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

Purpose: 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


INTRODUCTION
MRI at ultrahigh fields (UHF, static magnetic field B 0 ≥ 7 T) has shown great potential for improving image quality through increased SNR, and in many cases, improved image contrast. 1However, the increased spatial variation in the transmit (Tx) RF field (B 1 + ) results in corresponding inhomogeneous flip angle (FA) distributions when using conventional circularly polarized (CP) pulses.Parallel-transmit (pTx) pulses use multiple Tx channels, which can be driven with their own unique RF pulse form.The B 1 + field emerges as interference of the fields generated by the independent channels and is manipulated by the choice of their corresponding RF pulse forms.
Dynamic pTx pulses use channel-specific pulse shapes, generating temporally varying B 1 + fields.Throughout RF excitation, the phase of the preceding nuclear spins is affected by B 0 inhomogeneities but can additionally be manipulated by using complementary gradient fields. 2,3In total, dynamic pTx pulses offer more degrees of freedom for pulse design and thus a higher potential to produce more homogeneous FA distributions.These pulses are an essential requirement for generating uniform RF signal over the entirety of the head at 7 T 1 but have not been used in regular clinical practice yet.
Routine clinical use of dynamic pTx is often burdened by its complex optimization workflow.One major step toward clinical application is the concept of universal pulses (UPs), 4 which have been presented for various 3D pulse sequences in the head, 5,6 and the heart. 7These pulses are designed using pre-acquired B 1 + and B 0 maps from a group of subjects and significantly improve the FA homogeneity for unseen test cases compared with CP pulses.Because individually optimized pulses can further improve pulse performance, the concepts of standardized UPs (SUPs) 8 and fast online-customized (FOCUS) pulses have been proposed. 9These two approaches consist of a universal optimization of pulses and parameters before the scan and a subsequent individual optimization during the actual scan with acquired subject-specific field maps.SUPs use three-slice B 1 + maps acquired in < 10 s to derive a linear transformation of the predesigned universal RF pulse shapes.FOCUS pulses currently use B 1 + and B 0 maps across the whole volume in 47 s to perform a more comprehensive individual optimization of the pulses.UPs have also been proposed for large FAs and have shown to work on multiple commercially available coils 10 yet are designed to be used on distinct coil designs.On the contrary, FOCUS pulses have so far only been shown for small FAs, designed using the small-tip-angle (STA) approximation, 2 and only on one pTx coil.To broaden the application of FOCUS pulses, we extend this concept beyond the saturation pulse (STA) approximation by generating 180 • inversion pulses and evaluating their use on two pTx head coils.
Another challenge of UHF MRI is the increased specific absorption rate (SAR) exposure due to larger RF power requirements and its stronger local variation with reduced RF wavelength. 11Furthermore, because parallel transmission allows for varying amplitude and phase relationships between transmit elements, it is not sufficient to consider power absorbed by the entire body region and instead must be monitored locally in 10-g volumes. 12This detailed monitoring of local SAR exposure is regulated for UHF with limits specified by the International Electrotechnical Commission (IEC) guideline 60 601-2-33. 13valuation of local SAR with pTx requires electromagnetic field (EMF) simulations of the pTx RF coil using digital human body models.Given a 3D spatial distribution of conductivity, density, and electric fields, a body model simulation can be formulated into a set of so-called "Q-matrices," enabling a simple quadratic relationship between an applied multichannel voltage and local SAR. 14Nevertheless, estimation of local SAR remains computationally demanding, with EMF simulations often exceeding millions of voxels.A common solution for tractable local SAR estimation is by using virtual observation points (VOPs), which compress a large set of simulation Q-matrices into a smaller set of clustered local SAR points. 15VOPs are bounded by a percent overestimation with respect to a calculated "worst case" excitation vector, determined as the eigenvector associated with the largest eigenvalue of all VOPs.When generated from a diverse and realistic population of body model EMF simulations, VOPs are bounded above the true Q-matrices' local SAR for a particular pTx coil.
Another method for monitoring local SAR with pTx is to directly limit the peak RF power per transmit channel.In this scenario, the eigenvector from the largest eigenvalue of the full simulation set of Q-matrices (the ground truth "worst case") is used to determine the power limit.The power required to generate a specific local SAR threshold (such as IEC operating normal mode limits of 10 W/kg 13 ) is set as the upper limit for all channels.This again ensures no underestimation of SAR, but these per-channel power limits can be conservative for some applications.Nevertheless, such limits are often desirable for applications outside the brain such as in the body, where peak SAR values vary greatly with subject size and anatomy. 7his work explores both the pTx topics of B 1 + field homogenization and local SAR monitoring with comparisons in two coils each containing 8-Tx and 32-receive (Rx) elements: one commercially available and one self-built.For both coils, UPs and FOCUS pulses were generated for excitation and inversion.These pulses were used experimentally in healthy volunteers in a 3D T 1 -weighted MPRAGE sequence. 16The performance of these pulses was compared across coils in terms of normalized RMS error (NRMSE) and their local SAR contributions based on EMF-based VOP estimates and per-channel power estimates.

