Transcription
Hello everybody and welcome back. So, in the previous talk, we looked at the process of nuclear magnetic resonance, where we placed protons within an external magnetic field, and they aligned with that magnetic field, processing at a set frequency. We then applied a perpendicular radiofrequency magnetic pulse that caused those protons to start resonating in phase with one another and fanning out away from that longitudinal magnetization vector. That net magnetization vector then gained more and more transverse magnetization. And if we flip that net magnetization vector to 90 degrees, we completely lost the z-axis magnetization, the longitudinal magnetization, and at the same point, we've completely gained transverse magnetization. At 90 degrees, we have our maximum transverse magnetization vector. So, that process of nuclear magnetic resonance and the application of a radio frequency pulse caused loss of longitudinal magnetization and gain of transverse magnetization.
In the next two talks, we're going to look at the process of relaxation, which happens in two separate independent mechanisms. The first is the loss of transverse magnetization, otherwise known as T2 relaxation. The second process, which is independent of that first process, is what's known as T1 relaxation, or the gaining, regaining of longitudinal magnetization. So, in today's lecture, we're going to look at T2 relaxation, which is the loss of transverse magnetization.
Now, there are multiple different terms for this that I want to introduce you to. The first is what's known as spin-spin relaxation. We've seen in previous talks that the loss of transverse magnetization comes from these spins going out of phase with one another. As we stop that radio frequency pulse, the spins that were resonating in phase start to de-phase from one another, and the rate at which they de-phase depends on which tissue they're in. Now, that dephasing is primarily caused by spins interacting with one another. The way I like to remember this is that spin-spin has two S's here, so spin-spin is related to T2 relaxation. Now, if you take that analogy of spinning a basketball on your finger, if I had many people in the room and everyone was spinning a basketball on their finger, and the basketballs bumped into one another, those basketballs will start to lose some of their spin, and they will be de-phasing or spinning at different rates from the basketballs in the room. That is the process for the loss of phase in T2 relaxation.
Another term that you may come across is what's known as transverse decay, and this makes sense as protons de-phase, they lose their transverse or their net transverse magnetization vector, and we get a loss of signal because it's a transverse signal that we're measuring in our MRI machine. So, if you imagine these as basketballs, these protons here, and they're bouncing into one another, and as the spins interact with one another, the spins with different energy levels as well, the energy is transferred, and those spins become out of phase, and that's the predominant mechanism for the loss of transverse magnetization.
So, let's have a look at an example here. We have a unit of fat, represented by this orange color here, and a unit of CSF, represented by this blue color here. We've applied a radio frequency pulse that matches the precessional frequency of these net magnetization vectors and we flip that net magnetization vector to 90 degrees, our maximum signal. Now, what happens when we turn off that radio frequency pulse? While those precessing spins will now start to de-phase. And if you think about what fat is made up of, it's made up of long chains of triglycerides, where all the molecules are joined together. They can bump into each other really easily. If we take our room full of people with basketballs on their hands, fat has got chains of people holding hands with one another, and as they move around the room, they're much more likely to have their spins or the basketballs bump into one another. Water or CSF has free people walking around in the room, free to move as they please. They're not joined to other people in these long chains of fatty acids. So, water, they're less likely for the spins to interact with one another. There's more free movement in the room. So, you'll see that the phase of water or CSF stays much more in phase than fat does.
Let's have a look at these two separate tissues and see how they behave differently as they start to lose phase in the transverse plane. As you see in CSF here, the net magnetization vector is staying much more in phase. The spins aren't interacting as much as they are in fat, and we see that the signal generated from fat is lost much more quickly than the signal generated from CSF. So, now we can draw these curves here, which are our T2 relaxation curves that are dependent on the type of tissue through which the spins are spinning. Look in fat here, how out of phase those spins are, and as we know, as we get out of phase, our magnetization vectors in the XY plane start to cancel each other out, and after a period of time, we're getting complete loss of that signal in fat. The water has stayed relatively in phase with one another, and although we're still getting lots of signal because they're not perfectly in phase, that loss is much slower. And for each tissue, we can plot that free induction decay curve for the different tissues.
