The Physics of fMRI

April 13, 2009

I almost destroyed the backseat pocket of an airline seat this summer. The vandalism was inadvertent, assuredly, though the anger that fueled it was not. While waiting for my plane to take off, I had read a magazine article claiming to show that fMRI (functional magnetic resonance imaging) studies were “uncovering” the voting preferences of test subjects. An adjacent article announced that researchers could now predict the buying preferences of other test subjects using the same imaging technologies.

I almost destroyed the backseat pocket of an airline seat this summer. The vandalism was inadvertent, assuredly, though the anger that fueled it was not. While waiting for my plane to take off, I had read a magazine article claiming to show that fMRI (functional magnetic resonance imaging) studies were “uncovering” the voting preferences of test subjects. An adjacent article announced that researchers could now predict the buying preferences of other test subjects using the same imaging technologies.

I was puzzled. How could Fourier transforms performed on signals coming from someone’s cortex say anything about their politics? What could possibly have reduced the interpretation of these noninvasive imaging data to conceptual phrenology? I got so mad as I thought more about it that I jammed the articles back into the pocket, aggravating an already ripped inner seam.

The column you are reading is an attempt to push this admittedly hot reaction into a more positive direction . . . and for a good reason. There are growing numbers of articles in the popular press describing “breakthroughs” in our understanding of human cognition-and how noninvasive imaging data are changing the way we view the brain. Nothing wrong with that, certainly. There has been an explosion of studies using functional (f)MRI technologies and their like. But are the data being revealed strong enough to predict subjective behaviors, such as voting habits? As you can probably guess from my tone, the answer of this bioengineer is “no,” or at least “not yet.”

I have decided to do something positive about these “headlines.” For now, and in my next 2 columns, I will describe how fMRIs actually work and what is the least luxurious, most conservative way to interpret the view they give us about cognition. Given the conceptual and technical complexity, it is easy to misconstrue what imaging technologies can divulge about human cognition.

Starting with quarks (literally) and ending with scans of emotional behavior, we will explore some of the biophysical underpinnings of this promising (and may I say limited) technology. The hope is that by knowing a bit about the technical aspects of fMRI, we will better understand what it can-and cannot-measure. This will allow us to treat with greater skepticism, and more sobered excitement, the view that fMRIs are giving us about how our brains work. This first installment deals with some basic physics. I review a few properties about magnets and radio waves that you might not have thought about since your undergraduate days. In part 2, I will focus on the types of molecular interactions these magnets and radio waves actually measure when trained on an actively thinking brain. The third column will relate how this knowledge reveals both the strengths and limitations of using imaging technologies to discover aspects of human cognition.

THE 40,000-FOOT VIEW
We begin with the name. As you know, fMRI is short for functional magnetic resonance imaging. The core idea of fMRI has been around for a long time. Originally called just NMR (nuclear magnetic resonance), this technology found great utility in the organic and inorganic laboratories. When it came time to apply the technology to biological tissues (from ideas originally developed by Paul Lauterbur), the word “nuclear” was thought to have too many negative connotations. It was dropped in favor of the more socially compatible “functional.”

To understand how an fMRI scanner generates images, we have to break the machine down into its component parts. All fMRIs possess 3 general “gadgets.” The first is a device that can generate a powerful magnetic field. The second is a coil that can create powerful radio frequency pulses. The third is a high-speed computer, preloaded with a lot of very sophisticated signal processing software, all programmed to produce an image capable of making sense to a researcher.

How these 3 gadgets work together is fairly easy to understand, at least at the 40,000-foot level (Figure). The magnet in the fMRI transforms tissues into a visualizable state; the radio frequency pulses provide the signaling information necessary to discern them. The computer assembles the information from the radio frequency pulses into a form instantly recognizable to anyone who can read a weather map. Indeed, part of the problem with misinterpreting fMRIs is that the information seems so accessible.

To make sense of how these gad­gets work together, we have to understand how magnets and radio frequencies act at the subatomic level. These interactions are essentially the same physical processes you see on display every time you turn on your radio.

Why fMRIs need magnets
The most obvious characteristic of any fMRI machine is the magnet it carries. Modern magnets are constructed from superconducting wires cooled by helium. A typical fMRI can generate a magnetic field tens of thousands of times greater than the earth’s. The force generated is so strong that patients have to remove any metal items before entering the shielded privacy of the scanner. (That’s a safety issue. Flying metal objects, pulled off of uninspected individuals by the magnets, have injured and even killed people!)

Why do you need such beastly magnets? The reason has to do with the protons embedded in the biological tissues being examined and the odd motions these nuclear particles intrinsically possess. Three sets of facts describe why magnets are used.

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!