Transcription
Hello everybody, and welcome back. Today, we're going to be looking at the process of T1 relaxation. Now, this video follows on from the previous video where we looked at T2 relaxation. So, if you haven't watched that one, I'd highly recommend watching that one first, then coming across to this video.
Now, T1 relaxation is also known as spin-lattice relaxation. We saw in T2 relaxation, it was the interaction between spins, spin-spin relaxation, that caused the spins to dephase and ultimately lose transverse magnetization. And that's why T2 relaxation is often known as transverse decay.
In T1 relaxation, the spins interact with what is known as the lattice. Now, the lattice is the structural components, the macromolecules, the proteins that don't have spin themselves. But when spins interact with them, it causes those spins to start to gain longitudinal magnetization or start to realign with the main magnetic field.
Now, spin-lattice relaxation is also known as longitudinal recovery because those spins are starting to realign with the main magnetic field. We are gaining net longitudinal magnetization. We're recovering that longitudinal magnetization. In T2 relaxation, we are losing net transverse magnetization, that's why it's known as transverse decay. So, ultimately, what is happening here in T1 relaxation is the spins that were in the transverse plane are now realigning with the longitudinal plane, and we are regaining that longitudinal magnetization vector.
So, let's have a look at an actual example. Here we have the MRI machine with two separate tissues, fat on the left and CSF on the right. We've applied a radio frequency pulse that has caused the net magnetization vector to flip to 90 degrees. We have lost now the longitudinal magnetization vector and we're at maximum transverse magnetization vector. Now, when we switch off that radio frequency pulse, that B1 pulse, two things are going to happen, and these processes are separate. We'll get T2 relaxation, and at the same time, we're going to get T1 relaxation, independent processes from one another.
Now, we've looked at T2 relaxation where those spins start to dephase, and we get lots of transverse magnetization, we get transverse decay. Now, we're going to look at how longitudinal magnetization is regained within the sample. As that B1 radio frequency pulse is turned off, these spins will interact with the lattice. And we've talked about the lattice; it's the non-spin components that cause those spins to realign with the B0 field. Here, now, the rate at which spins realign is dependent on the type of tissue.
We've looked at the example of people within a room spinning a basketball on their finger, and we've said the basketball is coming into contact with one another, spin-spin interactions cause those basketballs to spin out of phase. That's synonymous with T2 relaxation. Now, if you picture people in the room, and there are chairs all over the room, or there are obstacles within the room, those chairs and obstacles aren't spinning, but the people walking around can trip over those chairs, interact with the lattice within the room, falling over would cause the basketball to tip like this into the longitudinal plane.
Now, in CSF, there are very few proteins or macromolecules or structural components, very few chairs within the room. So, the people walking around that room can walk around freely. The spin-spin interactions are less than say, in fat, and they're less likely to trip over the lattice within the room. So, in CSF, T1 relaxation also takes a long period of time.
Now, we've looked at fat being long chains of triglycerides, and we've said it's like people in the room holding hands with one another, and that's why T2 relaxation happens much quicker in fat. The basketballs are much more likely to bump into one another. Now, not only that, but in fat, there's more lattice within the sample, there are more structural components, non-spin lattice components, and that means that fat gains longitudinal magnetization quite quickly. What also happens in fat is the long triglyceride chains also move in response to that radio frequency pulse, meaning that the spins are more likely to come into contact with the surrounding lattice again, another reason why T1 relaxation happens faster in fat than it does in CSF.
So, let's see what happens over a period of time. We wait a period of time, and we see that in fat, we regain some longitudinal magnetization, and the same things happened in CSF. Now, this vector here, if we look in CSF, we've got our net magnetization vector. Initially, it was along the B0 plane. We flipped it to 90 degrees, and then over time, that is going to start to gain longitudinal relaxation until ultimately lying completely in the longitudinal plane.
Now, as this process is happening, as we are regaining longitudinal magnetization, we are also getting T2 relaxation happening at the same time, where these spins within the CSF are dephasing with one another. So, when the CSF starts to gain longitudinal magnetization at this stage, many of the CSF spins are out of phase with one another, and we've lost a lot of net transverse magnetization. Now, this gaining of longitudinal magnetization does account for some loss in transverse magnetization, but that pales in comparison to the transverse magnetization loss because of the dephasing of those spins. When we've regained some longitudinal magnetization at this point, we've likely lost all of the transverse magnetization because those spins are out of phase with one another. We can think of the net magnetization vector then as being just this longitudinal component here. That's really important. The transverse component does not equal this part of the vector because those spins are now out of phase, and because those spins are out of phase, the transverse component has canceled each other out, and we're left with a net magnetization vector in the longitudinal plane.
