Transcription
Hello everybody, and welcome back. Let's talk today about image quality in CT. Now, whenever we're trying to determine the quality of an image, we can assess four separate categories. We can look at the spatial resolution of an image, the noise in that image, the contrast resolution in that image, as well as if there are any artifacts or not.
Now, we've concentrated on artifacts in the previous talk, so I'm not going to talk about those today. But we're going to go through both spatial resolution and contrast resolution. See how we can measure them and how we can change that resolution within an image. Now, there's a lot to go through, so let's head straight into it.
We'll start with spatial resolution. Spatial resolution is the ability for us to separate two adjacent structures as being distinct entities within our image. If we've got two structures like this, they're sitting within the X-ray beam. We can separate them in the XY plane, the transaxial plane. That's what's known as transaxial resolution. And we want the ability to separate them in the Z axis, the longitudinal axis of our scan. This is what's known as Z-axis resolution.
Now, how do we go about measuring resolution within an image? Well, we can either measure transaxial resolution or we can measure Z-axis resolution. And the way we do that differs slightly. When measuring resolution, and you'll see later, when measuring noise, we can measure it either visually or we can measure it mathematically to get a quantitative measure for resolution.
Visually, we represent resolution by placing a phantom within the X-ray beam. Now, if we look at this phantom end-on, we can see that within the phantom, we place what's known as line pairs. Now, visual resolution is measured in line pairs per millimeter. You'll see that sometimes you'll see line pairs per centimeter, which is just a 10x multiple of that line pair per millimeter measurement. What we have is we have these line pairs here, alternating black and white stripes that you can see get narrower and narrower. The gap between those stripes gets smaller and smaller. The line pairs per centimeter or line pairs per millimeter gets larger. We've got more line pairs per unit distance. We can place that phantom within the CT machine and acquire an image of this slice here. We can then reconstruct that image and look at it on the computer.
Now we can visually assess when we can no longer see line pairs as being separate entities here. We can see all of the line pairs here. So we've got excellent spatial resolution within this current setup of our CT machine. And as we'll see later, there'll be certain cut-offs here where we can no longer see the line pairs as distinct from one another. And we can use the previous or the last visible line pairs as our spatial resolution. So this is a visual measure for transaxial resolution.
We can also have a visual measure for Z-axis resolution. If we were to look within this phantom here, we can see that there are these structures here that are adjacent to one another. They're changing height within the phantom and they're separated by a set distance from one another. Now that becomes incredibly important. We can see in this phantom they're equally spaced out, these highly attenuating structures within the phantom. In this example and in most phantoms, they're 0.5 mm apart, each one of these attenuating rods within the phantom. Now what happens if we place that phantom back into our CT machine? We're now looking at Z-axis resolution. These line pairs are continuous throughout the phantom. So our image would look something like this. But now these highly attenuating bars that we've placed along the Z-axis are also going to show up within our scan.
Now what does this mean? Well, we know the distance between each one of these bars. We know that there's 0.5 mm between these bars. So the reconstruction that we've used and the slice thickness that we've used will create this image. And we can calculate that slice thickness now by knowing the distance between here. So we know that this slice is somewhere between 1.5 mm thick and 2 mm thick because the gap between these are 0.5 mm. That's a visual way to see the slice thickness in the Z-axis. And the slice thickness is going to determine the lower limit of our resolution, especially if the pitch is one. We can't resolve anything smaller than the slice thickness because there's going to be partial volume averaging of the structures that lie within the slice. So that's how we visually determine resolution.
We can also use a mathematical calculation to determine resolution that gives us a quantitative measure of resolution. It's a method known as modulation transfer function. Now I'm going to describe this briefly here. What we can do is we can place a rod here that aligns with the Y-axis of our scan and we can acquire an image and reconstruct that image and display it on our screens here. Now this is the highly attenuating rod here. It's got high Hounsfield unit values allocated to it. We can take a cross-section of this image and plot the intensity values that have created this image along this cross-section. This is now going to be in the X-axis of our scan. We can plot that here. And we've made a graph that represents the attenuation values across this specific line. Notice how we haven't got perfectly crisp edges here. Because of the spatial resolution limit of our scan, we can't perfectly differentiate the edge of the attenuating rod from the phantom itself. This plot represents spatial location along the X-axis as well as signal intensity along the Y-axis.
