Optimal flip angles for in vivo liver 3D T₁ mapping and  B₁₊  mapping at 3T

The spoiled gradient recalled echo (SPGR) sequence with variable flip angles (FAs) enables whole liver $T_1$ mapping at high spatial resolutions but is strongly affected by $B_1^{+}$ inhomogeneities. The aim of this work was to study how the precision of acquired $T_1$ maps is affected by the $T_1$ and $B_1^{+}$ ranges observed in the liver at 3T, as well as how noise propagates from the acquired signals into the resulting $T_1$ map.

The $T_1$ variance was estimated through the Fisher information matrix with a total noise variance including, for the first time, the $B_1^{+}$ map noise as well as contributions from the SPGR noise.

Simulations were used to find the optimal FAs for both the $B_1^{+}$ mapping and $T_1$ mapping. The simulations results were validated in 10 volunteers.

Four optimized SPGR FAs of 2°, 2°, 15°, and 15° (TR = 4.1 ms) and $B_1^{+}$ map FAs of 65° and 130° achieved a $T_1$ coefficient of variation of 6.2 ± 1.7% across 10 volunteers and validated our theoretical model. Four optimal FAs outperformed five uniformly spaced FAs, saving the patient one breath-hold. For the liver $B_1^{+}$ and $T_1$ parameter space at 3T, a higher return in $T_1$ precision was obtained by investing FAs in the SPGR acquisition rather than in the $B_1^{+}$ map.

A novel framework was developed and validated to calculate the SPGR $T_1$ variance. This framework efficiently identifies optimal FA values and determines the total number of SPGR and $B_1^{+}$ measurements needed to achieve a desired $T_1$ precision.