Transcription
Hello everybody and welcome back. So, we're making our way through a series of talks looking at signal within blood vessels. And so far, we've seen that high velocity signal loss and turbulence can lead to dark blood vessels, can lead to hypointensity on our image. We then looked at the concept of flow related enhancement, how blood traveling into a slice that is unsaturated can give high signal. And we use flow related enhancement to generate time of flight MR angiography images. We've also been seeing how we can use saturation bands to prevent blood traveling from one direction from showing signal within our flow related enhancement or time of flight angiography images.
Today, we're going to focus on a phenomenon known as spin phase effect, and we'll see how traveling spins, spins that move whilst we're applying a gradient, will cause hypointensity within our image. And then we're going to look at the concept of gradient moment nulling, which is going to allow us to compensate for that loss of phase due to the movement of spins across the gradient. Both of these concepts are crucially important as we head on to our next talk, which is phase contrast MR angiography, a concept that people often struggle with.
So, we know that when we have a pulse sequence like this, there are many times when we apply a magnetic gradient across one dimension of our slice that we're imaging. We apply a slice selection gradient along the longitudinal axis that allows us to match a radiofrequency pulse and select a specific slice. We apply a frequency encoding gradient whilst we are acquiring our signal. And we apply a phase encoding gradient to generate phase differences along the Y-axis of our slice. Now, we know that all the spins within our slice, if we were to apply a gradient across that slice, what's going to happen? When we apply any of these gradients, there's going to be a frequency difference, a precessional frequency difference across the direction of that gradient based on the location across the gradient. There's going to be frequency differences.
Now, this example I'm going to show you as we apply the frequency encoding gradient, what happens to the precessional frequencies of these spins? We see that where the magnetic gradient is highest, we get a faster precessional frequency compared to where it's lowest. Now, whilst that gradient is being applied, we generate a frequency difference. When we switch that gradient off, when we reach the end of that gradient, those frequencies are going to become the base frequency, here, the frequency that's generated by our main magnetic field. What's happened is we've induced a phase difference across the slice because of those frequency differences. These spins are now out of phase with other spins based on the location across that gradient. Now, that phase difference, we compensate for using rephasing lobes. Here, we've seen that in slice selection gradient and in our frequency encoding gradient, we don't want to compensate for that phase difference in our phase encoding gradient because we want that phase difference to remain throughout our sequence here and allow us to figure out where signal is coming from along the Y-axis of our slice based on these phase differences.
Now, whilst we are applying that phase encoding gradient along that axis of the slice, we are inducing a frequency difference during that gradient. Once that gradient is switched off, that frequency difference has caused a difference in phase based on location in the slice, and that's what's causing the phase differences. Now, we can look at this in a different way. If we were to look at spins across a certain axis of our slice and we represent them using phase data here, these arrows here represent phase. If our spins are precessing at a certain frequency, if we were to look at the end of that spin and look at what phase the spin is in, we can represent that by this arrow here. Now, we're using the rotating frame here, the comparison of the phase compared to the endpoint along our gradient. Now, we apply this gradient along the slice here. The spins at this end of the slice are going to precess faster than the spins at this end of the slice whilst the gradient is on. And we can represent that phase change by these arrows here. Those that precess faster are going to have an increase in phase. There's going to be a positive phase change relative to the center or the null point of this gradient. Those that precess slower than the null point are going to have a negative phase change here. And we can see that the phase change along this gradient here is linear as we move across the gradient, we get incremental units of phase change that happens during any gradient that we apply in our pulse sequence.
Now, when we apply an equal and opposite gradient, such as in our slice selection gradient or our frequency encoding gradient, we can account for that phase change and cause rephasing of the spins. Now, this is assuming that the spins stay in the same location whilst we are applying these gradients. If a spin remains in the same location, it's going to receive an equal and opposite gradient that will allow for this rephasing, and this is a concept that we've looked at before.
Now, what happens when the spins are moving whilst the gradient is being applied? We apply a gradient across a slice and the spins move, say in blood vessels, whilst we are applying that gradient. What happens to the phase of those spins? Well, if we take a spin, for example, here at the null point, and this spin, say it's in blood vessels, is moving at a constant velocity across the gradient, and importantly, it's moving parallel to that gradient, the spin is going to accumulate phase as it moves across that gradient. And as it moves, we see that the phase accumulation is not linear, the phase accumulation is actually exponential. Now, if the velocity of that spin, the velocity of that blood, is constant throughout this gradient and the gradient strength remains constant, we can actually predict this phase change, and that is the basis of the spin phase effects.