Now remember, whenever we measure signal intensity, we can subdivide that signal intensity measure into multiple different frequency measures. We use an inverse Fourier transform to do that. Remember, any signal intensity plot can be deconstructed into sine waves of differing frequencies that when added together will make this signal intensity plot. We've covered that many times within this course. And we can do the very same here. We can plot a graph that has our modulation transfer function against spatial frequencies. When we're looking at this image, areas where the pixel values adjacent to one another don't change very much are what's known as low spatial frequency data. Where pixels change rapidly, like the edge of this attenuating bar here, that's what's known as high spatial frequency data. And it goes without saying that high spatial frequencies is what contributes to good spatial resolution within an image. So when spatial frequencies are low, our modulation transfer function is going to be normalized to one. Modulation transfer function is describing the capability of the system to transfer spatial resolution from our actual anatomy into spatial resolution within the image. How well does it transfer the contrast from our anatomy to the contrast within our image? The edges of our image, how accurately can it determine those images? That's what modulation transfer function is trying to represent.
So let's do an inverse Fourier transform of the signal that we've read out along this X-axis of our scan. When spatial frequencies are zero, the DC component of our signal here, the lowest frequency component of our signal, our modulation transfer function is going to be one. As spatial frequencies increase, our ability to differentiate where one structure ends and one structure starts, where pixel values change rapidly, gets less and less. And we make a threshold. It's generally a standardized threshold at 10% of the modulation transfer function. We call that our limiting spatial resolution. This gives us an objective measure of the spatial resolution limit for this current reconstruction method and for the parameters that we've set during the acquisition of this scan.
Now we can change various parameters. We can change the type of image reconstruction. We can do, we can change the filter that we apply to display our image. All of those changes are going to change the modulation transfer function or change the spatial resolution of our image. So you can see we can plot various different graphs depending on the parameters that we choose. And because the parameter changes that we're going to look at, the factors that influence spatial resolution make spatial resolution in our final image different, we're going to get different modulation transfer functions. I hope that's not too confusing.
You notice that some modulation transfer functions can actually give values higher than one. That's because in some kernels that we place on images, we are falsely sharpening the edges of that image, say in a bone kernel, a bone filter, where we want to get good resolution or good spatial resolution between bone and soft tissue. We want to see accurately if there's a small fracture within a bone. We're going to amplify, we looked at this earlier, we're going to amplify the higher spatial frequency data, and that's going to give us a sharper image. We're also going to get an image with more noise because we know that noise is located in the higher spatial frequencies as well. Noise represents rapid changes in adjacent pixel values. So we're going to get a sharper image. We're going to get a better modulation transfer function at certain spatial frequencies, but the image is also going to be noisier. It becomes at that cost. We can also set up our scan or an acquisition mode that has poorer spatial resolution. And we're going to look at some of the things that contribute to spatial resolution.
Now, so that's how we go about measuring spatial resolution. What actually influences that spatial resolution within our image? I like to think of these into two separate categories. The first being CT machine components that influence our spatial resolution and the second being scanning parameters. What parameters can we change when we acquire the image? What parameters can we change when we reconstruct the image?
So, let's start with the CT machine components that influence spatial resolution. They're more intuitive to me. The first being detector size. If we have large detectors, we're going to pick up a lot of X-rays. We're going to get high signal, but it's going to be at the cost of spatial resolution. If we pass X-rays towards our detectors here and try and create an image here, we're not able to resolve these two adjacent structures. Our final image is going to show it as one structure. If we decrease the detector size here and then create our image, we can see now we've got two separate structures. We've got smaller detectors. So, we're going to pick up fewer X-ray photons per detector. There's going to be lower signal-to-noise ratio, but we've got better spatial resolution. It makes sense.
