Transcription
Hello everybody and welcome back. So by now, we've spent most of our time looking at how exactly we generate an MRI signal. We've seen that if we place an element that has a non-zero spin within an external magnetic field, that element will process at a frequency known as the Larmor frequency. And that processional frequency is dependent on the gyromagnetic ratio of that element, as well as the strength of the external magnetic field.
We've also seen that if we apply a radio frequency pulse perpendicular to that main magnetic field, and that radio frequency pulse frequency matches the processional frequency of the spins, we get what's known as nuclear magnetic resonance, where these spins start to process or resonate in phase with one another, as well as start to fan out into the transverse plane. And what we get then is gaining of transverse magnetization, as well as loss of longitudinal or z-axis magnetization. And it's that transverse magnetization that we can actually measure as signal within our MRI machine.
Now, once we've gained transverse magnetization, we can then stop the radio frequency pulse. Once that radio frequency pulse has been stopped, two independent processes happen: T2 relaxation, or loss of transverse magnetization, predominantly due to the dephasing of spins, as well as T1 relaxation, or gain of longitudinal magnetization. Now, different tissues have different rates of both T2 and T1 relaxation, and it's the differences in those rates that give us contrast within our image. And we've also seen how we can manipulate the time to echo, or the TE time, as well as the time to repetition, or TR time, to weight our images, where we can get images that have predominantly T1 contrast differences shown in the image, or predominantly T2 contrast differences shown in the image.
That we are measuring that signal, but we've got no way of knowing where exactly that signal is coming from. MRI differs from x-ray or ultrasound or CT in the fact that the signal is actually being generated by the patient. It's coming from the patient. It's not like x-rays where we cast a shadow onto a detector, or ultrasound where we wait for these sound waves to come back, and the time it takes for those waves to come back allows us to plot the depth of the tissue boundaries. Here in MRI, the signal is actually coming from the patient. And in order to know where exactly in space that signal is coming from, we need to try and separate the various different signals on the Cartesian plane, which we've looked at before.
If we have three different coordinate values, a z-axis, an x-axis, and a y-axis values, if we know those three coordinates on this Cartesian plane as a frame of reference, we can say exactly where that signal is coming from in space within the patient. And that's what's known as spatial localization within MRI imaging.
Now, I'm going to separate this into three separate talks. The first is what's going to be known as slice selection. Here, we are trying to figure out where the signal is coming from along the z-axis, or along the longitudinal plane of our patient. Now, if we look at this patient within the MRI machine, when you're scrolling through an MRI image, you're looking at different slices that have been stacked upon one another. And you can see that the slice that we select along the z-axis of the patient has some width to it. So when you're looking at an MRI image, you're looking at a 2D image, a single slice that represents some width. There is some 3D data to those pixels on your screen, and in fact, those pixels represent what's known as a voxel. They've got some volume to them.
Now, when we select the slices, we're selecting along the z-axis of our Cartesian plane. We're selecting along this blue axis here, and the gradient that we use to select this slice is what's known as the slice selection gradient, and that's going to be our focus of today's talk. Now, if we take this slice out of the patient and place it on the Cartesian plane, you can see the slice we're selecting represents a z-axis value here. We can't separate the slice at the moment into y values and x values. Now, if we look at this slice head-on, we can see that that z-axis is coming in and out of the screen, just like we look at on our MRI images.
We then need a way to separate the signal coming from this slice into x-axis values and y-axis values. So if we have a patient here, we have an organ, and we have a lesion in that organ, we need to know that that signal coming from the lesion in the organ comes from a specific x-coordinate and a specific y-coordinate in that slice that we have selected. And so the next talk is going to be looking at the x-axis coordinates, known as the frequency encoding gradient. And after that, we're going to see how we can differentiate the y-axis components, known as the phase encoding gradients. But for now, let's focus on how exactly we can select a specific slice within the patient.
Now, if you take our patient within the MRI machine here, we've applied a main magnetic field, our B naught magnetic field, and the signal coming from this patient is going to come from those spins, predominantly hydrogen protons within water and within fat. So let's substitute our patient here for processing hydrogen spins. Now, this constant B naught means that these spins are all processing at the same frequency, known as the Larmor frequency. The gyromagnetic ratio and the strength of the magnetic field will cause these spins to process at a specific frequency.