Measurement system and data acquisition
All measurements were conducted as a multisite study at the University Hospital Erlangen and the Imaging Center of Excellence in Glasgow on two 7T whole-body MR systems (MAGNETOM Terra; Siemens Healthcare, Erlangen, Germany) with one commercially available 8-Tx/32-Rx head coil (Nova Medical, Wilmington, DE, USA) and one self-built 8-Tx/32-Rx head coil 17 in Erlangen and in Glasgow, respectively.Both coils were previously observed to have similar B 1 + performance, yet unlike the commercially available coil, the self-built coil also has eye cut-outs for subject comfort. 17SAR supervision was managed with fixed per-channel power limits for the commercial coil and the self-built coil with an EMF-based VOP model described subsequently.B 1 + /B 0 maps were acquired in the sequence preparation phase of any sequence using FOCUS pTx pulses.B 0 mapping was performed with a sagittal GRE sequence (TE 1 = 1.02 ms; TE 2 = 3.06 ms; resolution = 4.41 mm 3 isotropic; 52 slices; 0.88-mm slice gapping; FOV = 282 × 282 × 274 mm 3 ; acquisition time [TA] = 9.6 s).B 1 + mapping was performed using a transverse interferometric magnetization-prepared saturation recovery turbo FLASH sequence (TE = 1.63 ms; TR = 3.75 s; resolution = 4 × 4 × 5 mm 3 ; 25 slices; 5-mm slice gapping; FOV = 256 × 256 × 245; TA = 35 s). 18ll pTx pulses were used in a sagittal 3D-MPRAGE prototype sequence.The following timing parameters were applied based on the established clinical T 1 -weighted protocols from both sites: FA = 5 • , TR = 3 s, TI = 1.1 s, TA = 4 min 56 s, TE = 3.19 ms, FOV = 250 × 226 × 160 mm 3 , 1-mm 3 isotropic resolution, readout bandwidth = 250 Hz/Px, GRAPPA acceleration factor 3, and echo spacing (ES) = 6.9 ms using CP rectangular-shaped pulses and ES = 7.8 ms using pTx pulses.All previously acquired B 1 + and B 0 maps used for pulse design were interpolated into a 4 × 4 × 6 mm 3 matrix in sagittal orientation covering the FOV of the sequence.
Furthermore, a second 3D-MPRAGE protocol was created with 0.5-mm 3 isotropic resolution by doubling the previous scan matrix size.Due to SAR limitations, this additional scan was only performed in the self-built coil.
The only other sequence parameters that were adjusted to accommodate the higher resolution were TI = 1.37 s, TA = 9 min 15 s, bandwidth = 515 Hz/Px, and ES = 6.7 ms.
Before the study, pTx pulses were generated using eight training data sets each from both the commercially available and the self-built coils, which consisted of subject-specific B 1 + and B 0 maps and coil-specific local SAR estimation methods.For each coil, excitation and inversion pTx pulses were generated to use as UPs or as the initialization for FOCUS pulses and denoted accordingly as UP com/sb, ChPowLim/EMF /FOCUS com/sb, ChPowLim/EMF .Figure 1 shows an overview of the generated pulses for the two RF coils and corresponding SAR supervision strategies.
These pulses were evaluated on 132 data sets previously acquired with the commercially available coil and 12 data sets previously acquired with the self-built coil by performing Bloch simulations and SAR calculations derived from the respective VOP models.Three subjects, included in these evaluation data sets, were examined experimentally with prospective data collection using the commercially available coil and the 3D-MPRAGE sequence.Excitation and inversion pulses were designed for both pTx coils: UP/FOCUS com or UP/FOCUS sb .Similarly, 3 additional subjects not included in the evaluation data sets were examined with the same MPRAGE sequences using the self-built coil.One of those subjects was scanned at both sites.
The study was approved by the local ethical review boards, and all subjects provided informed consent before the scan at both sites.

