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

Purpose: The variable flip angle method derives T₁ 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 T₁ 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), T₁ , and a T₂ 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, T₁ ) = α'/α were determined. C_Δϕ was found to be independent of T₁ 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 T₂ 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 T₁ 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. © 2017 International Society for Magnetic Resonance in Medicine.