The Science of Everything Podcast - Episode 154: Magnetic Resonance Imaging

Episode Date: September 23, 2025

An overview of Magnetic Resonance Imaging (MRI), beginning from the basic physics of nuclear magnetic resonance, and covering the use of radiowaves to excite nuclear spin states, and the T1 and T2 modes of relaxation. We then explore how these phenomena are used to produce 3d images, including magnetic field gradients, frequency encoding, phase encoding, and Fourier transforms. We conclude with a discussion of functional imaging, including the haemodynamic response, the BOLD signal, echo planar imaging, and the steps of preprocesing. Recommended pre-listening is Episode 14: Principles of Quantum Mechanics, and Episode 61: Magnetism. If you enjoyed the podcast please consider supporting the show by making a PayPal donation or becoming a Patreon supporter. https://www.patreon.com/jamesfodor https://www.paypal.me/ScienceofEverything

Hello, you're listening to The Science of Everything podcast, episode 154, Magnetic Residence Imaging. I'm your host, James Fodor. So today we're going to talk about MRI or magnetic resonance imaging. We're going to cover the physics behind it, including how the excitation, the magnetic excitation occurs in the nucleus, how magnetic gradients are used to encode spatial information about the image. We're going to talk about how the image is reconstructed, the computational techniques underpinning that and we're also going to compare how structural versus functional imaging works and explain the differences there and we'll conclude with a bit of a discussion about post-processing of functional

imaging data. So this is a topic that's been requested a few times I think and is a particularly sort of interesting and tricky area that I don't think very well understood. So I think it should be an interesting episode. Recommended pre-listening is episode 14 principles of quantum mechanics and episode 61 on magnetism. So without further ado, let's get started and we'll begin by talking about nuclear magnetic resonance. MRI stands for magnetic resonance imaging. It's a medical imaging technique, which is also used in science, scientific research, which is able to generate pictures of the anatomy and physiological processes within the body. What makes MRI unique is that it's able to generate high-resolution images of soft tissue within the body, so without needing

to cut open any parts of the body, so it's non-invasive. It differs from other imaging modalities like CT or x-rays, which are primarily only useful for imaging hard tissues of the body, like bones, for example. It also has much higher resolution than other imaging modalities like PET scans or ultrasound. So because of this, MRI has attracted a lot of of interest over the years, both from researchers and the public. The name of the technique, magnetic resonance imaging, has actually been changed. Originally, it was called nuclear magnetic resonance imaging because that's the technique that it actually uses, but the nuclear was removed from the name because of the negative association the public has with the word nuclear.

So let me just briefly explain what the words in the name mean, and that also serves as an introduction into talking about the basic physics that's applied. So nuclear refers to the fact that the basis of the imaging scan is information about the nucleus of the atoms, in particularly water molecules, although we'll get to that in a moment. So it's information about the nucleus that's actually being detected, not the electrons. Magnetic refers to the fact that the technique relies on the magnetic properties of the nucleus, particularly the spin, which we'll get to in a moment. And resonance refers to the fact that it's resonant frequencies of the magnetic spin of the nucleus that is specifically used. Nuclear magnetic resonance is the physical process that is utilized to produce the images, hence nucleot magnetic resonance imaging or MRI for short.

Okay, so let's talk a bit about the physical underpinning. So, as I said, MRI exploits the magnetic properties of atomic nuclei, particularly hydrogen atoms in water molecules and also fat molecules. So these are abundant throughout the human body. So I mean, obviously any tissue is going to have significant amounts of water in it. So any scanning technique that utilizes the properties of water will be effective for the vast majority of tissues. And also hydrogen atoms in fat molecules can also be utilized. So specifically the way that it works is protons behave like tiny bar magnets owing to a property called spin. Now, I've talked about spin in the past.

It's rather counterintuitive because the word connotes this idea that there's like a tiny top that's spinning around on its axis. And that is sort of accurate in the sense that magnetic spin behaves as if, or it has the properties of a tiny top that's spinning on its central axis. However, we shouldn't think of spin as literally something spinning. It's a word that's used because of the similarity in the mathematics, not because we think there's anything literally spinning. All fundamental particles have intrinsic spin. It's a property that particles have in our universe for whatever reason, and it behaves as if, or the behavior of this property called spin is similar to that of the angular momentum of like a top spinning on its axis. Now protons specifically have two spin states. So we call this spin up and spin down.

neutrons also have spin, and this is why different elements have different nuclear spins, is because different elements, of course, have different numbers of protons and different numbers of neutrons depending on the isotope of the element. Now, for a given proton, or its spin can be in two states, so up or down or plus or minus a half is the way we typically write it because it turns out the value is half, but we didn't worry too much about that. We can just call it up and down. The lowest energy state is achieved when the nucleus essentially has a

balance of spin up and spin down. So if you have a single proton, then it will be spin up, but if you add a second proton, it will be spin down. And then if you add two more, one will be spin up, or one will be spin down and so forth, at least under normal conditions, right? So the normal tendency is for nucleons, neutrons, and protons to pair their spins. And so if there's an even number of protons plus neutrons in a nucleus, it will have zero net spin. And so it won't have these sort of magnetic resonance properties. But if the number of protons plus neutrons is odd, then there'll be one that's unpaired, this unpaired proton.

And that is what gives rise to nuclear magnetic resonant properties that we're interested in for MRI. Now, the reason why hydrogen atoms are so useful for this is because they always consist of just a single proton, a single unpaired proton, which therefore has spin up and, therefore, net positive spin. And so they're always susceptible to these nuclear magnetic resonance effects. So what happens when you put an atom that has a net spin, so like a single hydrogen atom, in an external magnetic field, so you turn on a big magnet and you put the atom in that magnetic field, what happens is that the spin of the proton within that atom becomes aligned to the external magnetic field, if it's strong enough, if there's a strong enough magnetic field.

This is because the spin property of protons and neutrons is a magnetic property, So it tends to align with external magnetic fields if those fields are strong enough. So by default, like if I just have a bunch of matter with unpaired protons in it, say a bunch of water, for example, the spins will be pointing in all different directions. So spin is a vector. It has a magnitude as well as a direction. When we say spin up, that doesn't literally mean it's pointing like up away from the surface of the earth. That's just a way of describing a positive half spin. So don't get confused there. Spin-up is not referring to the direction, it's just the magnitude and the sign.

But the actual vector orientations of my proton spins point in all possible directions. So you can imagine as if there are these tiny tops, two of them in each water molecule, and they're just pointing in different directions. So the net magnetization of that bunch of water will be zero. Each individual proton has a small component that it adds to the overall net magnetization. But because they're all pointing in different directions, they all cancel each other out. The only time when we see a net magnetization for the lump of water as a whole is if we place that water inside a strong magnetic field. And then all of the protons align with the external field. Again, if the field is strong enough, they'll all start pointing in the same direction,

which means then that instead of canceling out, the nucleus spins of the protons add up. They add together and form a strong net magnetization vector, which points along the direction. of the external field. Now, I've skipped over a detail here that's actually very important. So what I initially said was that when you place a bunch of water or henceforth, we can think of it as a lump of tissue like brain tissue, which is often what we're interested in imaging. So when you place a lump of tissue inside a strong magnetic field, what I said is that the spin of the unpaired protons in the water molecules within that tissue all align with the external magnetic field, and then they form a net magnetization vector that points along the direction of the field. But there's actually a couple of complications there

that are important. First, it's actually not true that all of the protons, the spins of all the protons align with the field. Actually, what happens is some of them align in the direction of the field, parallel to it, and some of them align in the opposite direction against the field, called anti-parallel. The parallel direction is a bit low in energy.

The anti-parallel direction is also fairly low in energy, but not quite as low. and so it's a slightly higher energy state. And the parallel and antiparralel offset each other, because obviously they're pointing in opposite directions, and so they cancel each other out. So the net magnetization vector of all of the protons in your tissue sample now consists of whatever's left over after the parallel

and anti-parallel protons spins cancel each other out. And because the parallel state, the spin vectors that point in the direction of the external field, because that is slightly lower energy, somewhat more protons will orient themselves in that direction, and somewhat fewer will orient themselves in the anti-parallel direction. And so although most of the spins will cancel out, parallel with antiparol, there'll be some net parallel vectors left over, and therefore a small but noticeable positive net magnetization in the direction parallel to the field. So it's not quite so simple as

that all of the protons align with the field. It's that actually most of them align either with the field or against the field, but there's a slight preference to aligning with the field, and so there's a there's a net overall magnetization in the direction of the field. Now, the second complication that I mentioned is that it's also not actually the case that the proton magnetization effect just align perfectly with the field. They just sort of start pointing in the direction of the field. If you think about the physics of that, that doesn't actually make a lot of sense. What happens is that when a proton is with a net magnetic spin is placed in a magnetic field, that external magnetic field exerts a torque on the magnetic moment of the proton.

