hello everybody and welcome back today I want to show you how we can generate these two seemingly very different images from the same data set that we've acquired during one single CT acquisition specifically I want to introduce the concept of postprocessing how we can take each and every pixel within this image and allocate a numerical value to that pixel that value is what's known as a CT number or a houndsfield unit and I'm going to show you how we go about calculating those houndsfield units we then can take the houndsfield units for each and every pixel in in this image and match those units to a grayscale value the matching process allows us to turn a numerical data set into an image that we can actually interpret and the grayscale value the way in which we match that grayscale to specific hfield units is what's known as windowing and I'm going to show you how manipulating that grayscale window can make these different images here now before we've gone about postprocessing and making these images a couple of steps have to have occurred before this process and I want to touch on those now those steps are what we're going to concentrate on after we've gone through this talk now we know that in this specific slice we're looking at a brain here a 3D model of the brain we're looking at a specific axial slice a volume of tissue within the patient this 2D image that we're seeing on our screen represents a volume a 3D Volume through the brain and each pixel corresponds to a specific voxel a volume element in the patient now we know in order to acquire the data for this specific slice the CT machine has to rotate at least 360 degrees around the patient and generate different projections and it's the data that we are reading through the detectors here that we're going to use to mathematically calculate the image here now when the CT machine is acquiring the data it's getting an analog signal that needs to be converted into a digital signal and then we need to pre-process some of that data we've talked about interpolation we might want to account for faulty detectors there's a lot of pre-processing that happens that then gives us raw data that raw data can be reconstructed and it's that reconstructed data that we're going to use to ultimately convert into houndsfield units and that process of reconstruction is going to be the topic of the next three talks now there two key data measures that the C machine needs to acquire we've talked about transmitted x-rays x-rays that have passed through the patient been attenuated as they pass through the patient and then hit our detectors we also need a reference intensity of the X-ray beam what is the intensity that we are projecting towards our patient and we can measure that on detected where that x-ray beam hasn't passed through a patient and it's the difference in the intensity that we're projecting towards the patient and the intensity that's actually being measured on our detectors that's going to help us determine the degree of attenuation as x-rays are passing through a specific line through the patient let's look at specific voxels here we've got a red voxel here that's on the insul cortex we can see it here in alati and we can see a separate purple vole here that's going to be in the white matter of the forceps minor here let's look at the this specific slice here and I'm going to look at this pixel here the purple pixel ultimately we need to figure out how much attenuation of the X-ray was due to the tissue within that specific voxel here and that process occurs during Reconstruction let's take a fictitious example here where we've only got this voxal of tissue with x-rays passing through it it hasn't passed through tissue beforehand and it hasn't passed through tissue afterwards the incident x-rays will hit this specific voxel and then head off towards our detector in this example say we've got 100 x-ray photons all of the same energy then hitting Al Vox of tissue a degree of attenuation is going to occur and that attenuation is either through the photo El electric effect or it's through scatter scattered x-rays aren't going to reach that detector in that line of the x-rays and that scatter can be Compton or R scatter a certain fraction of those x-rays will be attenuated and the rest will be transmitted in this example 10% of the photons have been attenuated the fraction of attenuation for a monochromatic beam over a known distance is what's known as the linear attenuation coefficient the linear attenuation coefficient is represented by this sign mu here I put a subscript P because we're talking about the purple pixel in our example so the linear attenuation coefficient tells us what fraction of these x-rays will be removed from a monoenergetic beam over a known distance so we know the pixel width here now the linear attenuation takes the combination of both the attenuation due to the the photoelectric effect the compon scatter and ra scatter we add up all that attenuation to get this linear attenuation coefficient value now the linear attenuation coefficient is dependent on a couple of things the first it's dependent on the energy of the X-ray beam that's heading towards our tissue higher energies will result in less attenuation it's more likely that x-rays will pass through that tissue because of those higher energies we've looked at the likelihood of the photoelectric effect it drops off rapidly as we increase incident x-ray energy so an increase in incident x-ray energy is going to result in a decrease in the linear attenuation coefficient in this tissue despite the tissue remaining the same it's also dependent on the density of the tissue here the more atoms that we have per cubic cimer the more likelihood there is going to be of having photoelectric or compon scatter interactions the same goes with the atomic number of the tissue the higher the atomic number of the tissue or the material the more likely there's going to be attenuation if we take iated contrast for instance that's got a much higher atomic number than the average atomic number of tissue and the last factor that is dependent on is electron density now when we're looking at tissues and CT Imaging this doesn't actually come into play as much as it would say in experimental studies the tissue density and the atomic number of the tissue play a large role in what linear attenuation coefficient is going to be ascribed to each pixel or each voxel within our image if we were to look at our red pixel for example here that attenuation could be different even even though we've got the same monochromatic x-ray beam heading towards that tissue that's based on the different tissue density and different atomic number of that tissue here we've got 20% of the X-ray photons being removed now we know that attenuation is not happening in a single Pixel it's happening in multiple pixels