Designing Rf Pulses with Optimal Specific Absorption Rate (sar) Characteristics and Exploring Excitation Fidelity, Sar and Pulse Duration Tradeoffs

INTRODUCTION: Recent methods of designing RF pulses for multi-coil TX systems have focused on solving regularized systems of equations. These techniques linearize the equations relating the RF waveforms to the resulting excitation and then penalize RF candidates with high peak and root-mean-square (RMS) voltages (VP and VRMS, respectively) in an attempt to limit SAR [1,2]. This is sensible because in single-coil systems, SAR scales directly with VP and VRMS. In multi-channel systems, however, the simultaneous transmission of pulses through multiple coils causes their E-fields to interact, possibly adding constructively, which may significantly affect SAR. We account for these interactions in RF design techniques for multi-coil TX systems by explicitly optimizing SAR. This builds on Zhu’s linear-algebraic formulation and optimization of SAR when designing RF pulses on P-channel TX systems [3], which requires knowledge of the steady state E-fields generated per unit of power sent to each TX coil, the tissue’s electrical properties and spatial sensitivity profiles (B1 maps) of each coil. Then we pose optimization problems that produce RF pulses with optimal SAR characteristics. In particular, we provide a closed-form solution for optimizing mean SAR, introduce a method to explore excitation fidelity, mean SAR and pulse duration tradeoffs, pose a constrained optimization problem that ensures 10g average SAR meets certain constraints, and show that RF pulses generated by a mean SAR optimization algorithm have better properties than those produced via Tikhonov regularization. METHODS: Regularized RF pulse design. For a P-channel TX system, linearizing and discretizing the equations relating the RF pulses played through each coil to the resultant excitation yields m=Abfull [2,4], where m is an Mx1 vector of the target excitation’s samples in the region of interest and bfull a PTx1 voltage vector of samples of the RF waveforms containing T samples of each coil’s RF pulse b1,p(t). A is an MxPT matrix incorporating each coil’s B1 map and the fixed k-space trajectory. An example of a regularized RF design algorithm is a Tikhonov regularization: min ||m-Abfull||2 + λ||bfull||2, with λ penalizing high-energy bfull candidates. Linear-algebraic formulation of SAR and design of RF pulses with optimal SAR characteristics. Analogously to Zhu [3], we derive a matrix-vector expression for s(r), the SAR at spatial location r, defined