SAR management
Local SAR monitoring is specific to each unique pTx coil, and in this study, the primary local SAR estimation methods were different for the two.For the commercial coil, fixed, per-channel power limits were used as provided by the coil manufacturer.This equates to eight real-valued local SAR checkpoints for every complex pTx configuration, one for each transmit elements.For the self-built coil, local SAR was monitored with VOPs derived from the coil's EMF simulation (CST Studio Suite; Dassault Systems, France).The VOP file was generated by concatenating nine data sets consisting of three body models, with each model placed in three positions along the z-direction in 10-mm increments.The VOPs were compressed with a 25% overestimation factor with respect to "worst case" configuration using the method in Eichfelder and Gebhardt, 15

F I G U R E 1
One commercial and one self-built coil were used for the measurements.Universal pulses (UPs) and corresponding parameters (energy regularization weight for excitation pulses, specific energy dose [SED] limit for inversion pulses) were generated for both coils using eight different B 1 + and B 0 maps as well as coil-specific specific absorption rate (SAR) supervision matrices (first and last virtual observation points [VOP] matrix).Fast online-customized (FOCUS) pulses were then generated based on the actual subject's B 1 + and B 0 maps acquired during the scan system errors was included.In total, these terms yielded a combined safety factor of 1.7. 17A final scaling factor of 1.2 was included, giving an overall safety factor of 2.04. 19o facilitate the comparison across the two coils with distinct SAR management methods, a set of per-channel power limits was also derived for the self-built coil as an alternative form of SAR supervision.Using the full simulation Q-matrices, the power limit was set to 0.78 W per channel, which would limit the peak local SAR to 10 W/kg for the "worst case" transmit configuration.Unlike the EMF-based supervision, the fixed per-channel limits are real-valued/non-phase-sensitive and are often much more conservative with overestimation.Using these per-channel power limits, a second set of UPs (inversion and excitation) were designed for the self-built coil.Both SAR methods (per-channel power limits and EMF-based VOPs) were then used in a scan using the two sets of UPs and online FOCUS pulses for the self-built coil in the same volunteer.Conversely, a set of EMF-based VOPs could not be derived for the commercial coil because the coil model simulation was not available.
For all healthy volunteer scans, the predicted and real-time local SAR estimates for the pTx MPRAGE sequence were recorded in the scanner log system.Scanner measurements and SAR calculations performed offline were compared for both the EMF-based VOPs and fixed, per-channel power limits of SAR estimation methods.

