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There is an excellent guide to MRI at mriquestions.com. Most images in these notes come from that site, courtesy of Allen D. Elster, MRIquestions.com.

Prior to a SE sequence, we can apply a 180-degree pulse. This changes the net magnetic field from $+M_0$ to $-M_0$. No phase coherence is added!

Tissues with different T1 will recover their net magnetic field at different rates.

TI = time of inversion = time from centre of inversion pulse to centre of next pulse (90-degree SE pulse) in the pulse sequence.

Can set TI to time that a particular tissue (e.g. fat) recovers to a net magetic field of zero. When the 90-degree pulse is then applied, that tissue gets no signal in the transverse field. So a "fat suppressed" pulse sequence would choose TI = 0.69 of T1$_\textrm{fat}$.

Recall that $M_z$ is not detected, so T1 cannot be recovered from $M_z = M_0 (1-e^{-t / \textrm{T1}})$.

Instead, we apply the 180-degree IR pulse and delay TI to let tissues with different T1 gain different amounts of $M_z$, which becomes $M_{xy}$ with the next 90-degree pulse. The magnitude of $M_{xy}$ can be recovered.

IR can also be used to increase the contrast between tissues with different T1 since they recover from $-M_0$ toward $+M_0$ at different rates.

But IR is slow.

STIR = Short TI Inversion Recovery. Has TI about 180ms so that fat has $M_z$ = 0 at that time and, hence, is black (i.e. has no signal).

FLAIR = Fluid-Attenuated Inversion Recovery. Has TI of 2.0s to 2.5s to null the $M_z$ of cerebro-spinal fluid (CSF). Has very long TR (8000ms) and long TE (140ms) for strong T2 weighting.