Transcription
Hello everybody and welcome back. Today we're going to discuss the phenomenon of nuclear magnetic resonance. In the previous talk, we looked at the various different magnets that were required to generate the magnetic fields in MRI imaging, and we saw that certain nuclei responded in a very particular way to those external magnetic fields.
Now, that response is what's governed by nuclear magnetic resonance. And in order to understand nuclear magnetic resonance, we first need to understand a concept known as spin. Now, throughout your studying, you're going to come across two separate models. The first is what's known as the classical model, and the second is the quantum mechanical model.
Now, the classical model is more intuitive, and it describes a charged particle rotating around its own axis with angular momentum. That movement of charge with angular momentum induces a magnetic field around that charged particle, and the strength and direction of that magnetic field can be represented by what's known as the magnetic moment, which we represent with this arrow here. The longer the arrow, the stronger the magnetic field around this spinning particle.
Now, importantly, this classical model is not actually what's happening within the particles within the body. It's a good way to think about what's happening, but these particles aren't actually spinning. And you'll see this model will fall short when we describe certain phenomena later on in this course. For example, a neutron has no charge, yet it has a magnetic moment. An uncharged neutron, if it was rotating on its own axis, wouldn't make a magnetic moment, yet it's what we observe in the physical world.
Now, how do we go about describing that magnetic moment within a neutron? Well, we need quantum physics in order to do that. Quantum physics is a bizarre world. It's less intuitive than the classical model, and within quantum physics, every property can be broken down into a discrete measurable value. When we think about quantum properties of an atom, such as charge, mass, color, and now spin, these are all properties that have distinct measurable values.
The way I like to think about it is looking at other quantum properties. If we look at an electron, for example, it has a quantum property known as charge. Now, charge is very difficult to describe to someone. What exactly is charge? It's very difficult to actually say what it is. What it does do, though, is it describes how that subatomic particle will react to other subatomic particles. We know that other subatomic particles with a negative charge will be repelled from the electron, and we know that opposite charges will attract. So, the quantum property there has described how that subatomic particle will react to an external force.
The same thing is happening with spin. It describes how that subatomic particle, or that particle, will react to an external magnetic field. We call this spin value spin angular momentum, and they have discrete measurable values. Protons, for example, like this proton here, is made up of quarks: two up quarks and one down quark, which each have their own spin values, and they are connected by gluons that hold those quarks tightly together in the proton. The proton itself has a net spin value of a half, and this spin value represents this spin angular momentum within the proton itself.
Now, you might be thinking that that's quite a difficult concept to get around. We can't make an electron more or less negatively charged; it has a set charge, the same as a proton has a set spin. In fact, electrons have a spin of a half, and neutrons have a spin of a half.
Now, when two neutrons are within the same nucleus, they both have a spin value of a half, but they have what's known as spin up and spin down. The two magnetic moments are in opposite directions and cancel each other out. In a nucleus that has an even number of protons and an even number of neutrons, the net spin value of that nucleus will be zero. Those proton pairs and neutron pairs would have canceled one another out, and the nucleus of that atom would have a net spin value of zero.
Now, any atom that has a spin value of zero will be unaffected by an external magnetic field. Now, if you think about the types of atoms within the human body, we think about oxygen, think about carbon, and think about hydrogen. Now, both Oxygen 16 and Carbon 12 both have an even number of protons and neutrons, and those even numbers mean that the spin values within those protons and neutrons cancel each other out. In hydrogen, we only have one proton; there's no neutron. Now, that proton has a spin value of a half, meaning the proton has its own magnetic moment and will be influenced by an external magnetic field.
Now, what I'm describing here is really only scraping the surface, and if you want to understand this in more depth, I'm going to link some articles and videos that you can read in your own time. Now, those principles that are linked below: the Pauli Exclusion Principle, the Heisenberg Uncertainty Principle, the Schrödinger equation, and entanglement, all of those are far beyond the scope of this course. Fortunately, when we're not trying to measure a single magnetic moment of a single proton itself, but rather measure a group of protons, we can take the net magnetization vector, the sum of all those magnetic moments, and use that net magnetization vector to calculate the MRI signal that we're generating. And that net magnetization vector acts very similarly to the classical model in physics. And later, if we come across a concept that is not explained by that classical model, I will refer back to this quantum mechanical model to explain how those phenomena are occurring.
So, why exactly do we use hydrogen? Well, I've alluded to it in the first place. There are many different atoms that will undergo nuclear magnetic resonance. All of these atoms here have a net spin that is not equal to zero. We mentioned Carbon 12 and Oxygen 16 earlier. These isotopes, because of the extra particle within the nucleus, mean that they have a net spin value and will ultimately undergo nuclear magnetic resonance. However, we use hydrogen one because it's the most abundant isotope in the body, and two, because the magnetic moment, that vector-like quality of the hydrogen proton itself, is the largest out of all of these isotopes here. It makes it a great candidate for MRI imaging, and not only is hydrogen abundant, but it's also abundant in various different tissues, so we can compare tissues to one another.
