T₁ mapping with the variable flip angle technique: A simple correction for insufficient spoiling of transverse magnetization

Purpose The variable flip angle method derives T 1 maps from radiofrequency‐spoiled gradient‐echo data sets, acquired with different flip angles α. Because the method assumes validity of the Ernst equation, insufficient spoiling of transverse magnetization yields errors in T 1 estimation, depending on the chosen radiofrequency‐spoiling phase increment (Δϕ). This paper presents a versatile correction method that uses modified flip angles α' to restore the validity of the Ernst equation. Methods Spoiled gradient‐echo signals were simulated for three commonly used phase increments Δϕ (50°/117°/150°), different values of α, repetition time (TR), T 1 , and a T 2 of 85 ms. For each parameter combination, α′ (for which the Ernst equation yielded the same signal) and a correction factor C Δϕ (α, TR, T 1 ) = α′/α were determined. C Δϕ was found to be independent of T 1 and fitted as polynomial C Δϕ (α, TR), allowing to calculate α′ for any protocol using this Δϕ. The accuracy of the correction method for T 2 values deviating from 85 ms was also determined. The method was tested in vitro and in vivo for variable flip angle scans with different acquisition parameters. Results The technique considerably improved the accuracy of variable flip angle–based T 1 maps in vitro and in vivo. Conclusions The proposed method allows for a simple correction of insufficient spoiling in gradient‐echo data. The required polynomial parameters are supplied for three common Δϕ. Magn Reson Med 79:3082–3092, 2018.