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This paper proposes a statistical framework to optimize and evaluate the MRparameter $T_1$ and $T_2$ mapping capabilities for quantitative MRI relaxometryapproaches. This analysis explores the intrinsic MR parameter estimateprecision 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), astatistical lower bound on the parameter estimate variance. Geometricallyinterpreting the new TNR efficiency definition reveals a more complete modeldescribing the factors controlling the $T_1$/$T_2$ mapping capabilities. Thispaper 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) anddriven equilibrium single pulse observation of $T_1$/$T_2$ (DESPOT) sequences.All pulse parameters are optimized to maximize the TNR efficiency withindifferent $T_1$ and $T_2$ ranges of interest. Monte Carlo simulations withnon-linear least square estimation (NLSE) of $T_1$/$T_2$ validated thetheoretical predictions on the estimator performances.

A Statistical Framework for Optimizing and Evaluating MRI of T1 and T2 Relaxometry Approaches