So this all comes down to how magnetic forces work. And if you've listened to the previous episodes where I talk about magnetism, I go through this. But magnetic forces are a bit strange. They don't act in the same direction as the magnetic moment. So they act perpendicular to it. So the magnetic moment is basically just like the direction that the spin is pointing in, right? So remember I mentioned that that spin always has a magnitude and a direction. So spin up and spin down, that refers to the magnitude of it. But the direction can be any direction. As I said, the protons, before they're put in the magnetic field, they're just pointing

in any old direction. But whatever direction it happens to be pointing in, when I then place that proton in an external magnetic field, or imagine I turn the field on, what happens is that that field will exert a torque on that proton, the magnetic moment of that proton. A torque is a force that causes rotation. so the proton will then start rotating. It won't just align to the external field and then sort of stop. What it does is it starts processing around the external field vector.

Again, this might seem initially strange, but the reason for this is just baked into how magnetic forces work. They always apply a torque to a magnetic moment. So unless the magnetic moment, the spin of the proton, happens to be already pointing perfectly parallel to the field, which is pretty unlikely, it will always be pointing slightly off in some direction, whether it's slightly to the left or slightly to the right or slightly up or down, whatever. It'll be pointing slightly off the direction of the field.

When that happens, the force that's exerted on the proton spin by the magnetic field will actually be perpendicular both to the direction of the spin and to the direction of the field. And so that is a torque. It causes rotation. So the situation is a little bit more complicated than how I initially. described it. Initially I said that when I have my massive tissue with the unpaired protons in it that have these nuclear spins, the spins are all pointing in different directions. When I turn on the field, the spins all align in the direction of the field or antiparrelal to the field, and there's a slight excess that are parallel relative

to antiparal. In fact, what happens is that the spins of the protons don't just align with the external field. They actually start rotating about that external field. In a sense, this is much the same thing because what we can do is we can convert our frame of reference to a rotating frame of reference, and then it's as if the protons are aligned with the external field. But they're not literally just pointing in a singular direction and staying there. They're actually rotating the direction of the magnetic moment is actually moving around, rotating, orbiting about the external field. And you can imagine it's like a kind of, they trace out a kind of a cone. So the direction of the magnetic moment points kind of in the direction of the external field, but not perfectly. That's like offset a little bit. And then it rotates, that vector rotates around

the external magnetic field, shaping out a cone, the flat side of which points in the direction of the external magnetic field like at the center. So you, now, why does this rotation about the external field matter very much? I mean, if you can just convert your frame of reference to a rotating frame of reference, so it's as if the protons are all pointing in the direction of the field. You know, why does this complication matter? Well, this complication is essential for understanding how magnetic resonance imaging works, because it turns out that the frequency with which protons are processing around the external field depends only on the magnitude of the external field. And it's not intuitive that this would be the case, but you can sort of show if you work

through the numbers that it is. If this weren't true, then magnetic resonance imaging wouldn't work. Because magnetic resonance imaging relies on this frequency always being the same, and depending only on the magnitude of the external field, it does not depend on any properties of the protons. In particular, it doesn't depend on the direction that the proton was initially pointing in. So the spin of the proton, the spin vector, the magnetic moment vector that points in some direction, right, it could initially point to the left or to the right, up or down, sideways, diagonally. Doesn't matter, right? Whatever direction it's pointing in, when you turn on the external field, the magnetic moment vector, the spin vector, it starts rotating about that external

field, about an axis that points along that external field, at the same frequency. Whatever the initial direction is, the frequency of rotation is the same. And that means that all of my protons in my sample of tissue, all of the unpaired protons in the water molecules, right, they're all pointing in different directions initially, the spins are pointing in different directions. But once I turn my external field on, they all start rotating about that external field, at the same frequency. That's crucial for the imaging to work. If the frequencies were all different depending

on the direction, it would be impossible to form an image. But because the frequencies are always the same, as long as the field is the same strength, is the uniform field across the tissue, then the frequency of procession will be identical. And this special frequency, which again depends only on the magnitude of the external field, is called the llama frequency.

Now, let's move to talk about the next element, which is excitation, and relaxation. So the way magnetic resonance imaging works is it applies a strong magnetic field which causes all of these unpaired protons to start processing around the external field at the same frequency, the

Larmor frequency. And then it applies excitations to the spins of the protons, leading them to relax in certain ways. And the way in which they relax, I'll explain what that means at the moment, but the way in which this excitation and relaxation pattern occurs is actually

how we measure the relaxation process and that's how we construct the image. So this part here, the relaxation excitation component is essential for understanding how the image is produced. So let's go through this. Now remember we start the protons, the spin of the protons, we start them processing around the magnetic field vector by just turning on that external magnetic field. They start processing around it at the law more frequency, right? But there's another thing that we can do in order to change the direction of the protons of processing in.

and that is we can apply a radio frequency. But basically we can turn on an electromagnetic field using a radio frequency generator, which is just, that's just another way to apply a magnetic field, right? So the static magnetic field that we initially used to generate the initial procession, that's a static magnetic field, but we can also use a varying magnetic field, and that's all an EM pulse is, right, a radio frequency pulse of electromagnetic radiation. it consists of varying electric and magnetic waves,

but we're interested in the magnetic waves part. So we can change the direction of procession of the protons by applying a short RF pulse, radio frequency pulse. If we apply the field at the right frequency for the right time, what we can actually do is we can rotate the vector of the net magnetization

a specified number of degrees. This is just affected by how long you, you have the RF pulse on for. So you need to make sure that it's at the right frequency in order to affect the Lamor procession because that that occurs at a certain frequency. So you tune your RF pulse to that same frequency, depending on the strength of your static magnetic field. And then you just calibrate for how long you need to turn the RF pulse on for in order to rotate the net magnetization vector. So that's the sum of all of the proton spin vector, summed all together. You just compute how long you need to turn on the RF pulse in order to rotate that by a

certain number of degrees. So you might want to do a 90 degree pulse, which rotates it by 90 degrees, or you might want to do a 120 degree pulse, which rotates it to pointing in the complete opposite direction. So both of those types of rotations are used in MRI. Now, we turn on our RF pulse. That rotates the net magnetization vector. Let's say to 90 degrees. Let's go with a 90 degree pulse. So that rotates, you can think of it as rotates the net magnetization vector from pointing, say, forwards, to now it points to the right. So we've rotated it by 90 degrees. This is a bit odd, right? Because now, instead of our protons processing about the direction of the external magnetic field, now they're actually processing 90 degrees to the magnetic field, which is a bit weird, right? Like, why would they

process 90 degrees to the magnetic field? Well, it's just because we've applied another magnetic field, which essentially causes them to process in a different direction. It rotates that magnetization vector to a 90 degree angle. So, of course, Our static field stays on the whole time. We haven't changed the static magnetic field, right? That field is always on. We've just applied a short radio frequency burst so that now the protons are processing 90 degrees to the field instead of parallel to the field. As soon as I turn off my radio frequency pulse, the protons are going to go back to their initial orientation, right?

They'll rotate back and go back to processing in the parallel to the external magnetic field. Obviously, that's what's making the process in the first place. they're not going to keep processing in a 90-degree angle, they're going to go back to where they were processing before. And this is key. This process here is called relaxation as it goes back from the excited 90-degree state, back to the initial parallel state. This is relaxation. But this process doesn't occur instantly. It takes a bit of time. It doesn't take very long, but it does take some time. And it's this process of the period of relaxation that we use to produce the images. And as it turns out, it's of course more complicated than that because there's actually two types of relaxation that we

need to discuss t1 and t2 relaxation and this actually is used to produce two different types of images t1 weighted images and t2 weighted images and we'll discuss the difference in a moment but let's talk about these two different types of relaxation now the easiest to understand i think is t1 relaxation so remember we've got our massive tissue with the unpaired protons we turn on our external field the protons start processing at the lammal frequency around this field. And we call this longitudinal magnetization that the magnetization vector that forms as the protons are all processing around parallel to the field. Remember, technically there's some that are parallel, some that are anti-parallel, but the net magnetization is due to the slight preference

towards the parallel to the anti-parallel because it's a slightly lower energy, right? In general, I will just ignore that, but remember, that's always in the background. So there's a net magnetization vector formed by the unpaired protons as they're processing about the field. We call that the longitudinal vector. Then I apply my IRA frequency, which rotates that longitudinal vector 90 degrees. So now it's pointing in what we call the transverse direction, like 90 degree plane to the original field. The T1 relaxation is what happens when that transverse vector essentially rotates back and goes back to pointing in the longitudinal direction. The spins go back to their original orientation as to orbiting about, processing about the external field. And the physical

mechanism by which this happens essentially is a transfer of energy from the spins to the lattice that surrounds them, basically the bonds between other atoms and the molecules as they all exist in the complex combination of the tissue. Energy is lost as it's dispersed out to other forms in the tissue, and then as that happens, the magnetization vector is then diminishes from the transverse direction and is recovered in the longitudinal direction. So basically we're just rotating back to the direction that the net magnetization was initially directed in. So that's T1 relaxation. That occurs over a period of, you know, one or two seconds in typical tissues. Now there's a second type of relaxation called T2 relaxation, and this actually happens much faster. This occurs over a few hundred milliseconds.

