Virtual Observation Points Research Articles

Hybrid algorithms for SAR matrix compression and the impact of post-processing on SAR calculation complexity.

This study proposes faster virtual observation point (VOP) compression as well as post-processing algorithms for specific absorption rate (SAR) matrix compression. Furthermore, it shows the relation between the number of channels and the computational burden for VOP-based SAR calculation. The proposed new algorithms combine the respective benefits of two different criteria for determining upper boundedness of SAR matrices by the VOPs. Comparisons of the old and new algorithms are performed for head coil arrays with various channel counts. The new post-processing algorithm is used to post-process the VOP sets of nine arrays, and the number of VOPs for a fixed median relative overestimation is compared. The new algorithms are faster than the old algorithms by a factor of two to more than 10. The compression efficiency (number of VOPs relative to initial number of SAR matrices) is identical. For a fixed median relative overestimation, the number of VOPs increases logarithmically with the number of RF coil channels when post-processing is applied. The new algorithms are much faster than previous algorithms. Post-processing is very beneficial for online SAR supervision of MRI systems with high channel counts, since for a given number of VOPs the relative SAR overestimation can be lowered.

A Mathematical Analysis of Clustering-Free Local SAR Compression Algorithms for MRI Safety in Parallel Transmission.

Parallel transmission (pTX) is a versatile solution to enable UHF MRI of the human body, where radiofrequency (RF) field inhomogeneity appears very challenging. Today, state of the art monitoring of the local SAR in pTX consists in evaluating the RF power deposition on specific SAR matrices called Virtual Observation Points (VOPs). It essentially relies on accurate electromagnetic simulations able to return the local SAR distribution inside the body in response to any applied pTX RF waveform. In order to reduce the number of SAR matrices to a value compatible with real time SAR monitoring ( << 103) , a VOP set is obtained by partitioning the SAR model into clusters, and associating a so- called dominant SAR matrix to every cluster. More recently, a clustering-free compression method was proposed, allowing for a significant reduction in the number of SAR matrices. The concept and derivation however assumed static RF shims and their extension to dynamic pTX is not straightforward, thereby casting doubt on the strict validity of the compression approach for these more complicated RF waveforms. In this work, we provide the mathematical framework to tackle this problem and find a rigorous justification of this criterion in the light of convex optimization theory. Our analysis led us to a variant of the clustering-free compression approach exploiting convex optimization. This new compression algorithm offers computational gains for large SAR models and for high-channel count pTX RF coils.

An 8-Channel Transceiver Coil for Carotid Artery Imaging at 7T Using an Optimized Shield Design.

To design and fabricate a transmit/receive (T/R) radiofrequency (RF) coil array for MRI of the carotid arteries at 7T with optimal shielding to improve transmit performance in parallel transmit (pTx) mode. The carotid coil included 8 total RF elements, with left and right subarrays, each consisting of 4 overlapping loops with RF shields. Electromagnetic (EM) simulations were performed to optimize and improve the transmit performance of the array by determining the optimal distance between the RF shield and each subarray. EM simulations were further used to calculate local specific absorption rate (SAR) matrices. Based on the SAR matrices, virtual observation points (VOPs) were applied to ensure safety during parallel transmission. The efficacy of the coil design was evaluated by measuring coil performance metrics when imaging a phantom and by acquiring in-vivo images. The optimal distance between the RF shield and each subarray was determined to be 45 mm. This resulted in a maximum B1+ efficiency of 1.23 μT/ √W in the carotid arteries and a peak, 10-g-average SAR per Watt of 0.86 kg-1 when transmitting in the nominal CP+ mode. Optimizing the RF shield resulted in up to 37% improvement in B1+ efficiency and 14% improvement in SAR efficiency compared to an unshielded design. Optimizing the distance between the RF shield and coil array provided significant improvement in the transmit characteristics of the bilateral carotid coil. The bilateral coil topology provides a compelling platform for imaging the carotid arteries with high field MRI.

Comparison of tight-fitting 7T parallel-transmit head array designs using excitation uniformity and local specific absorption rate metrics.

