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

Rapid, reliable quantification of MR relaxation parameters <inline-formula> <tex-math notation="LaTeX">$\textit{T}_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\textit{T}_{2}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$\textit{T}_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\textit{T}_{2}$ </tex-math></inline-formula> variation. However, <inline-formula> <tex-math notation="LaTeX">$T_{1}, T_{2}$ </tex-math></inline-formula> estimation with these sequences typically requires multiple scans with varied sets of acquisition parameters. This paper describes a systematic framework for selecting scan types (<italic>e.g.</italic>, combinations of SPGR and DESS scans) and optimizing their respective parameters (<italic>e.g.</italic>, 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 <inline-formula> <tex-math notation="LaTeX">$T_{1}, T_{2}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$T_{1}, T_{2}$ </tex-math></inline-formula> pooled sample standard deviations reflect CRB-based predictions. <italic>In vivo</italic> experiments show that in WM and GM, <inline-formula> <tex-math notation="LaTeX">$\textit{T}_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\textit{T}_{2}$ </tex-math></inline-formula> 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, <inline-formula> <tex-math notation="LaTeX">$\textit{T}_{1}$ </tex-math></inline-formula> 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.