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Physics of MRI 5: Relaxation and Image Contrast - Part 2a
Physics of MRI 5: Relaxation and Image Contrast - Part 2a
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Hi, my name is Marshall Sussman. I'm an MRI physicist at University Health Network, in University of Toronto. This lecture is gonna be the second part of my Relaxation and Image Contrast in MRI talk. So in first part of this lecture we briefly reviewed what image contrast is, and then we discussed a number of different MR mechanisms that can be used to generate contrast. So in this lecture what I'm gonna do is, I'm going to show how those contrast

mechanisms can be used within various different MR pulse sequences to create contrast. So the pulse sequences that I'm gonna be talking about are gradient echo and spin echo. So image contrast in image depends on a number of factors. So first is the tissue parameters. So this is proton density, T2, T2*, T1, which we've obviously mentioned, pulse sequence, and the pulse sequence parameters. So all three

of these things will affect the ultimate contrast we see in an image. Now often, when I interact with people who aren't necessarily really familiar with some of the details in MR physics, often, various different mnemonic devices are used. So people say if I have a short tear in my pulse sequence that gives me a T1-weighted contrast image. If I have a long TE

that gives me a T2-weighted contrast in my image. And that's true for many pulse sequence types, but it's not true in all cases. There are certain pulse sequences where these sets of parameters could give you different types of contrast. And really, in order to fully understand the contrast you're gonna generate in an image you really have to examine the pulse sequence, the parameters, and the underlying

contrast mechanisms. And it's really only from that complete understanding that you can really get a good comprehension of what types of contrast you're going to be generating. So with that in mind, let's move on to the first pulse sequence that we're gonna look at, Which is gradient echo. So this is one that we've looked at, a number of different times in the previous lectures, but I'm just gonna

briefly review it here. So basic pulse sequence timing diagram, you can see here, it starts with an RF pulse, which we know tips down the magnetization away from the external magnetic field. And we then turn on our gradients which is what move us through k-space to acquire our data. So initially, after we do our RF pulse, we always start at the center of k-space. We then turn on our Y gradient, and that

moves us up into a particular position in the vertical direction. We turn on our negative polarity X gradient which moves us out to the left hand side of k-space, and then that's followed by our positive polarity gradient, which sweeps out a complete line of k-space. And that's when we acquire our data. We then increase the strength of the Y gradient, and that moves us up to another

line in k-space, and repeat that same procedure. So we just simply step through this, repeat this procedure as many times as necessary in order to cover off all lines of k-space. Now within this basic gradient echo pulse sequence, there's three different adjustable parameters that we can manipulate. The first is the Flip angle or theta so that's really the RF pulse, and it's just simple

the angle that the magnetization makes with the external magnetic field. So this is something that we can control. The second parameter is the TR or the repetition time. And this is simply the time between the acquisition of adjacent k-space line. So essentially the time that it takes us to repeat this cycle. Third is the TE or the echo time, and this is defined at the time between when we first tip

our magnetization down, so we first put out our RF pulse and the time with which when we acquire the central portion of k-space. So in this case it's the center point of this gradient loop, cause that corresponds to when we go through the center of k-space. So in the next few slides I'm gonna show how these parameters can be used to modulate the contrast we see in an MR image. So first of

all, is the echo time or TE. So as we saw from the first part of the lecture, after we play at our RF pulse, the signal intensity decays away over time with T2* decay. So here we have, let's say this tissue here has a T2* value of T2A, T2A*. So the signal decays away like you see here. [BLANK_AUDIO] Now at this point in time here, when we go through the center of k-space which corresponds to this echo

time, the signal has therefore decayed away up till this point here. If we now have a second tissue with a different T2* value, so indicated by the red line, T2B*, then at the echo time, which again is the time we go through the center of k-space here, you can see that the signal will have decayed away, a different amount than the first one, again because it has a T2* value.

Now the contrast we're gonna get in our image, is simply gonna be the difference in signal intensity, at this point, at this echo time. So it's just gonna be e to the -t over T2A*, minus e to the -TE, over T2B*. So by setting up this echo time, we generate a T2*-weighted contrast in our image. Now what if we move the echo time to an earlier time point? So we've

now shortened the echo time TE to this point here. So again, the contrast we're gonna get in our image, is again just simply the difference in signal intensity between these two lines here. But in this case, because our echo time is shorter you can see that we haven't generated as much contrast, so there's less contrast in this case. So in general, when we shorten the TE we reduce the

T2*-weighted contrast in the case of gradient echo pulse sequence. Now I've been mentioning here that, the echo time, the TE in code contrast, which corresponds to the time we go through the center of k-space. But why is it the center of k-space is important, what's special about it? Well here we have a slide that I showed in my earlier talks on k-space. Here we have the

complete image and the corresponding k-space data that generates that image, again recall via Fourier transform. Now if instead of generating the image from the complete k-space data set, I just generate an image from the central portion of k-space, resulting image you see looks like this here. So in this case you can see, importantly, that we encode the contrast in this image.