The second component is the focal spot. When we think about the focal spot, we looked at this in the X-ray physics learning pathway, and we've touched on this at the start of this learning pathway. We have electrons being accelerated towards the anode and hitting the anode at the actual focal spot. They create then what's known as the effective focal spot, the focal spot size that's heading towards our patient. This is the effective focal spot width in the Z-axis. But we also have an effective focal spot width in the transaxial or the XY plane. That's determined by the width of the filament within the cathode as well as the beam shaping or the beam focusing down onto the focal spot. Now, ideally, we want a focal spot that's as small as possible, and you're going to see why now. But we can't focus the focal spot down onto too small a region onto the anode because the anode's not going to be able to tolerate all the heat over such a small focal spot. Spreading out the focal spot allows that heat to dissipate over a larger region in the focal spot. So it comes off at that trade-off. We have systems where we can vary where the focal spot lands on the anode and improve the heat tolerance. Not only that, but we can change the anode angle here. And you can see that changing the anode angle does little to the actual focal spot, but makes the effective focal spot much smaller.
So, let's take that effective focal spot and make it as small as possible. In an ideal world, we'd want a point source where our X-rays are coming from. So, we've made this focal spot really, really small. We place a patient between the focal spot and the detector, and we shine X-rays through that patient. They're going to cast a shadow onto our detector. Notice here how crisp the borders are here. We've got good spatial resolution. Now, we can't always get such a small focal spot. Generally, the focal spot is going to have some width. X-rays released from the focal spot are released in an isotropic manner. They're released in 360 degrees. So, X-rays coming from this point here are not only going to pass through this edge of the patient and through all of the patient. They're also going to cast a shadow on this edge of the patient. The same with the other side. Watch what happens.
Now, when these X-rays spread out towards our detector, we get what's known as a penumbra, a double shadow here, where we've got the main shadow being formed by the patient here, and then we've got this blurring at the edges of our anatomy. This blurring is known as a penumbra. It's what's known as geometric blur or geometric unsharpness. And we can see that geometric blur, which reduces spatial resolution, is a function of the focal spot size. The larger the focal spot size, the more geometric blur we get, the larger this penumbra is. But it's also a function of magnification. The closer the patient is to the source, the more magnification there's going to be, the more blur we're going to get. We can see this is our object-to-image distance. As this distance increases, we get more blur. And our source-to-object distance, this distance here, as that gets smaller, we get more geometric blur. Watch how that happens. As the patient heads closer to the detector and further away from the source, our blur gets smaller. As the patient gets closer to the source, further away from the detector, the blur gets greater. We get a decrease in spatial resolution. So, our focal spot size as well as how far the ISO center is away from our X-ray source is going to determine spatial resolution.
The last CT component that we're going to look at is what's known as detector offset. If we have two objects that we're trying to resolve and they lie on either side of the ISO center, this is the center of our CT scanner where the X-ray source is going to rotate around. If we pass X-rays through these two objects, we can see where those X-rays are going to land. They're going to land on the periphery of each one of these adjacent detectors here. It's going to be difficult to resolve these two objects. It's going to be a subtle change here, but what I'm going to show you is we're going to shift the CT machine by a quarter the distance of a detector. It's what's known as a quarter detector offset. Watch how the machine is just moved ever so slightly to the side. Notice how the ISO center has slightly shifted. The axis of rotation for this CT machine now is not going to be perfectly around the ISO center. It's going to be a quarter of the width of a detector off of that ISO center. Now when the CT machine rotates, it's not rotating around the ISO center. It's rotating just around the ISO center. If we redraw our lines through these two objects, now notice how they're no longer on adjacent detector elements, but they've got a detector element between them. We've created now a half offset on these detectors.
It's a difficult concept to visualize, and I think the best way to visualize it is to say we were imaging this dot here. Now, every time we created a projection around this dot here, we would register that projection here. This is a visual example of that. If there was no detector offset and we were to rotate around this object again, the next time we rotate around, we would get the same projections. Now, what a detector offset does is the first time we rotate around this object, we're going to get our projection data. The next set of projection data, the next rotation around this object is not going to perfectly align here. We're going to get a separate data set of the same object but at a slightly different angle. And if we were to repeat this process, you can see how we're filling in the gaps. We're creating slightly different views of the same object. If you're looking at a clock and you get that parallax when you're looking at two hands, if two hands were sitting over each other at the clock and you were looking at it head-on every time, you wouldn't be able to resolve those two objects. If you were to move your eyes to the side or open and close one eye, you'd be able to see those two hands separate from one another because we're creating different projections. That's what the detector offset does. So, those are the CT machine components.
