Bastien Guerin^{1,2}, Stephen F Cauley^{1,2}, Jorge F Villena^{3}, Athanasios G Polimeridis^{4}, Elfar Adalsteinsson^{5,6,7}, Luca Daniel^{7}, Jacob K White^{7}, and Lawrence L Wald^{1,2,5}

We extend our previously reported methodology for computation of the ultimate signal-to-noise ratio in realistic body models to the computation of the ultimate specific absorption rate (SAR) in the head of the Duke body model at 3 Tesla. We optimize 90° magnitude least-squares RF pulses subject to hundreds of thousands of SAR constraint for increasing numbers of electromagnetic fields in the basis set. As the size of the basis set increases, we show that the local SAR decreases toward a value that we call the “ultimate local SAR”.

[1] Guerin B et al. (2014). The ultimate SNR and SAR in realistic body models. Proceedings of the ISMRM, 22:617.

[2] Christ A et al. (2010). "The Virtual Family—development of surface-based anatomical models of two adults and two children for dosimetric simulations." Physics in medicine and biology 55(2): N23.

[3] Polimeridis A et al. (2014). "Stable FFT-JVIE solvers for fast analysis of highly inhomogeneous dielectric objects." Journal of Computational Physics 269: 280-296.

[4] Setsompop K et al. (2008). "Magnitude least squares optimization for parallel radio frequency excitation design demonstrated at 7 Tesla with eight channels." Magnetic Resonance in Medicine 59(4): 908-915.

[5] Massire A et al. (2013). "Design of non-selective refocusing pulses with phase-free rotation axis by gradient ascent pulse engineering algorithm in parallel transmission at 7T." Journal of Magnetic Resonance 230: 76-83.

[6] Zhao JJ et al. (2005). "A two level finite difference scheme for one dimensional Pennes’ bioheat equation." Applied Mathematics and Computation 171(1): 320-331.

[7] Boulant, N., et al. (2016). "Direct control of the temperature rise in parallel transmission by means of temperature virtual observation points: Simulations at 10.5 tesla." Magnetic Resonance in Medicine 75(1): 249-256.

Fig. 1. a: Cut through the Duke head model
non-uniform conductivity distribution at 128 MHz (3 T). b:
Perfusion distribution in Duke’s head. c: 3D view of the Duke head model (solid
red) and the associated Huygens surface (transparent green). The black space
beyond the Huygens surface is the “coil space”. The minimum distance between
the coil space and the head model is equal to 3 cm in this work. d: We
discretize continuous current distributions on the Huygens surface using
electric and magnetic dipoles. In this work, we place 263,862 dipoles at 43,977
distinct locations.

Fig. 2. a: Flip-angle RMSE vs local SAR
L-curves for increasing
number of basis fields (N ranges from 11 to
159 as shown on the legend of panel b). b:
Same curves, but with the “optimal
point” of
each curve shown as an open circle. The optimal
point is the point of highest curvature of the L-curve (see text for details on
how this was computed). The optimal points are linked to each other by a black
line, which we show as a function of N in Fig. 3.

Fig. 3: a: Local SAR of the optimal
points of the L-curves shown in Fig. 1 vs the number of fields in the basis
set. B: Evolution of the optimal point’ flip-angle error with the number of
basis fields.

Fig. 4: a: Flip-angle maps of the L-curve
optimal points for N=11, N=26, N=63 and N=159 basis fields. Below each map, the
RMSE and average flip-angle are indicated in white. b: Transverse view of the
SAR map through the local SAR hotspot for each optimal point of the N=11, 26,
63 and 159 L-curves. c: Maximum intensity projection of the SAR maps for each
optimal point/L-curve. Below each map, the global SAR and local SAR are
indicated in white (in W/kg).

Fig. 5: a: Transverse view of the
steady-state temperature map through the
temperature hotspot for increasing numbers of basis fields. b: Maximum
intensity projection of the steady-state temperature map for increasing fields
in the basis-set. Below each map, the maximum temperature hotspot is indicated
in white.