So the center of k-space still generates the contrast that we see in this image. The outer portion, so if we reconstruct the image just from the outer portion of k-space, you can see that we see the edge information, but there's really no contrast in the image. The image is essentially a uniform color. So that's the reason why the center of k-space is important, because that really encodes

the contrast in our image. So that's why we care about when we go through the center of k-space, and that's what we set our echo time to be. So just to summarize what we've got to date. The echo time, TE, corresponds to the time of acquisition of the center of k-space. The center of k-space, as we know, determines the image contrast, so therefore as a rule of thumb, the longer the TE, the heavier

the T2* weighting. So the more difference in T2* weighting we're gonna have between tissues with different T2* values. So here I just have an example of, this is an image of the heart, one acquired with an echo time of 2 ms, and one acquired with an echo time of 16 ms on a gradient echo scan. So if we compare say the myocardium and the blood in these two cases, you can

see in the one with a 16 millisecond echo time, there's a much larger contrast between the myocardium and the blood. Again because the myocardium has a much shorter T2* value. So it decayed away, much ore dramatically, in the 16 millisecond case, than it had in the 2 millisecond case. The next pulse sequence parameter we're gonna talk about is the

repetition time or TR. So recall the TR it's just simply the time between we acquired adjacent k-space line, so basically the time that we repeat this cycle. So let's look at what's going on with the magnetization. So initially we started out with our magnetization at its full, complete value. So let's say, as a value, for purposes of this discussion as one. So we then play out our pulse, and in this case let's assume

we have a 90 degree pulse, so that tips down the magnetization completely into this transverse plane here. Following that we have T2* decay. So the signal is then going to decay away completely. So following the magnetization decay, the magnetization will then regrow back towards its initial value due to T1 recovery. So here we have again this formula here, 1 - e to the -TR

over T1. Now if we set our TR to be long enough, then that magnetization will regrow back to its initial value. So in other words, the magnetization will regrow back to its initial state. But what happens if I set my TR to a shorter period of time, the magnetization doesn't regrow back to its initial value. Then instead of recovering completely, it will only recover partially. So let's say in this case, it only

recovers to a value of 0.8. So when we then foot the magnetization down, it now, instead of having a value of 1, it only has a value of 0.8. So when we then have our T2* decay on the next iteration, the signal intensity starts from a value of 0.8, and then decays away completely. It then regrows back to a value, again, of 0.8. It's decayed away completely, and we have the same TR value, so it goes back

to a value of 0.8. Now this is called, essentially, the steady state of the magnetization because the magnetization lies in a steady state on every single iteration. So it lies in exactly the same position on each iteration we do. So we tip the magnetization down, it decays, it then regrows back to a value of 0.8. We tip it down again, it decays away completely,

regrows back to a value of 0.8. So a steady state just simply means the magnetization is the same from one TR to the next. And in general, we almost always we'd acquire images when the magnetization is in a steady state. So now, let's examine the contrast it's generated as a result of a particular choice of repetition TR. So as we mentioned in the previous slide, this magnetization in

the red lies in the steady state. So we're constantly going between these two situations. We tip the magnetization down, it has a value of 0.8, it decays away to 0, then recovers to a value of 0.8, and the process is repeated. So it's the same each time. Now, this value of 0.8, the reason it recovered to this point, obviously, depends on the TR value. So if we change

the TR value to some other value, then the magnetization will recover to a different point. But the value that it recovers to also depends on the T1 value of the tissue. So for example, if I had tissue with a different T1 value as indicated by this green line here, so let's say I had a longer T1 value, then it would recover at a time TR to a different point. So in this case let's say it recovers only to

a value of 0.5. And important thing to note is that this magnetization also lies in its own steady state. So it's gonna continuously oscillate between, it's gonna decay away to, it's gonna be tipped down, and it's gonna decay away, and recover back to a value of 0.5. It's gonna be tipped down, decay away to 0, recover to a value of 0.5. If we look at this plot down on the right here, you can see that the red magnetization

is in a steady state where it has a value of 0.8, the green magnetization has a steady state value of 0.5. So in other words, we generate a contrast between these two signals, a T1-weighted contrast, which we capture when we tip the magnetization down. So in this case, the red magnetization would have a stronger signal intensity than the green one would.

And this is a contrast that depends on a T1 value. Now, if I change my TR, that's gonna change the relative amount of recovery between these two magnetization. So the relative T1-weighted contrast is gonna change if I adjust my TR. Now, as a general rule of thumb, the shorter the TR, the greater the T1 weighting because that means that the shorter one's gonna recover more quickly than tissues

with a longer T1 value. So TR affects the T1 weighting. Generally speaking, the shorter the TR value, the greater the T1 weighting. Now, there are some exceptions to this, of course, that if you have a very, very long TRs then the contrast basically disappears. And similarly if we had very, very short TRs then there really isn't much time

for a contrast to evolve so there overall won't be very much difference in signal intensity. [BLANK_AUDIO] Couple of additional comments on this contrast generated by TR. First of all, in this case, we always assume that the magnetization decays way to 0 each time. So that was sort of our steady state condition.

