Magnetic Resonance Imaging

[This is a transcript of the video embedded below. Some of the text may not make sense without the animations in the video.]

Magnetic Resonance Imaging is one of the most widely used imaging methods in medicine. A lot of you have probably had one taken. I have had one too. But how does it work? This is what we will talk about today.


Magnetic Resonance Imaging, or MRI for short, used to be called Nuclear Magnetic Resonance, but it was renamed out of fear that people would think the word “nuclear” has something to do with nuclear decay or radioactivity. But the reason it was called “nuclear magnetic resonance” has nothing to do with radioactivity, it is just that the thing which resonates is the atomic nucleus, or more precisely, the spin of the atomic nucleus.

Nuclear magnetic resonance was discovered already in the nineteen-forties by Felix Bloch and Edward Purcell. They received a Nobel Prize for their discovery in nineteen-fifty-two. The first human body scan using this technology was done in New York in nineteen-seventy-seven. Before I tell you how the physics of Magnetic Resonance Imaging works in detail, I first want to give you a simplified summary.

If you put an atomic nucleus into a time-independent magnetic field, it can spin. And if does spin, it spins with a very specific frequency, called the Larmor frequency, named after Joseph Larmor. This frequency depends on the type of nucleus. Usually the nucleus does not spin, it just sits there. But if you, in addition to the time-independent magnetic field, let an electromagnetic wave pass by the nucleus at just exactly the right resonance frequency, then the nucleus will extract energy from the electromagnetic wave and start spinning.

After the electromagnetic wave has travelled through, the nucleus will slowly stop spinning and release the energy it extracted from the wave, which you can measure. How much energy you measure depends on how many nuclei resonated with the electromagnetic wave. So, you can use the strength of the signal to tell how many nuclei of a particular type were in your sample.

For magnetic resonance imaging in the human body one typically targets hydrogen nuclei, of which there are a lot in water and fat. How bright the image is then tells you basically the amount of fat and water. Though one can also target other nuclei and measure other quantities, so some magnetic resonsnce images work differently. Magnetic Resonance Imaging is particularly good for examining soft tissue, whereas for a broken bone you’d normally use an X-ray.

In more detail, the physics works as follows. Atomic nuclei are made of neutrons and protons, and the neutrons and protons are each made of three quarks. Quarks have spin one half each and their spins combine to give the neutrons and protons also spin one half. The neutrons and protons then combine their spins to give a total spin to atomic nuclei, which may or may not be zero, depending on the number of neutrons and protons in the nucleus.

If the spin is nonzero, then the atomic nucleus has a magnetic moment, which means it will spin in a magnetic field at a frequency that depends on the composition of the nucleus and the strength of the magnetic field. This is the Larmor frequency that nuclear spin resonance works with. If you have atomic nuclei with spin in a strong magnetic field, then their spins will align with the magnetic field. Suppose we have a constant and homogeneous magnetic field pointing into direction z, then the nuclear spins will preferably also point in direction z. They will not all do that, because there is always some thermal motion. So, some of them will align in the opposite direction, though this is not energetically the most favorable state. Just how many point in each direction depends on the temperature. The net magnetic moment of all the nuclei is then called the magnetization, and it will point in direction z.

In an MRI machine, the z-direction points into the direction of the tube, so usually that’s from head to toe.

Now, if the magnetization does for whatever reason not point into direction z, then it will circle around the z direction, or precess, as the physicists say, in the transverse directions, which I have called x and y. And it will do that with a very specific frequency, which is the previously mentioned Larmor frequency. The Larmor frequency depends on a constant which itself depends on the type of nucleus, and is proportional to the strength of the magnetic field. Keep this in mind because it will become important later.

The key feature of magnetic resonance imaging is now that if you have a magnetization that points in direction z because of the homogenous magnetic field, and you apply an additional, transverse magnetic field that oscillates at the resonance frequency, then the magnetization will turn away from the z axis. You can calculate this with the Bloch-equation, named after the same Bloch who discovered nuclear magnetic resonance in the first place. For the following I have just integrated this differential equation. For more about differential equations, please check my earlier video.

What you see here is the magnetization that points in the z-direction, so that’s the direction of the time-independent magnetic field. And now a pulse of an electromagnetic wave come through. This pulse is not at the resonance frequency. As you can see, it doesn’t do much. And here is a pulse that is at the resonance frequency. As you see, the magnetization spirals down. How far it spirals down depends on how long you apply the transverse magnetic field. Now watch what happens after this. The magnetization slowly returns to its original direction.

Why does this happen? There are two things going on. One is that the nuclear spins interact with their environment, this is called spin-lattice relaxation and brings the z-direction of the magnetization back up. The other thing that happens is that the spins interact with each other, which is called spin-spin relaxation and it brings the transverse magnetization, the one in x and y direction, back to zero.

Each of these processes has a characteristic decay time, usually called T_1 and T_2. For soft tissue, these decay times are typically in the range of ten milliseconds to one second. What you measure in an MRI scan is then roughly speaking the energy that is released in the return of the nuclear spins to the z-direction and the time that takes. Somewhat less roughly speaking, you measure what’s called the free induction decay.

Another way to look at this process of resonance and decay is to look at the curve which the tip of the magnetization vector traces out in three dimensions. I have plotted this here for the resonant case. Again you see it spirals down during the pulse, and then relaxes back into the z-direction.

So, to summarize, for magnetic resonance imaging you have a constant magnetic field in one direction, and then you have a transverse electromagnetic wave, which oscillates at the resonance frequency. For this transverse field, you only use a short pulse which makes the nuclear spins point in the transverse direction. Then they turn back to the z-direction, and you can measure this.

I have left out one important thing, which is how do you manage to get a spatially resolved image and not just a count of all the nuclei. You do this by using a magnetic field with a strength that slightly changes from one place to another. Remember that I pointed out the resonance frequency is proportional to the magnetic field. Because of this, if you use a magnetic field that changes from one place to another, you can selectively target certain nuclei at a particular position. Usually one does that by using a gradient for the magnetic field, so then the images you get are slices through the body.

The magnetic fields used in MRI scanners for medical purposes are incredibly strong, typically a few Tesla. For comparison, that’s about a hundred thousand times stronger than the magnetic field of planet earth, and only a factor two or three below the strength of the magnets used at the Large Hadron Collider.

These strong magnetic fields do not harm the body, you just have to make sure to not take magnetic materials with you in the scanner. The resonance frequencies that fit to these strong magnetic fields are in the range of fifty to three-hundred Megahertz. These energies are far too small to break chemical bonds, which is why the electromagnetic waves used in Magnetic Resonance Imaging do not damage cells. There is however a small amount of energy deposited into the tissue by thermal motion, which can warm the tissue, especially at the higher frequency end. So one has to take care to not do these scans for a too long time.

So if you have an MRI taken, remember that it literally makes your atomic nuclei spin.