Now, in order to select a specific slice, we need these processing frequencies to be different along the z-axis. That's the basis for slice selection gradient. Now, in order to change the processional frequencies of these spins, we need to change the magnetic field strength along the z-axis. And we've seen this before. We've used gradient coils to apply a gradient magnetic field along the z-axis, or the longitudinal axis of our patient. And that's exactly what we do as a first step in slice selection. We apply a gradient field across the z-axis of the patient, and that gradient field means that there's a differential in magnetic field strength from one end of the patient to the other end of the patient.
Now, because that magnetic field strength differs at different locations along the z-axis, we get different processional frequencies along the z-axis. So the gradient field is causing these frequencies to differ based on the strength of the external magnetic field. Now, remember, this line here is not showing an angle change in the B naught field. It's showing a strength change. We can see that the strength of the magnetic field changes along that z-axis. The direction of that magnetic field is still purely along that z-axis.
Now, what we can do is try and select a specific slice based on these processional frequencies. We've seen that when we apply a radio frequency pulse that matches the processional frequency, that's when we get nuclear magnetic resonance and we get flipping of those spins into the transverse plane. Now, we can apply a radio frequency pulse to the entire length of the patient, and only the spins that match that radio frequency pulse will exhibit nuclear magnetic resonance. The other spins at differing frequencies won't flip into the transverse plane because those processional frequencies don't match that radio frequency pulse.
Now, when we apply a radiofrequency pulse at a certain frequency, say 60 megahertz, we don't apply that radio frequency pulse at exactly 60 megahertz. There's a slight range to that radio frequency pulse, and that's what's known as the radio frequency bandwidth. Maybe it goes from 55 megahertz to 60 megahertz. There's a 5 megahertz band at which that radio frequency pulse is being applied to the patient. So when we apply a radio frequency pulse, it's going to match up with certain processional frequencies within the patient here.
Now, you can see that that radio frequency pulse has some width to it. It's got a lower value and a higher value. There's a range known as the bandwidth of that radio frequency pulse. Now, this gradient that we've drawn here, you can think of that gradient as representing the different processional frequencies here. These processional frequencies are proportional to the strength of the magnetic field along the z-axis here, and this radio frequency bandwidth is showing the range of radio frequencies that we are exposing the entire patient to within the MRI machine.
Now, because this radio frequency matches the processional frequency of this specific slice, we'll get nuclear magnetic resonance within that particular slice, and we'll see that those spins now gain transverse magnetization, and that gives us a signal that we can actually measure. These other protons will not exhibit nuclear magnetic resonance because the radio frequency pulse frequency does not equal their processional frequency. Here, we've selected a specific slice. Now, this is the basis for slice selection.
Now, today, we're going to look at how we can move that slice along the patient. We want to image multiple points along the z-axis, and we want to see how we can increase or decrease the thickness of that slice. So let's start by looking at how we can move the slides along the z-axis, and that's what's known as slice selection. The first thing we can do is actually change the radio frequency pulse frequency. If we increase the radio frequency pulse frequency, we're going to match to a higher processional frequency proton. So let's see what happens as we increase that radio frequency pulse frequency. We shift our slides along the z-axis because we're now selecting for a higher processional frequency, and these protons are processing at a higher frequency because of that gradient field. There's a higher magnetic field strength further along the z-axis here.
Now, the second thing that we can do is not change the radio frequency pulse frequency, but change the gradient field itself. If we increase the magnetic field strength that these protons experience, we will change the processional frequencies of these protons. So as we increase that baseline gradient magnetic field, we'll see that at the same radio frequency pulse, we'll be selecting a different slice because now these processional frequencies have changed due to that increase in external magnetic field. Not only can we change the slice that we're selecting by changing the radio frequency pulse frequency or changing the gradient field or external magnetic field, we can, in theory, also move the patient along the z-axis. And as we move the patient, the slice that we're selecting will stay the same region within our z-axis, but the part of the patient that we're imaging will change as that patient moves along the z-axis. So there are three different ways that we can select the slice that we are trying to image.
