🧲 Hydrogen and the MR signal

Switch the magnet on, tip the protons with a radio pulse and watch the signal they give back.

Field strength Tissue

Larmor frequency at this field: 127.7 MHz

Drawn exaggerated and slowed: in a real 3 T scanner only a few protons in a million make the excess that lines up, and they turn about 128 million times a second.

Signal after the pulse: T2* decay

First 200 ms. The wiggle is the signal itself, drawn far slower than the real radio frequency.

Magnetisation along B0: T1 recovery

First 6 s. Dashed lines: the curve for this tissue and field.

Switch the magnet on to start.

How to read this

Magnet off: each hydrogen proton is a tiny magnet pointing any way, so together they cancel out. The net arrow on the right is zero.
Magnet on: the protons spin around the field direction (precession) at the Larmor frequency, and slightly more of them point along the field than against it. That small excess is the net magnetisation M. It builds up with time constant T1.
RF pulse: a short radio pulse at exactly the Larmor frequency tips M over by 90°. Now it turns in the sideways (x-y) plane and a coil picks it up as a radio signal.
Relaxation: the sideways signal fades quickly as the protons fall out of step (T2*, tens of milliseconds), while M grows back along the field more slowly (T1, about a second or two).

Try 7 T: the frequency goes up, T2* gets shorter and T1 longer. BOLD fMRI reads the signal during the fast T2* decay; the next page shows how blood oxygen changes it.

Key terms

B0: The scanner's main, always-on magnetic field, measured in tesla (T).
Precession: The wobbling turn of a spinning proton around the field direction, like a spinning top.
Larmor frequency: How fast protons precess: 42.58 MHz per tesla for hydrogen.
Net magnetisation (M): The sum of all the protons' tiny magnets in a voxel; the thing the scanner actually measures.
RF pulse: A short radio-frequency pulse that tips M away from B0.
T1: Time constant for M to grow back along B0 (to 63 % of full).
T2*: Time constant for the sideways signal to fade (to 37 %), from both random spin interactions (T2) and small field differences in the tissue.

Sources

Huettel S. A., Song A. W., McCarthy G. (2014). Functional Magnetic Resonance Imaging, 3rd ed., chapters 3–4. Sinauer.
Rooney W. D. et al. (2007). Magnetic field and tissue dependencies of human brain longitudinal ¹H₂O relaxation in vivo. Magnetic Resonance in Medicine 57: 308–318 (T1 values).
Peters A. M. et al. (2007). T2* measurements in human brain at 1.5, 3 and 7 T. Magnetic Resonance Imaging 25: 748–753 (T2* values).

Used in lessons 2, 3 of fMRI from zero.