Combined estimation of B1 and T1 for dynamic contrast-enhanced MRI by accounting for incomplete spoiling of transverse magnetization

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Abstract
Objective. The variable flip angle (VFA) method for longitudinal relaxation time (T 1) measurement is inherently sensitive to inaccuracies in the radiofRequency transmit field (B 1) and incomplete spoiling of transverse magnetization. The objective of this study is to devise a computational method that addresses the problems of incomplete spoiling and B 1 inhomogeneity in the estimation of T 1 using VFA method. Approach. Using an analytical expression of the gradient echo signal with account of incomplete spoiling, we first showed that ill-posedness in the simultaneous estimation of B 1 and T 1 can be lifted with the use of flip angles larger than the Ernst angle. We then devised a nonlinear optimization method based on this signal model of incomplete spoiling for simultaneous estimation of B 1 and T 1. Main results. We evaluated the proposed method on a graded-concentration phantom to show that the derived T 1 estimates offers an improvement over the regular VFA method and compares well with reference values measured by inversion recovery. Reduction of the number of flip angles from 17 to 5 yielded consistent results indicating that the proposed method is numerically stable. T 1 estimates derived from in-vivo brain imaging were consistent with literature values for gray and white matter tissues. Significance. Contrary to the common notion that B 1 correction in the VFA method for T 1 mapping should be performed separately, we show that combined estimation of B 1 and T 1 is feasible by the proposed method simply with the acquisition of 5 flip angles, as demonstrated on both phantom and in-vivo imaging data.

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