Synopsis

Mapping B₁+ inhomogeneity, using commonly available pulse sequences, is essential for widespread, accurate determination of T₁ using variable flip angle methods. We investigated the accuracy of B₁+ 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 B₁+ accuracy is affected by SNR, whereas the extent of B₁+ inhomogeneities imposes an upper limit on the FAs that can be employed. For a B₁+ inhomogeneity of ±40% and a SNR of 29 at 30°, the optimal FA pairs were found to lie between 43°/86° and 74°/148°.

Introduction

Methods

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 B₁+ 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 FA⁷.

The recommended range of nominal FA pairs varies with the range of B₁+ variations. As a guide, we characterized the B₁+ 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 FA⁷ was determined to be 1.105. Imaging parameters were: FOV=450*366mm², 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 T₁ values. Imaging parameters were: FOV=450*366mm², 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 T₁ 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*300mm² and slice thickness of 5mm.

Results and Discussion

Figure 2 shows the mean B₁+ bias as a function of nominal FA for an ideal rectangular pulse, considering three different B₁+ 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 B₁+, nominal FA pairs from 37°/74° until 90°/180° yield an accurate mean B₁+ estimate, with uncertainties within 5%. As the B₁+ 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 B₁+ bias for the GRE-EPI pulse. The slice profile effect generates a 6% underestimation of B₁+ for 60°, becoming progressively worse for larger angles. This leads to overestimation of T₁ values. Correcting for slice profile effects eliminates this bias (Figure 4). The suggested lower bound nominal FA pair for B₁+ variations up to 40% is 43°/86° to maintain the uncertainty in B₁+ estimation below 5%. The upper boundary is 74°/148°, above which the mean B₁+ estimate diverges. These recommended FA pairs are valid for this specific excitation pulse profile and scanner FA calibration.

The phantom T₁ with B₁+ 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 T₁ value histogram for these FA pairs, with mean consistent with the gold standard T₁ value (496±9ms).

Conclusion

Acknowledgements

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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