We tip the magnetization down, decays away to zero, then recovers back to it's steady state value. Typically, if that's not the case, we often tip away/g with something called spoiling. So that's just simply a gradient which dephases the demagnetization to get rid of any of the residual magnetization that's lying in the transverse plane. There's also RF spoiling, which is another way of

accomplishing the same thing. Another thing to consider is that I've assumed that when we tip the magnetization down we're capturing that T1-weighted contrast exactly as it's stored along the z axis here. But as we know, that if we have a TE that's not equal to zero, we're gonna start to have some T2*-weighted contrast evolve in our image. So if our TE is anything other than

zero then we're going to have, not only this T1-weighted contrast, but we're gonna have an additional T2*-weighted contrast that's superimposed on top of it. So we're gonna have sort of a mixture of both T1 and T2* weighting, which would complicate the interpretation of the image, cause it's hard to distinguish which mechanism is dominating. So typically, we wanna choose TE to be as short as possible in these

sort of gradient echo scans where we're trying to highlight T1-weighted contrast. We wanna choose TE as close to zero as we possibly can. Now let's move on to talk about the effects of flip angle on the contrast we have in a gradient echo pulse sequence. And again to examine this one we have to look at, again the magnetization, so in the previous case

we assumed that when we play our RF pulse we're tipping it down with a 90 degree pulse. So, in this case, let's generalize it, to say, we're gonna have an RF pulse with an angle theta. So, in this case, instead of the magnetization being completely tipped down in the transverse plane, it's only tipped down with angle theta. So at that point, instead of the magnetization, initially

had a value of one, but now in the transverse plane, where again we're our signal, it only has a value of 0.7 because we haven't tipped it completely down. So part of this magnetization lies along the z axis and part lies along the transverse plane. Okay, so once we do that, the signal we know decays away with T2* decay, just as before. So we assume that this signal disappears along

the transverse plane, and then once a signal's disappeared we're gonna then experience T1 recovery, and the magnetization is gonna regrow back to its initial value. But remember that unlike the previous case, it's not starting from zero because we didn't tip the magnetization completely down. Rather it's starting from this point of, in this case,

0.7. So the magnetization will then recover with this equation here. It's gonna start at 0.7 and recover back to its initial value. In this case, let's just assume we choose a particular TR, let's say, it's gonna recover back to a value of 0.9. And just to show you that this magnetization essentially recovers, this is basically the latter/g part of the T1 recovery curve. Cause initially, if we started

from zero it would recover like this, but in this case we don't have this portion of the curve cause we're starting at 0.7 already. So that's on the first iteration. We then have to tip the magnetization down again, but it actually gets to be quite complicated, because in general, the magnetization is gonna now start from a value of 0.9, it's gonna be tipped down to some value other than 0.7. And in general,

it's gonna take several iterations until we get into the steady state. So I'm not gonna draw the diagram here cause I 'd probably would have to go through four or five iterations of this until we finally get into the steady state. So generally speaking it's gonna take, if the angle is something other than 90, it's gonna take a longer period of time to get into this steady state of magnetization, but

we typically have to wait until we're in the steady state before we start imaging. Now what happens in terms of the contrast? So let's say we, again, flip our magnetization down with angle theta, it decays away, and then begins to recover. Now if we have two different magnetizations with different T1 values then obviously it will recover to different amounts. So if we plot the recovery on the

plot on the left, the shorter T1 value recovers more rapidly whereas the longer T1 value recovers more slowly. And again recall, they're starting from different points in time here at different values here. This is starting from value 0.5, this is starting from a value of 0.8. So in general, when we have different flip angles this also produces different T1-weighted contrasts. But unfortunately, the relationship

is quite complex between the two, and there really isn't a straightforward relationship between flip angle and T1-weighted contrast. As a rough guide, and this is only a very rough guide, larger flip angles generally produce a heavier T1 weighting, but that's not always the case. Here we just have an example, we have four different images of the brain acquired at different flip angles, 5 degrees,

20 degrees, 40 degrees, 90 degrees. And you can appreciate that the contrast of the brain tissue changes with differences in our flip angle. Okay, so let's just summarize what we've talked about so far with gradient echo. So we showed that there's three different parameters that we can vary in the pulse sequence. There's the flip angle theta, there's the echo time or TE, the time from the RF pulse

to the center of the acquisition of k-space, and there's the TR or the repetition time, which is just the time between the acquisition of adjacent k-space lines. We showed that if we have a longer TE, this is going to produce a heavier T2* weighting. If we have a shorter TR that's gonna produce a heavier T1 weighting. And finally, if we have a larger flip angle,

that's gonna, generally, produce/g a heavier T1 weighting although the relationship is complex, and it's not quite as straightforward. So now we're gonna move on to discussing some of the contrast mechanisms underlying spin echo. So just a brief review of the spin echo pulse sequence.

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