# The effect of and correction for through-slice dephasing on 2D gradient-echo double angle B 1 + mapping.

##### Belsley G., Tyler DJ., Robson MD., Tunnicliffe EM.

PURPOSE: To show that B 0 $$ {\mathrm{B}}_0 $$ variations through slice and slice profile effects are two major confounders affecting 2D dual angle B 1 + $$ {\mathrm{B}}_1^{+} $$ maps using gradient-echo signals and thus need to be corrected to obtain accurate B 1 + $$ {\mathrm{B}}_1^{+} $$ maps. METHODS: The 2D gradient-echo transverse complex signal was Bloch-simulated and integrated across the slice dimension including nonlinear variations in B 0 $$ {\mathrm{B}}_0 $$ inhomogeneities through slice. A nonlinear least squares fit was used to find the B 1 + $$ {\mathrm{B}}_1^{+} $$ factor corresponding to the best match between the two gradient-echo signals experimental ratio and the Bloch-simulated ratio. The correction was validated in phantom and in vivo at 3T. RESULTS: For our RF excitation pulse, the error in the B 1 + $$ {\mathrm{B}}_1^{+} $$ factor scales by approximately 3.8% for every 10 Hz/cm variation in B 0 $$ {\mathrm{B}}_0 $$ along the slice direction. Higher accuracy phantom B 1 + $$ {\mathrm{B}}_1^{+} $$ maps were obtained after applying the proposed correction; the root mean square B 1 + $$ {\mathrm{B}}_1^{+} $$ error relative to the gold standard B 1 + $$ {\mathrm{B}}_1^{+} $$ decreased from 6.4% to 2.6%. In vivo whole-liver T 1 $$ {\mathrm{T}}_1 $$ maps using the corrected B 1 + $$ {\mathrm{B}}_1^{+} $$ map registered a significant decrease in T 1 $$ {\mathrm{T}}_1 $$ gradient through slice. CONCLUSION: B 0 $$ {\mathrm{B}}_0 $$ inhomogeneities varying through slice were seen to have an impact on the accuracy of 2D double angle B 1 + $$ {\mathrm{B}}_1^{+} $$ maps using gradient-echo sequences. Consideration of this confounder is crucial for research relying on accurate knowledge of the true excitation flip angles, as is the case of T 1 $$ {\mathrm{T}}_1 $$ mapping using a spoiled gradient recalled echo sequence.