So it's more than 10 times faster than the T1 relaxation. But T2 relaxation is a little bit harder to understand, so I'll try to give the sense of it. Let's go back to the situation before we turn on the RF pulse. We've got all the unpaired protons in the water molecules. They all have their nuclear spin, right? That spin is pointing in all different directions. We then turn on the external field, and the magnetic moment that the spin of these unpaired protons then starts to process around the externally applied field.

at the same frequency for all of the different, all the different protons, that's the lumble frequency. And that's critical, the fact that they're all at the same frequency. Now I turn on my radio frequency, the short burst of the radio frequency, which rotates these spins from pointing parallel to the direction of the external field. Now they're pointing it in a 90 degree angle to the external field. And then, as soon as we get to that 90 degree rotation, I turn off that radio frequency. So that's gone now. So now we're just left with the original field that's now pointing 90 degree angles to the direction of the magnetization vector of all my protons.

But let's think about this. My proton spins were all processing around the external field vector, right? And what keeps them processing around at the same frequency is precisely that external field vector. But now I've rotated all of my proton spins 90 degrees to that external field vector. so that external field vector is not keeping them processing at the same rate anymore. So what happens is as soon as you turn off that RF frequency, which caused them to rotate 90 degrees, as soon as that's turned off,

basically their rates of spin quickly lose coherence, so they go all out of phase with each other. Basically, there's nothing keeping them tied to the Lamor frequency. What was keeping them tied to the Lamor frequency previously was the external magnetic field, but you've rotated them 90 degrees to that, so they're not being affected by it anymore, at least not until T1 relaxation happens and so they rotate back. But before that happens, they're not tied to that anymore.

And so basically what happens is that there's a rapid process of loss of coherence. It's called spin-spin relaxation. So that technically there's like complex quantum interactions between the spins and they interchange energy with each other and then with the lattice that they're embedded in. But we don't need to know the details of that. The point is that the spins quickly lose coherence with each other, which means that instead. So remember that net magnetization vector, it was pointing power.

to the initial field. We then rotated at 90 degrees and it's pointing 90 degrees to that field. But then as soon as we turn the RF frequency off that that caused that rotation, quickly, that net magnetization vector loses coherence and it goes to zero. And it goes to zero very quickly within, you know, within 100 milliseconds or so. And so this is T2 relaxation. T1 relaxation then happens after that. Well, I mean, technically it starts at the same time, right? But it's much slower. So T2 relaxation occurs within maybe 100 milliseconds. It actually depends on the different tissues have different time rates, but we'll get to that later. But let's say it's 100 milliseconds for T2 relaxation. Now the net magnetization vector has actually gone to zero. The

protons are still spinning, but they're all out of coherence, and they're not pointing parallel to the external field anymore because they've been rotated. So then gradually, as T1 relaxation occurs, the proton spins rotate back and begin pointing parallel to the initial field again. And again, technically they don't point parallel, but they're pointing, but they're pointing, but they start processing about that external field again, whereas previously they were rotated 90 degrees. So to go through the stages again, initially we have proton spins rotating parallel to the external field

at the same level frequency. Then we apply an RF burst, rotate them all 90 degrees. As soon as we turn that off, within 100 milliseconds after that, protons all lose coherence, and now there's no net magnetization field. And then another second or two after that, we have T1 relaxation occurring, and now the spins go back to processing about initial external magnetic field like they were originally.

So there's a series of stages there. Initial, then initial vector parallel to the external field, then net magnetization vector pointing perpendicular to that field, and then after T2 relaxation, there's no net magnetization vector, and then after T1 relaxation, now we return to the net magnetization vector pointing in the direction of the external field again. So those are the stages we go through. First excitation and then two stages of relaxation. First T2 relaxation after about 100 milliseconds and then T1 relaxation after one or two seconds. And after that, then we return back to our initial state. And remember, throughout this whole period, the external magnetic field, the original one has to be kept on.

Otherwise, the procession stops. And so this is all assuming that the external magnetic field is still applied. Now, there is a slight complication here, which of course more and more complications, which I'm going to mention briefly, but I'm not going to get too bogged down into the details. I'm just going to mention it for people who may have heard of it and be confused if I don't say anything about it. So we're about to talk about how these T1 and T2 relaxation times and the signals from them are used to produce images. But before we get to that, there's just another wrinkle that I need to mention, which is something called a spin echo sequence. And this is technically the more specific way that most modern MRI actually work.

So what I was explaining before is that we apply a 90 degree magnet, we apply a 90 degree rotation to the net magnetization vector, and then turn that off and it rotates back. Actually, the way that it's done when we use the spin echo sequence is that we first apply a 90 degree rotation, then we allow the spins to lose phase. They lose coherence. So basically, that's what happens there is we allow the T2 relaxation to occur, so they lose coherence. and then we apply 180 degree inversion pulse, which rotates all of the proton spin vectors by 180 degrees, so it flips them in the opposite direction. And then what actually happens is that initially they lost coherence,

then we rotate them 180 degrees, and then they actually come back into coherence again, and then lose coherence. The best way I can explain it is imagine you have a bunch of sticks, right, and you hold them in your fist pointing upwards above the table, right? When you let them go, they're all going to fall in different directions and then fall flat parallel to the table. right? Well imagine just as they finished falling you could somehow rotate them 180 degrees like

flip them upside down and then what they would actually do is that they would instead of falling down they would they would sort of rotate upwards and then return to their initial upward position right because you're just flipping the vectors around instead of falling down it's now kind of falling up right now you can't really do that when you're against the force of gravity right i don't know how you would make that work you can do that in a in a scanner by just applying the right magnetic resonance frequency to rotate the spins. So that's kind of what's happening. When the spins go out of phase, they're like all falling down in different directions, just like the sticks falling apart from each other and sort of falling in a circle on the table. But what you can do is you can apply a radio

frequency to quickly rotate the spins 180 degrees, which means they'll all sort of come up and point back in the same direction again briefly, and then they'll keep rotating and go out of phase again. Now, you might wonder what's the point of this. I mean, you get the same outcome. They still go a phase. It's just that we've added an extra step. The reason we do this is because it allows us to get more signal for our T2 relaxation. Because the way that T2 relaxation occurs is basically all of the proton spin vectors go from pointing at a 90 degree angle and then they quickly lose coherence and so they rotate away from that. After we perform the 180 degree inversion pulse, what they actually do is that they go from pointing in a negative 90 degrees through to

losing coherence and then they gain coherence and go back again to pointing in a 90 degree angle and then they lose coherence again. So what we do is we get sort of two lots of losing coherence instead of just one one period of losing coherence. They lose, they start coherent, they lose it, they gain it again and then they lose it again for good this time. So the benefit of that is just that we now get to double up. We get two rounds of losing coherence instead of just one, which gives us more signal. And that's the main benefit as I understand it. There may be other details. But the main benefit, as I understand that, this 180 degree inversion pulse that we use in the spin echo sequence, is that we get extra signal. Now, if you didn't understand that,

don't worry about it, just forget about the whole inversion pulse and spin echo thing. I mention it because you will hear that language when you're reading up about MRI sequences. And so that's what spin echo is. It's an extra trick for getting more signal out of the T2 relaxation period. But fundamentally, it's not really any different to if we just rotate the 90. degrees and then go back. So henceforth, I'm just going to be talking about it as if we don't use the spin echo, just to simplify things a bit, but just bear in mind that that is actually what's used in modern MRI. So at this point, you might be wondering, look, that's all very interesting. I've been talking for half an hour about how proton spins are affected by different

types of external fields and radio frequencies, and we can rotate them and so forth. But what does any of this have to do with forming an image of the inside of your body? Well, good question. And that's about what we're, that's about what we're going to get to and explain how we actually form the image using the nuclear magnetic resonance properties. The core link that we can draw between image formation and all of these, you know, complicated spin properties is that in our scanner, we have a radio frequency receiver coil, which is just a simple device that, basically just a piece of metal in a circuit, which when it's exposed to variable magnetic fields, it induces a current via Faraday's Law of Induction, and then we can measure the strength of that current.

