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The Physics of fMRI: Page 2 of 2

The Physics of fMRI: Page 2 of 2

First set
You may recall from your undergraduate physics days that single unpaired protons “spin” on their axes—and do so along random orientations. The unstable spinning causes these positively charged particles, protons, to “wobble,” like tiny spinning tops undergoing their last few rotations (see Figure).

Why does a proton spin? You probably also remember that protons are made of quarks (a proton has 3 of them), each paired with its strange antiquark cousin. These quarks and their paired colleagues do not sit still inside a proton. They have intrinsic spins, too, a fact that was used in the old days to explain the motion of the proton. That turns out not to be true. The quarks also display “orbital” motions relative to each other; it is now clear that the proton spins in part because of these internal orbital motions. There may be other contributing factors as well. In the truly goofy world of the quantum subatomic, we now know that quark/antiquark pairs continually flit in and out of existence inside a proton. These appearances/disappearances also appear to contribute to a proton’s motion.

Second set
The fact that a charged particle like a proton is in motion leads to a prediction. As you know, any charge that is also moving in space produces a magnetic field. Wobbly protons are by definition moving charged particles, even if held in the relatively firm grips of the molecules in which they are embedded (the classic example is hydrogen nuclei). As a result, these embedded-but-wiggly protons set up lilliputian magnetic fields. You can think of these protons as tiny bar magnets. Tissues in the human body are filled with hydrogen nuclei. They are thus filled with tiny bar magnets.

When the fMRI magnet is turned on, it applies a strong field to the biological tissues under examination. In reaction, these protons align their axes around the field lines dictated by the machine’s magnet. Or at least they try to. The alignment is not exact, which results in their axes rotating around the field lines in an inexact fashion. The protons “precess,” a term that refers to the change in the direction of the axis of any rotating object. This axis of rotation sweeps out a cone at a certain rate.

Third set
The last set of ideas has to do with the rate of the spinning proton held in thrall of the magnetic field. The time it takes for the wobbling proton to sweep out a cone exactly once is called the resonance frequency of the proton. Different protons sweep out cones with different resonance frequencies.

These differential frequencies also turn out to be important for understanding how fMRIs work. They have a direct hand in broadcasting the physical location of the atom in question, critical if you are interested in getting a picture of the tissue the atom inhabits. We must thus explore what determines the resonance frequency of a given proton at a given location. Unfortunately, that is not an easy question to answer, for there are many factors.

On resonance frequency
One factor that determines the proton’s resonance frequency has to do with the strength of the external magnetic field being applied. As you know, patients in an fMRI machine lay down in a tube. The magnetic field strength varies along the length of that tube, creating a gradient that is more powerful at the “head” end than at the “tail” end. The resonance frequency of a given proton is in part a function of where it finds itself in this gradient. (The specific resonance frequency of a given proton is called its Larmor frequency. A Larmor frequency is the natural resonance frequency of a spin system. It is calculated on the basis of 2 factors: the particular tissue being imaged and the aforementioned strength of the magnetic field.)

Because of these and other factors, the proton has the potential of broadcasting unique positional information to an observer. If you could figure out a way to extract this positional information (which means determining its specific resonance frequency), you could begin to image the origin of the source of the broadcast. These tiny little magnets could create an image, just like tiny grains of sand reveal a beautiful mosaic. The fMRI machines actually use magnets in part to set up the tissues so that they become “extraction competent.”

How that extraction occurs is the reason why we need the second and third parts of the fMRI device . . . a device that can generate radio frequencies and a really good computer that can make sense of the radio’s interactions with the tissues in the magnet. How they work together to give us an image is where we’re headed next.

WHY fMRIs NEED RADIOS
The second important gadget on a typical fMRI machine is a coil that can send out powerful radio frequency pulses aimed at the tissue to be examined. The machine transmits only on certain radio wave frequencies, which has the net effect of exciting some protons and not other particles in the sample. The proton is said to “flip.”

By “excite,” I really mean energy absorption. For this to happen, the radio frequency must have exactly the amount of energy it would take to make the proton flip from a low energy to a high energy state in the magnetic field. In other words, it must “resonate” with the nucleus. That’s the “R” in fMRI.

This energy absorption lies at the heart of the technology. The energy causes the proton to flip, which also causes it to come out of alignment with the magnetic field. Every proton that can interact with the radio frequency also will flip. Since you’ve got millions of potentials, you have millions of flips. Moieties that can’t absorb the energy don’t flip; they stay in their boring lower energy state . . . flips and non-flips in one space. For you digital fans out there, we have just created a bunch of ones and zeros. These are the building blocks nec­­essary to create an image.

So how are those ones and zeros detected? After a short period, the radio frequency pulse is turned off by the technician. In a few milliseconds, some of the protons that absorbed the radio frequency energy will begin to give some of it back. This release of energy causes the protons to realign themselves inside the strong magnetic field. There are detectors within the fMRI that are capable of measuring the time it takes for a proton to release this energy. It is this release of energy that the fMRI uses to create the image of the tissues. Only the moieties that absorbed the resonance frequency of the radio frequency pulse will flip in the first place, which means there is only a minority that can actually reverse themselves and dissipate their pre-absorbed energy. Enough of them come down, however, that a highly detailed image can emerge.

WHY fMRIs NEED COMPUTERS
We are not yet done, of course. The signals derived from all this flipping themselves inside the strong magnetic field. There are detectors within the fMRI that are capable of measuring the time it takes for a proton to release this energy. It is this release of energy that the fMRI uses to create the image of the tissues. Only the moieties that absorbed the resonance frequency of and resetting generate very complex datasets chock-full of ones and zeros. That’s why the third device in every fMRI is a computer. The machine’s coil picks up the signals derived from changes in the spin precession and feeds everything to the computer, which has been preloaded with a lot of sophisticated signal processing software. While the general nature of the processing is too complex for this space (unless you are comfortable with Fourier transforms), suffice it to say that a great deal of calculation and filtering goes on. There are usually injectable contrast dyes that assist during the imaging process. A picture eventually emerges and the activity within the tissue under examination becomes visible. Further software protocols can even mark differences in signals strengths with different colors. The image that emerges often looks like a Doppler weather scan showing earthy precipitation patterns.

None of the physics answers the questions about how fMRIs are used to detect and discriminate levels of neural activity, of course. Nor does it say very much about how vulnerable the images derived from such activity are to misinterpretation. But it is a start.

In the next column, I will drop down into the world of the thinking brain and address some biological issues. As we shall see, looking at how excited protons come down from their radio frequency–induced “high” has real implications for understanding human cognition—as long as we are careful about how we interpret what we observe. Prudent for the sake of airplane seats everywhere, at least for those flying in and out of Seattle!

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