We model the performance of parallel transmission (pTx) arrays with 8, 16, 24, and 32 channels and varying loop sizes built on a close-fitting helmet for brain imaging at 7 T and compare their local specific absorption rate (SAR) and flip-angle performances to that of birdcage coil (used as a baseline) and cylindrical 8-channel and 16-channel pTx coils (single-row and dual-row). We use the co-simulation approach along with MATLAB scripting for batch-mode simulation of the coils. For each coil, we extracted B1 + maps and SAR matrices, which we compressed using the virtual observation points algorithm, and designed slice-selective RF shimming pTx pulses with multiple local SAR and peak power constraints to generate L-curves in the transverse, coronal, and sagittal orientations. Helmet designs outperformed cylindrical pTx arrays at a constant number of channels in the flip-angle uniformity at a constant local SAR metric: up to 29% for 8-channel arrays, and up to 34% for 16-channel arrays, depending on the slice orientation. For all helmet arrays, increasing the loop diameter led to better local SAR versus flip-angle uniformity tradeoffs, although this effect was more pronounced for the 8-channel and 16-channel systems than the 24-channel and 32-channel systems, as the former have more limited degrees of freedom and therefore benefit more from loop-size optimization. Helmet pTx arrays significantly outperformed cylindrical arrays with the same number of channels in local SAR and flip-angle uniformity metrics. This improvement was especially pronounced for non-transverse slice excitations. Loop diameter optimization for helmets appears to favor large loops, compatible with nearest-neighbor decoupling by overlap.

Improved 1 H body imaging at 10.5 T: Validation and VOP-enabled imaging in vivo with a 16-channel transceiver dipole array.

To increase the RF coil performance and RF management for body imaging at 10.5 T by validating and evaluating a high-density 16-channel transceiver array, implementing virtual observation points (VOPs), and demonstrating specific absorption rate (SAR) constrained imaging in vivo. The inaccuracy of the electromagnetic model of the array was quantified based on B1 + and SAR data. Inter-subject variability was estimated using a new approach based on the relative SAR deviation of different RF shims between human body models. The pTx performance of the 16-channel array was assessed in simulation by comparison to a previously demonstrated 10-channel array. In vivo imaging of the prostate was performed demonstrating SAR-constrained static RF shimming and acquisition modes optimized for refocused echoes (AMORE). The model inaccuracy of 29% and the inter-subject variability of 85% resulted in a total safety factor of 1.91 for pelvis studies. For renal and cardiac imaging, inter-subject variabilities of 121% and 141% lead to total safety factors of 2.25 and 2.45, respectively. The shorter wavelength at 10.5 T supported the increased element density of the 16-channel array which in turn outperformed the 10-channel version for all investigated metrics. Peak 10 g local SAR reduction of more than 25% without a loss of image quality was achieved in vivo, allowing a theoretical improvement in measurement efficiency of up to 66%. By validating and characterizing a 16-channel dipole transceiver array, this work demonstrates, for the first time, a VOP-enabled RF coil for human torso imaging enabling increased pTx performance at 10.5 T.

Efficient optimization of chemical exchange saturation transfer MRI at 7 T using universal pulses and virtual observation points.

To optimize the homogeneity of the presaturation module in a Chemical Exchange Saturation Transfer (CEST) acquisition at 7 T using parallel transmission (pTx). An optimized pTx-CEST presaturation scheme based on precomputed universal pulses was designed. The optimization was performed by minimizing the L2-norm between the effective and a given target while imposing energy constraints under virtual observation points (VOPs) supervision. The proposed method was evaluated through simulations and experimentally, both in vitro, on a realistic human head phantom, and in vivo, on healthy volunteers. The results were compared with circular polarization (CP) presaturation and other pTx approaches previously proposed. All experiments were conducted on a 7 T MRI scanner using a commercial 8Tx/32Rx head coil. The simulations show that the proposed pTx strategy boosted with VOPs is superior to the CP mode and existent pTx approaches. While the best results are obtained with subject specific pulses, the gain provided by the use of VOPs renders the universal pulses superior to tailored pulses optimized under vendor provided SpecificAbsorptionRate(SAR) management. In the phantom, the glucose map was significantly more homogeneous than with CP (root mean square error [RMSE] 17% vs. 30%). The efficiency of the method for in vivo hydroxyl, glutamate and rNOE weighted CEST acquisitions was also demonstrated. The use of a pTx presaturation scheme based on universal pulses optimized under VOP SAR management is significantly benefiting CEST imaging at high magnetic field.

The effects of RF coils and SAR supervision strategies forclinically applicable nonselective parallel-transmit pulses at 7T.