That is specifically how we produce an image. We measure the current in this radio frequency receiver coil, which tells us about the magnitude of the magnetic field at the time that we were measuring it, and then we can use this to construct an image. So, okay, but how do we, we make an image out of that and aren't we the ones making the magnetic field in the first place? So there's a few things that we need to clarify here. So remember, there's, there's, scanners, MRI scanners often look like big donuts. And you sort of put the person in the, in the middle of the, in the hole in the donut, sort of elongated donuts, I suppose. So the person lies in the hole in the donut. And that donut is actually producing a very large static magnetic

field. So I'm not going to go into the details of explaining how we produce those fields. But basically, these days they use superconducting materials in a coil that surrounds, runs around the person. So that's inside the donut, right? The shape of that is just because of how magnetic fields work. You may recall from previous episodes we've talked about this. So if you have a moving current in one direction, so imagine we have a wire, we have a current that's running through that wire. That's a moving electric charges. By the right-hand rule, that produces a static magnetic field that circles around.

the wire. So if we want to produce a magnetic field that extends along the length of the person to do imaging in the person, what we want actually is a rounded coil, which then will produce a sort of linear magnetic field. Very hard to describe that in words, but basically the shape of the coil surrounding the person in the big donut is necessary to produce a kind of linear magnetic field, because that's ultimately what we want. We want a magnetic field that kind of runs along the length of the person's body and is as static as possible and consistent across that person's body. It won't be perfect. You technically have to have an extremely long coil indeed for that to be like perfectly, perfectly straight, but you know, we do the best we can. And so we have the

superconducting material, run an electric current through it. It produces a magnetic field. And we use a superconductor because it reduces the resistance, which allows us to produce a large magnetic field for a given amount of current. And we need to use then liquid, helium is used in order to keep at low temperature because superconductors are only working very low temperature. So it's all very sophisticated engineering setup and that's why these scanners cost millions of dollars. So anyway, all of this is to just produce the static magnetic field of a very high, very high intensity. So just for some context about how strong these magnetic fields are, the entire Earth, all of the outer core of the Earth that is, we think that the outer core, the movement of

charges in the outer core is what produces the Earth's magnetic field. The entire Earth produces a magnetic field of about 30 micro-Tesla. Standard MRI scanners these days typically have field strength of about 3 Tesla. So that's about 100,000 times stronger than the entire magnetic field of the Earth. So these are very strong magnetic fields, and that's why you can't bring any metal anywhere near these scanners because they'll just rip them out of your hands or out of your body, and there can be very serious injuries can occur if you're not careful. So all of this set up, the superconducting material and the donut shape and whatever, is just to produce the static external magnetic field that then you turn on when the scanner's turned on.

Now, that is a static field. It doesn't change over time or ideally over space either. And so our radio frequency receiver is not going to detect that, because its purpose is to detect changing magnetic field. So a changing magnetic field gets rise to a changing electric field, which is what we actually measure in our receiver. Now, in addition to that, we will also be applying a radio frequency. Remember, that's what does the excitation, the 90-degree rotation.

So we will pick up a current when we turn on our radio frequency excitation, but we'll just need to not... The point is that you don't record a signal at that time. When you're exciting, you don't record. a signal, you only record a signal during the relaxation process when your radio frequency signal is off. So although it is true that we're producing a strong static magnetic field and we're also turning on the excitation through radio frequency bursts, we're not actually recording a signal at the time we're doing the excitation and the static field doesn't result in any measurements because it's static. So the only signal that we should be measuring in our radio frequency receiver is due to the T1 and T2 relaxation of

the of the protons as they relax after we've excited the spins right we excited into 90 degrees then they relax back that produces a changing magnetic field because the magnetic field vectors are moving around there they're rotating backwards and that's what we measure with our radio frequency coil now by itself if this was the only if the degree if the aspects we've described so far was all that there was we wouldn't be able to produce any image with this information all we would really be able to do is measure the total magnetization vector from the proton spins in one mass of tissue, say, and then would be able to measure the total magnetization vector in another mass of tissue when we could compare them to each other. So based on, say, the magnitude of the signal and the time it took

for relaxation to occur, I might be able to tell you, well, this tissue has more fat in it, or it has more water in it, or something like that, right? So that's all we can really do at this point, but we can't actually produce any image because all the information in three spatial dimensions is all collapsed down. We only really have a single receiver coil that combines information from all three spatial dimensions. And so everything is sort of smushed on top of each other. It's as if you took all the pixels from an image and just average them out into a single pixel. You don't have any visual information there. It's all collapsed down into one. How do we actually extract useful three-dimensional information about the location of the signal

from this sort of clump of signal that is currently all we're measuring? Well, the key insight here is that spatial encoding, so information about parts of the tissue in different spatial locations, is encoded using magnetic field gradients. Now, what that means is simply that the static magnetic field that we're applying, you know, constantly throughout the process, it changes with position, it changes with the location within the tissue. So a uniform magnetic field is constant everywhere, but a magnetic field gradient changes the magnetic field depending on position. This is the key insight of magnetic resonance imaging that allows us to extract information about three-dimensional differences. Because essentially,

again, let's remember what information we're actually measuring in the radio receiver coil. we're measuring a current which is induced by a changing magnetic field, and the rate at which that magnetic field changes and the intensity of the field affect the current that we measure. So the current that we measure will tell us something about the tissue that produced that magnetization vector. So we can tell the difference between different types of tissue, but at the moment all spatial information is consolidated down into basically a single lump,

so there's no spatial structure. But if we could somehow extract spatial information, so we could basically tell where our signal was coming from, this part of the signal is coming from the left and this part of it's coming from the right, this part of it's coming from the top of the sample, this part of it's coming from the bottom of the sample. If we could somehow separate the signal out into spatial components, then we can actually produce an image from that. And that's what the spatial encoding allows us to do. So the simplest component of this is to just apply a magnetic field gradient in what's what's called the Z-axis, which is parallel to the magnetic field. So basically this means that it extends along the inside of the donut from the feet to the head of the person who's in there, right? So that's the Z-axis. So instead of having a uniform magnetic field, we can have a magnetic field that gets

stronger as you go from, let's say, the feet to the head of the person, in a linear gradient. So it gets progressively stronger as you go from one side of the donut to the other, like one end of the hole to the other, from feet to head. If we do that, that allows us to localize the RF excitation to only a thin slice of tissue, so 1 to 2 millimeters. Why is that? Well, because remember, the Lomor frequency depends only on the magnitude of the external field. Previously, we had the same external field along the entire length of the sample,

and so everything would be excited at one time, and so we'd get a signal that was affected by all parts of the tissue. But now what we're going to do is apply a magnetic filled gradient. And that means that each little slice of tissue along the Z-axis, so again, like from feet to head, each little slice of tissue will have a slightly different lemur frequency. And that means that we can excite only one slice at a time, just depending on whatever excitation frequency we give. We give the corresponding frequency of excitation, corresponding to whatever the lemur frequency is for that slice.

And then we can excite one slice at a time. That's a significant step forward, because now we're going to be. we can do everything that we said before, we excite, we relax, we measure the signal during relaxation, now we can do that one slice at a time. And so instead of having all information clumped together from three dimensions, now we can separate out one slice from another slice, and so we now have information along the sort of vertical direction from feet to head. Unfortunately, with the setup so far, we still have all of the information within a slice being clumped down together into a single pixel. So we're not quite to an image yet, but we're working in the right direction.

right, we've separated out one dimension. We just need to separate out the other two dimensions and we're there. But the second two dimensions are the trickiest to do. Now, you might think, well, we have three spatial dimensions, right? So we've used one of them. We've applied a field gradient, a magnetic field gradient in one spatial dimension, that the Z-axis, and that allowed us to separate off one dimension. Can't we just apply magnetic field gradients in the other two dimensions, and that will allow us to separate out information in those two dimensions as well, right? And then we get a three-dimensional image. Well, sort of, but not quite. That's a right idea, but it's, unfortunately, doesn't quite work that simply, but that is the general idea, but there's a

complication. So we can extract the information from a second spatial dimension, let's call it the x-axis, using the same principle of magnetic field gradient. And this is called frequency encoding, in this case. So the way that it works is, in addition to the variation of the magnetic field in the Z axis, so that's feet to toe, we now apply an additional magnetic field, which is perpendicular to the original one, which causes a magnetic field gradient now along the x-axis. So this means that the more frequency now varies linearly with the position along the x-axis. Let's say x-axis is like left to right, so from the left-year to the right here. So now we've got a second spatial dimension where we have a magnetic field gradient, and this means, again, that protons

at different locations across the x-axis process at different frequencies. So that means we can distinguish their position based on the frequency of the signal that we detect ultimately using our magnetic radio frequency receiver coil. Different protons will process at different frequencies and so we'll measure different frequencies of induced electric current in our radio frequency receiver coil and we'll therefore be able to sort of align that back, trace that back to oh okay so the low frequency a lower induced electric frequency must must correspond to a lower magnetic frequency, which occurs in this, you know, in this part of the x-axis, and then the higher frequency corresponds to a higher magnetic frequency, which is in

