Gabriela Belsley^{1}, Damian J. Tyler^{1}, Matthew D. Robson^{1,2}, and Elizabeth M. Tunnicliffe ^{1}

Mapping
B_{1}+ inhomogeneity, using commonly available pulse sequences, is essential for widespread,
accurate determination of T_{1} using variable flip angle methods. We investigated
the accuracy of B_{1}+ mapping with different flip angles (FA) using the double
angle method with a 2D multi-slice GRE-EPI sequence. At lower FAs, we found
that B_{1}+ accuracy is affected by SNR, whereas the extent of B_{1}+ inhomogeneities
imposes an upper limit on the FAs that can be employed. For a B_{1}+ inhomogeneity
of ±40% and a SNR of 29 at 30°, the optimal FA pairs were found
to lie between 43°/86° and 74°/148°.

Monte
Carlo simulations, using 10000 iterations, were performed to determine the
signal from an ideal rectangular pulse in the frequency domain and the GRE-EPI
RF pulse (Figure 1). These signals were corrupted with zero mean additive
complex Gaussian noise, with a signal-to-noise-ratio (SNR) of 29 at a nominal
FA of 30°. This SNR value was estimated from *in vivo* abdominal scans acquired with the same GRE-EPI sequence.
The DAM was used to estimate the apparent FA, with the B_{1}+ bias (correction
factor) calculated as the ratio between the estimated and nominal FA. Slice
profile effects were corrected by generating a look up table of the apparent FA
as a function of the nominal FA^{7}.

The
recommended range of nominal FA pairs varies with the range of B_{1}+ variations. As
a guide, we characterized the B_{1}+ mapping fidelities’ dependence on the FA pair
when the B1+ field is homogenous, or has uniformly distributed variations of
±20% and
±40%.

Phantom
images were acquired on a 3T MAGNETOM Prisma MRI scanner (Siemens Healthineers,
Erlangen, Germany) with a GRE-EPI 2D multi-slice acquisition. For this
excitation pulse, the scale factor between the slice centre FA and the nominal console
FA^{7} was determined to be 1.105. Imaging parameters were: FOV=450*366mm^{2},
matrix=128*104 with 15 slices, each of 8mm thickness and 2mm spacing between
slices; TR/TE=15s/12ms and nominal FA pairs of 30°/60° and 60°/120°,
corresponding to slice-centre FAs of 33°/66° and 66°/132°. A 3D VIBE SPGR Dixon
mapped the 3D T_{1} values. Imaging parameters were: FOV=450*366mm^{2}, matrix=320*260
with 16 slices of 3 mm thickness; TR/TE=4.1/1.23 ms, with FAs of 3°,6°,9°,12°,15°.
Gold standard T_{1} measurement used a spin echo inversion recovery experiment
with TR/TE= 10s/12ms, 8 TI values from 25 to 2000ms, matrix= 256*256, FOV=300*300mm^{2 }and
slice thickness of 5mm.

Figure
2 shows the mean B_{1}+ bias as a function of nominal FA for an ideal rectangular pulse,
considering three different B_{1}+ variation levels. The FA lower bound is
influenced by the SNR while the upper boundary is determined by the lack of
phase data from this product sequence. For a rectangular pulse with homogeneous
B_{1}+, nominal FA pairs from 37°/74° until 90°/180° yield an accurate mean B_{1}+
estimate, with uncertainties within
5%. As the B_{1}+ inhomogeneity increases to ±20% and ±40%, the
upper boundary of the FA decreases to 75°/150° and 65°/130°, respectively. Additionally,
the lower FA bound increases since smaller angles are more sensitive to noise.

Figure
3 illustrates the mean B_{1}+ bias for the GRE-EPI pulse. The slice profile effect
generates a 6% underestimation of B_{1}+ for 60°, becoming progressively worse for
larger angles. This leads to overestimation of T_{1} values. Correcting for slice profile
effects eliminates this bias (Figure 4). The suggested lower bound nominal FA pair
for B_{1}+ variations up to 40% is 43°/86° to maintain the uncertainty in B_{1}+
estimation below
5%. The upper boundary is 74°/148°, above which the mean B_{1}+
estimate diverges. These recommended FA pairs are valid for this specific excitation
pulse profile and scanner FA calibration.

The
phantom T_{1} with B_{1}+ corrections determined from nominal FAs of 30°/60° (Figure 5 a)) have a broader distribution (501±33ms) than that determined from nominal FAs of 60°/120° (493±24ms) (Figure 5 b)), consistent with the simulations. Figure 5 c) displays the T_{1} value histogram
for these FA pairs, with mean consistent with the gold standard T_{1} value (496±9ms).

This work was supported by funding from the Engineering and Physical Sciences Research Council (EPSRC) and Medical Research Council (MRC) [grant number EP/L016052/1] and the NIHR Oxford Biomedical Research Centre.

The authors would like to thank Aaron Hess and John McGonigle for useful discussions as well as Ferenc Mozes for providing the phantom.

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Figure 1: Slice profile as a function of distance from slice
centre for the GRE-EPI pulse (blue) and the rectangular pulse matching the 8mm slice
thickness (pink).

Figure 2: Percentage bias in B_{1}+ as a function of nominal
flip angle pair for different B_{1}+ ranges. The green, blue and pink curves correspond
to a homogeneous B_{1}+ field, ±20% and
±40% variations, respectively. This simulation considers an
ideal rectangular slice profile.

Figure 3: Percentage bias in B_{1}+ as a function of nominal
flip angle pair for different B_{1}+ ranges. The green, blue and pink curves correspond
to a homogeneous B_{1}+ field, ±20% and
±40% variations, respectively. This simulation considers the GRE-EPI pulse without slice profile correction.

Figure 4: Percentage bias in B_{1}+ as a function of nominal
flip angle pair for different B_{1}+ ranges. The green, blue and pink curves correspond
to a homogeneous B_{1}+ field, ±20% and
±40% variations, respectively. This simulation considers the GRE-EPI pulse with slice profile correction.

Figure 5: Phantom T_{1} maps using B_{1}+ DAM, including slice
profile correction, for nominal FA pairs of 30°/60° (a) and 60°/120° (b). Histogram of the T_{1} values obtained for the water region surrounding
the vials, doped with NiCl_{2} (c). Values obtained using nominal FA
pairs of 30°/60° and 60°/120° are shown in pink and blue, respectively. The
mean values and corresponding standard deviations are 501±33ms for 30°/60° and 493±24ms for 60°/120°. Gold
standard inversion recovery spin echo gave T1 of 496±9ms. Colour map scale
[300 600]ms.