Now, we selected a specific slice, say this slice here, and we got nuclear magnetic resonance only occurring along this slice. Now, how do we go about changing the thickness of that slice? Remember, as we increase the thickness, we'll have more protons that are experiencing nuclear magnetic resonance, more resonating protons within the transverse plane, and ultimately getting more signal. We will lose some z-axis resolution, but we'll be getting more signal, and there's certain times where we want our slice to be thicker or our slice to be thinner.
Now, the first way that we can increase the slice thickness is by changing the bandwidth of the radio frequency pulse. If we increase the ranges of the radio frequency pulse frequencies, we are going to be getting more nuclear magnetic resonance because we're covering a wider range of processional frequencies here. Now, you can see our slices got thicker because this bandwidth has got thicker. We are covering a wider range of processional frequencies. Now, at the same increased bandwidth, if we wanted to decrease the slice thickness, what we could do is actually change the gradient of the external magnetic field. If we increase that gradient, we make the difference between the magnetic field at the one end of the z-axis and the other end of the z-axis, we make that difference bigger. We can see that we ultimately narrow the slice thickness. We've still got that increased bandwidth, but the range of radio frequency pulses falls along a smaller part of this gradient graph here, and again, we get a smaller slice thickness. So you can see that changing the radio frequency pulse bandwidth, as well as changing the steepness of the gradient magnetic field, both play a role in these slice thickness that we are selecting in the z-axis.
Now, as I mentioned before, this slice has some thickness to it, and we know that the protons within this slice aren't perfectly on top of one another in the z-axis. There's some width to that slice. Now, with that width comes a particular problem, and that's what's known as slice phase. You'll see that the gradient field that is experienced at this part of the slice will be different from the gradient field experienced at this part of the slice. There's still a gradient field occurring here that is being covered by the entire radio frequency pulse bandwidth.
Now, as we allow those spins to spin, we will see that although they are resonating in phase with one another, they are resonating at a frequency that is dependent on the radio frequency pulse and the gradient field that these spins are experiencing. And you can see that these spins are out of phase with one another because of this differential gradients here. Now, what we can do is apply what's known as a re-phasing gradient after we've applied our slice selection gradient here. Now, the re-phasing gradient means that we will apply an equal and opposite gradient in the other direction along the z-axis. That equal and opposite gradient will allow these spins to now spin in phase with one another. Initially, this side of the slice was experiencing a low magnetic field, and once we applied the re-phasing gradient, it experienced a high magnetic field. And if we average our slice selection gradient and the re-phasing gradient out, that entire slice that we've selected will have experienced these same amount of external magnetic field, allowing these spins to spin in phase with one another. And that's what's known as the re-phasing gradient.
So let's now recap the entire process that has allowed us to select a specific slice along the z-axis of our patient. Now, the MRI machine constantly has a B naught, an external magnetic field along the z-axis, that never gets switched off, no matter which type of pulse sequence you're doing. There will always be a B naught along the z-axis of the patient. And that's why when we represent what's happening along our specific pulse sequence, we don't actually have a line here for B naught. It's always there, whether we're taking an image or not, that MRI machine is on, and that B naught is on.
Now, we've seen that when we want to generate signal within our MRI image, we need to apply a radio frequency pulse, and here we've applied a 90-degree radio frequency pulse. These graphs, if you're unfamiliar with them, represent time along this axis here. Now, we apply a radio frequency pulse for a specific period of time. That causes the spins to flip to 90 degrees in the transverse plane. They've got maximum transverse magnetization. At that same time, we need to be applying this slice selection gradient, the gradient that we've been looking at throughout this talk, that gradient along the z-axis of the patient.
Now, because we are applying the slice selection gradient, this 90-degree RF pulse, that is released at a specific frequency, or at least a specific frequency bandwidth, will only cause certain spins to exhibit nuclear magnetic resonance and flip into the transverse plane. And it's only those spins with a processional frequency that matches the frequency of the radio frequency pulse that will flip. And that's the basis for selecting the specific slice. We then looked at why we need to apply a re-phasing gradient after the slice selection gradient to account for the differences in the spins along that thickness of the slice. And this re-phasing gradient will mean that all the spins within that slice, along the entire z-axis of that slice, will be resonating in phase with one another.