this part of the axis. And you can kind of draw a correspondence between these frequencies that we measure in our electric field, in our radio frequency receiver, correspond to these locations along the x-axis, and you can map them back. So this is a little different to how our first dimension worked. Remember, our first dimension actually worked by simply only exciting one slice at a time. So when we apply that excitation frequency, you just apply it at the right frequency to excite one slice, and then it relaxes back, and you measure the signal from just that slice. This is a little bit different because we don't just excite like one location along the X axis at a time. You excite the whole thing, but when we're measuring the resulting signal,

you essentially, you measure all of the frequencies at once and then are able to extract them using a technique called Fourier analysis or Fourier transatlose. which separates out the frequencies. So just think of it like this. When we measure the T1 and T2 relaxations from all of the protons across the x-axis, they're all relaxing back, but they're relaxing back at slightly different frequencies, right? That's because they're a little more frequencies are a bit different. And so the radio frequency receiver coil will be measuring all of those at the same time. So there's all of these, this superposition, this summation, this combination of all of of these changes in the magnetic field across the x-axis because of the difference in the

normal frequency. So we measure all of those at once, but we can use this mathematical technique that separates out the frequencies to then see, ah, yes, so here's one frequency in our electric field that corresponds to the protons in this exposition. Here's another frequency that corresponds to the protons in a different position and so forth. So we can map them directly back. And now we have a mechanism for isolating a signal to somewhere along the end of the end. x-axis. So now we've isolated two dimensions. We can, we use slice selection with the variation in the static magnetic field along the z-direction. We use slice selection to pick a slice from somewhere from head to toe. And then we use the, what's called the frequency encoding.

This additional gradient of additional magnetic field in the x-axis, which changes the lemur frequency. And thereby allows us to determine where along the x-axis a given signal comes from, and thereby map back our measure. signals, radio frequency signals, to different parts of the x. So that's two dimensions. But in order to construct a full three-dimensional image, we need information about the final dimension, which we'll call the y-axis. That's essentially like up and down. So from the back of the head to the front of the head. Now how do we encode this information? Now you might imagine, well, let's just apply another frequency encoding, right? Like just like we did with the x

axis, we apply a gradient in the x direction to get x information. Why can't we apply a gradient in the Y direction and then we get Y information. It turns out that that's not going to work. And the reason why it doesn't work is essentially because there's no way for us to distinguish. If we have one axis of a variation, like the X axis, we can then map different frequencies to different positions on the axis. But if now we have two axes at the same time, there's actually no way for us to tell whether a given frequency maps to like this point on the X axis or this point on the Y axis. All we have is a frequency range. And so that provides us with one dimension of information. And we can't really reliably separate that out into

x-axis versus y-axis. I mean, there's complicated things you could imagine doing as to like, well, maybe they both contribute to the frequency, but then there's still going to be a problem because let me just simplify the discussion a little bit. Imagine that I have a two-dimensional axis and I plot a number on it that's just the sum of those two axes, like one plus two equals three. So I plot a three on the plot. The problem is that 1 plus 2 is equal to 3, and 2 plus 1 is also equal to 3. So how do I know if the information that I've recorded comes from x equals 2, y equals 1, or if it's come from x equals 1, y equals 2?

You see, there's no way to distinguish those two cases because they sum to the same thing, and it's that sum is all I measure, the sort of aggregate frequency, if you like, in the radio frequency coil. So I mean, I've simplified it a little bit, but that's the essential problem that if I just do the same thing but in the y-axis in addition to the x-axis then i get this this inability to distinguish where my where the signal has come from so that process of just repeating the same thing again in the y-axis won't work but we can do something kind of similar so instead of applying this what's called frequency encoding we use something a bit different that's called phase encoding and what this actually

means is that we just switch on a time-bearing radio frequency pulse that matches the lemore frequency briefly and then quickly switch it off again. So we briefly switch it on and briefly switch it off. Now, if we just did that for all y-axis positions at the same time, or for the same time, then all that would do is slightly shift the frequencies of everything the same amount, and that would be fairly pointless, right? We wouldn't get any signal from that. The trick is that we turn on this radio frequency pulse for slightly different times at different and why locations. So let's think about what that does. Basically what we're doing is remember that our Lomor frequencies are our protons all processing about the external magnetic field. And we're turning on

a very short pulse. This is not the 90 degree rotation pulse, right? This is another thing. This is a phase encoding pulse. So it's a second pulse for a different purpose. We turn it on for a short period of time and then turn it off. When we do that, what that's going to do is it's going to rotate a proton spin by a little bit, but not by very much. And then it will keep processing at the same rate. I mean, obviously then there'll be T2 relaxation, right? But this is just, this is before the relaxation occurs, right? Before the T2 relaxation, before everything goes back, you'll rotate the procession vector by a small amount, and it will keep processing there. Now, the trick is, if we turn on this radio frequency pulse for slightly different periods of time, depending on your y-axis,

what will actually happen is that all of my protons will get slightly out of phase with each other. You turn on the radio frequency pulse, it rotates it a little bit, and then you turn it off, and it stops, and then the procession is occurring. Let's say at one degree relative to, let's say they all start off at zero degree. You turn it on for a little bit, for one degree, and then you stop, and it's processing at one degree relative to your external magnetic field. And then in the next, so like a next millimeter down, you turn the radio frequency off after two, you know, milliseconds or whatever period of time it is. And now the protons at that location are processing at two degrees. And now I move another millimeter along in the y-axis. And I keep the radio frequency pulse on for three milliseconds.

And now they're processing at three degrees relative to the initial static field and so on. And you see now what we have is a phase encoding. All of the proton vectors are processing at the same rate. They're just now at slightly different angles relative to the initial magnetic field. Now, again, those are going to relax, back fairly quickly, but this is before that relaxation happens. So then what happens is we first apply our phase encoding signal, and then we apply the excitation signal, which does the 90 degree rotation. So think of it as the phase encoding signal gives each position on the y-axis a small

angle relative to the external magnetic field, and then they all get the same excitation signal, which rotates them all by 90 degrees, and then they all relax back. And it's that magnetic field changes that occur as they relax back that are picked up by our radio frequency receiver. But because of this phase signal that we've given, the pattern of the variation in the magnetic field over time as everything relaxes back is changed. It's a bit complicated to explain how, but because of the phase offset, what we get is a different overall combination of signals. And we can, again, using a Fourier transform, we can measure that on our radio frequency coil. It's a bit complicated because a single gradient of phase differences, you know, the one I'd

explained how, you know, as you move along the X direction, you add an increment to the, to like the amount of time you keep that excitation signal on. And so you form this phase gradient where they're all slightly offset from each other. A single gradient of that, of that phase encoding actually only gives you like one piece of information about the Y axis. So to simplify it, you could imagine it tells you enough information to determine whether something, whether a pixel is like in the top half or in the bottom half. It's more complicated in that because we're working in frequency space after the Fourier transform, but I don't want to get into all that here.

Suffice it to say that we need more than one phasing coding gradient. You actually need one for each pixel that you want to measure. So suppose that I want to be able to isolate the location of a given signal to within one part in a hundred along the y-axis. Well, that means you need to do 100 phasing coding instances. So you need to repeat this phasing coding process a hundred times in order to get this information about 100 different intervals along the, along the y-axis. So let's summarize now. What we want to do is we want to be able to separate out the signals that we're measuring in our radio frequency core. So this is an induced electric current that's induced by changes in the magnetic field. We need to separate these out based on the spatial location of where

the signal is coming from so that we can produce an image. And to do that, we use a combination of variable magnetic fields, frequency encoding, and phase encoding. And it all comes down to kind of the same thing. It's changing the magnetic field strength in accordance with the location in three-dimensional space, but there's a slight difference to how we do it in each dimension so that we can separate out the dimensions from each other. In the Z-axis, that's feet to head, we use slice selection. So that's changing the magnitude of the static field so that we can just excite one slice at a time

and thereby just measure one slice at a time. So we actually only get a signal from one slice. So that's kind of very straightforward and simple. To encode information about the x-axis, we use frequency encoding. So we actually vary the static magnetic field now by the X direction. That's left to right. And in doing that, we measure actually all of the locations

along the x-axis at once, but then using a Fourier transform, we can extract information that says, this frequency of magnetic field corresponds to this location in the x-axis, and this other frequency corresponds to this location the x-axis and so on. So that allows us information about position in the x-axis. And finally, we use a series of phase encoding gradients to give us the extra piece of information we need about the y-axis. So that's like front to back of the head. And so we actually need to repeat that