more specifically happening in multiple adjacent voxels as those x-rays are passing through the patient let's look at this example here and I want to show you why the term linear here can be quite confusing in this example after the x-rays have traveled a set distance here we've lost 20 x-rays or 20% of the X-ray photons here if we were to place the exact same voxal of tissue here adjacent to our previous voxal we will get a 20% reduction in the intensity of the X-ray photons here but the absolute number difference is now 16 not 20 we can repeat this process by placing the same voxel adjacent to the next voxel and you'll see that each time that voxal of tissue is attenuating the X-ray Beam by 20% but our absolute number of X-ray photons that are being reduced is smaller and smaller as we move on here we're getting a reduction at 13 x-ray photons and 10 x-ray photons and we can see that represented on the graph here this graph is showing us how the absolute number of X-ray photons as they're passing through a set volume of tissue reduces in an exponential fashion or negative exponential fashion rather than a linear fashion the the linear part here means that the fraction removed is the same now we can represent this Photon loss using this formula here n not here with the subscript note is the X-ray intensity or the number of X-ray photons that are being released from the anode of the CT machine heading towards our patient and here is the intensity or number of X-ray photons that are actually measured by our detector this part of the equation here is showing us what fraction of these incident protons are being removed from the beam and that will allow us to see what the remainder that is being transmitted towards our detector the linear attenuation as that increases it's going to decrease the value of this fraction we're going to get a smaller percentage of xray photons being transmitted through the same with increasing the distance the further we travel through a tissue the more attenuation there's going to be ultimately the number of X-ray photons reaching our detector is going to be lower so in this example I can calculate a linear attenuation coefficient for these specific voxul of tissue this is assuming that these are 1 cm wide it's just easy for my calculations here now importantly we can take this exact same voxal of tissue it's got the same tissue density and it's got the same average atomic number but we can change the linear attenuation coefficient by reducing or increasing the incident x-ray Photon energy if we were to send a much lower intensity beam towards these voxel here we could get a linear attenuation coefficient that's much different for the the same tissue that difference here is purely based on the differences in photon energy with lower Photon energies we're much more likely to get the photo electric effect specifically but also more likely to get Compton and ra scatter and that results in more x-rays being removed from the beam in this example we're getting 50% of the x-rays being removed through each volume of tissue here now importantly when we're looking at clinical examples we haven't got the same voxal of tissue adjacent to one another we've got multiple voxul of tissues all with differing tissues differing tissue densities and different average atomic numbers so we're passing through a volume of tissue with adjacent voxels here and we know that this volume of tissue ideally will be within the field of view of our CT machine we talked about how we calculate that field of view we' got x-rays of a certain intensity reaching that volume of tissue and then exiting towards our detector now these linear attenuation coefficients of adjacent voxal are different from one another and we need to manipulate this formula because now we don't have a single linear tenation coefficient but we've got multiple linear tenation coefficients now this is a known value we know the incident x-ray intensity and we know the transmitted x-ray intensity that's being detected by our detectors we also know this distance here the field of view that we've calculated before this is the distance that we're trying to accurately calculate linear attenuation coefficient values for and this we can represent by the term X here x being the width of each individual voxal that we're trying to calculate and N being the number of voxal within that total width so we can now rewrite this equation like this we know these values here we know the pixel width and now we can add up all these linear attenuation coefficients we can rearrange this formula I don't want to get too much into it but here we've rearranged the formula and we've got our variables on one side of the formula and we've got our known values on the other side of the for formula this is going to be a numerical value that we can actually use to reconstruct these images the goal of reconstruction is again to make multiple simultaneous equations from all the different projections that we've generated around 360° around the patient and then solve for these variables using the simultaneous equations now for now I'm not going to talk about how we go about solving those variables but say that we can say that for each voxel within our image we can accurately calculate the linear attenuation coefficient in that voxel I'm going to show you some examples here now remember these linear generation coefficients are specific for the scan that we're doing specific for the energy of the beam that we're sending towards our patient if that energy of the beam the average energy of the beam were to change these linear attenuation values will change also it's important to note that these linear attenuation values not going to be the same for all fat within the body visceral fats or subcutaneous fats are going to have different densities and between patients we're going to get different densities we know that people have different bone densities depending on their age or depending on their sex so these are just just examples here you don't need to learn these here now what if we take these linear attenuation coefficient values we've made an array say a 512 by 512 pixel array and we've placed the linear attenuation coefficient in each one of these pixels can't we then convert those to a gray scale and make an image well let's do that let's get a gray scale from black to white here and all the Grays in between we make our lowest linear attenuation coefficient air we make that black and we make our highest bone we make that white if we were to place all of these these tissues here on the scale that' all be very close to one another the difference between fat and between uh gray matter sorry this is white matter and gray matter is only 0.022 here there's a problem when it comes to the scale if we were to try and generate this image it would end up looking like