Transcription
Hello everybody and welcome back. Today we're going to be looking at CT profusion imaging. And it's my hope that by the end of this talk, you'll be able to look at these images and understand what they represent. And not only that, but look at the images and understand the calculations required to generate the values that have been used to create these images.
Now, CT profusion imaging is a dynamic study. It's representing changes in attenuation over time. And those changes in attenuation come from contrast that we've administered to the patient. And we use that contrast administration and the subsequent changes in Houndsfield unit values as a proxy for blood flow. Blood flow in arteries, blood flow in veins, and most importantly, blood flow within tissues in the microvascular beds that peruse the tissues. And in this example, we're going to be focusing on the brain. So let's have a look at an example.
Here we have a patient that presents with an eskeemic stroke. They've got a focal neurological deficit. We've taken an uncontrasted CT scan to check that that deficit wasn't from say, a mass or from a hemorrhage in the brain. And this is in fact an eskeemic stroke. We can see there's a clot within the right MCA. What we want to do with perfusion imaging is figure out what effect this clot has had on the perfusion of the tissues to which it supplies. Not only that, but we want to somehow be able to differentiate which regions of the brain have irreversible damage. We call that the core infarct, and which regions of the brain are hyperprofusing. They're at risk, but they're still salvageable if we were to remove this clot here.
So, what we do, the first thing we do is we administer contrast. Once we've administered contrast, we take multiple scans at the level that we're interested in. We want to continually scan the region of the brain. We can see here contrast now within the anterior cerebral arteries. We can see it in the middle cerebral arteries. And you can see very obviously here in the right MCA territory, we've got underperfusion. There's no contrast in this region here. What we then do is we repeatedly scan and monitor the contrast changes in tissues. And it's this density change or contrast change over time that's going to allow us to generate those profusion CT images.
So what we can do is look at this image here, and we can see that different regions of the image are going to respond differently to contrast administration. And for every voxel, we want to see those changes over time. Remember, it's a dynamic study. It's not one static snapshot of the brain. So for each of these regions, let's take the red, the green, and the blue region here, arterial, tissue, and venous regions here, and plot them over time. Plot the contrast concentration or the Houndsfield units over time here. And you'll see that the different tissues respond differently to contrast administration. We get what's known as the arterial input function. And we get the tissue attenuation curve that we're going to look at today. And it's these graphs, the changes in contrast concentration over time in specific regions of the brain that will allow us to generate key metrics. And it's those key metrics that will allow us to determine whether a region of the brain is core and unrecoverable, or whether a region of the brain is at risk but salvageable if we were to remove the clot.
So what are those key metrics? Well, firstly, we can calculate what's known as cerebral blood flow. Cerebral blood flow is saying, in a particular region of interest, how much blood is flowing through that mass of tissue per minute. We measure that in milliliters per 100 grams per minute. The next parameter that we want to look at is what's known as cerebral blood volume. We want to figure out how much blood is flowing through that region over a period of time. It's a volume of blood. The next parameter we're going to look at is what's known as mean transit time, the average time it takes blood to move through our region of interest. And lastly, we're going to look at a time-based measurement known as time to peak or T-max. They're two different measurements. They measure similar things though. And I'm going to show you how they're different later on. It's going to be a major focus of the talk. But what they're essentially measuring is from the contrast administration to the patient, how long does it take for the maximum contrast concentration to be reached in our region of interest? And I'm going to show you how we can use these four parameters to determine whether we've got core infarct tissue or whether we've got penumbra at risk salvageable tissue.
So let's look at a clinical example, and hopefully by going through this clinical example, you can get an appreciation for what these parameters represent. So we have a patient here who again presents with a clot within the MCA. This is the left MCA here. You can see a dense MCA. It's a non-contrast CT scan. We always start with a non-contrast to check that there's no hemorrhage. Then we can do an angiogram, and we can see there's a disruption in the MCA here. But you can see that we are getting perfusion past that disruption. Either it's an incomplete occlusion, or we have collaterals supplying the MCA territory here. After our angio, we can then perform our profusion imaging. First calculations that we're going to make is for each voxel or each pixel within the image, we're going to calculate the cerebral blood flow. You can see now in the MCA territory, we've got a reduction in cerebral blood flow compared to the normal contralateral side. And the beauty of these measurements are, you can compare sides of the brain. They can be compared relative to one another. So we've got a reduction in cerebral blood flow. But how can we figure out if any of this region is salvageable?
