Andreas Lesch^{1}, Christoph Aigner^{2}, and Rudolf Stollberger^{1}

^{1}Institute of Medical Engineering, Graz University of Technology, Graz, Austria, ^{2}Physikalisch-Technische Bundesanstalt (PTB), Braunschweig and Berlin, Berlin-Charlottenburg, Germany

For many applications in MRI fast and accurate $$$B_1^+$$$ -mapping is an important prerequisite to correct for spatially varying RF-field variations. We recently proposed a reconstruction algorithm to reconstruct highly undersampled Bloch Siegert data, which was applied to 3T data. In this work we investigated the applicability of this algorithm to 7T data in terms of accuracy and possible acquisition time. We could successfully show that the proposed algorithm can be applied to 7T data with only slightly increased error compared to 3T. The minimum scan time at 7T is in the order of 45s-1min for a 3D volume.

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

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

For further details we refer to

A spherical phantom and a healthy subject were scanned on a 7T system (Magnetom, Siemens, Erlangen, Germany) with a 1Tx32Rx head coil (Nova Medical, Wilmington, USA) according to the local IRB approved protocol. The following scan parameters were used to acquire the phantom data: FOV=200x200mm, slab thickness=150mm, acquisition matrix=128x128x30, $$$TR/TE=160/15ms$$$, $$$T_{pulse}=10ms$$$, $$$\alpha_{BS}=1000°$$$,$$$f_{BS}=5kHz$$$. The in-vivo dataset was acquired using: FOV=256x192mm, slab thickness=80mm, acquisition matrix=128x96x16, $$$TR/TE=377/10ms$$$ and 25% slice oversampling. A Fermi shaped BS pulse with duration $$$T_{pulse}=7ms$$$, $$$\alpha_{BS}=600°$$$ on-resonant equivalent flip angle and a resonance offset of $$$f_{BS}=4kHz$$$ leading to a pulse constant $$$K_{BS}=70.93rad/G^2$$$ was used. The regularization parameters $$$\mu$$$ and $$$\lambda$$$ were adjusted doing a parameter sweep to $$$\mu=1.1\cdot 10^{-2}$$$ and $$$\lambda=10$$$.

Data were retrospectively subsampled using a block pattern with different sizes, where only $$$n\times m$$$ lines in k-space center were acquired as described in

^{1} Deoni SCL, Rutt BK, Peters TM. Rapid combined
T1 and T2 mapping using gradient recalled acquisition in the steady state. Magn Reson Med. 2003;49:515–526.

^{2}
Schmitt P, Griswold MA, Jakob PM, et al. Inversion recovery TrueFISP: quantification of T1, T2, and spin density.
Magn Reson Med. 2004;51:661–667.

^{3}
Katscher U, Boernert P, Leussler C, van den Brink JS. Transmit SENSE. Magn Reson Med.
2003;49:144–150.

^{4} Zhu Y. Parallel excitation with an array of
transmit coils. Magn Reson Med. 2004;51:775–784.

^{5} Sacolick LI, Wiesinger F, Hancu I, Vogel MW. B1
mapping by Bloch–Siegert shift. Magn Reson Med. 2010;63:1315–1322.

^{6} Zaiss M, Bachert R. Chemical exchange
saturation transfer (CEST) and MR Z-spectroscopy in vivo: a review of
theoretical approaches and methods. Phys. Med. Biol. 58 (2013) R221–R269.

^{7} Lesch A, Schlöegl 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

^{8} Bredies K, Kunisch K, Pock T. Total
generalized variation. SIAM J Imaging Sci. 2010;3:492–526.

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

Figure 1:
B_{1}^{+} map in μT for fully sampled reference, low
resolution estimate and the result of the proposed variational reconstruction algorithm for a
retrospectively subsampled dataset in a spherical phantom for a
block pattern with size of 12 x 4, 12 x 6, 12 x 8 and 8 x 8. The
results are shown as a transversal and a sagittal slice through the 3D‐dataset. The right part of each
column shows the error map for
the corresponding result as normalized error in percent of the desired B_{1} peak_{ }magnitude. The MAE is given as
the mean of the error map over the
whole phantom.

Figure 2:
B_{1}^{+} map in μT for fully sampled reference, low
resolution estimate and the result of the proposed variational reconstruction algorithm for a
retrospectively subsampled dataset in the brain of a healthy volunteer for a
block pattern with size of 8 x 4, 10 x 6, 12 x 6 and 14 x 10. The
results are shown as central slice of the 3D‐dataset. The right part of each
column shows the error map for
the corresponding result as normalized error in percent of the desired B_{1} peak magnitude. The MAE is given as
the mean of the error map over the
whole 3D‐brain inside the cranial bone structure for each case.

Figure 3:
Error histogram for the retrospectively subsampled in-vivo dataset
compared to the fully sampled reference in
percent of the desired B_{1}^{+}
peak magnitude for block sizes of 8 × 4, 12 × 6 and 14 × 10 encodings in the k‐space center. The error histograms are shown for zero padded low resolution
estimate and the result of our proposed variational reconstruction algorithm.

Table 1:
MAE, medAE and q_{90%} inside the cranial bone structure of the
in-vivo dataset for different block sizes in percent of the desired B_{1} peak magnitude. The values are given for the
zero padded low resolution estimate and the result of the proposed variational
reconstruction algorithm.