this very little useful clinical information here our bone is all blown out we haven't got much differentiation in our bone we can't see the outer table or the inner table of the skull bone here we can't even see the sutures we've got no useful information there and we can't tell really anything about the gray and white matter that's sitting within the cerebrum here there's another issue here is that the difference between the linear attenuation coefficient of air and compared to say water is about a thousandfold difference it's a thousandfold difference here the difference between water and bone is about a 2 and 1/2 fold difference so the scale is all off here but that's not our biggest issue here the biggest issue when it comes to using linear attenuation coefficient values and translating them directly into an image is that these values are going to change depending on the X-ray intensities that are incident on the patient I've said that a couple of times now now why is that important well the linear attenuation value change is different for different tissues in bone we get a lot more photoelectric effect than we do in say soft tissue so if we increase x-ray intensities we're going to get a rapid drop off in attenuation through bone and that's not proportional to the drop off in attenuation in soft tissue what we want to do is somehow stand standardize these values to a single value and that's exactly what we're going to do so we're going to change the scale and we're going to standardize these values how do we go about doing that well we want to convert linear tenation coefficient values into C numbers or houndsfield units now in order to convert these numbers we use this formula here and it's simple if you go through it the houndsfield unit for a specific voxal of tissue we take the calculated linear attenuation coefficient of that voxel and we subtract the linear attenu coefficient of water dividing that value by the linear tenation coefficient of water what this does is it standardizes the linear attenuation to water so everything is in reference to water now why is this important well we can do an experiment where we place water within the CT machine and we measure the attenuation values now we've got a reference value it's a way of calibrating our CT machine we can then take the calculated value here say of white matter and enter it into this formula getting a hfield unit value if we were to only use this part of the formula we would again be dealing with decimals to the third or fourth decimal place and that's why we multiply this by a constant we multiply it by a thousand so we're dealing with whole numbers here it's much more usable it's much more user friendly that's the value of this constant here we standardize that linear attenuation to water now what if there was water in that voxal itself well water's linear attenuation will be the same here the top our numerator of this equation would be zero our hounds field unit for water will always be zero now that's really handy because anything that has a positive Hound field unit value is going to be more attenuating than water and everything that has a negative houndsfield unit value is going to be less attenuating than water so we've got a standard Point water's houndsfield unit value is always going to be zero we can then plot those hfield unit values on a scale now remember if the X-ray intens changes water's houndsfield unit value is not going to change the houndsfield unit values for the other tissues are going to change ever so slightly less drastically than our linear attenuation coefficients because we've now referenced them or standardized them to water air is also a value that changes very minimally because Air's linear attenuation is so low this here this part of the equation is very close to minus one okay so now we've converted our linear attenuation coefficient values into CT numbers or Hound field units you can see these round numbers they're much easier to deal with than these multiple decimals here and we can see that the changing of houndsfield units just a couple of houndsfield units is going to represent a very small change in the actual density or linear attenuation coefficient here and that small change we can link to a grayscale value and see those differences so let's try and do that let's bracket the tissues that we actually want to see in our image let's go from air to Bone now importantly if you used the bone calculation here you're going to get a value that's higher than th000 I've just used a th000 here because that's of a often a reference standard for bone and remember these are always going to change these linear tenation coefficient values we also want to set a midpoint what's the middle of that range that we've selected here and the middle of this range is going to be zero you'll see why that becomes important later and let's apply a grayscale value to these Hound field units now the process of applying this grayscale value to the Hound field units is what's known as windowing windowing is what's going to manipulate or postprocess our image there's two key points when it comes to windowing the first is what's known as window width what's the range of hfield units that we want to represent within our image within the grayscale part of our image the second is what's known as window level what's the midpoint of that window width that we've selected here the example zero now we can take those houndsfield units that we have in an array of our image and convert them to actual grayscale values that we display on the screen and generates our image here again this image is slightly better we can see some more contrast within the bone here but there's still very little contrast within the cerebrum here now what happens if we want to see the differences in the cerebrum what if we want to see where the CSF is in relation to the brain or what if we want to see differences between white matter and gray matter we're going to need to change this window now why do we need to change this window can't we zoom in here and maybe click on it and see what the differences are while the human eye can only really interpret 30 to 50 Shades of Gray different and here we're dealing in an 8bit system with 256 different Shades of Gray 256 Shades of Gray spread out over 2,000 houndsfield units only every seven or eight houndsfield units are we going to get a change in a shade of gray and we can see here that these houndsfield units are very close to each other the human eye is not going to be able to interpret these differences so to get around this what we do is we narrow our window we want the contrast to occur over a smaller range of houndsfield units this comes at a compromise though everything in this example above 80 hfield units is going to appear white in our image everything below zero hfield units is going to