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

PURPOSE: The spoiled gradient recalled echo (SPGR) sequence with variable flip angles (FAs) enables whole liver T 1 $$ {T}_1 $$ mapping at high spatial resolutions but is strongly affected by B 1 + $$ {B}_1^{+} $$ inhomogeneities. The aim of this work was to study how the precision of acquired T 1 $$ {T}_1 $$ maps is affected by the T 1 $$ {T}_1 $$ and B 1 + $$ {B}_1^{+} $$ ranges observed in the liver at 3T, as well as how noise propagates from the acquired signals into the resulting T 1 $$ {T}_1 $$ map. THEORY: The T 1 $$ {T}_1 $$ variance was estimated through the Fisher information matrix with a total noise variance including, for the first time, the B 1 + $$ {B}_1^{+} $$ map noise as well as contributions from the SPGR noise. METHODS: Simulations were used to find the optimal FAs for both the B 1 + $$ {B}_1^{+} $$ mapping and T 1 $$ {T}_1 $$ mapping. The simulations results were validated in 10 volunteers. RESULTS: Four optimized SPGR FAs of 2°, 2°, 15°, and 15° (TR = 4.1 ms) and B 1 + $$ {B}_1^{+} $$ map FAs of 65° and 130° achieved a T 1 $$ {T}_1 $$ 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 + $$ {B}_1^{+} $$ and T 1 $$ {T}_1 $$ parameter space at 3T, a higher return in T 1 $$ {T}_1 $$ precision was obtained by investing FAs in the SPGR acquisition rather than in the B 1 + $$ {B}_1^{+} $$ map. CONCLUSION: A novel framework was developed and validated to calculate the SPGR T 1 $$ {T}_1 $$ variance. This framework efficiently identifies optimal FA values and determines the total number of SPGR and B 1 + $$ {B}_1^{+} $$ measurements needed to achieve a desired T 1 $$ {T}_1 $$ precision.