Now, we've seen that the hydrogen proton itself has a non-zero spin value. It's got a spin value of a half, and because it has a non-zero spin value, it will have a magnetic moment, that vector-like property describing the magnetic field around that proton. Now, throughout this course, I'm going to refer to hydrogens either as free hydrogens or as protons, because a hydrogen is just one proton, or I will refer to them as spins. All three of those are synonyms that you will see used interchangeably.
So, when we look at the hydrogen proton itself, we say it has a net magnetic moment. Now, in fact, in the quantum world, that hydrogen proton can exist both to spin up and spin down states simultaneously, and only when we go about measuring that magnetic moment can we say with certainty whether that hydrogen is spin up or spin down. We should rather think about the net magnetic moment of a group of hydrogens, where we sum all those little magnetic moments to get one net magnetization vector. And that's why I'll represent a net magnetization vector without the proton attached. When you see a vector like this, I'm talking about a group of hydrogen protons.
Now, the magnetic moment describes how those hydrogen protons will respond to an external magnetic field. So, it goes without saying that the magnetic moment and the spin value of the proton itself are linked in some way. Now, in order to link the magnitude of the magnetic moment to the spin of the proton itself, we use a value that's known as the gyromagnetic ratio. Now, this is a value that's worth learning if you're studying for an MRI physics exam. This kind of question comes up a lot. The hydrogen atom has a gyromagnetic ratio of 42.5 megahertz per Tesla, and if we times the gyromagnetic ratio by the spin, we will get a magnetic moment value here. Now, you'll see later that the gyromagnetic ratio becomes really important when determining the precessional frequency of those hydrogen atoms in a magnetic field.
The gyromagnetic ratio, as you can see here, links a specific atom to that atom's spin and gives us the magnitude of the magnetic moment. Now, we've said that when an atom with a non-zero spin is placed in a magnetic field, that atom will align with the magnetic field and it will precess at a certain frequency. Now, the frequency at which that atom will precess, I've mentioned before, is related to the strength of the magnetic field and the type of atom that it is.
Now, we can use the gyromagnetic ratio and the strength of the magnetic field strength in order to calculate what's known as the Larmor frequency. If we take the specific gyromagnetic ratio of the atom of interest and we times it or multiply it by the strength of the magnetic field, we will get a frequency value that's known as the Larmor frequency, and this is a key principle in MRI imaging. If we know the magnetic field strength, say it's one Tesla, and we know the gyromagnetic ratio of the proton or atom that we are trying to image, we can calculate the precessional frequency of that hydrogen proton. That becomes really important because when we start adding that RF pulse, we want the radio frequency pulse to match the precessional frequency. If the main magnetic field strength went to 1.5 Tesla, our frequency would increase by 50%. You can see that multiplying a Tesla value with the gyromagnetic ratio means that the Tesla in the unit here will be canceled out, and our frequency will be in megahertz.
Now, importantly, what the Larmor frequency is calculating is the precessional frequency of the atom of interest. In our case, it's hydrogen. Now, if you think about spinning a basketball on your finger, firstly, if the basketball wasn't spinning, it would just fall off. We need that angular momentum in order for that basketball to stay on our finger as it's pulled down by gravity. And you'll see when people spin a basketball on their finger, they move their finger from side to side ever so slightly in order to keep that basketball spinning. You can think of that as the precessional frequency. If that basketball were to change, if you were to make it a tennis ball, your frequency would have to change. The frequency is dependent on the type of atom that is in that magnetic field.
Now, as those protons align with the magnetic field, we've said that some will be spin up and some will be spin down, and there will be an energy difference between these two, where the net magnetization vector will lie parallel to the external magnetic field, and we'll get what is known as a net magnetization vector. As you can see, these precessing protons are precessing out of phase. They're at the same frequency but different phase because they're in different phases. The XY, the transverse magnetization values cancel each other out, and we have a net magnetization that is directly along the longitudinal or Z axis.
Now, if we take this net magnetization vector and place it within the MRI machine, this should not be precessing. And I want to make this clear throughout this course: whenever I show a net magnetization vector that is precessing within the MRI scanner, I am not saying that this net magnetization vector has any transverse magnetization yet. What I want to show you here is that the hydrogen atoms that are causing this net magnetization vector are precessing at a set frequency. The magnetization vector itself should be dead still because those transverse magnetization values are canceling each other out. Those hydrogen atoms are out of phase.
This frequency becomes really important for when we want to induce transverse magnetization. So, we can calculate the specific frequency of the net magnetization vector by using the Larmor equation here. Now, once we've calculated that specific precession frequency, we can apply a radio frequency pulse that matches that frequency. That radio frequency pulse, as we've seen, is called B1. It's perpendicular to the main magnetic field. If I'm spinning that basketball on my finger like this, and someone gives a force to my arm perpendicular to the gravitational field, I'm going to fan my finger out in order to carry on balancing that basketball, and the axis of that basketball is also going to change. The same thing happens when we apply a radio frequency magnetic force at the same frequency as those atoms are precessing. Energy will be applied into the system, and that net magnetization vector will be knocked off the longitudinal or Z plane. We will gain some transverse magnetization.