To investigate the effects of using different parallel-transmit (pTx) head coils and specific absorption rate (SAR) supervision strategies on pTx pulse design for ultrahigh-field MRI using a 3D-MPRAGE sequence. The PTx universal pulses (UPs) and fast online-customized (FOCUS) pulses were designed with pre-acquired data sets (B0 , B1 + maps, specific absorption rate [SAR] supervision data) from two different 8 transmit/32 receive head coils on two 7T whole-body MR systems. For one coil, the SAR supervision model consisted of per-channel RF power limits. In the other coil, SAR estimations were done with both per-channel RF power limits as well as virtual observation points (VOPs) derived from electromagnetic field (EMF) simulations using three virtual human body models at three different positions. All pulses were made for nonselective excitation and inversion and evaluated on 132 B0 , B1 + , and SAR supervision datasets obtained with one coil and 12 from the other. At both sites, 3 subjects were examined using MPRAGE sequences that used UP/FOCUS pulses generated for both coils. For some subjects, the UPs underperformed when simulated on a different coil from which they were derived, whereas FOCUS pulses still showed acceptable performance in that case. FOCUS inversion pulses outperformed adiabatic pulses when scaled to the same local SAR level. For the self-built coil, the use of VOPs showed reliable overestimation compared with the ground-truth EMF simulations, predicting about 52% lower local SAR for inversion pulses compared with per-channel power limits. FOCUS inversion pulses offer a low-SAR alternative to adiabatic pulses and benefit from using EMF-based VOPs for SAR estimation.

An investigation into the dependence of virtual observation point-based specific absorption rate calculation complexity on number of channels.

This study aims to find a relation between the number of channels and the computational burden for specific absorption rate (SAR) calculation using virtual observation point-based SAR compression. Eleven different arrays of rectangular loops covering a cylinder of fixed size around the head of an anatomically correct voxel model were simulated. The resulting Q-matrices were compressed with 2 different compression algorithms, with the overestimation fixed to a certain fraction of worst-case SAR, median SAR, or minimum SAR. The latter 2 were calculated from 1e6 normalized random excitation vectors. The number of virtual observation points increased with the number of channels to the power of 2.3-3.7, depending on the compression algorithm when holding the relative error fixed. Together with the increase in the size of the Q-matrices (and therefore the size of the virtual observation points), the total increase in computational burden with the number of channels was to the power of 4.3-5.7. The computational cost emphasizes the need to use the best possible compression algorithms when moving to high channel counts.

A Nested Eight-Channel Transmit Array With Open-Face Concept for Human Brain Imaging at 7 Tesla

Purpose: Parallel transmit technology for MRI at 7 tesla will significantly benefit from high performance transmit arrays that offer high transmit efficiency and low mutual coupling between the individual array elements. A novel dual-mode transmit array with nested array elements has been developed to support imaging the human brain in both the single-channel (sTx) and parallel-transmit (pTx) excitation modes of a 7 tesla MRI scanner. In this work, the design, implementation, validation, specific absorption rate (SAR) management, and performance of the head coil is presented.Methods: The transmit array consisted of a nested arrangement to improve decoupling between the second-neighboring elements. Two large cut-outs were introduced in the RF shield for an open-face design to reduce claustrophobia and to allow patient monitoring. A hardware interface allows the coil to be used in both the sTx and pTx modes. SAR monitoring is done with virtual observation points (VOP) derived from human body models. The transmit efficiency and coverage is compared with the commercial single-channel and parallel-transmit head coils.Results: Decoupling inductors between the second-neighboring coil elements reduced the coupling to less than −20 dB. Local SAR estimates from the electromagnetic (EM) simulations were always less than the EM-based VOPs, which in turn were always less than scanner predictions and measurements for static and dynamic pTx waveforms. In sTx mode, we demonstrate improved coverage of the brain compared to the commercial sTx coil. The transmit efficiency is within 10% of the commercial pTx coil despite the two large cut-outs in the RF shield. In pTx mode, improved signal homogeneity was shown when the Universal Pulse was used for acquisition in vivo.Conclusion: A novel head coil which includes a nested eight-channel transmit array has been presented. The large cut-outs improve patient monitoring and reduce claustrophobia. For pTx mode, the EM simulation and VOP-based SAR management provided greater flexibility to apply pTx methods without the limitations of SAR constraints. For scanning in vivo, the coil was shown to provide an improved coverage in sTx mode compared to a standard commercial head coil.

