Commonplace Book

Bloch

Watch magnetisation tip, precess, fan out and relax, following the Bloch equations. Pick a pulse sequence and run it, or tip the spins yourself. Drag the sphere to turn it.

|Mxy|, the signal Mz Mx′, My′ T2 decay T2*
t
Mx′
My′
Mz
|Mxy|

Sequence

Tip the spins

Tissue

Rough values at 3 T.

Field

View

What you're looking at

The sphere is drawn in the rotating frame, which turns with the spins at the Larmor frequency, so spins exactly on resonance stand still. B0 points up the z axis. Each thin arrow is an isochromat, a group of spins that see the same field; the thick one is their sum, M, the magnetisation you can measure. Its part in the x′y′ plane is the signal a coil picks up.

The spread gives the isochromats a Lorentzian range of frequencies, the way a slightly uneven field does. They fan out and the signal decays with T2*, faster than T2 alone. A 180° pulse flips the fan over so it closes again into a spin echo; only true T2 decay is left, which the CPMG train makes plain. Inversion recovery shows T1: the signal vanishes when the 90° pulse lands at T1 ln 2, as Mz crosses zero.

Pulses are hard pulses, drawn slowly so you can follow them; relaxation stops while they play. The lab frame adds the Larmor precession back, a turn a second rather than a hundred million.