Let's look at some scanning parameters that are going to influence our spatial resolution. Now we saw this visual representation of spatial resolution earlier. Depending on the kernel that we apply to our image, depending on what parts or what features of the image we want to highlight and which we want to suppress, we're going to get different spatial resolution. A bone kernel is going to give us very crisp spatial resolution. A soft tissue kernel is going to give us less spatial resolution but better subtle contrast resolution. The bone kernel, as we mentioned earlier, is going to give us a noisier image but with better spatial resolution. So the type of filter or the type of kernel that we apply in our reconstruction algorithm is going to influence the spatial resolution within an image.
The next parameter that we can look at is the pixel size. Now we know that pixel size is a function of the field of view size as well as the matrix size. Here we've got a 9x9 matrix. Again, we've got two objects that we want to resolve. If this is the final image that we're creating and each one of these pixels or voxels is going to have a Hounsfield unit value associated to it, we're not going to be able to resolve these two adjacent structures. This pixel size is a limiting factor for the image display spatial resolution. If we were to increase the matrix size, we're going to decrease the pixel size. We've now got an 18x8 matrix. You can see when we reconstruct this image, we're now going to be able to resolve these two objects from one another. They're going to be distinct from each other. This is a fairly simple concept, but you can see how smaller pixels give us better spatial resolution. Now, having larger pixels doesn't mean we're not going to detect these objects. If we had a highly attenuating very small object here, it would still be detected and represented in that pixel, but it's not improving our spatial resolution. So it's not a function of can we detect something being there or not. It's a function of can we separate two adjacent structures from one another.
The next scanning parameter we'll look at is what's known as the number of projections as well as the pitch. They go hand in hand. Remember when the X-ray source rotates around a patient, we are filling a data space known as a sinogram. The rate at which we can sample the detectors, i.e., the rate at which we can fill each column within the sinogram, determines the number of projections that we have around this region of anatomy. And it's the number of projections that give us our theoretical limit for how many voxels we can separate this anatomy into and ultimately display. Fewer projections means we're either going to have to rely on interpolation of the data, filling in some of the missing data, or we're going to have to create an image with lower spatial resolution. The pitch is the same. High pitch means we're not going to scan all of the regions of anatomy and we need to fill in some of the missing data, again, interpolate that data. A pitch of less than one means that regions of anatomy are going to be scanned more than once. We're going to effectively have more projections of an individual piece of anatomy. And more projections, more data, allows us better spatial resolution. Now, if you think about pitch, we're talking about spatial resolution in the Z-axis. So lower pitch values give us better spatial resolution in the Z-axis as well as in the XY plane because we're sampling data more than once.
Z-axis resolution is also affected by what's known as the slice thickness. We mentioned this earlier. Now the cone angle that's determined by the collimators in the Z-axis is going to determine our beam width. So here's the cone angle here. The beam width is the width of the beam that's heading towards the detectors in the Z-axis. Remember we've got the XY plane there, the Z-axis going across the width of the beam. So here's our beam width that gets larger as it heads out towards the detector because of that cone angle. The slice thickness isn't necessarily the same as the beam width. The slice thickness is determined by the number of detectors or the number of rows of detectors that we use to reconstruct the image that we're displaying. We can either use one row of detectors or we can bin multiple rows of detectors together and use all the data from those rows to make one slice of our image. Here we get more signal, less noise, but we get less spatial resolution in the Z-axis because we get partial volume averaging of tissues that lie within this slice thickness. Thinner slices are going to give us better spatial resolution.
So that's spatial resolution. You can see we've got CT machine components and scanning parameter components. And you would have noticed while I was mentioning some of those factors that influence spatial resolution, we were talking about signal and we were talking about noise. A lot of these factors have overlap. You'll see especially when we look at noise and contrast now, how much overlap there is.
So let's get into looking at noise. What is noise and where does it come from? What's the source of noise in our image? We can think about noise as coming from three separate sources. The first and most common source or the predominant source of noise is what's known as quantum or statistical noise. We looked at this when we looked at iterative reconstruction. We saw that noise wasn't distributed in a Gaussian or a normal curve within our image. It was asymmetric in distribution based on the X-ray energy heading towards the detectors. We call that distribution plus-on noise distribution. When an X-ray beam is heading towards an array of detectors, the actual number of X-rays that are going to fall on each of the individual detectors is going to vary slightly from each detector to the next. And that variance, that standard deviation in the number of X-rays that land on those detectors is described by Poisson noise distribution. That randomness of how X-rays fall is what's known as quantum noise. And that's the predominant cause of noise in an image.