Post-processing algorithms for specific absorption rate compression.

Compression of local specific absorption rate (SAR) matrices is essential for enabling SAR monitoring and efficient pulse calculation in parallel transmission. Improvements in compression result in lower error margin and/or lower number of virtual observation points (VOPs). The purpose of this work is to introduce two algorithms for post-processing of already compressed VOP sets. One calculates individual overestimation matrices for the VOPs to reduce overestimation, the other identifies redundant VOPs. The first algorithm was evaluated for VOP sets calculated for three different transmit arrays with either 8 or 16 channels. For each array, two different overestimation matrices were used to generate the VOP sets. Each post-processed VOP set was evaluated using one million random excitation vectors and the results compared to the VOP set before post-processing. The second algorithm was evaluated by utilizing the same random excitation vectors and comparing the results after removal of the redundant VOPs with the results before removal to verify that these were identical. The first algorithm reduced the mean overestimation by up to four fifths compared to the original set, while keeping the number of VOPs constant. The second algorithm decreased the number of VOPs generated by a compression with Eichfelder and Gebhardt's algorithm by more than 40% in 40% of the investigated cases and by more than 20% in 73% of the investigated cases. Two post-processing algorithms are presented that enhance previously compressed VOP sets by improving the accuracy per number of VOPs.

Performance analysis of integrated RF microstrip transmit antenna arrays with high channel count for body imaging at 7 T.

The aim of the current study was to investigate the performance of integrated RF transmit arrays with high channel count consisting of meander microstrip antennas for body imaging at 7 T and to optimize the position and number of transmit elements. RF simulations using multiring antenna arrays placed behind the bore liner were performed for realistic exposure conditions for body imaging. Simulations were performed for arrays with as few as eight elements and for arrays with high channel counts of up to 48 elements. The B1+ field was evaluated regarding the degrees of freedom for RF shimming in the abdomen. Worst-case specific absorption rate (SARwc ), SAR overestimation in the matrix compression, the number of virtual observation points (VOPs) and SAR efficiency were evaluated. Constrained RF shimming was performed in differently oriented regions of interest in the body, and the deviation from a target B1+ field was evaluated. Results show that integrated multiring arrays are able to generate homogeneous B1+ field distributions for large FOVs, especially for coronal/sagittal slices, and thus enable body imaging at 7 T with a clinical workflow; however, a low duty cycle or a high SAR is required to achieve homogeneous B1+ distributions and to exploit the full potential. In conclusion, integrated arrays allow for high element counts that have high degrees of freedom for the pulse optimization but also produce high SARwc , which reduces the SAR accuracy in the VOP compression for low-SAR protocols, leading to a potential reduction in array performance. Smaller SAR overestimations can increase SAR accuracy, but lead to a high number of VOPs, which increases the computational cost for VOP evaluation and makes online SAR monitoring or pulse optimization challenging. Arrays with interleaved rings showed the best results in the study.

Local SAR compression algorithm with improved compression, speed, and flexibility.

Local specific absorption rate (SAR) compression algorithms are essential for enabling online SAR monitoring in parallel transmission. A better compression resulting in a lower number of virtual observation points improves speed of SAR calculation for online supervision and pulse design. An iterative expansion of an existing algorithm presented by Lee et al is proposed in this work. The original algorithm is used within a loop, making use of the virtual observation points from the previous iteration as the starting subvolume, while decreasing the overestimation with each iteration. This algorithm is evaluated on the SAR matrices of three different simulated arrays. The number of virtual observation points is approximately halved with the new algorithm, while at the same time the compression time is reduced with speed-up factors of up to 2.5. The new algorithm improves the original algorithm in terms of compression rate and speed.

Fast online-customized (FOCUS) parallel transmission pulses: A combination of universal pulses and individual optimization.