Parallel-transmit pulse design
Pulse design optimizations were performed with MATLAB R2020a (The MathWorks, Natick, MA, WA).The 5 • excitation pulses (duration = 1 ms, 30-μs gradient ramp) were generated with the method described in Herrler et al. 9 The excitation pulses use an extended spiral nonselective (SPINS) gradient trajectory 20 and an energy regularization weight , as this strategy was previously proven stable. 9Additionally, because the excitation pulse design falls within the STA approximation regime, complex RF pulse shapes could be calculated quickly and were sufficient to address the individual changes to B 1 + and B 0 for the highly dynamic SPINS trajectory.The UP RF optimization was then calculated using the variable exchange algorithm 21 on eight training data sets altogether.Online customization of the RF shapes was performed with that same algorithm using the final UPs as starting points.All pTx excitation pulses were compared with a CP 5 • excitation pulse of 100-μs duration, which was scaled accordingly using the mean reference voltage among all training data sets for comparability to UPs.For the additional 0.5-mm isotropic MPRAGE sequences performed in the self-built coil, FOCUS pulses were designed with stronger regularization of the specific energy dose (SED).The pTx inversion pulses were based on a k T -point trajectory 22 consisting of six k T points.This trajectory was chosen to facilitate a large tip-angle (LTA) design.Despite the anticipated benefits of more complex trajectories, 23 a stable and fast online pulse design in the nonlinear LTA regime was only tractable when using the simpler k T -point trajectory.The LTA optimization algorithm was an interior point-based algorithm proposed by Majewski 24 denoted as "IpOpt" below.The IpOpt optimizes RF magnitudes, phases, k T -point locations, and subpulse durations under strict SED and gradient slew rate constraints.The first step of the optimization (k T -point locations, subpulse durations, and RF magnitudes and phases) was calculated with the IpOpt using the eight training data sets combined.The initialization values were optimized without any SED constraints starting from six CP rectangular-shaped subpulses with channel magnitudes of 175 V and without any gradient blips.
In the next step, combined optimization variables (COVs) for the inversion pulse COV Inv were defined.These included the transmit k-space locations of five of the six k T -points (k Ti , for i  {1, 2, … , 5} and dim  {x, y, z}), with the last k T point always located in the center of transmit k-space.Additionally, a scaling factor c Tsub for the subpulse durations was introduced (starting value = 1), and a limit for the local SED exposure in J/kg was imposed directly as SED lim (starting value: SED estimate of an adiabatic HS4 pulse [duration = 12.8 ms, bandwidth = 1660 Hz] with nominal voltage of 350 V derived from the corresponding SAR supervision mode).In total, the inversion COVs contained the following parameters: To evaluate a single set of COVs, FOCUS pulses were designed with the IpOpt for each of the N p = 8 training data sets.To assess the homogeneity of the FA distribution, a Bloch simulation was performed, and (FA-)NRMSE values for each individually optimized pulse p were calculated as Here, (v) denotes the simulated FA in voxel v among N v voxels in total, and  t denotes the target FA of 180 • for inversion.It has been shown that local FA dropouts may occur when using spokes or k T points 25 and need to be considered by the optimization.Therefore, a basic brain extraction algorithm was performed after the optimization, and the minimum FA when neglecting the lowest second percentile within the brain, denoted as  min,p , was included in the universal offline optimization as a lower bound (see subsequently).To assess the pulse's contribution to the sequence's local SAR deposition, the corresponding maximum local SED value (SED p ) was calculated.To find the optimal COV Inv , the following was minimized with the global search function from MATLAB (similar to equation 6 in Herrler et al 9 ) with a time limit of 1 day: where target values NRMSE t = 0.05,  t = 180 • , and SED t = SED HS4,Unom=350V in J/kg.This formula imposes exponentially weighted SED values, yet the COVs include a hard SED limit to find a more general tradeoff between local SED exposure and homogeneity.The initial UPs were then generated based on these optimized COV Inv and using the IpOpt with all training data sets at once (same as the starting pulse for the optimization of COV Inv ).To calculate the UPs, 500 pseudo-randomly generated starting values were used to initialize the nonconvex IpOpt optimization.The starting values of the subpulses had both random RF magnitudes and phases (magnitudes are derived from the described initial Ups and multiplied by uniformly distributed numbers between 0.8 and 1.2; phases are uniformly distributed numbers between 0 and 2π).For each of the random initialization pulses, an IpOpt optimization was then performed with all training sets.The 500 resulting candidate solutions for the final UP were then associated with an NRMSE value using Equation (2), and the candidate corresponding to the lowest cost value was identified as the optimal solution.For FOCUS pulses, B 1 + and B 0 maps acquired at the beginning of the examination were exported to another computer and used for pulse design, as the IpOpt optimization was not fully integrated into the scanner software yet.The pulses were then reimported to the host computer to be played out by the sequences.It took approximately 13 s to customize an inversion pulse and about 9 s for an excitation pulse.