phase encoding step where we rotate the proton spins a slightly different amount based on their y position. And so we then apply a different gradient, apply a different gradient each time. So like if you want a hundred increments along the y-axis, you'll need to do that a hundred times. time with a slightly different phase encoding gradient. So the slice selection plus the frequency encoding plus the phase encoding altogether gives us three dimensions of information that allows us to localize each sort of bit of signal to one three-dimensional location. This is called a voxel. It's the three-dimensional analog of a pixel. And a single voxel in a high-resolution image might be like one cubic millimeter. So basically that means each slice is about one millimeter thick. And the frequency encoding along the x-axis allows us to specify position to within 1 millimeter, and then the phase encoding gradients along the

y-axis allow us also to then specify location on the y-axis to within 1 millimeter. And so then overall we can say this signal corresponds to this location within 3 dimensions, and then the magnitude of electric field that we measure in this location gives us a pixel intensity of this amount. And these electric fields that we measure as are always ultimately driven by or caused by the magnetization relaxation as the system returns back to a equilibrium state. And remember that there is two types of this relaxation, and either type of which can be the basis for a given image. So we can use the changing magnetic field in response to T1 relaxation to make an image, or in response to T2 relaxation to form an image. Structural images, like the ones that

give you a static, high-resolution image of your brain. So they typically use T-1 weighting. And what that means is the intensity of the voxels is determined by the electric field that's measured over the period of time it takes the T1 relaxation to occur. Remember, T1 is the type of relaxation where the longitudinal magnetization vector is recovered. So we go from, we start with, to revise, we start with the protons processing about the external field, we rotate them by 90 degrees, and then almost immediately the rotated proton processing, start to go out of phase with each other. So that's T2 relaxation. That occurs very quickly. And then slightly longer, the proton magnetization vectors then rotate back, they return to their

initial orientation, and then start processing about the external field again. That's the T1 time. So the T1 is the longer time that is associated with the recovery of the longitudinal magnetic vector. And so a T1 weighted image is one in which the pixel intensity is determined based on the signal over a period of time that it takes T1 recovery to occur, T1 relaxation to occur. Whereas a T2 weighted image, and T2 weighted imagery is used in functional imagery, which gives you a time signal of intensities, we'll talk about that in a moment. T2 weighted imagery is essentially the same, except that the voxal intensity is based on the electric field that's measured over periods of time relevant to T2 relaxation.

And essentially you can choose the exact time that you measure the field signals at in order to maximize the signal that you get from each of these two different types of decay. So now to put all the pieces together and explain how exactly we produce an image, we need to have enough information to specify where each voxel, the signal corresponding to each voxel and where it's located in three-dimensional space. First, what we do is we have our strong magnetic field. We've got our protons processing about that. magnetic field, we then apply our 90 degree excitation, and at the same time we apply our slice selection, so that excitation actually determines the slice selection, because we specify the excitation so that it has the right frequency to excite only one slice in our Z-direction. So that already localizes one dimension. Then we apply one of our phase encoding gradients. So remember, if we want, say, a 100-by-100 pixel image, we'll pick one of our, we'll start

with one of the 100 phase encoding gradients that we need. And then just after that, we apply a frequency encoding. So we apply a new magnetic field that varies the strength of the static magnetic field, but in the X direction. This is different from the gradient in the, that's parallel to the direction of the field. That's used for slice selection. This is a frequency encoding gradient that is along the X direction. So we apply that just at the time when we read off the echo. We read off the relaxation, either the T1 or the T2 relaxation, depending on what type of image we're making. And we read that off at the same time as we apply the frequency encoding. And so what we're going to measure then is the signals corresponding to all of the pixels

along one line of the X axis at a single point on the Y axis and at a single slice on the Z-axis. So we pick a slice, we pick a phase encoding gradient, and then we measure, and then we apply the frequency encoding vector and measure all of the x pixels in one go, because we use the Fourier transform them to separate those out from each other. And then we repeat that over and over again, so we pick one phase encoding gradient, we apply a frequency encoding gradient, and then we take a measurement of the relaxation time, and then we turn the frequency encoding off, and we stop measuring, and then we increment the phase encoding, so we apply a new in phasing coding

gradient. Frequency encoding on, measurement on, and turn that off, new frequency encoding gradient, and so forth. And the way it works is that so because each individual measurement doesn't take very long to take, it only takes a couple of milliseconds, we can actually go through the entire sequence of phasing codings and collect all like 100, collect all 100 points within that for a single or maybe a couple of excitations. So it's not like we have to wait the full recovery time for each, time we do a new frequency encoding gradient. Initially that's how it worked with the very first imaging and it took hours and hours to image even very simple things. But now the scanners have improved and the technology has improved such that within one or maybe a few excitations, you can go through a full range of phase encoding gradients. And for each one of those, you do a full frequency encoding gradient. So that basically means that we can do a whole slice in only a couple of excitations. And each excitation only takes a couple of seconds to, to, well,

wait for the relaxation time. So you can do a slice in only a few seconds, which means then that if you're doing like 100 slices or 200 slices over in a high resolution structural scan, then you can complete a scan in only a few minutes. So you just do one slice at a time. You go through, you do one excitation, go through the phasing coding gradient, the full range of them, so like 100 or 200 phasing coding steps, each of which has the full range of frequency encoding. So then once you've gone through that, you've got all of the X and the Y information for a single slice and then you increment do the next slice and so on. So that's why it takes a few minutes to go through a full structural scan because you're collecting information from all three

dimensions. Now as usual I have simplified this a little bit because modern structural scanning actually doesn't use slice selection. It uses a technique, a 3D paradigm, 3D flash is one of the more common one that's used which actually uses two types of phase encoding gradients plus frequency encoding instead of slice selection. But, and again, the details of that are not really important. It's a slightly different way of doing functionally the same thing. So I'm going to ignore that complexity from now on, and I'm just going to talk about slice selection, particularly because we're now moving on to talk about functional imaging, which don't use slice selection. But just bear that in mind if you're someone who's familiar with this, that yes, technically modern

structural scanning doesn't typically use slice selection. It uses two-dimensional phase encoding. but to keep it simple, I'm just going to focus on the slice selection method. Now, at this point, we then move to the final part of the podcast where I'm going to talk about functional magnetic resonance imaging. So so far, we've talked about how you make an image of the body, or say a particular part of the body, like the brain, because that's particularly what functional imaging is useful. So you make an image of the soft tissue in the brain at a static point in time.

So a single structural image may take several minutes to produce, During that period of time, the person is asked to stay as still as possible, so they're not moving around and distorting the image. And you're not going to image any changes that happen within that time. The idea is that you're measuring just the structure of the tissue which doesn't change over short periods of time, normally, right? Functional magnetic resonance imaging, instead of just measuring a single structure at one point in time, what it wants to do is measure changes within the tissue over a fairly short period of time, usually on the order of a few minutes, or maybe up to an hour. And specifically, we're interested in measuring the function of the tissue, basically in terms of its electrical activity. We want to measure the activity of the brain to make inferences about what's happening as the person thinks about something,

or sort of the mental representations or processes that occur as someone is processing information or thinking about something, remembering something and so forth. So that's the sense in which fMRI or functional magnetic resonance imaging, that's the sense in which it is functional because we're trying to measure, we're trying to tell something about the functional. of the brain, not just its structure. So if you think about a static MRI image as producing a three-dimensional picture, what functional magnetic resonance imaging does is it produces a three-dimensional video that you can sort of watch over time. So how was this done? Well, functional magnetic resonance imaging relies on something called the bold signal. That's B-O-L-D in capital letters. That stands for

blood oxygen-level dependent signal. And the name is fairly descriptive because the signal that we can measure is dependent on the blood oxygen levels of the tissue in a particular brain region. So let's step back a bit and explain how that works. Ideally, what we would like to measure is the electrical activity corresponding to neurons within a particular region of the cortex. We think that the firing rates of neurons is what corresponds to, that is brain activity, essentially. That's how information processing and the brain occurs. Unfortunately, it's very difficult to measure the electrical activity of neurons directly. Each neuron is very small and the electrical fields are quite faint and they're blocked by the skull and even the membranes over the brain dull them a little bit.

