Nicolas Boulant^{1}, Vincent Gras^{1}, Alexis Amadon^{1}, Michel Luong^{2}, Guillaume Ferrand^{2}, and Alexandre Vignaud^{1}

SAR calculations in parallel transmission (pTx) typically rely on electromagnetic simulations performed on generic models. Uncertainties however often exist due to tolerances in the lumped element values, cable losses, phase offsets and different coupling between transmit elements. Additional uncertainties in SAR evaluation include intersubject variability and exam supervision. In this work, we review a workflow that has been implemented in our laboratory with home-made and commercial pTx coils at 7T. Based on this strategy, nearly 100 healthy volunteers have been scanned with no reported incidents, while still allowing to exploit pTx to mitigate efficiently the RF inhomogeneity problem.

The
strategy consists of analyzing three fundamental uncertainties leading to three
(concatenated) individual safety factors applied to the SAR prediction and
incorporated into Virtual Observation Points (VOP)^{1} matrices
provided to the scanner for real-time supervision.

Coil
modelling: SAR margins related to imperfect coil modelling are
computed for a phantom of known geometry, electric properties and position. Our
reference phantom is a 16 cm diameter spherical agar-gel phantom with 4 g/l
NaCl (σ=0.78
S/m and ε_{r}=72
at 298 MHz). Electromagnetic simulations are performed with appropriate
software after tuning/matching the array in the numerical domain^{2}. Transmit
B_{1} maps are measured and compared to the simulated ones. For
unaccounted cable losses, phase offsets and different coupling, as demonstrated
elsewhere^{3,4} simulated electromagnetic fields can be tuned by
appropriate linear combinations. Thus we calibrate
our B_{1} simulations by fitting each measured complex B_{1} map as a linear combination of the simulated ones. For the k^{th} transmit channel, one obtains $$$B_{1,k}^{measured}\approx B_{1,k}^{cal}=\sum_{n=1}^N \alpha_{k,n} B_{1,n}^{sim}$$$, where N
is the number of channels and [α_{ij}] is the so-called
calibration matrix, which likewise returns calibrated electric fields. The remaining discrepancy between the measured and
simulated B_{1} maps is quantified and propagated into a SAR
amplification factor^{5}. MR thermometry is performed on the phantom
for two modes of excitation to control that the peak measured temperature rise is
within the computed margin and that the heating patterns match. The calibration
matrix, determined with phantom data, is then applied to the generic head model
E-field simulations. This extrapolation is rigorous when involving cable-related
phase offsets and losses, while uncertainties in the tuning/matching variations
of the transmit coil are taken into account in the intersubject variability
factor. The calibration matrix with the reference phantom is controlled each
day in-vivo experiments are scheduled to control any possible fault that could
impact the SAR calculations^{6}.

Intersubject
variability: EM simulations are generally performed on generic models.
As a result, we have proposed a statistical analysis to assess the sensitivity
of the SAR with respect to different parameters such as head length, head width
and position^{7}. If the SAR behavior is smooth enough for small
variations, knowing the statistics^{8} of the different parameters
allows calculating the output SAR statistics^{7}, the latter being
pulse-dependent. Safety factors can then be determined based on risk analysis.

Exam supervision: Real-time supervision based on directional couplers (Dico) incorporates uncertainties in the amplitude and phase of the transmit RF voltage (in our case 10 % and 5°). To address this, we maximize the SAR for many random RF pulses based on this uncertainty, to return a last SAR amplification factor.

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[2] M. Kozlov and R. Turner. Fast MRI coil analysis based on 3-D electromagnetic and RF circuit co-simulation. J of Magn Reson 200:147-152 (2009).

[3] A. Beqiri, J. W. Hand, J. V. Hajnal and S. J. Malik. Comparison between simulated decoupling regimes for SAR prediction in parallel transmit MRI. Magn Reson in Med 74:1423-1434 (2015).

[4] P. Vernickel, C. Findeklee, J. Eichmann and I. Graesslin. Active digital decoupling for multi-channel transmit MRI systems. Proc of the 15th ISMRM meeting, p 170 (2007).

[5] G. Ferrand, M. Luong, A. Amadon and N. Boulant. Mathematical tools to define SAR margins for phased array coil in-vivo applications given E-field uncertainties. Proc of the 23rd ISMRM meeting, p 3763 (2015).

[6] J. Hoffmann, A. Henning, I. A. Giapitzakis, K. Scheffler, G. Shajan, R. Pohmann and N. Avdievich. Safety testing and operational procedures for self-developed radiofrequency coils. NMR in Biomed 29:1131-1144 (2016).

[7] M. Le Garrec, V. Gras, M-F Hang, G. Ferrand, M. Luong and N. Boulant. Probabilistic analysis of the specific absorption rate intersubject variability safety factor in parallel transmission MRI. Magn Reson in Med 78:1217-1223 (2017).

[8] R. Ball, C. Shu, P. Xi, M. Rioux, Y. Luximon, J. Molenbroek. A comparison between chinese and caucasian head shapes. Applied Ergonomics 41:832-839 (2010).

[9] International Electrotechnical Commission. Medical equipment part 2-33: particular requirements for the basic safety and essential performance of magnetic resonance equipment for medical diagnosis. 3rd ed. Geneva: International Electrotechnical Commission 2011;601:2-33.

[10] N. Boulant, X. Wu, G. Adriany, S. Schmitter, K. Uğurbil and P-F Van de Moortele. Direct control of the temperature rise in parallel transmission by means of temperature virtual observation points: Simulations at 10.5 tesla. Magn Reson in Med 75:249-256 (2016).