## The Basic Physics Behind fMRI

Each atomic nucleus that is affected by magnetism (those having an odd number of protons or neutrons or both) spins like a gyroscope when placed within a magnetic field. Remember that in a gyroscope the axis of rotation itself rotates. This rotation is called precession; the same thing happens to each nucleus. The frequency of this precession is proportional to the strength of the magnetic field, with the constant of proportionality being determined by the atomic species' gyromagnetic ratio.

For hydrogen, which is the current basis of fMRI, the constant is approximately 42MHz per Tesla. A Tesla is a measure of the strength of the magnetic field. One Tesla is 10,000 gauss; a gauss is roughly the strength of the earth's magnetic field. A standard ``high-field'' MR scanner has a main field strength of 1.5 Tesla; this field strength is achieved through the use of superconducting materials, but that is another story.

As the nuclei precess, the probability distribution of the directions that their axes are pointing is determined by the strength of the field. Quantum mechanics says that they will either point with the field or against it; they can't be in-between. The stronger the field the more concentrated the distribution pointing in the direction of the field (or rather in the opposite direction to the field; there is a local minimum in the energy function in exactly the opposite direction when the nucleus is a dipole). This distribution also depends on the energy state of the system; the more energy the nuclei contain the more likely they are to be flipped the other way.

This fact is the key to magnetic resonance. When we inject a little energy into the system, at the frequency of precession, it is absorbed by some of the atoms. They get flipped to point "uphill" against the magnetic field. After a while they flip back to their ground stat, emitting this energy. The scanner detects the emitted energy and uses it to construct an image.

Fiasco is a toolkit for analysis of functional brain images developed at the CMU Department of Statistics. See the Fiasco Home Page for more information.
fiasco@stat.cmu.edu