Simulation data
An evaluation of all pTx excitation pulses showed that the UPs performed worse regarding (FA-)NRMSE when used on the opposite coil for which it was generated.At the same time, all UP excitation pulses performed better than the CP excitation with a "universal" average scaling.All FOCUS pulse performance increase when using electromagnetic field (EMF)-based VOPs.Generally, the VOP-based SED estimates of the self-built coil are lower than per-channel power limits of the same coil (52% lower) and the commercial coil (67% lower).When applied to the self-built coil and using EMF-based VOPs, all FOCUS pulses show very similar and good performance When FOCUS sb pulses (subscript "sb" denotes optimization initialized with UPs of the self-built coil) are applied on the commercial coil, they show only slightly worse homogeneity but much higher SED than FOCUS com (subscript "com" denotes initialization with UPs of commercial coil).Importantly, the customization of all FOCUS pulses is always done for the subject and coil it is applied on.
The simulated NRMSE and SED values of all pTx inversion pulses and an HS4 adiabatic inversion CP pulse are shown in Figure 2 for data sets (B 1 + maps, B 0 maps, VOPs) from both coils.To better distinguish the effects of using different coils versus different SAR supervision strategies, UP and FOCUS pulses were generated with self-built coil data sets but using per-channel power limits as well (subscripts "sb, ChPowLim" vs. EMF-based based "sb, EMF").The nominal voltage for the adiabatic pulses was set to 400 V.This is lower than if set by the vendor-provided routine based on a transmitter voltage calibration, but is necessary to reduce SAR below the first level limit of 20 W/kg when using the per-channel power limits supervision.The proportion of commercial coil data sets in which UP sb,EMF shows lower NRMSE than UP com was only 3.0%, but FOCUS sb,EMF outperformed FOCUS com in 28.8% of the commercial coil data sets.When using only brain voxels for customization, FOCUS com /FOCUS sb,EMF reach NRMSE values of 3.2%/3.4% on average within the brain compared with 7.9%/8.5% in all valid voxels in commercial coil data sets.Notably, UP sb,EMF shows higher SED estimates than UP com on commercial coil data sets but lower on self-built coil data sets.In general, the EMF-derived VOPs in the self-built coil provide approximately 52% lower SED estimations than the fixed per-channel power limits.
Figure 3 plots a pair of FOCUS excitation and inversion RF pulse and gradient waveforms designed for the self-built coil.For every time point of each of the pulses, the instantaneous pulse SED was calculated using the uncompressed electromagnetic-field simulation Q-matrices, the EMF-based VOPs (used in the self-built coil), and the "VOPs" enforcing fixed, per-channel power limits (used in commercial coil and also derived for the self-built coil).The SED for each respective calculation was then normalized to the maximum of the Q-matrices' value and plotted for comparison.As anticipated, EMF-based VOP estimates are greater than all Q-matrix SED values; Comparison of RF waveforms, gradient waveforms, and relative instantaneous SED for FOCUS excitation (left) and inversion pulses (right) designed for the self-built coil.Magnitude pTx RF waveforms for eight transmit channels (top row).Excitation gradients for pTx waveforms (middle row).Time-resolved SED for both pulses calculated using the full EMF model Q-matrices before VOP compression (salmon orange), the compressed EMF VOPs used in the self-built coil (sea green), and the fixed per-channel power limit SAR monitoring method used in the commercial coil (crimson red) (bottom row).All relative SED is normalized to the maximum SED value of the Q-matrices' estimate meanwhile, the per-channel power limit estimates are even greater still.
Figure 4 shows the simulated local SAR given a fixed 1-W input power for 10 000 uniformly distributed random shim 8-Tx configurations generated using MAT-LAB's rand/randi functions.Each shim vector was normalized to unit norm length and used to estimate local SAR for the full EMF Q-matrices, the compressed EMF-based VOPs, and the fixed per-channel power limit VOP method-all based on the coil simulation of the self-built coil.The 1-W local SAR values for all configurations are displayed as histograms to show the distribution of local SAR values.Additionally, the local SAR for each configuration using uncompressed EMF Q-matrices and the compressed EMF-based VOPs were plotted against each other in a scatterplot to ensure the VOP overestimation condition held true for every simulated value.Finally, a one-to-one plot of the EMF-based and per-channel power limit local SAR is compared, showing that in nearly every case the per-channel power limits overestimate SAR compared with the EMF-based approach.One exception was found when the random vector had a Euclidean distance that was very close to the "worst case" configuration of the EMF-based VOPs, which is unique to the "worst case" derived from the uncompressed simulation to determine the per-channel power limits.In this case, the difference in SAR estimates was 0.01 W/kg.

