Purpose

Parallel transmission (pTx) so far has suffered from a time-consuming workflow necessitating the measurement of field maps and online pulse design. Universal pulses were recently proposed to spare the pTx user this cumbersome procedure1. Assuming a certain reproducibility of B1+ maps across subjects, the approach consists of blindly applying pulses that were designed, offline, to work robustly over a database made of several B1+/DB0 maps. The performance of these pulses was demonstrated numerically and experimentally at 7T in head imaging¹. In this work we investigate numerically the reproducibility of these maps to propose database matching strategies and minimum size of database to achieve sufficient robustness.

Methods

The coil under study was the 8 Tx-Rx Rapid biomedical coil (Rapid biomedical, Rimpar, Germany). Our home-made female 9-tissues surface-based head model underwent translations in Z (TZ), translations in Y (TY), deformations in head length (HL) and head breadth (HB) that were considered significant given the adult Caucasian statistics² (up to $$$\sqrt{6}$$$ standard deviations). A total of 33 electromagnetic (EM) simulations was executed by varying these parameters one by one or simultaneously in the HFSS (Ansys, Canonsburg, PA, USA) solver. The correlations between the returned field maps were then calculated over the intersection of their brain masks (the region used to design the RF pulses) in the laboratory frame (method #1) or in the “brain frame”, after undoing the translations in TZ and TY (method #2) (Fig.1). Universal pulses were designed for one small tip angle kT-points excitation³ on three different databases consisting of: D1 (subjects #1-33), D2 (subjects #1-20 corresponding to 0≤TZ≤+36 mm) and D3 (subjects #14-33 corresponding to –36 mm ≤ TZ ≤ 0). Each pulse design consisted of minimizing the worst flip angle normalized root mean square error (FA-NRMSE) across subjects in the corresponding databases¹, under explicit constraints⁴. For more realistic calculations, $$$\Delta B_0$$$ maps were synthetized for each head configuration⁵. Once a pulse was designed, individual FA-NRMSEs were computed for each of the 33 subjects using a Bloch simulation, thus allowing to determine a potential gain in partitioning the full database according to intervals in Z. Finally, to analyze the impact of the size of the database on the robustness of the NRMSE, the same kT-points universal pulse was designed on databases made of N = 2 and up to 26 subjects, taken randomly out of the 33 subjects. For each N, the procedure was repeated 20 times to select randomly 20 different subsets out of the possible combinations.

Results

Figure 2 reports the channel-by-channel B1+ correlations between the reference model and the models obtained by varying TZ, TY, HL or HB. Method #2 reveals that the maps are highly similar when the brain maps are realigned, indicating a relative “attachment” of the B1+ maps to the head. Method #1 on the other hand reveals that the most sensitive transformation otherwise is TZ. Figure 3 shows the FA-NRMSE results across the 33 subjects, for the universal kT-points pulses and for the different partitioning strategies. In agreement with the correlations, Z is found in this case to be the most sensitive parameter and consequently, segmenting the database according to the Z position of the head can improve the universal pulses NRMSEs. Figure 4 finally shows that the FA-NRMSEs across the 33 subjects roughly converges when the number of subjects included in the universal pulse design exceeds 20 subjects.

Discussion and conclusion

This work presents a B1+ maps intersubject variability study to propose database matching strategies for universal pulses. In the frame attached to the brains, the B1+ maps are highly similar and provide additional motivation for finding non selective kT-point pulses able to produce fairly homogeneous FA profiles disregarding possible variations in the position or the size of the head. By partitioning the full database (33 head models) into Z intervals for database matching, the universal pulse design performance indeed could be noticeably improved. The minimum size of the database to obtain the NRMSE robustness over 33 different models in this work was estimated at around 20. While this number certainly increases the computing demand compared to subject-based tailored solutions, it remains reasonable considering that the calculation is performed offline. Finally, the variations enforced on the average head model to perform this study explored large, somewhat unlikely occurring values from a statistical standpoint². As a result, the worst case NRMSEs in Fig.4 correspond most likely to rare scenarios, so that the size of the database can possibly be decreased further at around N = 12.

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2013-2018), ERC Grant Agreement n. 309674.

References

[1] Gras V et al. MRM doi: 10.1002/mrm.26148. [2] Ball R et al. Applied ergonomics 2010 ;41 :832-839. [3] Cloos M et al. MRM 2012;67 :72-80. [4] Hoyos-Idrobo et al. IEEE Trans Med Imag 2014 ;33 :739-748. [5] Salomir R et al. Concepts Magn Reson Part B 2003;19B:26-34.