Interpolative computation of spin-lattice relaxation times from signal ratios

An iterative linear interpolation is described for computing T1 estimates from image-signal ratios that are monotonous functions of T1. Whether the function decreases or increases with T1, the same algorithm described applies. The iterative process converges readily. Narrowing the whereabouts of T1 sought in lookup tables to T1 regions just small enough to require only a few subsequent interpolations tends to shorten overall T1 image computing time. Used with imaging methods for which the function is readily evaluated, the iterative interpolation allows a rapid and precise T1 computation compatible with variable choice of pulse-sequence parameters. The flexibility is suitable to stochastic analysis of T1 measurement from signal ratios. Examples of applications to computing the stochastic uncertainty represented either by crude indicators or by standard statistical quantities are given. A method of stochastic simulation yielding the statistical quantities is described.