Now, you'll see that I've written T2 star decay here, and not T2 decay. Now, whenever you put an asterisk somewhere, it means that there's some terms and conditions. And the reason for this T2 star decay is because the actual measurable decay that we measure on the MRI machine, the drop-off of signal that we were looking at at the previous slide, is not purely due to the spins interacting with one another. T2 relaxation, in an ideal world, would only be getting loss of that transverse magnetization vector from spins interacting with one another, spin-spin relaxation. Now, in the real world, we get loss of signal because of spin-spin relaxation, but we also get loss of signal due to magnetic field inhomogeneities, which we're going to look at next.
Before we move into that, I want to draw your attention to these T2 star time constants here. At the beginning of our radio frequency pulse, once we flip those net magnetization vectors to 90 degrees, we have maximum signal, and all those protons are in phase with one another. We have 100% of the transverse signal at 90 degrees. This is our transverse magnetization vector. Now, as time goes by, we get loss of that signal because of the dephasing of those atoms, and it happens at different rates depending on the tissue we're in. When 63% of that signal has been lost, or we have 37% of the transverse magnetization vector left, that time constant, the amount of time it takes to get to that point, is what's known as T2 star, or T2 star decay. And we can use these values to get contrast in our tissues later.
Now, in an ideal world, we wouldn't want T2 star, we would want a T2 value, which would represent 63% loss in the transverse magnetization vector purely due to spin-spin interactions, not due to magnetic field inhomogeneities. And this curve here would be known as our T2 relaxation curve. We've seen that the T2 star relaxation curve happens much quicker in tissues.
Now, if we have a look at our MRI machine here, in an ideal world, the magnetic field would be homogeneous. It would be exactly the same, no matter where the protons are within this magnetic field. Now, there are three separate mechanisms that make this magnetic field inhomogeneous and cause that T2 star decay. The first is that the MRI scanner itself can't make a perfect strength magnetic field that's equal all the way through the transverse plane. The coils are going to have differing magnetic field strains the further away from the coils you get. So, that's the first reason for magnetic field inhomogeneity. The second mechanism is that there could be a substance within the patient, either metal or calcium or dense cortical bone, that causes disruption in the local magnetic fields here. And that's why in a patient that has a metal device, you'll often see T2 signal is completely lost around that device. That's because of the localized changes in the magnetic field strength. And the last thing is when spins start to de-phase with one another, the magnetization vectors are becoming out of phase with one another, and they can disrupt the local magnetic field as well. And so we don't get perfect magnetic field lines in the longitudinal plane here. So, all three of those mechanisms cause the magnetic field to be inhomogeneous.
Now, because the field is inhomogeneous, a proton that is sitting here will experience a different magnetic field strength to a proton that is sitting at a different location. And we've seen that when protons or spins experience different magnetic field strengths, they will spin at different rates. We look back to our Larmor frequency, a different magnetic field strength will cause the dephasing to be increased because the rates of change of those precessional values will be different between those two protons. And that's what's responsible for this T2 star effect occurring.
Now, our T2 star, or the free induction decay curve, will always be less than the T2 value, the T2 relaxation value. And in imaging, we want to try and compensate for this reduction or increased rate of loss of transverse magnetization. And there actually is a mechanism for which we can compensate for these local field inhomogeneities. So, let's have a look at how we go about compensating for that T2 star decay when we are trying to produce an image.
The first thing we need to do is apply a 90-degree RF pulse that is perpendicular to the main magnetic field. Once we've applied that 90-degree RF pulse and turn it off, we will get relaxation, T2 relaxation, where we get loss of transverse magnetization. Now, in an ideal world, the transverse magnetization loss will be due only to spin-spin interactions, where spins are transferring energy and they start becoming out of phase because of that transfer of energy between the two spins. That is what's known as our T2 decay, or T2 relaxation. Now, what actually happens in the real world is we get spin-spin interactions, which cause that loss of transverse magnetization, and we get local magnetic field inhomogeneities, which causes this T2 star decay to occur. So, this is what we want, this T2 relaxation. This is what we're actually measuring because of the inhomogeneities within the magnetic field.
So, what has actually happened here? Well, we've taken our longitudinal net magnetization vector and flipped it to 90 degrees with that 90-degree RF pulse. We've completely lost longitudinal magnetization, and we've now got a maximum transverse magnetization. We've got maximum T2 signal here. Now, what's going to happen is these spins in the same voxel within our image are going to de-phase with one another. If we look at it end on, they're going to de-phase like this. Some of them will move faster than others, and that's mainly due to the spin-spin interaction between the different spins. But we've also seen that there is differing strengths of magnetic field strength because of that local inhomogeneity in the magnetic field. Now, the one that's experiencing a higher magnetic field strength is going to de-phase quicker than the one that's experiencing a lower magnetic field strength. So, we've flipped it to 90 degrees, and we're getting de-phasing of these spins.
