Transcription
Hello everybody, and welcome back. So, we've looked now at how a spin that's moving through a slice, whilst we're applying a gradient across that slice, will change phase as it moves across that gradient. And the degree of phase change is actually predictable, so long as that spin is moving at a constant velocity parallel to the gradient that we're applying, and the gradient field strength remains the same. And this is what's known as spin phase effects. And we've also seen we can use a specific pulse sequence known as gradient moment nulling, that allows us to compensate for those phase changes, whether spins are stationary or whether they're moving through the slice.
Now, it's my hope that we can build upon these concepts to go about explaining how we generate a phase contrast MRA image. Now, as a reminder, spin phase effects occurs differently between moving spins and stationary spins. When stationary spins experience a magnetic field gradient, the phase change occurs in a linear fashion. For each each unit of time that we apply that gradient, we will get a unit of phase change. Moving spins that are moving at a constant velocity parallel to that gradient will get incrementally more and more phase change for each unit of time that we're applying that gradient. And it's this phase change difference that allows us to create a phase contrast MRA.
Now, importantly, the degree of phase change in a moving spin is represented by this formula here, where phase change is a product of a constant and the amount of time that we're applying the gradient. And you can see that the amount of time we're applying the gradient leads to exponential changes in phase. And this constant here is a product of how fast that spin is moving through the gradient. And we're going to look at that closer in this talk, as well as how strong that gradient is. You can imagine the stronger the gradient, the more phase change we're going to get as that spin moves across a gradient.
So, how then do we go about creating a phase contrast Mr. Angiography image? Now, importantly, there are multiple different mechanisms, subtle differences between how different manufacturers and how different pulse sequences go about creating a phase contrast MRA. What I want to focus on today is the core underlying principle that underpins all different phase contrast MRAs. If we have a stationary spin, a spin that's moving at a certain speed, and another spin that's moving at a faster speed, here we are going to get different changes as those spins move across a gradient.
So, what we can do first is apply a gradient across the slice. And we assume that these spins are moving parallel to that gradient at a constant velocity. This gradient here, we can see we get an increase in magnetic field strength as spins move from left to right on our image here. So, let's see what happens to the phase as these spins move. The first stationary spin is going to experience a linear change in phase. The slower spin that's moving across the slice will experience a a single unit of phase change for this given period of time that we're applying the gradient. The last spin that is moving faster across the slice will also experience a unit of phase change, but it will experience more phase change than the preceding spin because it's traveling a longer distance across that gradient.
So, let's look now as these spins move across the gradient for this period of time, whilst the gradient remains constant. We can see that the stationary spin gains a small amount of phase. The moving spin gains more phase than the stationary spin, and a spin that moves faster gains even more phase. For each one of these spins here, we have said they've gained one unit of phase. If you cast your mind back to that phase diagram, for the first unit of time that we apply our gradients, each spin is going to get one unit of phase. The degree of phase is different based on the velocities, but we call that one unit.
Now, in every phase contrast MRA, we apply an equal and opposite gradient in the other direction. It has the same amplitude here, the same steepness of gradient, but now as the spins move, they're moving in the same direction. They're going to move along a magnetic field strength that is getting smaller and smaller. We're going to lose phase relative to the null point. We can see that as it moves along a gradient that is getting weaker and weaker, we're going to slow down, relatively speaking, the precessional frequencies and regain some of that phase.
Now, we've said for the first period of time, a stationary spin is going to gain one unit of phase. And the second period of time, as long as the gradient is equal and opposite, the stationary spin hasn't moved along that gradient. It's stationary by nature. It is then going to regain one unit of phase. It's a linear fashion. For every period of time, we gain or lose one unit of phase. For moving spins, we've seen that in the second period of time with a gradient, we are going to gain three units of phase. In that first period of time, we get one unit, then three units, then five units. If that's complicated to you, go back to the previous talk where we look at spin phase effects.
Now, this spin gained one unit of phase in the positive direction as it moved along a positive gradient. Now it's going to lose three units of phase as it moves along this negative gradient here. The same happens with this spin, but those three units are more because the initial unit is larger due to that increased velocity of the spin. So, let's watch these spins closely as they move along that gradient. Notice how the stationary spin has regained its phase, and the net phase change over this period of time is zero. It's gone back to the same phase that it started at.
Spins that were moving across the gradient here had initially gained phase with this positive gradient here, but then lost more phase as it headed further and further along this gradient through the slice. Remember, this only works when it's moving parallel to the gradient. The spin that was moving fastest lost the most amount of phase, and that's because this constant here is proportional to the velocity that that spin is traveling. The higher the velocity, the more phase change there's going to be.
Now, when this gradient is switched off, we can see that the degree of phase change is proportional to the velocity that those spins were traveling through the slice. If there's no phase change, we can assume that that spin was stationary. If there's a certain degree of phase change, we can actually calculate the velocity that that spin was traveling along the slice due to the degree of phase change. The faster the spin is moving through the slice, the more phase loss that we're going to get as it moves across these gradients.