Well, if we look at the table here I've used for reference. Now, these are reference values that many institutions use, but these change between institutions and change between studies. So, don't use these as fact. I try to give you trends more than absolute values. A penumbra is considered to have reduced cerebral blood flow in the region of 50 to 30% of the contralateral side. And core infarct is considered generally to be anything under 30% of the cerebral blood flow on the contralateral side. We can then calculate cerebral blood volume. You can see there's a difference between core infarct and penumbra when it comes to cerebral blood volume. So let's do that for this patient. And notice how this region here has actually got increased cerebral blood volume compared to the contralateral side, which doesn't seem to make sense. We've got a reduction in cerebral blood flow. What this represents is the penumbra of this lesion here. Here we've got reactive or compensatory vasodilation allowing this eskeemic tissue to try and get more blood, to try and get more oxygen. So because of the reduction in cerebral blood flow, the rate of blood traveling through this region, that region of the brain has vasodilated, allowing for the absolute blood volume to be more. This region here though hasn't had that compensatory mechanism, and we can assume that this is the core infarct. This is unsalvageable tissue.
So we've done CBF and CBV. Let's look at the mean transit time. Now, the mean transit time, as I'm going to show you later, is a function of the CBV and the CBF. And we can see that blood takes longer to move through this region here as opposed to the surrounding tissues. And lastly, we can look at the time-based measurements where we can calculate the time to peak and the T-max values. And hopefully by the end of this talk, you'll understand the differences between the two. It's showing us the amount of time it takes for the concentration of the contrast within that specific pixel to reach its peak. And it's delayed in the region of the left middle cerebral artery in both the time to peak and T-max regions. Notice here, just mark this, bookmark this, the regions that are unaffected in T-max are almost zero here. There's no delay in the T-max values. Here, when you look at the time to peak values, even in the normal healthy tissue, there's a delay between administering the contrast and the peak concentration in those tissues.
Now, this patient actually had the clot removed, allowing for reperfusion and hopefully allowing for recovery of that penumbra that we've identified in these images. And I'm going to show you just for completeness sake, the pre and post thrombectomy images. We can see here the internal carotid artery filling with contrast. We can see it bifurcating into the anterior cerebral artery and the middle cerebral artery, which abruptly ends here. And as we play this further on, we can see that there's some collateral supply of the temporal lobe here where we were getting that hypoperfusion of the tissues. And then we can see this contrast eventually heading out through the dural venous sinuses out towards the internal jugular vein. Let's look at what this looked like after the clot was removed. We can see now the contrast coming through the left internal carotid artery, flowing freely through the middle cerebral artery. And look how much more perfusion we're getting within that temporal lobe. We're not relying on those collaterals to supply blood to that region. And again, we can follow that contrast out. So it was the perfusion imaging that allowed us to see, actually, wait, we've got salvageable tissue here. This patient will benefit from a mechanical thrombectomy.
Well, how then do we go about generating these parameters here and ultimately creating the images that we've seen in that clinical example? Well, first, what we need to create is what's known as a time-attenuation curve, and it describes exactly what it is: how does attenuation in a specific voxel change over time after contrast administration? And the first time-attenuation curve that we want to generate is what's known as the arterial input function. We place our region of interest over a main artery, normally the anterior cerebral artery or the middle cerebral artery. What we then do is repeatedly scan this region of the brain and calculate how the Houndsfield units change in that region of interest, and we can plot that change over time. After we've plotted that change, we can plot a graph that best fits the measurements that we created. We are measuring discrete measurements at a set time interval. In this example, every 3 seconds in this region of interest. Time zero is when we are injecting contrast. We are injecting a large bolus of contrast to a patient. That contrast needs to head up into the left side of the heart and ultimately be pumped towards the brain and then be registered in this anterior cerebral artery. That's why we've got this time delay here. This marks where the contrast starts reaching the anterior cerebral artery, and then we can see a peak in contrast until it fades off. That's what's known as our arterial input function.
The rate at which blood enters the brain is obviously going to influence the rate at which blood perfuses the actual brain tissue. We can see that the arterial input function is slightly different to the venous system. We can see we've placed a marker over the superior sagittal sinus here, and it takes longer for contrast to reach the dural venous sinuses. That makes sense. It needs to go through the brain tissue first before being absorbed into the dural venous sinuses. But notice how much overlap there is here. Blood is still arriving into the arterial system, and we've already got blood leaving through the venous system. It's a dynamic process. All the blood doesn't come to the arteries first, then go to the tissues, and then go to the veins. There's overlap because this is a continual dynamic process. And the last time-attenuation curve that we need to generate is what's actually happening at the tissue level at our region of interest here. We're not over a vessel now. Now we're looking at how tissue is responding to that administration of contrast. The contrast is coming in the microvascular beds. It's going to enter the tissues and it's going to leave the tissues in a very set way depending on the viability of the tissues. So let's plot the contrast in tissue over time, and we can see that the peak is much lower than in the arterial and venous systems. Again, we can fit a curve to represent that tissue attenuation curve. Now, this looks like this peak isn't very high. That's just because of the scale of the Houndsfield units here. We can rescale that, and you see that the tissue attenuation curve also creates a peak like this. Okay.