Now, as the tissues gain their longitudinal magnetization, we can use this x-axis here as a proxy for the longitudinal magnetization vector, and that becomes really important in T1 relaxation. As we wait more time, we see that fat again is gaining the longitudinal magnetization faster than it is in CSF, and we can plot this on this graph here. The y-axis here being the longitudinal magnetization, the net longitudinal magnetization, and the y-axis ends in 100 here, where we've got full recovery of longitudinal magnetization. And we can see that fat is gaining that longitudinal magnetization faster than water is. That's because in CSF, there's less lattice for interaction to occur. And not only in fat is there more lattice, but spin-lattice interaction is more likely to occur because of how those triglycerides react to the magnetic field.
As we wait more time, we can see now in fat, we've regained 100% of that longitudinal magnetization, and the CSF sample is slowly regaining that longitudinal magnetization. And it's these differences here that allow us to get T1 contrast within an image. We saw in transverse relaxation that was looking at T2 differences within the image. Here, now, we're looking at how we get T1 differences, and that's what we're going to focus on in this talk.
Now, for the various different tissues, you can plot these on a graph, the same that we did with T2 relaxation. Now, we saw that T2 relaxation was a loss of signal, a decay in signal. T1 relaxation is a gain of signal; it's longitudinal recovery. We are gaining or regaining that longitudinal magnetization vector. So, here we can see that fat gains faster than muscle, and muscle gains faster than CSF. And again, we can use a time constant here known as the T1 time constant.
In T2 decay, we looked at the time it took to lose 63% of the transverse magnetization signal. Here, in T1 relaxation, we're looking at the time it takes to gain or regain 63% of the longitudinal magnetization vector. That time is what's known as the T1 time constant. Now, this isn't an arbitrary number. 63% is used in both of those equations because there is an equation that looks at the T1 and T2 relaxation constants, and that equation is out of the scope of this lecture series. But what you need to know here is that the T1 time constant is much longer in CSF than it is in fat.
Now, why do I keep comparing CSF and fat? The predominant signal generated in the MRI is either coming from water or it's coming from fat. That's where the most free hydrogen atoms are available to generate signal in MRI imaging. Now, you would have seen that in T2 relaxation, we had a concept known as T2 star. Why then do we not get T1 star relaxation? What was causing T2 star relaxation? T2 star was the extra loss of decay away from the T2 relaxation curve that was due to magnetic field inhomogeneities, the differences in the magnetic field strength throughout the magnetic field caused the spins to dephase faster than they would usually just from spin-spin interactions. Some spins were experiencing a higher magnetic field and therefore resonating faster, and some spins were experiencing a lower magnetic field and therefore resonating slower. And because of the differences in those speeds of resonance or speeds of procession, we got lots of transverse magnetization.
In T1 relaxation, the magnetic field is responsible for gaining longitudinal magnetization, and differences in magnetic field strength will result in slight differences in the longitudinal relaxation. However, because the magnetic field is inhomogeneous, some of those spins will experience a weaker magnetic field and gain longitudinal magnetization slower, and some will experience a stronger magnetic field and gain longitudinal magnetization slightly faster. If we average out those differences, we're going to get gaining of longitudinal magnetization at roughly the average magnetic field strength, and that gaining of longitudinal magnetization then will be equal to the T1 time. The regaining of longitudinal magnetization has nothing to do with the phase of the spins. We saw that in T2 loss, it has everything to do with the phase of the spins and that magnetic field inhomogeneity, whether it be stronger or whether it be weaker magnetic fields cause dephasing. That dephasing doesn't affect this longitudinal magnetization, and we get a time constant known as T1 that is the average of that magnetic field.
So, let's then compare our T2 relaxation and T1 relaxation, specifically looking at the lens of time to echo and time to repetition. We saw that in T2 relaxation, the TE time highlighted the differences in T2 relaxation between the different tissues. We can see here that changing the TE time in T2 relaxation highlighted the T2 contrast differences between the various tissues. And if we used a really short time to echo, we got high signal but no contrast between those tissues. We negated the T2 differences between these tissues, but we still got signal from that sample. As we waited slightly longer, we have still got signal coming from the sample, but the signals differ because of the differences in T2 relaxation. And if we waited even longer for a really long TE time, we'd get very low signal and very little contrast between the tissues.
Now, when we look at T2 relaxation, this is something that we can directly measure because we are looking at transverse magnetization, and it's transverse magnetization that we can measure with the coils within the MRI machine. And that time to echo is the time that we actually measure that signal. Now, if we look at T1 relaxation, what are we gaining? We're gaining longitudinal magnetization, and we can't measure that longitudinal magnetization because it's within the same plane as our main magnetic field. We can't place coils there to measure that longitudinal magnetization. So, how then do we go about highlighting the differences in longitudinal magnetization? The differences in longitudinal magnetization rates is what is going to give us the T1 contrast differences within the tissues.
