Spatial and precessional frequencies

Here’s a top tip for any student of MRI physics: never say a sentence about “frequencies” without specifying what type of frequencies you mean. So “frequency relates to position” is not allowed.

Always use these:

  • precessional frequencies
  • spatial frequencies

Precessional frequencies are the speed with which the magnetic direction of a hydrogen proton (or spin isochromat) rotates around the direction of the magnetic field it experiences. We talk about precessional frequencies, when discussing what’s physically happing to our sample, and when we’re referring to the Larmor equation.

Spatial frequencies are real waves in actual space. Draw a wave with your hand in front of you. Congratulations, a spatial frequency. Now draw a wave with a smaller wavelength. Voilà, a higher spatial frequency. We talk about spatial frequencies when we’re talking about k-space, the signal from the sample, and encoding.

So, precessional frequency relates to position. K-space is a map of spatial frequencies, which are what we record in an MRI experiment. Precessional frequencies refer to individual parts of the sample or patient. Spatial frequencies affect the whole image, and come from the whole sample/patient.

It gets a bit more complicated.

When talking about precessional frequencies, we should state whether we are referring to the magnetic direction of individual hydrogen protons (spins”), or microscopic groups of spins which experience the same magnetic field strength: spin isochromats. This is because the magnetic direction of a single hydrogen proton wanders around slowly (and precesses quickly) all the time. There is a tendency for the wandering of each spin to be more with the main external magnetic field (B0) than against it, and so overall, a net magnetisation forms. This net magnetisation—of many spins—we call Mz. Because Mz is the sum of many spins, it doesn’t “wander” like the individual spins. It doesn’t precess around the external magnetic field either, unless an RF pulse moves it away from it’s default position aligned with B0; Mz is equal to the equilibrium value M0 when no RF pulse has been applied (thermal equilibrium). We do not talk of “Mz” or “M0” for a single spin.

So, if you see pictures of magnetisation vectors being manipulated by RF pulses, it should be referring to the net magnetisation of a large number of spins: a spin isochromat.

Read more on the net magnetisation page of the main site.