appear black fat and air are going to look exactly the same they're going to be black water is going to be black now what's happened to our window width and our window level our window width now is 80 Hound field units and our window level is going to be 40 Hound field unit you can see how the level describes where we are along this scale and the width describes how wide wide we are covering how many hfield units we're covering this is what's known as a brain window and look what happens to our image when we apply that brain window there's a drastic difference now let's look at what's actually happened our bone has been blown out it's white we can't tell the difference between the outer table and the inner table and the spongy bone between them we've got much more contrast detail between our white matter and our gray matter because of this narrowed down window look at the difference in the grayscale values even between such small changes in houndsfield units the fat we can no longer see the subcutaneous fat here look how it just looks like the patient's head ends in bone and then it just goes out to air if you look at our previous image you can see that subcutaneous fat there because fat was included in our grayscale it's now no longer included we can still see the temporalis muscle because that's sitting within the soundfield unit uh window here and depending on the clinical question we're trying to ask we can change this window in multiple different ways in the abdomen we're going to be using very different Windows to what we're using in the brain now in the question bank that I'll link below this talk I'm going to leave for you reference slides showing the different window that we use and I'm going to link these cases so you can play around with the window yourself this window that I've changed to now you see we've got a wider window everything below 400 is going to be black our window width is now 1,400 and our window level is going to be 300 700 above 700 below look what that does to our image we've now created a bone window CT we want to keep air black because it's important in bone window CT to see if we've got numac Cranium we want to be able to see air within the cranium if we've got fractures within the bone see how we can see the sutures now better we can see the landroid suture here so the window allows us to answer different questions allows us to get contrast in the tissues that we're interested in so hopefully you can see how we go from that raw data acquisition there's some form of calculation that happens that it gives us linear attenuation coefficient values and we now know what those linear attenuation coefficient values rep present we also know how to convert those using this formula here into C numbers or houndsfield units say the same thing we can then take those Hound houndsfield units place them on a scale and then put a gray scale that matches those houndsfield units and where we place those gray scales and how wide that gray scale is is what's known as winding and will manipulate our image now why have I talked about this prior to talking about the pre-processing and the Reconstruction well the calculations that going to actually figuring out what the linear attenuation coefficient in a voxal is is a little bit more complicated than I may have suggested in theory the answer seems simple we generate multiple attenuation data points from different angles around the patient we got projection data from all those different angles and then we back calculate we calculate those simultaneous equations we figure out those unknown variables and then we use those to do what we've done in this talk it's a little bit more difficult than that in practice this was the example that we looked at first now they two key differences in real life we don't create a monoenergetic beam say this one that we were looking at all those x-ray photons had the same energy we create a poly chromatic a polyenergetic beam that has an average intensity this is the quality of the X-ray beam the number of photons in the X-ray beam is the quantity of the X-ray beam now if our linear tenation coefficient was the same as what we looked at before we would see that we' get 80 photons coming through but what's happened here we preferentially attenuated lower energy x-rays we know that attenuation happens more at lower energies therefore the average energy of our beam has increased if we were to place another voxel of tissue here what's changed the average energy has changed we know that with higher incident x-ray energies we're going to get a lower linear attenuation coefficient we're going to reduce the fraction of x-rays that we are removing from this beam the beam then as a result has a higher x-ray energy a higher average energy and as this process continues we proportionately remove a smaller and smaller fraction of x-rays whilst our beam is simultaneously having an higher average energy and if you think about this across the entire length of a patient the average energy of the beam can change quite a lot this is what's known as x-ray beam hardening the absolute number of x-rays as well as change that reaches our detector so that value that we are that's reaching our detector is not perfect for the linear attenuation that's happened through our patient it's quite quite hard now to solve that simultaneous equation with an incorrect answer not only that but we can have scattered x-ray photons that are coming from different areas but are contributing to the linear tenation that we're calculating in this specific line across our image so scatter in combination with beam hardening of a polychromatic beam is going to make the calculation much more difficult you know that in order to solve simultaneous equations we need very accurate answers when we're using this formula here or rearranging this formula here our answers are going to vary as we rotate around the patient the degree of beam hardening is going to be different we're going to pass through different lengths of bone different widths of tissue and that really muddles the data now this is one point where I'm really grateful for the physicists that have come up with CT Imaging with reconstruction of data they've somehow managed to design systems that can still culate or at least very accurately estimate the linear attenuation coefficient in pixels without needing extremely accurate data and those are the processes that we're going to look at in future talks the Reconstruction processes we're going to look at simple back projection and filtered or convolution back projection we're going to look at iterative reconstruction and fua based methods and how physicists have got around this point how they've managed to use really messy data but still create accurate images so if you're interested in that join me in the next talk until then goodbye everybody