To mitigate spatial flip angle (FA) variations under strict specific absorption rate (SAR) constraints for ultra-high field MRI using a combination of universal parallel transmit (pTx) pulses and fast subject-specific optimization. Data sets consisting of B0 , maps, and virtual observation point (VOP) data were acquired from 72 subjects (study groups of 48/12 healthy Europeans/Asians and 12 Europeans with pathological or incidental findings) using an 8Tx/32Rx head coil on a 7T whole-body MR system. Combined optimization values (COV) were defined as combination of spiral-nonselective (SPINS) trajectory parameters and an energy regularization weight. A set of COV was optimized universally by simulating the individual RF pulse optimizations of 12 training data sets (healthy Europeans). Subsequently, corresponding universal pulses (UPs) were calculated. Using COV and UPs, individually optimized pulses (IOPs) were calculated during the sequence preparation phase (maximum 15 s). Two different UPs and IOPs were evaluated by calculating their normalized root-mean-square error (NRMSE) of the FA and SAR in simulations of all data sets. Seven additional subjects were examined using an MPRAGE sequence that uses the designed pTx excitation pulses and a conventional adiabatic inversion. All pTx pulses resulted in decreased mean NRMSE compared to a circularly polarized (CP) pulse (CP = ~28%, UPs = ~17%, and IOPs = ~12%). UPs and IOPs improved homogeneity for all subjects. Differences in NRMSE between study groups were much lower than differences between different pulse types. UPs can be used to generate fast online-customized (FOCUS) pulses gaining lower NRMSE and/or lower SAR values.

Global and peak local specific absorption rate control on parallel transmit systems using k-means SAR compression model.

To improve the specific absorption rate (SAR) compression model capability in parallel transmission (pTx) MRI systems. A k-means clustering method is proposed to group voxels with similar SAR behaviors in the scanned object, providing a controlled upper-bounded estimation of peak local SARs. This k-means compression model and the conventional virtual observation point (VOP) model were tested in a pTx MRI framework. The pTx pulse design with different SAR controlling schemes was simulated using a numerical human head model and an eight-channel 7T coil array. Multiple criteria (including RF power, global and peak local SARs, and excitation accuracy) were compared for the performance testing. The k-means compression model generated a narrower overestimation bound, leading to a more accurate local SAR estimation. Among different pTx pulse design approaches, the k-means compression model showed the best trade-off between the SAR and excitation accuracy. The developed SAR compression model is advantageous for pTx framework given the narrower overestimation bound and control over the compression ratio. Results also illustrate that a moderate increase of maximum RF power can be useful for reducing the maximum local SAR deposition.

Modelling and B1 Shim Analysis of 16-Element Transceiver Array at 7 T.

The work examines the workflow of using commercially available software for electromagnetic modelling and validation of a transceiver array coil operating at 298 MHz for magnetic resonance imaging and spectroscopy at 7 T. The coneshaped, tight-fit parallel transmit head array consists of two rows with eight loop coils per row and transmits two distinct spatial distributions by means of B 1 shimming. Considerations for finite-difference time-domain simulation setup and post-processing with circuit-domain co-simulation are examined, as is the generation of virtual observation points suitable for online safety monitoring.

An 8-channel transceiver 7-channel receive RF coil setup for high SNR ultrahigh-field MRI of the shoulder at 7T.

In this work, we present an 8-channel transceiver (Tx/Rx) 7-channel receive (Rx) radiofrequency (RF) coil setup for 7 T ultrahigh-field MR imaging of the shoulder. A C-shaped 8-channel Tx/Rx coil was combined with an anatomically close-fitting 7-channel Rx-only coil. The safety and performance parameters of this coil setup were evaluated on the bench and in phantom experiments. The 7 T MR imaging performance of the shoulder RF coil setup was evaluated in in vivo measurements using a 3D DESS, a 2D PD-weighted TSE sequence, and safety supervision based on virtual observation points. Distinct SNR gain and acceleration capabilities provided by the additional 7-channel Rx-only coil were demonstrated in phantom and in vivo measurements. The power efficiency indicated good performance of each channel and a maximum B1+ of 19 μT if the hardware RF power limits of the MR system were exploited. MR imaging of the shoulder was demonstrated with clinically excellent image quality and submillimeter spatial resolution. The presented 8-channel transceiver 7-channel receive RF coil setup was successfully applied for in vivo 7 T MRI of the shoulder providing a clear SNR gain vs the transceiver array without the additional receive array. Homogeneous images across the shoulder region were obtained using 8-channel subject-specific phase-only RF shimming.

A method to approximate maximum local SAR in multichannel transmit MR systems without transmit phase information.