Now, what happens is over time, these spins will de-phase with one another, and they will also start gaining longitudinal magnetization. Now, the one is de-phasing faster than the other. What we want to do is be able to re-phase these two spins with one another. And the way we do that is by applying what's known as a 180-degree radio frequency pulse. It's the same radio frequency pulse, this 90-degree radio frequency pulse, same magnitude, but for twice the duration. So, what has happened now? One spin is de-phasing faster than another spin, and we apply a 180-degree RF pulse. So, let me get this right here. This is the faster one, the blue is the slower one. We apply a 180-degree radio frequency pulse. We are flipping those spins now 180 degrees here is our main magnetic field. Now, the leading spin is the slow spin, and the trailing spin is the fast spin. We're spinning or precessing in this direction. Now, what is going to happen over time is the faster spin is going to catch up with the slower or the lagging spin. And if we wait the exact same period of time between our 90 and 180-degree pulse, what will happen is those spins will now become in phase with one another because of that 180-degree pulse. And we have gained now that net magnetization vector in the transverse plane. Our spins have re-phased with one another. And you can see that represented by this graph here, is that as the spins start to re-phase with one another, we get an increase in that transverse magnetization vector because of that 180-degree flip and then allowing those spins now to catch up with one another and sync up, giving us a maximum net transverse magnetization vector. And what we can do then is sample the signal at this point. And if we sample the signal at this point, you'll notice that that signal is the same as the T2 relaxation, the signal we're measuring now at the time to echo. And you can see now why it's called an echo. It's the same as what we would have gotten if the loss of transverse magnetization was only because of spin-to-spin interactions or T2 relaxation. And it's this mechanism, which we're going to look at later in a pulse sequence called spin echo sequences, that allows us to regain that T2 relaxation and account for those local inhomogeneities in the magnetic field. And we can do this for all the different tissues, all the different voxels within our patient, and plot these values over time.
Now, importantly, we can place this 180-degree RF pulse wherever we want to place it, and then measure the echo at the same distance between the 90-degree RF pulse and the 180-degree RF pulse. This distance and this distance is the same. We can make this TE time much shorter, or we can make it much longer. A shorter TE time will give us higher signal, and a longer TE time is going to give us lower signal. And if we plot those signals over time, depending on the different tissues that we're trying to image, we can see that T2 relaxation curve. It takes much longer in CSF because those hydrogen protons are able to move freely. In fat, you think of people holding hands in the room, spinning basketballs in those long triglyceride chains, the basketballs are going to bump into each other, and that spin-spin interaction is going to cause a loss of transverse magnetization. And that happens even faster in muscle.
Now, we've seen that we can choose the time to echo when we're going to sample this tissue. If we sample really early, a short time to echo, we flip that longitudinal magnetization vector into 90 degrees, switch off the RF pulse, and immediately sample the tissue. What we get is a short time to echo. Now, you'll see that the signal here is high for the muscle, for the fat, and for the CSF. We're going to have a high signal, and there's going to be no contrast between these tissues. We've got very little difference in the T2 relaxation times between these tissues. If we wait a longer period of time and make our echo slightly longer, you'll see that the signal has decreased, but the contrast between the various different tissues has increased. Our muscle signal is going to be much lower, it's going to be represented darker on the MRI. Fat is lower than CSF, but higher than muscle. And now CSF is still giving us a bright signal value. Waiting or prolonging the T2 times going to increase the contrast between those two tissues. So, you can see how changing TE time changes the contrast, and that contrast is based on the T2 relaxation differences between these tissues.
Now, we can wait even longer and have a third time to echo here, where we've now got very little signal. And again, we've lost contrast here. There's very slight grayscale differences, but now it's difficult to tell the CSF from the fat and from the muscle. So, if you wait too long without time to echo, we're going to lose that transverse magnetization vector and not have any signal to detect. Now, hopefully, this graph shows you that change in the TE will highlight the differences in T2 relaxation differences between the various different types of tissues.
In the next talk, we're going to be looking at T1 relaxation, and I'm going to show you how we can use T1 relaxation differences in order to see the T1 differences between tissues. So, until that talk, I'll see you all then. Goodbye, everybody.