So let's go about calculating these parameters. I've kept them down here because these are what we're trying to calculate ultimately. The first parameter is easy. It's our time to peak from the moment we administered the contrast. How long does it take for the tissue attenuation curve to reach its peak? That's what's known as the time to peak. Now, the time to peak value has a couple of shortfalls. It doesn't account for the dispersion of contrast before it reaches the brain. It doesn't account for say, a stenosis in the internal carotid artery. Anything that's causing delay for the contrast to reach the brain is going to be included in that time to peak value. And this delay may not be due to the eskeemic stroke that we're trying to assess. Not only that, but the time to peak value is not independent of the arterial supply. We can't supply a bolus of contrast at one time point. It has to be given to the patient over a period of time. We administer that bolus, and the rate at which that contrast is administered is also going to influence the rate at which we reach our peak here. This is just important to note.
Next, we can calculate our cerebral blood flow. If we were looking at this graph, we're basically looking at the rate of change of concentration. And the rate of change is going to give us a proxy for the cerebral blood flow. So, we can take the maximum slope of this graph. We would have gotten this by deriving this graph using the derivative of this graph and finding its peak. And we can calculate the maximum slope. We can use that maximum slope, the change in Houndsfield units over a change in time to calculate the cerebral blood flow. Again, this calculation is not independent. It's dependent on the arterial input function. And we're going to look later how we can uncouple the arterial input function from the cerebral blood flow. But for now, this is a way to calculate cerebral blood flow, or at least estimate cerebral blood flow in our voxel of interest.
Next, we can look at this curve and say how much contrast has traveled through this voxel of interest over this period of time that we've been sampling. And that's what's known as our cerebral blood volume, or the cerebral blood volume. And to calculate the cerebral blood volume, we calculate the area under this curve. Again, another principle from calculus. So the cerebral blood volume we saw in the penumbra can actually be raised as opposed to normal tissue. In our infarct, the cerebral blood volume is going to be decreased. Our cerebral blood flow will be decreased. So the curve of this graph will be more gradual, and the area under the curve will be less in a core infarct.
Lastly, we want to calculate the mean transit time. Now I've said to you that the cerebral blood flow measurement is not an accurate measurement. It's more of an estimation, and it's better when you're comparing two tissues and not trying to get absolute values. Later on, when I show you deconvolution processes, we can use a cerebral blood flow and the cerebral blood volume to calculate mean transit time. And that's actually how it's done in modern CT scanners. We can use this time-attenuation curve and say, what is the average value of contrast over time? The values of contrast over time averaged out, and divide that by the total contrast that's been administered in this time, and get an approximate for the mean transit time for the amount of time that it takes on average for blood to move through our region of interest. But I'll show you a better way to calculate this later.
Now I've said that using the time-attenuation curves that we've generated here alone to calculate these parameters have some shortfalls, and those shortfalls center around two main concepts. The first is this delay that happens before contrast actually reaches the brain. Contrast is going to disperse before reaching the brain, and there are many factors that cause delay for contrast to reach the brain. If a patient is bradycardic, say, or they've got a poor cardiac output, it's going to take longer for that contrast to reach the anterior cerebral artery. Again, if there's stenosis in the internal carotid arteries, we can't at the moment have a tissue attenuation curve that's independent of our arterial input function as well. So, let me place that arterial input function over this graph. Notice how this arterial input function overlaps with our tissue attenuation curve in our region of interest. The rate at which we administer contrast, the amount of contrast that's coming, as well as the physiological factors from the patient that determine how quickly that contrast gets to the tissue is all going to change the shape of this curve here. And ultimately, it's going to change the cerebral blood flow.