To calculate local specific absorption rate (SAR) correctly, both the amplitude and phase of the signal in each transmit channel have to be known. In this work, we propose a method to derive a conservative upper bound for the local SAR, with a reasonable safety margin without knowledge of the transmit phases of the channels. The proposed method uses virtual observation points (VOPs). Correction factors are calculated for each set of VOPs that prevent underestimation of local SAR when the VOPs are applied with the correct amplitudes but fixed phases. The proposed method proved to be superior to the worst-case calculation based on the maximum eigenvalue of the VOPs. The mean overestimation for six coil setups could be reduced, whereas no underestimation of the maximum local SAR occurred. In the best investigated case, the overestimation could be reduced from a factor of 3.3 to a factor of 1.7. The upper bound for the local SAR calculated with the proposed method allows a fast estimation of the local SAR based on power measurements in the transmit channels and facilitates SAR monitoring in systems that do not have the capability to monitor transmit phases. Magn Reson Med 78:805-811, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Local SAR, global SAR, and power-constrained large-flip-angle pulses with optimal control and virtual observation points.

To present a constrained optimal-control (OC) framework for designing large-flip-angle parallel-transmit (pTx) pulses satisfying hardware peak-power as well as regulatory local and global specific-absorption-rate (SAR) limits. The application is 2D and 3D spatial-selective 90° and 180° pulses. The OC gradient-ascent-pulse-engineering method with exact gradients and the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is proposed. Local SAR is constrained by the virtual-observation-points method. Two numerical models facilitated the optimizations, a torso at 3 T and a head at 7 T, both in eight-channel pTx coils and acceleration-factors up to 4. The proposed approach yielded excellent flip-angle distributions. Enforcing the local-SAR constraint, as opposed to peak power alone, reduced the local SAR 7 and 5-fold with the 2D torso excitation and inversion pulse, respectively. The root-mean-square errors of the magnetization profiles increased less than 5% with the acceleration factor of 4. A local and global SAR, and peak-power constrained OC large-flip-angle pTx pulse design was presented, and numerically validated for 2D and 3D spatial-selective 90° and 180° pulses at 3 T and 7 T. Magn Reson Med 77:374-384, 2017. © 2015 Wiley Periodicals, Inc.

Direct control of the temperature rise in parallel transmission by means of temperature virtual observation points: Simulations at 10.5 Tesla.

A method using parallel transmission to mitigate B1+ inhomogeneity while explicitly constraining the temperature rise is reported and compared with a more traditional SAR-constrained pulse design. Finite difference time domain simulations are performed on a numerical human head model and for a 16-channel coil at 10.5 Tesla. Based on a set of presimulations, a virtual observation point compression model for the temperature rise is derived. This compact representation is then used in a nonlinear programming algorithm for pulse design under explicit temperature rise constraints. In the example of a time-of-flight sequence, radiofrequency pulse performance in some cases is increased by a factor of two compared with SAR-constrained pulses, while temperature rise is directly and efficiently controlled. Pulse performance can be gained by relaxing the SAR constraints, but at the expense of a loss of direct control on temperature. Given the importance of accurate safety control at ultrahigh field and the lack of direct correspondence between SAR and temperature, this work motivates the need for thorough thermal studies in normal in vivo conditions. The tools presented here will possibly contribute to safer and more efficient MR exams.

Design of parallel transmission pulses for simultaneous multislice with explicit control for peak power and local specific absorption rate.

To design parallel transmit (pTx) simultaneous multislice (SMS) spokes pulses with explicit control for peak power and local and global specific absorption rate (SAR). We design SMS pTx least-squares and magnitude least squares spokes pulses while constraining local SAR using the virtual observation points (VOPs) compression of SAR matrices. We evaluate our approach in simulations of a head (7T) and a body (3T) coil with eight channels arranged in two z-rows. For many of our simulations, control of average power by Tikhonov regularization of the SMS pTx spokes pulse design yielded pulses that violated hardware and SAR safety limits. On the other hand, control of peak power alone yielded pulses that violated local SAR limits. Pulses optimized with control of both local SAR and peak power satisfied all constraints and therefore had the best excitation performance under limited power and SAR constraints. These results extend our previous results for single slice pTx excitations but are more pronounced because of the large power demands and SAR of SMS pulses. Explicit control of local SAR and peak power is required to generate optimal SMS pTx excitations satisfying both the system's hardware limits and regulatory safety limits.