Optimizing MR Scan Design for Model-Based ${T}_{1}$ , ${T}_{2}$ Estimation From Steady-State Sequences

Rapid, reliable quantification of MR relaxation parameters
$\textit{T}_{1}$
and
$\textit{T}_{2}$
is desirable for many clinical applications. Steady-state sequences such as Spoiled Gradient-Recalled Echo (SPGR) and Dual-Echo Steady-State (DESS) are fast and well-suited for relaxometry because the signals they produce are quite sensitive to
$\textit{T}_{1}$
and
$\textit{T}_{2}$
variation. However,
$T_{1}, T_{2}$
estimation with these sequences typically requires multiple scans with varied sets of acquisition parameters. This paper describes a systematic framework for selecting scan types (
e.g.
, combinations of SPGR and DESS scans) and optimizing their respective parameters (
e.g.
, flip angles and repetition times). The method is based on a Cramér-Rao Bound (CRB)-inspired min-max optimization that finds scan parameter combinations that robustly enable precise object parameter estimation. We apply this technique to optimize combinations of SPGR and DESS scans for
$T_{1}, T_{2}$
relaxometry in white matter (WM) and grey matter (GM) regions of the human brain at 3T field strength. Phantom accuracy experiments show that SPGR/DESS scan combinations are in excellent agreement with reference measurements. Phantom precision experiments show that trends in
$T_{1}, T_{2}$
pooled sample standard deviations reflect CRB-based predictions.
In vivo
experiments show that in WM and GM,
$\textit{T}_{1}$
and
$\textit{T}_{2}$
estimates from a pair of optimized DESS scans exhibit precision (but not necessarily accuracy) comparable to that of optimized combinations of SPGR and DESS scans. To our knowledge,
$\textit{T}_{1}$
maps from DESS acquisitions alone are new. This example application illustrates that scan optimization may help reveal new parameter mapping techniques from combinations of established pulse sequences.