Transcription
Hello everybody, and welcome to the CT Physics course. This is the first in a series of videos that build on from one another, and the purpose of today's talk is just to provide an introduction, a road map that you can use to plot your journey through CT physics.
And we're going to start at the very beginning by defining what exactly CT is and looking at the CT machine. You can see the CT machine here with the outer gantry, the table which the patient lies on, and lasers to ensure that the patient's lying directly in the middle of the CT machine, and you'll see why that becomes important later on. If I remove this outer casing, we can see the inner workings of the CT machine: an x-ray source, the place where the patient is going to lie, and then detectors here.
Now, at its very core, CT or computed tomography utilizes x-ray radiation to generate attenuation data through a single slice of a patient around multiple different angles around that patient. The word tomography has its origins in the Greek word "tomos" meaning section or slice. We're taking a picture of a section or slice of the patient.
Now, this CT machine is going to need to rotate around the patient, and whilst we're rotating the CT machine, we're gathering attenuation data from all different angles around that patient. All of that data is gathered by these detector elements here, and it's going to be digitized and stored and later processed into an image. The process of processing that data into an image is complex, it's computationally heavy, and it can only feasibly be done by computers, hence the term computed tomography.
Now, we're going to look at these processes in a bit more detail here in future talks. We're going to come back to each one of these topics and fill in all the finer details. So we have our CT machine here, and it's rotating rapidly around a patient like this, all the while gathering data.
Now, let's look at what happens in a single rotation of this CT machine. We're going to place a fake patient in the middle here, a very simple patient. The dark regions here are not attenuating any x-rays. These lighter regions are attenuating x-rays to some degree. What we can do is plot the degree of attenuation on a graph. You can see this graph here. The part where the x-ray is traveling through the most attenuating material is going to give us our highest attenuation value. As we head out to the peripheries of these objects, they get thinner. Essentially, there's less distance for the x-rays to travel through those objects, and you can see how attenuation tapers off here. The regions where there's no x-ray attenuation, we've got no attenuation plotted on our graph.
Now, what we can do is change the angle of the CT or the incident x-rays as the CT machine rotates, and we can see how that data changes when we change the angle here. There are going to be certain points where x-rays are going to pass between these two objects and create two separate regions of attenuation on our graph here. This x-axis on our graph represents the detector here, and we can digitize these values here, these analog values here, and plot them over time on something that's known as a sinogram, which I'm going to show you how that's generated here. Let's look at one rotation of this CT machine here, see how the graph is changing, and see how we're generating that sinogram.
Now, obviously, this is an extremely simple example. The human body has tissues with differing attenuation, and it's complex. It's not just two single objects within the human body. What we're going to do is generate this data here. The sinogram that we've generated here shows us how the attenuation within the tissues have changed over time. One, and as time passes, we are also changing the angle of incidence towards the patient here. We're rotating the CT machine around here, so this is showing different angles, the data at different angles along the one single rotation of the CT machine.
What we can then do here is store that data, but also process that data. And turning that data into an image that we can use clinically is what's known as image reconstruction, data processing, and ultimately display of an image. Acquiring the image and storing the image is a separate process. We're going to label that data acquisition and storage.
Importantly, data acquisition, the scanning parameters that we choose initially here: the tube peak voltage, the filament current, the region of anatomy, the coverage that we're going to cover with a patient, the pitch of our CT machine, the relationship between how fast the patient is moving through the CT scanner and how fast the CT scanner is rotating, or whether we're going to use contrast. All of these decisions that we make at this data acquisition part of our CT scan are decisions that are made once. Once we've acquired that data, we can't then go and change the data that we're recording here. If we wanted a different set of data, we would have to repeat that CT scan.
On the other end of the spectrum, we can create multiple different types of images using different algorithms depending on the clinical question or the image that we're trying to create here. We're going to cover all of these processes in later talks. We're going to look at back projection, we'll look at the convolution kernels or algorithms of filtered back projection, we'll look at F transformation and F-based reconstruction, as well as iterative reconstruction, which is the most commonly used in current CT systems.
