Synopsis

A method is presented to perform B₁⁺-mapping simultaneously with high dynamic range and high SNR by optimally combining data from acquisitions with different acquisition parameters. Reconstruction of the B₁⁺-maps is performed using dictionary matching methods. This approach is applicable to various B₁⁺-mapping sequences. Examples based on the AFI sequence are shown in both numeric simulations and a phantom experiment in the presence of a severe B₁⁺ hot-spot. The performance of the proposed methods largely exceeds that of classic AFI sequences, simultaneously matching low-flip-angle acquisitions in dynamic range and high-flip-angle acquisitions in SNR, at identical acquisition times.

Introduction

Reliable B₁⁺-mapping is required for many MR-applications, such as calibration of parallel-transmit systems. The dynamic range required for such measurements can be large, unlike for homogeneous volume-transmit coils. Most methods for B₁⁺-mapping exhibit a cyclic signal dependence on transmit field strength, limiting dynamic range^1,2. Low acquisition flip angles increase dynamic range, but often reduce SNR below acceptable levels.

Reconstruction of B₁⁺-maps from inversion of analytic signal equations imposes stringent constraints on the signals produced by the MR sequences. These constraints can be alleviated by reconstructing B₁⁺-maps via dictionary matching, an approach that can be extended to match vectors of signals acquired at each sample location from a set of MR sequences. In particular, acquisitions with different flip angles of non-integer ratio permit to disambiguate B₁ values over a dynamic range that can exceed that of the individual acquisitions. We propose to optimally combine signals with varying cyclic dependences from several acquisitions to reconstruct high-dynamic-range, high-SNR B₁⁺-maps.

Furthermore, this framework readily permits taking into account effects like intra-voxel B₁⁺-gradients that may be of importance in the presence of B₁ hot-spots. Numeric simulations and experimental data from a phantom containing a copper wire producing a B₁⁺ hot-spot is presented.

Numeric simulations

Fig. 1 shows the acquisition schemes examined. Signals were simulated from simple signal equations as a function of local B₁⁺, T₁ and flip angles. Signal equations for da-hdrAFI are:

$$S_1=\frac{1-E_2+\left(1-E_1\right)E_2\cos{\left(\lambda\alpha_2\right)}}{1-E_1E_2\cos{\left(\lambda\alpha_1\right)}\cos{\left(\lambda\alpha_2\right)}}\sin{\left(\lambda\alpha_1\right)}$$

$$S_2=\frac{1-E_1+\left(1-E_2\right)E_1\cos{\left(\lambda\alpha_1\right)}}{1-E_1E_2\cos{\left(\lambda\alpha_1\right)}\cos{\left(\lambda\alpha_2\right)}}\sin{\left(\lambda\alpha_2\right)}$$

$$E_{1/2}=\exp{\left(-\frac{TR_{1/2}}{T_1}\right)}$$

$$\lambda=\frac{B_1}{B_{1,nom}}$$

Monte Carlo simulations were performed on data simulated for B₁⁺-values up to a range of 1.5 to 10-fold the nominal B₁⁺, and for T₁-values in a range between 100ms and 4000ms. White noise of a realistic amplitude common to all acquisitions (1600 realizations for each B₁/T₁ combination) was added to the data and dictionary-based reconstruction was performed, for four acquisition schemes. In all acquisition schemes (consisting of 2 sequences each), TR₁ was fixed to 15ms and total acquisition time to 400ms per k-space line.

a) cAFI (2 signals per voxel), optimized to perform best for B₁⁺-values up to 1.5 times the nominal B₁⁺, leading to α=53.2°, n=12.3. Simulations were performed for two signal averages, to match the other examined sequences in acquisition time, increasing the SNR of the data accordingly.

b) cAFI as in a) optimized for B₁ values up to 10 times the nominal B₁⁺, leading to α=11.2°, n=12.3, 2 averages.

c) hdrAFI (four signals per voxel), optimized for B₁⁺-values up to 10 times the nominal B₁⁺, leading to α₁=84.3°, α₂=33.2°, n₁=2.0, n₂=22.6.

d) da-hdrAFI (four signals per voxel), optimized for B₁⁺-values up to 10 times the nominal B₁⁺, leading to α_1,1=112.9°, α_2,1=29.5°, α_1,2=6.6°, α_2,2=52.4°, n₁=21.2, n₂=3.4. Results are presented in Fig. 2.

Phantom experiments

To evaluate hdrAFI in the presence of a severe B₁⁺ hot-spot, a 20-cm copper wire of 3-mm diameter was immersed in a large phantom constructed according to ASTM-F2182-09 and filled with saline solution. The wire placed along the lateral wall was insulated along its length, with the tips in contact with the medium. Strong RF-induced currents in the wire are expected. Data were acquired on a Philips 3-T TX Achieva using the TX/RX whole body coil. Three B₁⁺ acquisition schemes were compared:

a) cAFI parameterized for low dynamic range (α=49.0°, n=6.3, 2 averages, t_acq=291s)

b) cAFI parameterized for high dynamic range (α=13.0°, n=5.9, 2 averages, t_acq=280s)

c) hdrAFI, combining one of each of the above acquisitions (t_acq=286s).

The data were acquired in 3D, FOV 448x128x220mm³, voxel size 2x2x10mm³, TR₁=15ms, TE=3.1ms. Data were reconstructed via dictionary matching. Results are presented in Fig. 3.

Discussion & Conclusions

The proposed method constitutes a promising technique to increase dynamic range of B₁⁺-mapping without decreasing sensitivity in regions of low B₁. Minimum acquisition time is increased, however, contrary to other methods³ all data acquired contribute to the final B₁ map, making the method SNR efficient. Doubling acquisition time may permit to increase dynamic range by a factor of 6 or more. Here, a dictionary approach was chosen to reconstruct B₁ maps. Non-linear fitting could equally be employed to reconstruct these data⁴. Numeric simulations show outstanding results. Phantom experiments show significantly improved B₁⁺-maps. The proposed method is however sensitive to the precise parametrization of the sequences, as ambiguities in the dictionary can potentially lead to large reconstruction errors. Realistic modeling of the acquisition process and its imperfections will be necessary to derive optimal and robust acquisition parameters reaping maximum benefit from the method, while avoiding strongly non-linear error propagation from the acquired data to the reconstructed B₁ maps.

This method is not specific to AFI and should be similarly applicable to DREAM sequences².

Acknowledgements

References

1. Yarnykh VL. Actual Flip-Angle Imaging in the Pulsed Steady State: A Method for Rapid Three-Dimensional Mapping of the Transmitted Radiofrequency Field. Magn Reson Med. 2007;57(1):192-200.

2. Nehrke K et al. DREAM - A Novel Approach of Robust, Ultrafast, Multislice B1 Mapping. Magn Reson Med. 2012;68(5):1517-1526.

3. Padormo F et al. Large Dynamic Range Relative B1+ Mapping. Magn Reson Med. 2016;76(2):490-499.

4. Hurley SA et al. Simultaneous Variable Flip Angle-Actual Flip Angle Imaging Method for Improved Accuracy and Precision of Three-Dimensional T1 and B1 Measurements. Magn Reson Med. 2012;68(1):54-64.