- Proof:
- The equation for a repeated inversion recovery sequence is
- where
- TI = inversion time
- TR = repetition time
- T
_{1}= spin-lattice relaxation time - T
_{2}= spin-spin relaxation time - r = spin density
- k = proportionality constant

We start with the Bloch equations introduced in Chapter 3. The signal in a pulse sequence is proportional to the amount of longitudinal magnetization rotated in to the xy-plane. For this reason, we only need to examine the component which describes in differential form the time (t) evolution of the M

Integration yields

and evaluating between the limits yields the following equations.

Which after rearrangement gives the IR equation.