MRI Machines and You

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Quantum Mechanics + Radio Waves = Pictures of your Brain

Big Ideas: 
  • MRI takes advantage of quantum mechanics to get pictures you couldn't otherwise get

We have new technology that can look inside your brain! With Quantum Mechanics!  Actually, it's not that new. It's called an MRI machine (Magnetic Resonance Imaging), and odds are there's one at your local hospital. But it does use quantum mechanics to look inside your brain.

 

As some of you will know, quantum mechanics was developed in response to some things that classical mechanics (eg, forces, blocks and planes, weird arrangements of frictionless pulleys and massless strings) couldn't explain. Two of the ideas that came out of quantum mechanics are relevant here. One is that light, rather than being a continuous wave, is composed of a bunch of little bits of light, called photons, at certain energies, and those energies are determined by the wavelength, which our eyes see as “colour” (American eyes see “color”). The second thing is related to the first, and that is that electrons in an atom can only have certain energies, not just any energy, and can jump between these energies by absorbing or emitting a photon. This means, among other things, that if you put energy into an atom, say by running electricity through a gas, the light that comes out will come out only at a few special wavelengths, not every wavelength, and those wavelengths will be determined by the jumps between the allowed energies in the atom. This was used to explain spectral lines back in the day, and today the principle is used to make florescent lights, which is why florescent lights, especially older ones, tend to have a much less “natural” feel than incandescent ones (which produce all wavelengths). The take home message here: light consists of photons, and atoms can only have certain energies.

 

MRI makes use of the same type of phenomenon, with two important, and related, differences. They stem from the fact that what we are dealing with now is magnetic rather than electric. Also, the things that are jumping up and down in energy are not electrons whizzing around an atom, but magnetic states of the nucleus. So a short review of the nucleus is in order. The nucleus, as hopefully you remember, is a bunch of protons and neutrons stuck together. It is very small, contains most of the mass of the atom, and has a positive charge (since the protons are positive and the neutrons neutral). If the nucleus is spinning, it acts like a tiny magnet, in exactly the same way that a current put through a looped wire makes an electromagnet.

 

 

Except that it's not quite exactly like an electromagnet, since the nucleus is so small that it follows the rules of quantum mechanics, so the amount it is spinning by, which in a fit of imagination physicists called the “spin” of the nucleus, can only take on certain values. This means that the nucleus is a little magnet that can only take on certain magnetizednessess. Magnetobilities? Magnetizations? (Bonus points if you can figure out which of those words is right.) For the simplest case, the case that is used in MRI scans, the nucleus (of hydrogen) has two magnetizations (okay, so I gave that one away, but I'm also not actually handing out bonus points), which physicists call “up” and “down”. In ordinary conditions, up and down have exactly the same energy.

 

 

But, if you apply what we call a "magnetic field" to the nucleus, then the two spins aren't at the same energy any more. You can think of a magnetic field as being like putting some extra magnets lined up in one direction around the nucleus. The spin that lines up with these "magnets" (remember, north wants to be close to south), will have a lower energy than the one that doesn't. In the image below you can see that the nucleus on the left is lined up with the extra, "field" magnets, so that the N's are all closest to the S's. But the one on the right isn't; the S on the nucleus is facing the S on the "field" magnet. This means it's at a higher energy.

 

 

Since the nucleus is governed by quantum mechanics, it can't just move from one spin to the other, it has to jump, and when it does that, it has to either absorb a photon (if it's moving from the low energy state in line with the magnetic field to the high energy state opposite it) or release a photon (if the opposite happens). In the diagram below I've drawn the photons as fuzzy blue things with a wave inside them. After all, even in quantum mechanics, the total amount of energy has to stay the same, so if the nucleus loses some energy, it has to go somewhere. The "somewhere" is, in this case, a photon. I should mention that the photons that are involved with nuclear spins have way, way less energy and way, way longer wavelengths than the photons that make up visible light. But they're still photons, and they obey the same rules about energy conservation and quantum mechanics.

 

 

So how does this all let us get an image of your brain? Well, first you stick your head in a magnetic field. This gives all the hydrogen atoms in your head (there's a lot of them!) an energy split. If you wait a while, they'll all be in the state that's lined up with the magnetic field, so they will all absorb photons of a certain energy, but not other energies. What we really want, though, is a slice-by-slice view, so that we can see what's going on. To understand how we get that, we need to remember that the energy difference between the up and down states of the proton (ie, between the state in which it's lined up with the other magnets and the state in which it isn't) depends on how strong the other magnets are, which we call the magnetic field strength. So, if we make a field (a set of external magnets) that changes in strength as we move along, like this,

 

then we know that the photons that will be absorbed by the hydrogen atoms as we move along will also change, like this:

 

So now, if we pick a particular energy, and only use photons at that energy, we they will only be absorbed by the atoms at the position that has the right magnetic field strength. We can add to our graph here photons at one energy:

 

Now that we know how to get only the only the atoms in one slice absorbing our photons, the only thing left to do is stick your head in the field and go.

 

 

And voila!  You have a picture of your brain. At least, after you've ran it all through a computer. You can't just put a piece of film in the machine and get anything, since there's radio waves flying everywhere. A computer, though, can pick up all those radio waves and figure out which ones were absorbed by the brain, and where that happened. Then it puts all that data together into an image:

 

 

The computer uses the photon wavelengths to determine position and the number of absorbed photons to determine the brightness in the picture. So to summarize: nuclei can behave like little magnets. We can use radio photons to flip those little magnets back and forth. If we change our magnetic field strength, we can make only certain nuclei absorb our radio photons. We can use a computer to put that all together and get a picture. Yay!

Comments

Wow, this was so great!!

Wow, this was so great!! Thank you :)

Thank you so much! I'm

Thank you so much! I'm learning about MRIs for my A-level physics but the textbook doesn't explain it at all which was frustrating. This was really helpful, thanks again :D

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