What we want to figure out in profusion imaging is what's the actual response of the tissue itself, independent of the arterial input function. We want to say, if we gave all of the contrast at one point, if there was a way of us to just give all the contrast at once to that voxel of interest, how would it respond to that contrast? How would it process that blood? How long would it take blood to get through that region? We want to know how that tissue will respond because ultimately that's going to show us the function of that tissue, how well that tissue is being perfused. And to do that, we use a method known as deconvolution. And deconvolution is going to improve particularly on these two values, the cerebral blood flow and the time to peak, which we're actually going to calculate a value known as T-max. That ultimately is going to affect our mean transit time and make that more accurate and make it independent of dispersion or transit time, as well as the arterial input function.
So how do we go about doing that? Well, we create what's known as the impulse residue function. The impulse residue function says how would the tissue respond independently of the arterial input function. So we have the arterial input function here. We say, what if we took all that contrast and administered it in one go at time zero? We accounted for that delay that it took to get to the anterior cerebral artery. We want to say how would the tissue react to contrast at one point. We create what's known as a fraction of contrast in the tissue. We say all of the contrast has reached the tissue. How then does that contrast leave the tissue over the period of time that we're measuring? This is what's known as the tissue response. It's the impulse residue function. And this is what we're actually going to try and calculate. And if we manage to calculate this, we'll get a much more accurate calculation of cerebral blood flow.
Now, we can't physically measure this because that's not actually happening in the patient. We need to mathematically model this. So, how then do we model the impulse residue function and calculate the cerebral blood flow? Well, we use this equation. I'm going to take you through this equation step by step and show you how we go about calculating the cerebral blood flow and the impulse residue function. This here is our tissue attenuation curve. How the tissue has responded to the bolus of contrast that was given clinically at the rates that we gave it. This is our arterial input function. How contrast changed in the anterior cerebral artery in our example. If we convolute this, means convolution here. If we convolute the arterial input function and our impulse residue function and scale it by the scalar value of cerebral blood flow, we will get the measured tissue attenuation curve that we've been plotting with the green line. Don't worry if that doesn't make sense. We're going to go through this step by step.
So in this equation, we have two known measurements. We've measured these values. The impulse residue function we haven't been able to calculate. That's an unknown. And the cerebral blood flow scalar value is an unknown variable. Now when we were measuring these values, they were discrete values. We were measuring at set points in time. In our example, every 3 seconds. What we can do is we can take those discrete values over time and put them in an array. Putting them in an array is what's known as discretizing the values. We haven't got continuous values with that line of best fit. We're taking the actual discrete values, and we can rejig this formula to create a second formula. This is our values measured over time in the tissue of interest, and that's equal to a matrix that we've created out of the arterial input function. We've got two unknowns here. We want to combine the cerebral blood flow and our impulse residue function and calculate for them as a whole. We can't calculate two unknown variables in this equation yet.
So what we do is this array that we create is what's known as a Toeplitz matrix. We take the arterial input function and we convert it into a matrix that has the convolution function baked into it. I've mentioned this here because those of you who are interested can go and read about this further outside the scope of this talk. But the way in which we arrange this array, we created purely out of the arterial input function. But the diagonal values in this array remain the same in the bottom left-hand side of our array. In the top right-hand side of our array, we have zero values. This allows us to deconvolve, or to take the arterial input function out of the impulse residue function. We then can combine the cerebral blood flow and the impulse residue function into a function known as H. Now, the mathematics isn't important here. Understanding what we're doing is, and we're going to get to what we're actually doing.
Now we can isolate H using this equation. Again, this looks complicated, but what we've done here is we've applied what's known as a singular value decomposition. This equation here is very sensitive to subtle changes. And those subtle changes get propagated throughout the equation. And what we want to do is create a threshold value, and values underneath that threshold we're not going to include. That prevents noise and things like that in our image from being propagated through the data and giving us inaccurate measurements. We only want values that are above a certain threshold to be included in this equation. That's what we're doing here. We're also deconvoluting this arterial input function away from this H function that we're trying to isolate. We're essentially moving the arterial input function to the other side of the equation here. This is just our discretized values of our tissue attenuation curve here. H then can be plotted as a function over time. We say H over time equals the scalar value of cerebral blood flow multiplied by the impulse residue function.
Now what are we calculating here? The impulse residue function is how each tissue responds to that immediate, that theoretical immediate bolus of contrast. Cerebral blood flow shows us how blood is moving through that region of interest. This equation is the most important equation when it comes to the deconvolution method in calculating the parameters that we use for profusion imaging. It's what's known as a tissue residue function. It describes how the tissues respond to a bolus of contrast. And we can plot that tissue residue function over time.
