams as if these are all single element continuous wave transducers and now you might be wondering well what does a post wave transducer beam look like and to be honest it's really not that much different it's just a matter of where the beam is in space compared to that pulse so if we look at these two images the one on the left is our continuous wave it's just always there it's always getting electrical voltage making a sound wave beams coming out constantly on our pulse waves that electrical voltage comes down interacts with the pct crystal and a quick short pulse is sent out but that pulse has to travel in space over time that's how we get that hourglass shape it has to move out of the crystal through the near zone to the focus and then into the far field and that'll happen but it happens over time and because the pulse stops the beam will also stop and then it has to kind of reproduce that traveling again where on the continuous wave it's just always constantly making that near zone focus and far zone so every time a pulse comes through near zone focus and far zone have to be created it'll be created over time and then we wait for echoes to come back beam is created over time again wait for echoes to come back remember we talked about the idea of pulse duration where we have that period of time of creating the pulse going out and then we have our pulse repetition period which is the time creation plus the waiting time so same shape just a difference of waiting for the whole pulse to be created now this may not have been something that you were considering but it is at least worth mentioning because this is going to have actually a very large clinical impact on you as a sonographer so is the intensity the same all the way through the beam so the giants that we've been using so far show the beam narrowing at its natural focus and it would make sense that as the beam narrows we are going to see more intensity because if you remember back to your intensity formula intensity is equal to the power over area squared so if we're reducing that area or the width of the beam we are going to see an increase in the intensity so for the most part we will always say that the focus the narrowest part of the beam is the most intense part of the beam however it gets a little bit more complex than that when we are actually using the beam in soft tissue or in a medium that's going to cause attenuation so again all the images that we've been using are not taking attenuation into account so we're acting as if they could just go on and on and on forever but that's not true in the clinical setting the beam comes in it's going to lose some of that power because of attenuation but it's also going to gain some of that power because of narrowing so there's a fine balance of losing intensity and increasing intensity based on how far the beam has traveled and the width of the beam so in reality what we see is the strongest point is actually just above the focus and that is because attenuation hasn't quite gotten to the point of reducing that intensity to counteract the amount of narrowing that will occur at the focus so again if we think about it we've got the sound coming out of the transducer it's attenuating along this line so it is getting weaker as we go through so this part of the beam attenuation-wise is stronger than this part of the beam but the second factor that we need to look at then is what's happening to the area we have more area up here compared to the less area down here so now for just looking at area we've got less intensity here because of the larger area compared to the intensity with the narrow area at the focus so again attenuation wise more intensity less intensity being widthwise less intensity more intensity combining these two thoughts together then tells us that right above the focus ends up being the most intense part because we still aren't attenuating all the way through this area but we are still experiencing a reduction in area and this idea is actually very clinically significant because we often will tell you as instructors that you should place your focus at or below the area of interest so over here we have our focal zone on a machine if you have this little eye bar shape cursor on the side this usually represents a focal zone if you just have like a little arrow here and not the spacer that usually represents a focal point so the machine is showing us a focal zone here with the focal point in the middle of it and when we are using a transducer and an ultrasound system that allows for focal point movement we will want to take this and move it just at or just below the area of interest so we can utilize that intensity and the narrowness to provide the best image because our stronger beam is going to return better echoes and that narrow beam is going to provide better lateral resolution which helps with our detail the concept of the focus and lateral resolution we're going to talk a lot more about in the next unit when we get into our resolutions but this is a nice kind of little precursor about why we need to think about how that beam is changing in space and the intensity within that beam remember in this unit we have been talking about single element transducers creating one continuous wave beam now we know that continuous wave beams cannot create images but we did just kind of get done talking about how pulse wave beams look very similar to our continuous wave beams and we know that our pulse wave beams do create images i think it's easy for students to kind of look at how quickly our pictures are made and how seamless it seems and think that maybe just that one beam coming out of the transducer is creating the whole entire image but that's not true what ends up happening is that one beam is going to create one scan line and then we put a ton of scan lines together to create the full frame or image this is also a great opportunity to point out that our modern transducers have multiple pct crystals not just the one crystal that we've been talking about so far so as we learn about transducers we're going to start to learn more about how the pzt crystals work together to create a beam or a scan line and then we'll learn more about how the machine creates each scan line to create a full frame and it's just amazing how quickly the machine can do that and make it look like a seamless movie to our eyes so there's lots more to come on the image creation and the beams and the pzt crystals all working together this is a great jumping off point of taking that knowledge of the single element transducers and now we're going to see how to apply them to our multi-element transducers that we use currently and that brings us to the end of unit 9 bm anatomy so make sure to head back to your workbook and work through some of those activities that we have in the back review the nerd check questions again those are open-ended questions that you can use to test your knowledge and recall the information that i presented in this unit remember we had some big formulas in this unit but it's the relationships that we can pull from those formulas that are going to be ultimately what you need to know and just like the transducer anatomy be prepared to be able to label anatomy and talk about each region and how they are related to one another