Secondly, we can think of electronic noise. Our detector's ability to accurately measure X-rays that are landing on the detector. Our ability to send those electrical impulses towards our computers for processing. When we amplify the signal, we're going to add some noise. Each of those components is going to add noise into the final image, the final calculations that we display on the screen. And last, we can think about reconstruction noise. We said that blur is introduced into an image based on the point spread function, especially when we were looking at filtered back projection. Noise is the same in filtered back projection. We're spreading out noise throughout the image as we back-project all the various different projections. And that spreading out of noise happens in a predictable way based on this point spread function. So noise can be introduced in multiple different ways.
And how do we go about then measuring that noise? Again, we can measure it visually or we can measure it quantitatively or mathematically. A visual representation uses another phantom where we've got regions of the phantom that are only six Hounsfield units different from the background phantom. And visually we can see where we can no longer see these little dots within the phantom. Now, each one of these circles has the same Hounsfield unit values. But as the circles get smaller and smaller, our ability to differentiate them from the background decreases because of the noise in the image. See the graininess here. So that's how we can determine noise visually.
We can also take a sample of this phantom of the background noise here and we can plot the signal within this sample on a graph. We can plot the variation in signal here and we can see what's the standard deviation of the variation in signal from within this sample here. We take that standard deviation value and we can perform a function similar to what we did in the modulation transfer function, but instead now we're going to create what's known as a noise power spectrum. Now this calculation is outside of the scope of this talk, but what the noise power spectrum does or what it represents, it represents the spatial frequency data that we've gained from here, how noise is distributed in the image, but it also gives what's known as the texture of the noise within an image. We know how noise is spread out predictably within an image in filtered back projection. We need to think about noise as not being independent. Each part of an image, each noise region on an image is not independent of the rest of the image. There's dependence on how we've spread data within the image. I don't want to confuse you too much here. When we think about spatial resolution, we're looking at two points and saying, can we differentiate them from one another? Noise, we can't look at just one small region of an image. We're not comparing individual pixels to one another. We're looking at how noise is spread throughout the entire image. And this noise power spectrum is going to give us an idea of that. Know that this exists. Know that there are different mechanisms for measuring noise, both visual and quantitative. And that's probably about the level that we need to know.
So how then do we go about improving our signal-to-noise ratio? Noise is going to obscure our ability to differentiate structures. If we increase signal and keep background noise the same, we're going to increase the true anatomy signal and decrease the contribution that noise has to play into blurring the true signal. Again, I'm going to separate this into two categories. Either we can increase signal or we can make changes to our image processing and reconstruction to improve signal to noise.
Now how do we go about increasing signal? We can increase the number of X-rays and the time those X-rays are heading towards our detector. It's going to give us more signal. The milliampere-seconds again. We can increase the KVP as well. That's going to increase the number and the average energy of X-rays that are heading towards our detector. The beam is more penetrating. More X-rays are going to reach the detector. Pitch, as we mentioned, when we're looking at spatial resolution, is going to result in more data, more projections, more signal. And slice thickness, too. The thicker our slices, the more signal reaching the detector for a specific slice that we're reconstructing. If we take multiple rows of detectors, we've got more signal that we're going to bin together and create our specific slice or image that we're looking at. Our voxels essentially become bigger in the Z-axis. Tube current modulation allows us to increase the tube current when we've got thicker regions of anatomy and when we've got more dense regions of anatomy. Again, improving signal that's reaching the detector. Making our detectors more efficient. Reducing the amount of electronic noise that we have is going to improve our signal-to-noise ratio. And I've put in brackets patient size. We can't change the patient size, but we've seen in larger patients, we've got more tissue for the X-rays to penetrate. We saw when we looked at photon starvation in artifacts, got very noisy images with patients that are larger, and if we don't accommodate for that using our MAS and our KVP, we're going to introduce more noise into the image.