Now, as you'll remember from the T2 relaxation talk, we then apply a 180-degree radio frequency pulse, and that 180-degree radio frequency pulse will allow those spins to start to re-phase with one another and account for the T2 star differences within the tissues. Now, if that sounds like Greek to you, go back to that T2 relaxation talk and see why we apply this 180-degree radio frequency pulse. Now, at the same time difference between the 90 and 180-degree radio frequency pulse, we then sample the signal within our tissue. At this point, all the signal that we measure in the MRI machine is coming from this specific slice because only this specific slice has been tipped into the transverse plane.
Now, a lot of people get confused. This slice selection gradient, the gradient that we're applying along the z-axis, is only on while the radio frequency pulse is on. The times between the radio frequency pulse or between the slice selection gradient, the only magnetic field at this stage that the patient is experiencing is the main magnetic field. We flip those spins into the transverse plane. We then switch off the radio frequency pulse, and we switch off the slice selection gradient. We get that T2 and T1 relaxation of those spins. And at this time to echo, when we sample, we are only measuring the differences in the T2 relaxation at this time to echo.
Now, some people get confused thinking, but if we've switched the slice selection gradient off, how do we know that that signal is coming from exactly this slice? While all the other spins here throughout this pulse sequence have just been processing with the main magnetic field, and when we apply that slice selection gradient, those processional frequencies aren't matching up with this radio frequency pulse, so they never flip into the transverse plane. So even though the slice selection gradient and the radio frequency pulse has been switched off prior to the time to echo, it's only those that were selected during this period of time that will exhibit transverse magnetization. And remember, we can only measure transverse magnetization.
So now we've got to the stage where we've selected a specific slice within our patient, and that slice covers one transverse plane across the patient. Now, the signal that we're measuring within the coils of our MRI machine is coming from that entire slice. There's no way at the moment for that MRI machine to figure out where along that slice this signal is coming from. All those net transverse magnetization vectors are being added to and taken away from one another, and we're just getting one long trace coming into our coil as those spins resonate within the slice. We need to now figure out a way in which we can take that signal that is being generated from this slice and tease out where exactly that signal is coming from along the x-axis, as well as along the y-axis of this particular slice. At the moment, with the pulse sequence that we've done here, we've got all of these spins resonating at the same resonance frequency, in phase with one another.
Now, they're resonating at the same frequency because they are experiencing these same external magnetic field. They're experiencing that B naught magnetic field, and at this time to echo, they have lost a certain amount of transverse magnetization and gained a certain amount of longitudinal magnetization. Now, these spins are all spinning in phase, coming from this entire slice, and we've got no way, as it currently stands, of differentiating where that signal is coming from along the x-axis, as well as the y-axis.
Now, in the next talk, we're going to add another line to our pulse sequence here that will allow us to differentiate where the signals are coming from along the x-axis of that slice. Once we figured out where the signal is coming from along the x-axis of the slice, we need to then add another line to our pulse sequence in order then to differentiate where the signal is coming from along the y-axis of our slice. And those two happen in completely separate processes. So we're going to talk about them in two separate talks. And hopefully, by the end of these three talks, we'll be able to understand exactly how an MRI machine knows exactly where the specific signal is coming from within the patient.
Now, these three sections are very confusing, and you might need to go back to them multiple times. And as you've seen, you might need to actually revisit the talks that we've done prior to these. I'd encourage you to spend a lot of time making sure you understand the concepts before moving on to the next talk. And again, if you're studying for a specific physics exam, I've linked in the top line in the description below question banks that I've curated from past papers that allow you to test yourself and see where your knowledge gaps are and where you need to focus on more before for your exam. So go and check those out if you are studying for a specific exam. Otherwise, I'll see you all in the next talk, where we're going to look at x-axis frequency encoding gradients. So until then, goodbye everybody.