In order to calculate that phase change, the change in phase, we can use this formula here. Now, this formula makes a couple of assumptions. It makes the assumption that our gradient strength remains the same, and it makes the assumption that the spin is moving at a constant velocity parallel to that gradient. Now, we can calculate the phase change using this formula here, which is a constant. The constant is determined by the velocity of the blood or the velocity of the spin, as well as the strength of the gradient and the period of time that we apply that gradient for. You can see that the longer we apply the gradient, the more the phase shift, there's an exponential phase shift here.
Now, we can look at two separate types of spins, spins that are moving across the gradient or spins that remain stationary. Here, we can see that a spin that remains stationary and has a gradient applied to it will gain phase in a linear fashion. For each period of time that we apply that gradient, the stationary spins are going to gain one unit of phase. So, we can calculate the phase change in stationary spins using this formula here. If our gradient remains constant, our phase change is going to increase in a linear fashion. If we were to look at a moving spin, a spin that was moving along that gradient at a constant velocity and that gradient was constant, we'd see that the phase change is actually exponential. In the first unit of time, we are going to gain one unit of phase. Now, remember, this graph here is showing units of phase. These aren't the same y-axis for stationary and x-axis spins. This is showing the proportion of phase change. So, for one unit of time, 1 to the power of 2 is 1, we are going to gain one unit of phase. If we were to continue applying that same gradient for another unit of time, you can see now that we've applied two units of time for a constant velocity spin moving parallel to that gradient at a specific gradient, we'll see that 2 units of time to the power of 2 is 4. In our second unit of time here, we've gained an additional three units of phase, one unit of phase initially, three units of phase in the next period of time. If that spin were to continue moving and we still had the same gradients applied, we would see that we would gain an extra five units of phase. We've gone one unit, three units, five units. We're getting incrementally more and more phase as that spin moves along the gradient, and it makes sense. If the spin starts at one location and it's going at a specific precessional frequency and it moves along the gradient, as it moves, it's going to gain the precessional frequency, it's going to precess faster and faster. If it's moving along the positive side of our gradients, those frequency changes are cumulative, they build on from one another. We get an exponential increase in phase change as that spin is moving along the gradient. So, three units of time, 3 to the power of 2 is 9, we get nine units of phase change. You can see how the phase in a moving spin has changed drastically, whereas the phase in a stationary spin has only changed a small amount over this period of time.
Now, it's these spin phase effects in moving spins that causes loss of signal within blood vessels. Remember, with a stationary spin, we apply a gradient and we apply an equal and opposite gradient that allows for rephasing of those spins, and we get the normal signal. Signal loss in an MRI image is due to the degree of phase coherence. As spins dephase more and more, we get loss of signal. Moving spins experience much more dephasing or much more phase incoherence because of that phase change, and ultimately give less and less signal as a result of them moving across the gradient.
So, let's revisit how we compensate for those phase changes in our pulse sequence. Now, we've looked at rephasing lobes, and we've seen how rephasing lobes can allow for rephasing of stationary spins. Let's look what happens to those moving spins when we use those normal rephasing lobes like we use in our slice selection gradient or our frequency encoding gradient. We have a pulse sequence that occurs over a period of time, and we apply a gradient for a specific period of time along the slice here. The gradient strength is represented by this G here, and the period of time is the time across this axis here, represented by T here. We're looking at this part of the graph. Both our moving spin and our stationary spin are going to gain one unit of phase, and we can see that represented here. Now, the moving spin will only gain one unit of phase if it's moving at a constant velocity and it's moving parallel to that gradient.