Experimental data
Figure 5 shows T 1 -weighted MPRAGE images and corresponding simulated FA maps of 1 subject that were acquired with the commercial coil using various pulses for excitation and inversion.Figure 6 displays a range of T 1 -weighted MPRAGE images acquired for this study in multiple volunteers with the commercial and self-built pTx coil.For all volunteers, the same five scans are shown: HS4 adiabatic inversion with CP-mode excitation, UP com pulses, UP sb, EMF pulses, FOCUS com pulses, and FOCUS sb, EMF pulses.
Local SAR measurements predicted by the 7T scanner are compared in Table 1 for both SAR management methods (EMF-based or fixed per-channel limits) in the self-built coil.In a single subject, MPRAGE scans with UPs and FOCUS pulses were repeated, applying both SAR supervision methods.In all cases, the local SAR reported using the EMF-based VOPs was lower than when using fixed, per-channel limits.In fact, the scanner operated within IEC local SAR normal mode (up to 10 W/kg in the head) for the EMF-based method, whereas it was within first level mode (10-20 W/kg) frequently for the per-channel limits approach.
Figure 7 compares the FOCUS pTx MPRAGE images in Subject 5 using the self-built coil at 1-mm 3 and 0.5-mm 3

F I G U R E 4
A, Histogram comparison of local SAR for full EMF simulation model Q-matrices (purple), VOPs compressed from electromagnetic (EM) simulation (sea green), and fixed per-channel power limit SAR monitoring derived for the same coil model (crimson red) across 10 000 random shim vectors applied with 1-W input power The x-axis shows the full distribution of local SAR across the three SAR estimate methods, which is dominated by the distribution from the fixed per-channel limit estimates.B, Local SAR estimates for the full Q-matrices (x-axis) against the EMF-based VOPs (y-axis) for the same shim configuration.As guaranteed by the VOP compression method, the EMF-based VOP estimates always overestimate SAR compared with the full uncompressed Q-matrices.C, Local SAR estimates for EMF-based VOPs (x-axis) compared with the per-channel power limits (y-axis).The only instance where the per-channel power limits are less conservative is a very specific vector that has the closest Euclidean distance to the EMF VOPs "worst case" vector compared with all other random vectors.This case is highlighted in the pink circle, and the local SAR value for the EMF-based VOP estimate is 2.78 W/kg, whereas the per-channel power limits is 2.77 W/kg MPRAGE images acquired with the commercial coil and simulated corresponding FA maps of the used excitation and inversion pulses using either adiabatic HS4 + CP pulses as well as UPs or FOCUS pulses designed for the two different coils (subscript "com"/"sb" refer to commercial/self-built coil data sets used for the offline UP design).The adiabatic and UP com /FOCUS com inversion pulses show no artifacts, whereas UP sb, EMF /FOCUS sb, EMF show B 1 + -related artifacts in the center of the brain as well as B 0 -related artifacts near the nasal cavity.All pTx excitation pulses show lower NRMSE values than the CP mode.In general, the agreement between the simulated inversion and excitation flip-angle maps and the experimental images is limited by the accuracy of the B 1 + and B 0 maps.The accordance of the simulated maps and experimental images appears to be usable F I G U R E 6 MPRAGE images of 3 subjects per coil using either adiabatic HS4 and CP pulses, UP, or FOCUS pulses optimized for both coils ("com" indicates the commercial coil, "sb" the self-built coil).Subject 3 was scanned with both coils.Image artifacts caused by imperfect pulse design are marked with orange arrows.As also indicated by Figure 2, adiabatic pulses and UPs for inversion show in the B 1 + shading cerebellum of some subjects.UPs are generally prone to B 0 -related artifacts near the paranasal sinus but also in the temporal lobe.When used by the commercial coil, UP sb in particular shows poor inversion in the center of the brain, whereas UP com still performs well when used by the self-built coil.FOCUS pulses show more comparable and robust performance across different subjects, as well as less-severe B 0 -related artifacts