What we also get here is some direction to where these spins are moving. Are they moving up the gradient or are they moving down the gradient? Spins that are moving from left to right are going to have phase changes that are net negative because during the second gradient here, the negative gradient here, we're getting more phase change than we were getting in the first gradient. So, spins that are moving from left to right here are going to have a net negative phase change here. If these spins are moving from right to left in our image, remember blood can flow in both directions through our slice, our net phase change would be positive.
So, this phase change, the magnitude of the phase change, gives us information as to how fast these spins were moving through the slice. And the direction of the phase change gives us clues as to which directions the spins were moving in that slice.
Now, what we can do is acquire multiple different K spaces with different phase contrast gradients that we've applied here. We need to apply this at the bare minimum in all three orthogonal planes in the Cartesian plane here. If we apply a gradient along the longitudinal axis in the slice selection gradient direction here, we will see that spins that are moving through the slice and remain within that slice are going to experience a phase change during this positive and negative gradient. This phase contrast gradient here, only spins that are moving in that Z direction will experience the full phase change here because those are parallel to the gradient that we've applied.
In order to see spins that are moving along the X axis of our slice, we need to repeat the sequence, but now these gradients need to occur along the X axis of our slice, separate to our frequency encoding gradients. Again, we need to at the bare minimum have one of these sequences having this gradient occurring across the Y axis of our slice. This will detect movement in the Y plane, the X plane, and the Z plane.
Now, as you know, blood doesn't only flow through the slice in the Z axis or flow perpendicular or parallel to our slice. We can have blood flowing diagonally through our slice. And ideally, we want to use more than three separate sequences here, more than just the X, Y, and Z planes. And what we can do is apply this phase contrast gradient at the same time in both the X axis and the Y axis, and we'll get a combination vector that will allow us to assess flow diagonally through our slice. So, ideally, we want to do this more than three times, six times, 12 times to assess what the phase change is in multiple different planes in our slice.
Now, the phase change is what's used to generate signal in our image. We are not measuring transverse magnetization. We want to compare phase changes over time through multiple iterations of this pulse sequence. Where there is more phase change, we're going to represent those regions as bright, and that's what's known as a magnitude image, where the magnitude of phase change is going to give us brightness on our image. And we can go about generating an image that looks something like this here. You might see that this represents our sinuses, our dural venous sinuses, as blood is flowing away from the brain back to systemic circulation. You can see that we are representing blood flow in all different directions here. We've applied this phase contrast gradient both in the X axis, the Y axis, the Z axis to allow us to generate this magnitude image here.
Now, without getting too complicated, there are multiple different ways that we can represent phase contrast MRA images. This is a magnitude image, where any phase change is represented as brightness on the image. You can see that the background tissue that remains stationary, there's no phase change with that phase contrast M sequence, so it's represented as dark on our image here. We can have a phase image, where the direction of flow becomes important. Spins that are moving through the slice in one direction will be represented by a certain grayscale, and spins that are moving in another direction will appear darker. The way that we can manipulate the data and ultimately represent the data in an MRI image varies drastically. What I want you to understand is how that bipolar gradient is going to give us that phase shift information that allows us to see what spins are moving and which spins are stationary.
Now, importantly, when we're looking at this image here, you might be wondering why can't I see the carotids coming up into this image? Why can't I see arterial blood flow in the brain here? Now, what we've done is selected for a specific velocity within this image, and we only want to represent spins that are traveling at that specific velocity. And I want to introduce you to a concept that is crucially important to phase contrast MRA, and that's a concept known as velocity encoding.
Now, in our first example, we had a gradient across our slice that was a specific magnitude. What happens if we took those same spins, but we applied a gradient that was had a higher amplitude, that had a steeper gradient? We would represent that gradient with a higher amplitude here. You can see that the gradient here, across the same distance, is much deeper. Now, as these traveling spins, these moving spins, move across this gradient, they're going to experience higher magnetic field strengths than our initial example. Those higher magnetic field strengths, if you think back to your Larmor equation, are going to induce a further or a greater change in frequency and ultimately a greater phase change.
Now, let's take this example here with a greater magnetic field strength. We'll see now that because the magnetic field strength is stronger, we get a greater change in phase here over this period of time. Here we get one unit of phase change, and that unit of phase change is proportional to the gradient field strength as well as the velocity that these spins are moving. You can see that even the stationary spin has gained more phase because of this stronger gradient. Our moving spin now has gained double the amount of phase that it did in our first example, and same here. Now, this one unit of phase change is much larger. So, when we reverse that gradient, now this one unit will be three units of phase change in the opposite direction.