Now, I showed you what the impulse residue function looked like. It looked like this. If all of the contrast arrived immediately at our voxel at the time that we were injecting the contrast, how would that voxel respond? Obviously, the contrast doesn't arrive immediately at the voxel. It has to be in the artery first. It has to make its way to the voxel. This scalar value, the cerebral blood flow value, describes the dynamics of the blood, how the blood is flowing towards that voxel. We can scale this input residue function that we've got here by the dot product of the cerebral blood flow. And that's going to change our graph here. We're now plotting the tissue residue function. We're now plotting H of T over time here. And we're getting values that are milliliters per 100 grams per minute. We're getting cerebral blood flow values. So it goes without saying that our max cerebral blood flow is here. That's going to be the max of H of T, the max of the tissue residue function.
We can now take this cerebral blood flow value and use it to calculate our mean transit time. An accurate mean transit time that's independent of delay. Independent of delay from contrast administration to contrast reaching the voxel. And it's independent of the arterial input function. We simply take the cerebral blood volume, the area under the curve of the initial tissue attenuation curve that we drew, and we divide that by the cerebral blood flow. We take the total volume of blood and divide it by the rate at which blood is moving through that tissue, and we get the mean time that it takes for blood to move through that tissue. We can also calculate the T-max here. The time at which this function reaches its maximum. So when we reach the max CBF here, we get a time that's known as T-max. Now, generally speaking, we can use T-max values of 6 seconds as being under 6 seconds generally considered as normal. Above 6 seconds, that tissue is now vulnerable tissue. It's either penumbra or core infarct. Some institutions or some papers use above eight or above 10 seconds as a value for core infarct, but that changes between places.
So we've now calculated much more accurate measurements of cerebral blood flow, mean transit time, and T-max. It might be useful to think of the differences of the non-deconvolution methods and the deconvolution methods for calculating these parameters as traffic heading out into a suburb. We think of the brain as multiple pathways of blood can get to the different regions of the brain. Same as if we're driving into a local suburb that's contained. Either we can let cars come in one by one as if we're giving contrast. Those cars can either turn off before going to the suburb. They might not go to their home. They might go to the shops first and then go to their home. But every car that's going into that suburb is going to go to every house within the suburb. What we're doing when we're using deconvolution methods, we're saying to everyone, you're going to arrive at the start of the suburb. You're all going to be on the same road at exactly the same time, and you're all going to drive to your house as quick as possible. They're going to be some roadblocks, like a thromboembolus, that's going to prevent blood from traveling its normal path to its home, and they're going to have to take an alternative route to reach their home. Measuring the cerebral blood flow and measuring the T-max here, the time it takes for a specific car to get to its specific location, its specific voxel in the image, is independent of what happened before the car reached the suburb, before they left work or left school. It only started measuring from when it reached the beginning of that suburb, the main road into the suburb. So that's only showing us what delays occurred within the suburb. It shows us what delays occurred because of a thrombus within the brain. It doesn't account for anything that happened outside of the brain. So, it gives us much more accurate readings.
Now, I know that some of the math here can be quite confusing. What's important is to understand what those images at the beginning meant. Now that we've gone through these, I'd encourage you to go back to the start of this video and go through that clinical case and look at those images and see what we are representing in each one of those images and how we've gone about calculating those values. I've left this here to show you how we calculate the values in the non-deconvolution methods and in the deconvolution methods. Cerebral blood flow is a slope of the graph, or it's the max point of our tissue residue function. Cerebral blood volume is the area under the curve, or the tissue attenuation curve. Mean transit time is either the average tissue contrast over time divided by the total tissue contrast, or in the deconvolution method, it's our cerebral blood volume that we've calculated here divided by the cerebral blood flow that we've calculated here. We can't calculate time to peak in the deconvolution method. We calculate the maximum concentration in our tissue attenuation curve at a given point in time after contrast administration. And lastly, T-max, which is a much better measure than time to peak because it accounts for that arterial input function and the delay of contrast to the brain. We calculate that by finding the time at which the tissue residue function is at its maximum.
So that brings us to the end of profusion imaging. I know there's a lot to go through in that talk, and some of the mathematics can be complicated. I've mentioned the Toeplitz matrix, and I've mentioned SVD deconvolution. If you're interested in the mathematics, I'd highly encourage you to do some research around those topics and see how these equations actually come to life. For those of you that aren't interested in the mathematics, focus on these parameters and what they actually mean clinically. We're going to end off our entire physics learning pathway by looking at an introduction to photon counting CT. That's going to be the topic of the next talk. So, I'll see you all there. Goodbye everybody.