Well, in order to do this, we need to look at how we actually go about creating these signals. The pulse sequence here, the first thing we do is apply a 90-degree RF pulse to lose all of that longitudinal magnetization and gain all of the transverse magnetization. We then sample the signal at a time known as the time to echo, the TE time. And as we've seen, a very short time to echo results in high signal but very little T2 differences in the tissue. The longer we wait for that time to echo, the more the T2 differences are, the more those spins are allowed to dephase at their set rate for the tissue, and we highlight those T2 differences. We then wait a long period of time as all those spins start to regain longitudinal magnetization and lie in the longitudinal plane. Then, at a given period of time, we repeat that 90-degree RF pulse. That's our time to repetition. As we repeat that 90-degree RF pulse, we re-flip that net magnetization vector into the transverse plane.
So, let's have a look at what that means for the T1 relaxation times within our image. Now, importantly, when we talk about T1 relaxation, we're talking about the gaining of the longitudinal magnetization vector. If we look at CSF and fat, for example, fat gains the longitudinal magnetization vector quicker than CSF does. That's what we've looked at already in this talk. Now, in this longitudinal plane, we can actually use this x-axis vector value as the net magnetization vector for the sample because the spins here in the T2 or the transverse plane have now dephased. The transverse plane has canceled everything out. We've got a net magnetization vector equal to this x-axis value. The same happens in CSF. So, at any given period of time, we've got longitudinal magnetization vectors that are equal to the x-axis value of that longitudinal magnetization. So, that period of time, we've got a short longitudinal magnetization vector for CSF and a long longitudinal magnetization vector for fat.
If we then apply that 90-degree RF pulse at this period of time, which represents the longitudinal magnetization vectors differences between the CSF and the fat, here's what will happen then. The net longitudinal magnetization vectors for CSF and for fat will be the y-axis value for the transverse magnetization at the time of repetition. Here, you'll see that now that we flip that vector, flip the longitudinal magnetization vector, the differences in signal between fat and between CSF is quite large.
So, let's now look at two periods of time where we can do the time to repetition within our T1 relaxation. As we do a short time to repetition, we get what we've just looked at here. The CSF has regained very little longitudinal magnetization, or MZ. Fat has regained a lot of the longitudinal magnetization here. So, what have we got at this period TR1? We've got fat that has regained a lot of longitudinal magnetization and CSF which has only regained a small amount of longitudinal magnetization. If we repeat the 90-degree RF pulse at this stage, the value of the y-axis in the transverse plane is going to be equal to the amount of longitudinal magnetization that the different tissues have gained at that point. So, a short TR time means that we haven't allowed full longitudinal magnetization to occur, and we've still got differences between these tissues.
Now, because we have flipped the longitudinal magnetization vector into the transverse plane, we can now sample that signal. And if we have a very short TE time here, we negate the T2 differences in the tissue. We'll see that the signal coming from fat is going to be much higher than the signal coming from CSF. What we've done here is we've highlighted the T1 relaxation differences within these tissues. You can see here the signal for fat is much brighter, signal for CSF is darker. And when we look at T1 weighted images, we'll see that CSF is dark and fat is bright. That's because of these shorter TR times that's highlighting the T1 differences in the tissues.
If we wait a longer period of time and have a TR time that is long, we have allowed those tissues to regain their longitudinal magnetization, and the longitudinal magnetization vector between the two different tissues is going to be similar. We then apply the 90-degree RF pulse, and the signal from those tissues is now very similar. We can see if we sample those signals at a very short TE time, we'll have high signal with very little T2 differences because at TE time is really short, the T2 differences haven't had time to come about, and we've got very little T1 differences because we've allowed the sample to regain the longitudinal magnetization vector. And this is a sequence we're going to look at later, known as a proton density weighted image, where we negate the T1 differences from a long time to repetition and we negate the T2 differences by using a short TE time.
Changing the TE results in changes in T2 contrast, and now you can see that changing the TR, the time to repetition, results in highlighting the T1 differences. In the next talk, we are going to look at how we use these TE and TR times to weight our images, to weight them either towards the T2 contrast differences or towards the T1 contrast differences, or somewhere in between, known as proton density weighting.
Now, importantly, every image has some T2 contribution and some T1 contribution to contrast in the image. So, if you want to learn how to do that, join me in the next talk where we will look at weighting of MRI images. Until then, goodbye everybody.