So direct measurement of electrical signal is possible. So we can use, we can do that in EEG. So electroencephalograms, that's when people have electrodes placed on their skulls and it measures their brain activity. It has very poor spatial resolution. Even more extreme, you can actually implant electrodes insert electrodes into a person's cortex, but that is dangerous and so is usually only done for people who are going to have a brain surgery for some other reason, usually to locate the particular part of their brain that's responsible for triggering seizures. So this sort of research is done on them. So on healthy people, we can usually only put the electrodes on the surface of the skull, and that doesn't give you a very good spatial resolution. So instead, we can

use the magnetic signal that's produced by the brain. But the magnetic signal is not produced directly by neurons. Well, I mean, there is a weak magnetic signal, but that's not the one we measure. Instead, what we do is we rely on differences in the magnetic properties between oxygenated and deoxygenated blood. And that's the key here. That's why it's oxygen level dependent. When a neuron is firing, so when it's active, it uses energy. It requires glucose in order to restore the electrical potential to the baseline level to allow it to keep firing. This takes energy. Neurals don't store very much glucose within the cell, so they need to take in that energy from the bloodstream. This means that when a specific region of the cortex increases in activity,

so it starts to activate, it extracts oxygen from its local capillary network, which leads to an initial small dip in the amount of oxygenated hemoglobin in that area and an increase in the amount of deoxygenated hemoglobin. So hemoglobin is the protein that carries oxygen in our red blood cells. And after a lag of a few seconds, maybe two to six seconds, the blood flow within that region of the cortex increases and it delivers a surplus of oxygenated hemoglobin and washes away the deoxygenated hemoglobin. So this leads to an actual, an overshoot of the amount of oxygenated hemoglobin in that region. And then it's gradually used up over time as the tissue returns to equilibrium. So there's this initial dip in the amount of oxygenated hemoglobin,

which is fairly small, and then a large increase following a few seconds. Now, the reason this is relevant is because oxygenated versus deoxygenated hemoglobin have different magnetic properties. Deoxygenated hemoglobin is paramagnetic, which means it is affected by magnetic fields, whereas oxygenated hemoglobin is diamagnetic, which means it's not very much affected by magnetic fields. The effect of this is that paramagnetic blood, so the deoxygenated blood, it interferes with the local magnetic field. Remember when we put a brain in an fMRI machine, we turn on our external magnetic field.

That's a very strong magnetic field. That produces a fairly homogeneous field. Obviously, we have the gradation in the Z direction that we talked about. But other than that, it's fairly homogenous. It's the same throughout. However, when we have this deoxygenated hemoglobin, it actually introduces inhomogeneities in the signals, the disruptions of the magnetic field,

because deoxyhemoglobin is paramagnetic. So it's affected by the magnetic field and in turn disrupts that magnetic field. The more deoxyhemoglobin we have, the more disrupted the signal is. And the less signal we overall observe because of the interference that's produced. Conversely, the more oxygenated hemoglobin we have, the better is the signal we observe. The stronger the signal we observe because there's less interference in our homogenous magnetic field. So this means that after that initial dip, when the cerebral blood flow brings in all this oxygenated hemoglobin to the site of increased brain activity within that local area of cortex, the blood overall

becomes more diamagnetic, which means it interacts less with the external magnetic field that we've applied. And this leads to greater field homogeneity, which means we observe a stronger magnetic signal from that region. So the long and the short of it is that at least for those few seconds for which the bold signal lasts, whenever there's activity in a particular region of the cortex, we observe a stronger magnetic field signal in that region. And it's localized to that region within a few millimeters of where the activity is localized to. Now, this change in the magnetic signal as a result of neural activity is called the hemodynamic

response. The main problem with it is that it lags several seconds after the initial neural activity. We've been able to measure this using simultaneous fMRI and electrode recordings in the brain, where we can directly compare the ball signal to the actual signal to the actual. actual neural activity. And we see that they correspond pretty well, but there's a several-second delay, like three to six seconds usually of time it takes for the bold signal to ramp up after the actual firing of the neurons. So that's the main downside of this bold signal technique is that it does have this lag time. But when you're processing the data, you can obviously

take that into account. The problem is that not every neuron is the same. So different neurons and different parts of, well, a signal neuron doesn't have a bold signal. It's a combination of neurons in a given area, but different types of neurons in different regions of the brain have different hemodynamic response functions. So there's the shape of the peak and the time it takes is slightly different. So that does lead to a bit of noise, actually quite a lot of extra noise in the signal. But nevertheless, we can still use this bold signal to fairly reliably give us information about the neural firings in that region of cortex, which is what we're really interested in. So again, the long and the short of it is when you have neurons firing in a given region of

the cortex, like a few cubic millimeters, that leads to an increase, after a few seconds to delay, an increase in the amount of oxygenated hemoglobin in that area, which in turn leads to an increase in the magnetic field that's measured in that area, because oxygenated hemoglobin interferes less than deoxygenated hemoglobin, so we get a stronger magnetic signal that's measured, and this is our bold response. And it is specific in time and in space two regions of the brain that experience greater neural activity. So it has a resolution of maybe within a millimeter or two and a temporal resolution of a few seconds. It takes a few seconds for the signals ramp up and down. So that means that we can use the bold signal with a strong enough

external magnetic field in order to produce a essentially a three-dimensional video of brain activity within a resolution of a millimeter or two and a temporal resolution of a second or two. So that's pretty cool, right? There is obviously a lot of noise in the signal because there's a lot of sort of approximations we're making and it's very indirect. We don't directly measure the neural activity. We measure the differences in magnetic field sensitivity that are caused by differences in hemoglobin versus oxygenated, versus deoxygenated hemoglobin, which in turn result from bloodstream responses to changes in the amount of glucose within the cells that is in turn affected by neural activity. So it's quite indirect, which means there is a lot of, noise and it is temporarily delayed relative to the neural activity but there still is a lot of signal there and we can use that to infer which parts of the brain are being activated in response to a particular task or a particular type of stimulus that the participant is observing or thinking about while they are in the scanner so let's put the pieces together and then explain how we form how we produce this functional image so usually what we do is that we perform slice selection so that happens the

the same way as it does in a structural scan. And then we apply the phase encoding gradient. And so remember that you actually have to do a bunch of those. So we will apply one iteration of the phase encoding gradient, turn on the frequency encoding signal, and then take a measurement. And then we'll keep doing that until we've covered all of the phase gradients that we need to cover the full y-axis. The challenge in functional imaging is that we need to collect the entire volume very quickly. Obviously, we can't take several minutes to collect the entire volume. like we do in structural scanning, because we're trying to measure what happens as the person is thinking in real time. Ideally, we'd like to have a resolution of less than 100 milliseconds,

because that's roughly the amount of time it takes to sort of process a stimuli, like reaction time is on the order of a couple of hundred milliseconds. In practice, we can usually only get it down to maybe one second at best, although a lot of studies will have like a two-second temporal resolution. So that means that we need to collect the entire three-dimensional image in less than a second. So it has to be done much faster than a structural. scan. And that means that there are some compromises. It means you have less signal to noise ratio. So the image you get as much blurrier and it's also lower resolution. I mean, that contributes

to the blurriness as well. So less signal to noise and lower spatial resolution. But you can still get a fairly good image. So usually the way it works is that we have to go through a full phase encoding series of phase encoding gradients and the corresponding frequency encoding gradients. we have to do that within only a few tens of milliseconds, because we need to collect all of the slices within, let's say, about a second, if we're going for a T.R. a temporal resolution of about one second. So this means we have, if we have, say, about 60 slices, that's a sort of a fairly common number.

That means that we can have about 30 milliseconds to collect each slice. So what we'll do is we'll do in excitation, which determines which slice we're selecting, based on the frequency that we use. And then we run through the full range of phase encoding gradients and within each of those, applying the corresponding frequency encoding gradient at the same time. We'll run through the full lot of those,

so maybe there'll be 60 different phase encoding gradients, allowing us to have a resolution of about like 60 pixels along the y-axis. And similarly, there'll be like a resolution of 60 along the frequency encoding, so along the x-axis. It will take maybe half a millisecond to go through each, phase encoding gradient. So half a millisecond, you apply the phase encoding gradient, apply the frequency encoding gradient, take a measurement. And then sort of straight away, as soon as you finish that, another half a second, you apply the next phase encoding gradient.

Next one, next one, next one, next one. You go through the full lot of 60, and then you're done with that slice, and then you allow the relaxation to finish, and then you apply a new excitation and select the new slice. So it's very, very fast. You have a lower resolution than you do in the structural scans. Remember I said that typically you might have a a matrix of like 200 by 200 by 200 or something like that, 100 or 200, whereas in the functional scans, it's more like 60 by 60, something like that. So you'll have a lower spatial resolution and a lower signal to noise ratio as well, because you're going much more quickly through all of the signal collections.

But the upside is that you're able to finish much faster. Instead of taking several minutes to do a scan, you can do an entire three-dimensional volume in only about a second or two. And this allows you to then construct a three-dimensional video over time to watch how different parts of the brain activate and deactivate or have a higher or lower signal measured in them over time. Now to finish up, I'll just mention briefly about some of the steps that we have to take to analyze functional data. Because although it's often described as your brain lighting up in response to a particular signal or stimulus or part of your brain lighting up, that's really very misleading. because there's no light in your brain, right? Your brain doesn't literally light up.