Now, importantly, this radio frequency pulse needs to match the precessional frequency of those hydrogen atoms in order to induce this resonance. Now, resonance is two things. The first is it's applying energy to cause that net magnetization vector to fan out. The second is that because the radio frequency pulse matches the precessional frequency, those hydrogen spins start to spin in phase with one another. They are no longer out of phase, and because they are in phase with one another, we actually get a vector forming where we can measure the XY plane or the transverse magnetization.
Now, importantly, we only get transverse magnetization when the hydrogen nuclei are in phase, and when they're in phase, they're undergoing what is known as resonance. Now, if we apply a radio frequency pulse for a certain period of time, we are flipping that net magnetization vector by a certain angle known as the flip angle. Now, at a flip angle of say, 60 degrees here, we will measure a certain signal if we place a coil transverse to our main magnetic field here, and that signal can be read out. The signal strength, the amplitude of that signal, is proportional to the transverse magnetization of those in-phase precessing hydrogen atoms.
If we apply that radio frequency pulse for a longer period of time, that flip angle will keep getting bigger until it reaches 90 degrees. That is when we get the maximum signal for our hydrogen nuclei. The net magnetization vector is now 90 degrees to our main magnetic field, and you can see the amplitude of this signal is higher here. So, the application of a radio frequency pulse allows us to induce resonance. Resonance allows us to get transverse magnetization, and transverse magnetization allows us to measure a signal.
Now, when we are looking at a gradient that's applied in the longitudinal direction, we can calculate the specific frequency with the Larmor equation for a specific point along this gradient. If we know the magnetic field strength here, we will know that the Larmor frequency will be higher for these hydrogen atoms along this XY plane here. The gyromagnetic ratio for the hydrogen atoms or hydrogen protons within the sample remains the same, but the magnetic field strength changes. That changing magnetic field strength changes the frequency of the hydrogen protons that are precessing within the tissues, and we can select a specific slice that matches that frequency and have a radio frequency pulse that selects for just that specific slice. Again, the radio frequency pulse will only work if you are pushing it at the precessional frequency. If my precessional frequency is different to my radio frequency pulse, they are not going to match up, and that energy is not going to be transferred to those precessing, now resonant hydrogen protons.
So, not only does resonance allow us to measure signal, but it also allows us to select a specific group of hydrogen atoms based on the Larmor frequency of those hydrogen atoms. Now, what I've alluded to is that when we apply a radio frequency pulse, it takes time for those now in-phase precessing hydrogen atoms to gain transverse magnetization. That takes a period of time. If we apply a radio frequency pulse that matches the precessional frequency for a certain period of time, that makes that net magnetization vector 45 degrees, we will get a certain signal. If we wait that exact same period of time, continually applying that radio frequency pulse, that magnetization vector will now be 90 degrees. We'll have gained maximum transverse magnetization. Interestingly, this takes half the time to generate the signal, but the signal generated at 45 degrees is 70% of the signal generated at 90 degrees. And we're going to come across sequences later where we need to measure the signal quickly, and we need to use short flip angles. We can't afford to wait all that time for the radio frequency pulse to get into 90 degrees, and despite using small flip angles, we are still generating a proportionally higher signal for the time it took to flip that net magnetization vector 45 degrees.
Now, when we looked at the classical model with that actual spinning charged particle creating a magnetic moment, we would think that the radio frequency pulse could only flip those protons to 90 degrees. If we tried to flip in more than 90 degrees, the magnetic dipole of that specific proton would be opposite to the main magnetic field, and we wouldn't be able to push it past 90 degrees. Now, the quantum properties of a proton means that if we apply the radio frequency pulse for double the amount of time that it took to flip the net magnetization vector to 90 degrees, we can in fact flip that net magnetization vector a full 180 degrees. We've again lost all transverse magnetization, but now this vector is sitting in the higher energy state, anti-parallel to the main magnetic field. And this is because the proton can exist in both the spin up and spin down states. And you'll see as we go on throughout this course, there are multiple pulse sequences when we are required to flip the net magnetization vector a full 180 degrees, and then we wait for that net magnetization vector to return to its resting state. And you'll see why that's extremely helpful when trying to generate a true T2 signal instead of a T2 star free induction decay signal, but that is for another talk.
I hope nuclear magnetic resonance has made some sense to you. Spin angular momentum is responsible for a magnetic moment within a proton. That magnetic moment means that proton will align with an external magnetic field and precess at a frequency that's dependent on the strength of that magnetic field and the type of atom that we're looking at. And we can then use that precessional frequency to apply a force perpendicular to that precessional frequency and induce resonance within those hydrogen atoms. That entire process is what's known as nuclear magnetic resonance.
So, I'll see you all in the next talk, where we're going to look at the loss of transverse signal once we flip that net magnetization vector 90 degrees. How then do we go about measuring the loss of that net magnetization vector? So, I'll see you all in that talk. Goodbye, everybody.