Now, I've said to you that the data that we've acquired and stored, we can process to create different types of images depending on what we're looking for clinically. Essentially, what we've created here is a matrix of attenuation values at specific locations within an array. We're looking at a single slice of a patient, and each pixel within this image correlates to a specific voxel within the patient, a small volume of tissue at a specific location in that patient.
Now, let's have a closer look at what we can do with this matrix or this array of data to manipulate the images that we're creating. I've said to you, each point in this image, each pixel in this image has an attenuation value. Now, we use a value known as a Hounsfield unit. A Hounsfield unit correlates to the degree of attenuation at a specific point or a specific pixel within an image, and that Hounsfield unit has been standardized relative to the attenuation of water. We say that water has an attenuation value of zero Hounsfield units. Anything that attenuates x-rays less than water is going to have negative Hounsfield unit values. Anything that's more dense or attenuates x-rays more than water is going to have positive Hounsfield unit values.
Now, we can't see numbers. We can't look at a table of numbers and say, "Oh, that's definitely a brain." What we need to do is convert that into an image that we can visually process, and we do that by applying the grayscale and matching that to specific Hounsfield units. Now, we can move that grayscale, we can spread out that grayscale and correlate that grayscale to specific Hounsfield units, which represent the degree of attenuation. You can see with this current grayscale value, we've got bone being very bright and water being almost black here.
Now, what we've done essentially is we've created an array. We've created a table of numbers that correlate to specific locations within this image. That array has numbers for it, Hounsfield units, representing attenuation, representing a single slice within a patient. Now, with CT scanning, we create multiple arrays that we can stack on top of one another. And because we can stack the data on top of one another and correlate those Hounsfield units to specific grayscale values, what we can create is a scrollable axial image here. We can scroll through the anatomy, scroll through that array of numbers.
Now, we've also created a stack of arrays, and they're the same dimensions, and they're representing continuous regions of anatomy within the patient. Why can't we take that array and cut it at a different angle and represent the Hounsfield units from that angle? That's exactly what we can do in multiplanar reformatting. We can take our original data set and create coronal images, sagittal images from the same data set. These are representing the same data that was acquired in that initial image because it's from the same data set. We can cross-correlate accurately between these images. You can see these faint green lines here represent exactly where our axial slice is located, exactly where our sagittal plane is, and exactly where our coronal plane is here. I've isolated the pineal gland, which is highly attenuating to x-rays, it's been calcified here, and we can cross-correlate in this multiplanar reformatting. We don't have to take different images in the coronal plane and in the sagittal plane and somehow stitch them together.
Now, we've allocated a specific grayscale value to specific Hounsfield units here. What if we were interested in say, just the bones? What we can do is shift that grayscale across to the Hounsfield units that correlate mostly to bones. Anything outside of the regions of that grayscale is either going to be completely black or completely white. What we've done is shifted the grayscale window. This process is called windowing. We've created here a bone-windowed CT scan, and this process of moving the window, changing the window level and changing the window width is going to be the subject of a complete talk where we look at Hounsfield units and windowing.
Essentially, with this data set that we've created, there are hundreds of different ways that we can manipulate this data and display the data differently depending on the clinical question that we're answering. We can even figure out where the surfaces are here and place an external, an artificial external light source and create a 3D image like this where it looks like a light is shining on the surface of the bones here. We're getting shadows formed. This is all computer algorithms from the same initial data set. The possibilities here are endless, but it relies on the fact that we've taken the sufficient data initially in that data acquisition mode.
So we've looked now at data acquisition and we've looked at image processing. Those are two of the three major facets in CT imaging. The third facet is the patient. Is the CT scan going to answer the clinical question that we're after? Are there other examinations or investigations that we can do that will still provide us with the same clinical answer without exposing the patient to ionizing radiation? What region of anatomy do we need to cover? Do we need to give contrast? These are all decisions that we need to make with regards to the patient themselves.
