  This paper proposes a statistical framework to optimize and evaluate the MR
parameter $T_1$ and $T_2$ mapping capabilities for quantitative MRI relaxometry
approaches. This analysis explores the intrinsic MR parameter estimate
precision per unit scan time, termed the $T_{1,2}$-to-noise ratio (TNR)
efficiency, for different ranges of biologically realistic relaxation times.
The TNR efficiency is defined in terms of the Cramer-Rao bound (CRB), a
statistical lower bound on the parameter estimate variance. Geometrically
interpreting the new TNR efficiency definition reveals a more complete model
describing the factors controlling the $T_1$/$T_2$ mapping capabilities. This
paper compares $T_1$ mapping approaches including the inversion recovery (IR)
family sequences and the Look-Locker (LL) sequence and simultaneous $T_1$ and
$T_2$ mapping approaches including the spin-echo inversion recovery (SEIR) and
driven equilibrium single pulse observation of $T_1$/$T_2$ (DESPOT) sequences.
All pulse parameters are optimized to maximize the TNR efficiency within
different $T_1$ and $T_2$ ranges of interest. Monte Carlo simulations with
non-linear least square estimation (NLSE) of $T_1$/$T_2$ validated the
theoretical predictions on the estimator performances.