The images that you see with parts of them in color or shown in a brighter light, that's just a way of representing the signal after lots of processing. So don't get too confused about that. I think sometimes the way it's described is a bit misleading because there's no literal lighting up. What happens is that after we measure the bold signal,

as we've been discussing, you measure your three-dimensional video over, say, one hour of a task. Maybe the person has been given different images to look at or different sounds to listen to or different tasks to think about. The tasks that you're giving them obviously depends on what question you're interested in asking and what parts of the brain you want to investigate. But you'll have some tasks. They'll do that while in the scanner. You take the three-dimensional video of their brain during that task. And then you need to go through a series of pre-processing steps in order to actually extract useful information about that.

So I'll just briefly highlight what some of these steps are in case you're in. interested or have heard about these before. So first you do something called slice time correction. This adjusts for the fact that different slices in a volume are acquired at different times. We've just talked about that, right? You have to do one slice at a time. Actually, newer methods can do multiple slices at once, but they still can't do all of the slices at once. So in the traditional version, you do one slice at a time, and you have to correct for the fact that those signals were required a slightly different time. So you sort of offset them so that you adjust the data back so that the slices are aligned in temporal reference to each other.

You then have to do something called head motion correction. So basically the person's head is in the scanner. You want it to remain completely fixed in place, not rotating and not translating in any direction, so that you get the best signal possible. Any movement introduces blurring in the image. But everyone moves their head a little bit, and because the person is alive,

you can't rely on it to be perfectly static. So you need to correct. for that and we use rigid body transformations and rotations to try to correct for the motion. Although, you know, that's never perfect, and so it's better to prevent the motion altogether, but we still need to make those corrections for what motion does remain. Then there's something called distortion correction, so this compensates for the fact that it's never possible to have a perfectly homogenous magnetic field. Remember that we do have the gradient due to slice selection and then the x, the x, the x,

Sisc gradient, which gives us our frequency encoding. But I mean, apart from those, there are still going to be in homogeneities, like differences in the magnetic field strength in different places in the scanner, which is not ideal, but it's never possible to make a perfectly homogenous magnetic field of that strength. So these magnetic field in homogeneities introduce distortions into the image, which there are fancy techniques for trying to reduce the extent of them. But again, we can ever do it perfectly, but it's a way to reduce the impact of these. And these can actually be quite severe. So it is important to do that distortion correction and to try and ensure to calibrate the scanner regularly to ensure that the distortion is

minimized. Then what we do is something called co-registration. So we align the subject's functional images to a high-resolution structural scan. So normally what you'll do is you do a structural scan first. You'll just say, the patient just relax. We'll measure your, we'll take an image of your brain for a few minutes. That will give you a high-resolution structural scan. And then you'll actually start the task. You'll ask them to, you know, process the images or whatever you're doing. And you then get the three-dimensional video that I mentioned. That's the functional imaging. What you then want to do is align all the first functional images to the one high-dimensional structural image so that the functional images can be,

so we can essentially say which part of the brain that they correspond to, because it's a bit hard to see with the functional image. It's lower resolution. So if you align everything to the high-resolution image, you can use that images as like a reference point. So co-registration is the process of like aligning everything to that high resolution map. Then there's a step called normalization. That's where we, because each individual's brain is actually quite different, and if you look at a number of MRIs, you can actually see there's a large variation in size and shape of the brain.

But there's like a lot of similarities, but there's also a lot of differences as well, depending on what level of detail you're looking at. Overall shape is similar, but size and details can vary quite a lot. So what we do is we have standard templates, which we then align by warping in a complex ways, we align everyone's individual scans to that common template, which allows us to compare across individuals more easily.

There's then various forms of noise removal that are used, so like removing motion artifacts, scanner drift, physiological noises due to heart rate and things like that to improve the signal to noise ratio. So only after we do all of these steps do we actually get to a series of images, functional images that are actually useful. And then what we have to do is we have to apply different, and then what we do is we apply different statistical models

to extract the signal that we're interested in. Because again, the brain doesn't literally light up. The brain is constantly doing stuff. And so if you look at a raw or even like a pre-processed functional magnetic resonance image video, it doesn't look like very much. It just looks like a brain shape with parts of it flashing a little bit gray than others, right? It's very boring, actually. In order to extract a useful information out of it,

but what we have to do is statistically determine which parts of the brain are more active than others in different conditions. So to take a very simple example that was done using the very earliest fMRI studies, basically they would just flash a light, and they would do that a number of times. And then what they would do is that they would see which parts of the brain are more activated when that light is flashing compared to when the light was not flashing. Because all parts of the brain are activated to some extent, but if you repeat the same stimulus multiple times and average over those times and then compare different parts of the brain, how active are they in this condition, but in the light on condition versus the light off condition, you can get a contrast.

And so that's actually how the brain signals are extracted, how these activation maps are produced is by comparing different conditions where there's one type of stimulus versus not that stimulus or a different stimulus. To look at those early studies, what they find is that the back of the brain, the occipital cortex, which is known to be associated with the vision, was more activated when the flash was present than when it wasn't, whereas other parts of the brain there wasn't really much of a difference. So it doesn't mean that the rest of the brain wasn't doing anything. It just means that the rest of the brain was sort of roughly equally activated when the light was flashing versus when it wasn't. And what we're interested in is the

parts of the brain that are differentially activated by that specific stimulus. And that's what we actually are trying to ultimately measure when we're extracting this information from the functional scans. And so that's how at the end of the day we're able to produce these maps showing parts of the brain, quote-unquote, lighting up. What they're actually showing is the output of a statistical process which is inferring which parts of the brain were more activated, specifically when that stimulus was present or when that task was being performed relative to other parts of the brain. And that does need to be borne in mind because any model like this can go wrong and deliver incorrect results if there are incorrect assumptions have been made. Incorrect steps have been taken during the processing. And there are many cases of this happening in FMRI research.

So there's many things that researchers can do to get different results. And so there needs to be an appropriate caution applied when interpreting these results. When done well, it can give very informative insights about how stimuli a process, processed in the brain and where they're processed. When done poorly, it can basically just give you garbage. So you have to be careful and not overinterpret the results and be a bit skeptical about exactly how the stimulus was presented and how the data was processed and what model they used and so forth. That brings us to an end of today's episode. I know it's quite a complex topic. I try to make it as reasonably simple as I could.

Let me just cover very briefly the key concept of how magnetic resonance imaging works as a brief summary. Recall that it relies fundamentally on the fact that protons have this property of intrinsic spin, which is a magnetic property, which means that they act as if they are a tiny magnet spinning like a top. Ordinarily, the spins of different protons point in different directions, but when we apply a strong external magnetic field pointing in one direction, then the spins of each proton start to process about that external field at the same frequency, the frequency only depending on the strength of the field. That's called the Lamor frequency. And we can use this fact to produce images of tissue when it's been exposed to this high-intensity magnetic field

by first applying radio frequencies to excite these proton spins so that they essentially rotate a 90 degrees and then gradually they relax back. And we can measure the electrical signals that result from the changing magnetic signals. So as the magnetic field rotates back, the proton spins rotate back to their original orientation. That's a change in the magnetic field. So that elicits a change in the electric field in our circuit via Faraday's Law of Induction. That's what we actually directly measure in our radio frequency receiver coil. We measure the change in the electrical field due to the changes in the magnetic fields.

as the protons are relaxing back to their initial state as they process around the external field. That by itself doesn't give you an image, but we can use this excitation and relaxation steps in combination with cleverly constructed ways of extracting spatial information out. So you recall we vary the intensity of the magnetic field along the Z-axis, the toe-to-head axis, in order to get information about which slice of the body we're dealing with. We can then apply a frequency gradient. along the X direction to get information about left to right information. And then finally, we can apply a phase encoding step to get in, or a series of steps,

in order to get information about the y-axis, the front-to-back of the head direction. So combining all of these together and using fancy techniques like Fourier transforms, we can determine where in the three dimensions of the brain a given piece of signal came from and thereby construct the voxile intensity corresponding to that region in three-dimensional space. That is how we construct a structural image. We can extend that to construct a functional image over time, a 3D video, by using the difference in oxygenated versus deoxygenated hemoglobin. It's different magnetic properties.

So that when a region of brain is relatively activated, it's firing a lot of action potentials, that actually results in a more intense magnetic signal because of the effect of the oxygenated hemoglobin. And thereby we can compare the magnetic intensity of different brain regions at different times when the participant is presented with a different stimulus or a different task, and thereby extract information about which parts of the brain are more or less involved in particular types of tasks, and therefore use that information to construct these brain activation maps. So I hope you found this episode interesting. If you'd like to sort of support the podcast, you can do so in a number of ways. You can share the podcast with a friend.

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