It's these three facets that we need to think about when acquiring a CT scan because they all relate to the two major outcomes of CT scanning. The first is image quality. Is this CT scan going to be of sufficient quality that allows us to make a diagnosis or allows us to rule out a diagnosis? That comes at the trade-off of radiation dose. We're always trying to minimize radiation dose. We're exposing the patient to x-rays, to ionizing radiation, often over large regions of anatomy.
Now, these two qualities, these two outcomes are often opposing. When we try and increase image quality, we often have to do that by increasing radiation dose. The same goes with trying to reduce radiation dose; we're often reducing image quality. And I would encourage you throughout this course to keep these two outcomes at the forefront of your mind. They're incredibly important. You'll see that these type of questions come up over and over again in exams, and rightly so, because they're so important.
If any of you have done any of my previous physics past paper question banks that I'll link below in the description, you'll know that I take questions from past papers and rank them in order of frequency. I try and bring up the most common questions that come up in exams. Having looked at CT questions, related to image quality and radiation dose come up over 40% of the time. These are incredibly important things that we need to keep at the forefront of our mind.
So we've now looked at the three major facets and we've looked at image quality and radiation dose. We're going to go into each one of these in later talks, and I want to shift gears a little bit and look at something that I feel is foundational to CT before we go into the specific lectures. Whenever you're learning a new subject, there's often a topic that you need to know in order to understand that subject. If you were trying to learn a new language that utilized a different alphabet system to the one that you're used to, there's no ways that you'll be able to learn that language, to read that language, to write in that language, to understand that language without knowing the alphabet of that language. For me, this is the alphabet of CT.
You may have thought to yourself, "Can't I take a frontal radiograph and a lateral radiograph, put them at right angles to one another, and cross-correlate the attenuation data and create a CT?" After all, we've exposed the region of anatomy that we're interested in at two separate angles. Surely we can see from the front, see from the side, and see where that attenuation is going to be and ultimately plot a CT scan? Can't we put them at right angles, take the specific slice that we're interested in, look at the attenuation values on that specific slice, and then project those attenuation values across the slice from the frontal side and from the lateral side, and then somehow mathematically calculate where these attenuation values cross and figure out what the attenuation value is at these crosshairs, at these regions here?
If you blow your eyes at this, you can see where the vertebrae are and where the heart is. You can see where the lungs are less attenuating lungs, and you can see where x-rays aren't passing through any patient at all. They're unattenuated, they're transmitted all the way through to our detector. Is there not some way that we can create a CT scan from this? Well, I want to show you why that's impossible, why we need multiple views, and why CT is so data-intensive by creating all of this data at different angles.
Let's take a simple matrix that's 2x2. We've got four variables here. We're trying to figure out the attenuation of these four variables: W, X, Y, and Z. If we were to take a frontal radiograph of these four variables, we place detectors on the one side of the patient and we pass x-rays through that patient, we can get attenuation calculations here, how much those x-rays have been attenuated. We can do the same from 90 degrees, effectively taking a lateral radiograph of this 4x4 matrix. We've now created attenuation values for the rows and the columns in this matrix. We can then go about working out how these attenuation values have come about. We can add these two variables, do the same here, and do the same from our different view. We've essentially created four separate equations that will help us to calculate what these variables are. Got four variables and four equations, and if you know anything about simultaneous equations, this will be enough to go and calculate the values of these variables. You see, this adds up to 7, 13, 5, and 15. We can confidently say that these are the attenuation values in each one of these pixels within the matrix, and we can apply a grayscale to those if we want to create an image. So we've created a very basic image here.
In our image, we've got 512 by 512 pixels. Can this be extrapolated out further? When we increase the number of pixels, we've now increased the matrix size to 3x3. We've got nine variables here. Again, we can take a frontal and a lateral and create different equations here. Now we've created six separate equations. We've got six equations and nine variables to calculate. Whenever you have more variables than you have equations, like we have here, you cannot confidently calculate each of these variables. In fact, we've got an infinite number of solutions to this specific set of variables.