Next we can look at image processing and reconstruction. We spend quite a lot of time in the iterative reconstruction talk looking at how we can counteract the plus-on noise distribution within our image. In iterative reconstruction, we're not back-projecting all of that noise data from multiple different projections and reinforcing that noise. We're actually getting less noise with each iteration within our cycle. Placing a soft tissue filter, again, we're going to lose spatial resolution, but we're going to get better subtle contrast resolution. That's often when we're looking at, say, gray and white matter in the brain. We haven't got great spatial resolution. We can't see the edges of the bone well, but we can see that differentiation between subtle Hounsfield unit changes between gray and white matter. And again, increasing the pixel size. This could be in either part here. We've got more signal per voxel. We've got more data to create each voxel. That's either by increasing our field of view or decreasing the matrix size, making the pixels bigger.
So that's noise. We're going to finish off by briefly looking at contrast. And we only need to look at this briefly because contrast and noise have such an overlap. Anything that reduces noise is generally going to improve our contrast. Our ability to separate tissues that of subtle different densities. So we've looked at all of those factors that improve noise. Those factors are going to improve contrast. The one exception to this is KVP. If we increase the KVP, we're reducing noise. The beam becomes more penetrating. We get more signal to our detectors and the signal-to-noise ratio is going to improve. However, we get less attenuation, proportionally less attenuation, and it's attenuation differences that we're trying to tell apart in contrast resolution. Increasing KVP is going to make those differences less. A lower KVP allows for more X-ray interactions, more photoelectric effect, and Compton scatter, and allows us to better delineate tissues with subtle contrast differences. So, that's the one exception. KVP improves noise but it worsens contrast. Increasing KVP. We also saw that blur in our reconstruction, especially in back projection images, is going to decrease our spatial resolution as well as decreasing contrast resolution. We can't see the differences in these two structures as well because of blur. So reconstruction methods are also going to worsen contrast or improve contrast.
And ultimately what we want is good contrast between tissues of different densities. If we look at these two images here, we can see they are the same patients, but we got very different contrast values here. The brain parenchyma is different between the two images. The way in which we visualize the bone, the spatial resolution of the bone is different. And we can see that there are multiple factors that play into our contrast resolution. And these are great examples here. Notice how the tissue composition drastically influences the contrast resolution in the image. Bone is very dense. Soft tissue is much less dense. We've got good contrast resolution between soft tissue and bone, especially in this windowing. Notice how we've got a dense clot within the right MCA here. This clot is much more dense than the blood or the CSF or even the surrounding brain tissue. That tissue composition difference is going to give us contrast in the image. Secondly, we can look at contrast agents on the right-hand side. We've given the patient contrast. We can see contrast in the left ICA in the left middle cerebral artery. Here we can't see contrast in the right middle cerebral artery because of this clot here. Contrast agent is going to allow us to get better contrast in our image.
Next, we can look at the windowing, the width and the level of the window. How we window our images is going to determine what contrast we get in our image. Remember, we've assigned Hounsfield unit values to each one of the voxels in the image. How we then apply a grayscale to those Hounsfield unit values, known as windowing, is going to determine contrast in the displayed image. It's not changing the underlying data, the calculations that we've made, the linear attenuation coefficients, and the Hounsfield units value. It's changing the grayscale that we're using to display the image and ultimately the contrast that we see visually. And lastly, we can talk about the kernel or the filter that we apply to these images. A bone filter is going to give us great contrast between bone and the surrounding soft tissues. Soft tissue filters, as I mentioned earlier, gives us better low contrast resolution between, say, gray matter and white matter.
So that brings us to the end of image quality. There's so much to cover. I've tried to cover the major factors that influence spatial resolution, noise, and contrast within an image. Knowing how changes in certain parameters or changes in the CT machine influence these various image quality factors and how they overlap with one another. How noise overlaps with contrast and how spatial resolution overlaps with noise is important for understanding image quality. There's so much to cover here and as a result, this always comes up in exams. I'd encourage you to go through the question bank that I've linked below. We've got many different examples. I ask the questions in multiple different ways to ensure that we understand how these various parameters interact with one another.
So that brings us to the end of image quality in CT. Next, we're going to look at a specific CT acquisition known as CT perfusion imaging. So I'll see you all in that talk. Until then, goodbye everybody.