Synopsis

In this work we investigate the feasibility of a double shot acquisition for 3D Bloch-Siegert B₁⁺ mapping. Therefore, we combine the previously proposed variational reconstruction algorithm for highly subsampled Bloch-Siegert data with an EPI readout. The acquired dataset was retrospectively under-sampled and the reconstruction results are compared to the fully sampled reference, a zero padded low resolution estimate and to results acquired with a much more robust GRE readout. We can show that the results are in good accordance to the fully sampled reference and the GRE acquisition for acceleration factors of up to 100 making double shot acquisition possible.

Introduction

Fast and accurate quantification of the $$$B_{1}^+$$$-field and the resulting flip angle is a crucial calibration step at high and ultra-high field strength for various applications in MRI. A very promising approach to map the $$$B_{1}^+$$$-field is based on the Bloch-Siegert shift caused by an off-resonant RF-pulse¹ that allows usage of short repetition times (TR). However, the Bloch-Siegert method is limited by high RF-energy deposition and therefore restricts the minimal possible TR due to patient safety constraints. In the case of 3D acquisition, the SAR limitations lead to unacceptable long acquisition times. To overcome this limitation fast acquisition strategies like EPI^2,3 or spiral^3,4 readouts were proposed on the one hand and on the other hand compressed sensing (CS) based reconstruction algorithms for under-sampled data^5,6. This work combines a previous developed CS reconstruction framework with fast under-sampled EPI acquistion to acquire 3D volumes with a double shot measurement for ultrafast 3D volume $$$B_{1}^+$$$-mapping below 1s.

Methods

A 3D-EPI-SE sequence with segmented acquisition in slice encoding direction with an echo train length of 128 was implemented using the open source sequence development tool Pulseq⁷. Figure 1 depicts the main sequence elements and their timing. We used a slice selective excitation pulse with an flip angle of 25° and a non-selective rectangular refocusing pulse together with symmetric crusher gradients. An off-resonant Bloch-Siegert pulse with a duration $$$T_{BS}=8ms$$$, a resonance offset $$$\Delta\omega_{BS}=4kHz$$$ and an on-resonant equivalent flip angle $$$\alpha_{BS}=1000°$$$ leading to a pulse constant $$$K_{BS}=35.7rad/G^2$$$ was inserted between the excitation and refocusing pulse. With this sequence we acquired a 3D-dataset of a cylindrical water phantom on a 3T MR system (Skyra, Siemens, Erlangen, Germany). The following imaging parameters were used, leading to a total acquisition time of $$$T_{aq}=22s$$$: $$$FOV=250mm$$$, matrix size $$$128\times 128\times 32$$$, 37.5% slice oversampling, readout bandwidth of 2041Hz/pixel, $$$TR/TE=250/105ms$$$ and a resolution of 5mm in slice direction.

The variational reconstruction algorithm for subsampled Bloch-Siegert measurements is described in⁶ and consists of a two-step procedure. Both steps are defined by solving an optimization problem. In the first step a TGV-regularization term^8,9, which enforces piecewise smooth solutions, is applied to reconstruct the magnitude and phase of the underlying image. In the second step a smoothness constraint is applied to stabilize the spatial smoothness of the underlying $$$B_{1+}$$$-field defined as follows (for further details we refer to⁶):

$$\hat{u}=\arg\min_u\frac{\lambda}{2}\parallel\,k_+-\mathcal{F}\left(u\right)\,\parallel_2^2+TGV\left(u\right)$$

$$\hat{v}=\arg\min_v\frac{\mu}{2}\parallel\,k_--\mathcal{F}\left(\hat{u}\,\cdot\,v\right)\,\parallel_2^2+\parallel\nabla\,v\parallel_2^2=e^{-j2\phi_{BS}}$$

The regularization parameters $$$\lambda$$$ and $$$\mu$$$ where chosen as follows: $$$\lambda=64$$$ and $$$\mu=15\cdot 10^{-4}$$$.

To investigate the potential of the proposed method for a two shot acquisition, the fully sampled dataset was retrospectively under-sampled using block sampling patterns of different sizes, summarized in Table 1. For the evaluation the mean absolute error (MAE) compared to the fully sampled reference, its median (medAE) and its 99% ($$$q_{99\%}$$$) quantile were used. Additionally a fully sampled Bloch-Siegert 3D-dataset with a GRE based sequence was acquired for reference purposes ($$$T_{aq}=15min$$$).

Results

Discussion and Conclusion

Acknowledgements

References

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² Duan Q, Souheil IJ, van Gelderen P, Sunil P, Jeff DH. Implementation and validation of fast whole‐brain B1 mapping based on Bloch–Siegert shift and EPI readout. In Proceedings of the 21st Annual Meeting of ISMRM, Melbourne, Australia, 2012; p. 609.

³ Saranathan M, Khalighi MM, Glover GH, Pandit P, Rutt BK. Efficient Bloch–Siegert B1(+) mapping using spiral and echoplanar readouts. Magn Reson Med. 2013;70:1669–1673.

⁴ Khalighi M, Glover G, Pandit P, et al. Single‐shot spiral based Bloch–Siegert B1+ mapping. In Proceedings of the 19th Annual Meeting of ISMRM, Montreal, Quebec, Canada, 2011; p. 578.

⁵ Sharma A, Tadanki S, Jankiewicz M, Grissom WA. Highlyaccelerated Bloch–Siegert ­B1+ ­ mapping using joint autocalibrated parallel image reconstruction. Magn Reson Med. 2014;71:1470–1477.

⁶ Lesch A, Schloegl M, Holler M, Bredies K, Stollberger R. Ultrafast 3D Bloch–Siegert B‐mapping using variational modeling. Magn Reson Med. 2018; DOI: 10.1002/mrm.27434

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⁹ Knoll F, Bredies K, Pock T, Stollberger R. Second order total generalized variation (TGV) for MRI. Magn Reson Med. 2011;65:480–491.