Now, it doesn't mean that we don't have solutions. I've said we've got an infinite number of solutions. We could, in fact, allocate numbers here, attenuation values that make these equations true. This adds up to 16, 10, 10, 7, 16, and 13. So it's not saying that there isn't an answer to this. We've got a patient that has specific attenuation values. There is an answer. We can't calculate with the data from those two views, with the data that we've got from our detectors, we can't accurately calculate these values here. Watch how these numbers change here, but they still remain true for the equations that we created. These still add up to 16, 10, 10, 7, 16, and 13. If we were to apply a grayscale value, say to these, this would be the image that we generate that would still comply with the equations that we've generated. But this image that we looked at previously also answers the variables in these equations that we've made. We've created two completely different images from the two views that we've looked at.
So hopefully that convinces you that we can't just take a frontal or a lateral radiograph. Now, how many angles would we need? How many equations would we need to say, create this image here, which has got 512 by 512 pixels? Well, we would need to generate more than a quarter million equations to solve for this image here. You can see why it's called computed tomography. No human is feasibly going to solve 262,000 different simultaneous equations. We're going to need at least 512 different views. If we've got 512 detectors, that will give us a number of equations here.
Now, when I was looking at this for the first time, I kept coming back to the fact that, can't, isn't there another way to try and calculate these without having to get all of those simultaneous equations? And what really convinced me that there isn't another way is by looking at a Sudoku, and hopefully this will make the penny drop. There are more possible Sudokus than there are stars in the sky. There are so many ways that you can make a Sudoku here, yet we know that the rules of a Sudoku means that in each row and in each column, there needs to be the numbers 1 to N. That means that if we were to look at these numbers in here as attenuation values and then measure the degree of attenuation as we went through the rows and as we went through the columns, all of them would add up to 45 arbitrary units. Now, later on, we're going to look at attenuation passing through a patient; it's not a linear process, and we're going to account for that later, but let's stick to the basics here. This Sudoku, if we had two detectors, would detect 45 in each row, in each column. We can now change that Sudoku. We've still got 1 to N in each column. Again, those detectors are not going to measure any difference. No matter what Sudoku we use, the detectors can't detect that change. They need multiple different angles. They need at least nine different angles here if we were to have nine detectors to create those 81 different simultaneous equations and solve for these 81 variables.
Now, that's actually quite powerful. We've got more Sudokus than there are stars in the sky, yet we only need, with a nine-detector CT scan, we only need nine different angles to figure out where these variables are placed. You can see how powerful it is. We can get very accurate images, and that's a benefit of CT. We get very good spatial resolution. And once we've acquired that data and stored that data, we can do so much. We can manipulate that data and create multiple different images.
So that's what I want to cover today: the three major facets of CT, the patient, data acquisition and storage, and image processing and display, and how they relate to image quality and radiation dose, and then looking at why we need multiple angles within a CT machine. And hopefully, I've given you a feeling as to how we're going to process that data and ultimately create our image.
In our next talk, we're going to look at the inner workings of a CT machine. We're going to go through each one of these components, and we're going to look at how a CT machine is able to rotate like this while simultaneously acquiring the data. Now, to do that, we are going to actually virtually build our own CT machine together. I'm going to take you through each one of these steps and describe the various components that we're adding to create our CT machine. We'll also look at the generations of CT machines and how we can change our scanning parameters depending on the data that we're trying to acquire.
Again, as a reminder, in the first line of the description, I've linked a question bank. To date, we've helped over 4,500 students not only pass but excel in their Radiology Physics Exam. So if you're studying for a physics exam, it's a really high-yield resource to figure out what you know, what you don't know, where you need to work on more, and where you don't.
Now, I'll see you all in in the next video where we're going to dive into the CT machine, the hardware itself. Until then, goodbye everybody.