Now, we apply an equal and opposite gradient. We've used this before. We see that for an equal and opposite gradient of the same period of time, a stationary spin is going to experience one unit of phase change, but it's going to experience a negative phase change because our gradient is in the opposite direction. So, our stationary spin is going to regain that one unit of phase change that it had lost during the first gradient. Our moving spin, however, is still moving along this gradient. It's experiencing the first unit of phase change during our first gradient. It's going to experience more phase change during the second period of time, and we've seen that during the second period of time, as long as that spin is still moving along that gradient, we're going to experience three units of phase change. Now, because this gradient is in the opposite direction, we're going to experience three units of phase change in the opposite direction. Our moving spins are not going to rephase, they're not going to gain phase coherence and give signal. Our moving spins are going to overshoot here and lose phase as a result of this second gradient. So, we can see that these rephasing gradients that we use only work for stationary spins. Moving spins still experience phase incoherence, and as a result, we're going to get low signal on our MRI image when we have spins that are moving across the slice during the period of time that we are applying a gradient to that slice.
Now, it turns out we can compensate for this movement of moving spins through a slice whilst the gradient is being applied using something that's known as gradient moment nulling. Now, gradient moment nulling compensates for this phase loss as spins move through a slice. Not only does it compensate for phase loss for moving spins, it still compensates for phase loss for stationary spins, and we're going to go through how we go about achieving this. We initially apply the same gradient across the slice. This could be our slice selection gradient, our frequency encoding gradient, and we apply it for a period of time. We've seen that both our stationary spins and moving spins are going to gain one unit of phase. This is the first period of time here.
Now comes the kicker. In our second gradient, we are going to apply an opposite gradient of twice the strength, of twice the amplitude here. This gradient is twice as strong and in the opposite direction of our initial gradients. What happens to our stationary spins? We apply a gradient for a period of time, but now our constant, which is dependent on the gradient field strength, is twice the strength. Our gradient field strength is twice the strength. We've got two times the constant. Instead of losing one unit of phase, we are going to lose two units of phase. It's twice the field strength here. Our stationary spin is going to dephase two units here because of this twice the field strength.
What happens with our moving spins? Our moving spins, we see for another period of time, are going to lose three units of phase. But our constant again is twice as high. Our gradient is twice as high. The velocity remains the same, and we know that this constant is based on the velocity and the gradient field strength, but our gradient field strength is twice that of the initial gradient. So, instead of losing three units of phase, this moving spin, as it travels across the steeper gradient, is going to lose six units of phase. This spin is going to lose or dephase six units.
Now, we can see the stationary spins and the moving spins are completely different phases from where they were initially. Now, what happens if we apply our last gradient here for the same period of time that we applied each one of these gradients? We apply the same gradient that we applied initially. Our stationary spin, as we know, is going to gain one unit of phase. It's going to rephase. This sequence here, where we apply a specific field strength gradient in one direction, apply the gradient that's twice as strong in the opposite direction, and then reapply that same gradient, will allow stationary spins to rephase with one another.
Now, what happens in moving spins, assuming that they are moving at a constant velocity parallel to this gradient? Well, we know for the third period of time, as that spin is moving further and further along that slice, along that gradient, we're going to get five units of phase change. Given that our gradient is the same as the initial gradient, those five units of phase change are going to be in the positive direction. This spin now is moving across the positive direction of our gradient, it's gaining frequency, and as a result, it's going to gain phase. We are going to gain five units of phase. Five units of phase is going to cause this moving spin to rephase. That's the beauty of gradient moment nulling. It's an ingenious method to allow for rephasing of both stationary spins and moving spins. If we have spins that are moving through our slice whilst we are applying a gradient, but we use this gradient moment nulling technique where we apply these specific sequence of gradients, we are going to get signal from spins that are moving through the slice, and it doesn't matter what the velocity of those spins are. It only matters that the velocity is constant, assuming the velocity is constant, because we're dealing with ratios here, with units of phase change, not absolute values of phase change. We can see that whatever unit of phase change occurs over these periods of time, gradient moment nulling is going to allow for rephasing of both stationary and moving spins.
Now, these concepts are often difficult for people to grasp, but it's really important to understand both spin phase effects, the change of phase as spins move across the gradient, as well as gradient moment nulling, in order to understand our next concept, which we're going to look at, which is phase contrast MR angiography. We use these phase changes to allow us to generate an MR angiography image that allows us to look at moving spins specifically and get rid of signal coming from stationary spins. Now, that's what we're going to look at in our next talk.
Now, gradient moment nulling is a question that I've seen come up over and over again in past papers. It really assesses whether you truly understand the underlying physics related to moving spins within an MRI slice, and I've included these type of questions in the question bank that I've linked below. Otherwise, I'll see you all in our next talk where we look at phase contrast MR. Until then, goodbye everybody.