Data-driven optimized flip angle selection for T1 estimation from spoiled gradient echo acquisitions

Abstract

Purpose: Define criteria for selection of optimal flip angle sets for T1 estimation and evaluate effects on T1 mapping.

Theory and methods: Flip angle sets for spoiled gradient echo-based T1 mapping were selected by minimizing T1 estimate variance weighted by the joint density of M0 and T1 in an initial acquisition. The effect of optimized flip angle selection on T1 estimate error was measured using simulations and experimental data in the human and rat brain.

Results: For two-point acquisitions, optimized angle sets were similar to those proposed by other groups and, therefore, performed similarly. For multipoint acquisitions, optimal angle sets for T1 mapping in the brain consisted of a repetition of two angles. Implementation of optimal angles reduced T1 estimate variance by 30-40% compared with a multipoint acquisition using a range of angles. Performance of the optimal angle set was equivalent to that of a repetition of the two-angle set selected using criteria proposed by other researchers.

Conclusion: Repetition of two carefully selected flip angles notably improves the precision of resulting T1 estimates compared with acquisitions using a range of flip angles. This work provides a flexible and widely applicable optimization method of particular use for those who repeatedly perform T1 estimation. Magn Reson Med 76:792-802, 2016. © 2015 Wiley Periodicals, Inc.

Keywords: SPGR; T1 mapping; error propagation; flip angle selection.

FIG. 1

Representative input to flip angle selection algorithm. Initial estimates of (a) T₁ map and (b) M₀ map in the human brain based on an inversion recovery data set. (c) Joint density distribution of T₁ and M₀ based on the maps in (a) and (b). (d) Flip angle minimization objective function, shown here for 2 flip angle selection for the purposes of visualization.

FIG. 2

T₁ bias (a, d, g), standard deviation (b, e, h), and RMSE (c, f, i) maps based on simulations of T₁ mapping in the human brain using 10-angle acquisitions at SNR = 20. a–c correspond to simulation results using the 10 angles selected with our proposed method; d–f correspond to results using the 10-point range angle set; g–i correspond to results using a the 10-point repeat set. All measurements are in units of ms.

FIG. 3

(a–e) RMSE in T₁ estimates from simulations of 2, 4, 6, 8, and 10-angle SPGR acquisitions, respectively. (f) Bias, standard deviation, and RMSE in T₁ estimates plotted versus number of acquisition flip angles. The estimate variance is the primary contributor to error in the T₁ estimate. All measurements are in units of ms.

FIG. 4

Maps of inter-scan standard deviation in T₁ show reduced variation when the 10-point optimal angle set (b) or 10-point repeat angle set (c) is used compared to the 10-point range angle set (a). See Table 1 for specific angle sets used for acquisition. T₁ maps of the rat brain (c) prior to flip angle optimization and (d) after flip angle optimization 10-point optimal angle set) show an increase in the average T₁ estimate in the rat brain by 15.8 ms, more easily observable in (e) the T₁ difference map (difference = optimal – 10-point range). Smoothed joint density functions of T₁ and M₀ (f) prior to and (g) following flip angle optimization also show this slight shift, along with the elimination of a small population of voxels with high initial T₁ estimates (T₁ > 1.5 s, white arrows). (T₁ map, difference map, and P(T₁, M₀) are not shown for the 10-point repeat angle set because results are nearly identical to those for the 10-point optimal angle set under visual inspection.)