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

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.