Now, what happens as these spins carry on moving through our slice? The phase changes much more drastic because of the steeper gradient. The velocities haven't changed. The only thing that's changed is the steepness of the gradient, the strength of the gradient that we were applying across whatever axis of our slice we're trying to get this information from. This spin here, for example, has moved from left to right. If we were to look at where it started its phase, the same as the stationary spin, we would perhaps think that the spin has only gained a small amount of phase. Now, if the MRI machine was detecting this phase change and it only sampled here and here, you may see how the MRI machine might think that this spin was moving much more slower than it was and moving in the opposite direction. See how phase change direction here is a a positive phase change? A net positive phase change. In our initial example, we had a net negative phase change for all spins that were moving left to right.
What's happened here is we've passed the 180 degrees of phase change. Now, as we pass the 180 degrees of phase change, we lose our ability to figure out which direction these spins are flowing, because after 180 degrees, we no longer know whether that spin had gained phase because it was moving at a specific velocity along the gradient, or whether it had gained phase this way because it was moving opposite and slower.
Now, what our velocity encoding gradient does, it allows us to select a gradient that's gradual enough to prevent going past the 180 degrees in phase change. If spins are moving very fast, they're going to change their phase very fast, and we're going to need a much shallower gradient. A shallower gradient will prevent that phase change from happening too rapidly.
Now, what parameters here are causing phase change? The first is the velocity that these spins are moving. You see that the faster spins move, the more phase change we're getting. Now, we can't change how fast spins are moving. If we're looking at a blood vessel, spins are going to travel at a specific velocity based on the cardiac output of that patient. If we're looking at flow of CSF, CSF generally flows at a certain speed, but if you've got say aqueductal stenosis, there might be faster CSF flow through that aqueduct. We don't know the velocity. What we need to do is estimate the velocity and tell that to the MRI machine. And we give that velocity in centimeters per second. Say we think CSF is going to be flowing at about 8 centimeters per second in our region of interest here, we can tell the MRI machine we want to be able to accurately detect velocities that are 8 centimeters per second or less, 8 centimeters per second or slower.
What the machine can then do is change two parameters, two parameters that we have control over. The first is the gradient field strength. It can make the gradient field strength steeper. When we've got slow flow like 8 centimeters per second, we can allow for more phase change, as long as it doesn't go past that 180 degrees. The other thing you can do is reduce the period of time or increase the period of time that we apply that gradient. The longer we apply the gradient, the more phase change we're going to get.
Now, if we say set this to 200 centimeters per second, but we're interested in spins that are moving at 5 centimeters per second, what we're going to do is apply a gradient that's much too shallow. We're not going to accurately be able to represent that slow flow. We want to match this gradient and match the period of time that we're applying the gradient to the velocities that we're interested in here. The closer we can get these gradients to the velocities where we get maximum phase shift here, the more accurately we're going to represent that phase shift.
The reverse is also true. If we set a gradient that's too high, or we apply the gradient for too long, we set our velocity encoding to a value that's too low, and we're looking at arterial blood where blood's moving much faster than 8 centimeters per second, we are going to get phase shift that goes over the 180 degrees, and we're going to get what's known as aliasing. We're going to lose that directional information here. Not only do we lose which direction the spins are flowing in, we can't calculate whether it's going left to right or right to left, we also can't back calculate the velocity that these spins are moving, because we've passed the 180 degrees. We don't know how many phase shifts have occurred because our gradient was too steep or we applied the gradient for too long.
Now, hopefully that makes sense. A little bit difficult concept to get around. Now, you may be wondering what are the advantages of doing phase contrast angiography? We looked at time of flight angiography, and that worked well. Well, again, phase contrast angiography doesn't require us to give contrast. And when we did time of flight angiography, we saw that that it was the unsaturated spins entering the slice that were providing a signal. But we said that if tissues have a very short T1, they regain their longitudinal magnetization very quickly, they could also still provide signal, they don't become saturated. Some stationary tissue could provide signal. And when we look at contrast enhanced angiography in our next talk, we'll also see that T1 values of tissues become very important. Phase contrast angiography doesn't rely on the T1 values of tissues, it relies on phase differences, and not signal differences, not transverse magnetization differences within tissues.
Not only that, but we can see that phase contrast angiography allows us to get information in multiple different planes. In time of flight angiography, we saw that if spins were running through a plane, we could get saturation and lose quality of spins running in the image. It was better when spins were running perpendicular to our slice. Now, there are disadvantages to phase contrast angiography. The major one being, we have to repeat the sequence so many times in multiple different planes just to get any valuable information. And that's the biggest downfall. It takes incredibly long to generate phase contrast angiography images. And also, because we can't get every single axis within our slice, we can get a reduction in our accuracy compared to time of flight angiography images.
Now, we're going to move on to the final talk in this Mr. Angiography series, where we look at contrast enhanced Mr. Angiography. So, until then, I'll see you all there. Goodbye everybody.