T A B L E 1
Comparison of experimental local SAR predictions measured by the scanner in the pTx MPRAGE sequence for both SAR management methods (EMF-based VOPs and per-channel power limits) Note: All local SAR values are listed as a percentage of the maximum permitted (20 W/kg for first-level mode).All pulses were designed for and used in the self-built pTx coil and the same subject.The following four MPRAGE scans were performed twice: UP inversion and excitation designed with EMF-based VOPs, UP inversion and excitation designed with fixed per-channel power limits, FOCUS inversion and excitation initialized with the EMF-based UPs, and FOCUS inversion and excitation initialized with the fixed per-channel power limits UPs.In the first series of scans, the local SAR was supervised with the EMF-based VOPs (values in second column), and in the second series of same scans, the fixed per-channel power limit supervision was used (values in third column).The ratio of these two scanner local SAR estimates are reported in the last column.

pTx MPRAGE pulses EMF-based
supervision only.The yellow box windows show a zoomed region that highlights the increase in resolution for each plane of view.With the higher resolution, the length of the readout train increases with the 0.5-mm 3 acquisition, which changes the T 1 -weighted contrast in the image.

DISCUSSION
In this work we extended the concept of universal optimization and online customization to the LTA domain and developed clinically applicable pTx inversion pulses based on 6 k T points that use individually optimized gradient and RF pulse shapes.Their robust performance was shown for N = 132 commercial coil and N = 12 self-built coil data sets and may allow them to serve as a low-SAR alternative to adiabatic inversion pulses.PTx UPs and FOCUS pulses designed for excitation consisted of a SPINS gradient trajectory and online-customized RF shapes.The comparison of UP and FOCUS pTx excitation and inversion pulses was evaluated in two separate 8-Tx RF head coils of similar design: one self-built and one provided commercially.
Along with pulse performance, the use of two different SAR supervision strategies of the coils was compared.When applied on a distinct coil to the one used for pulse optimization, we found strong artifacts with UPs for particular subjects.For example, in Figure 5 the UP inversion pulse designed for the self-built coil produced an

F I G U R E 7
Comparison of MPRAGE images using the self-built pTx coil in the same volunteer acquired with FOCUS pulses and SAR supervision EMF-based VOPs.Images with 1-mm 3 isotropic (acquisition time [TA] = 4 min 56 s) (top row) and with 0.5-mm 3 isotropic resolution (TA = 9 min 15 s) (bottom row).Yellow boxes capture a zoomed region to appreciate the resolution differences.The difference in T 1 contrast between the two resolutions is attributed to the longer readout time for the 0.5-mm 3 acquisition.The same higher-resolution 0.5-mm 3 scan was not possible in the commercial coil due to more restrictive SAR management with fixed per-channel power limits artifact in the center of the brain when used on the commercial coil.In a previous study, both coils had very similar B 1 + fields when compared with the same imaging phantom, yet the self-built coil had an approximate 10% reduction in peak B 1 + attributed to the RF shield eye cutouts. 17eanwhile, FOCUS pulses show more stable performance when designed from the opposite coil UP, yet still perform worse than when designed from the native coil UP.
The performance of pTx pulses not only varied with the coil used in its design, but also with the subject's geometry and anatomy.Just like in the original description of UPs, 4 the largest variation was observed with improper patient positioning, in which all pTx pulses were unable to effectively homogenize the entire brain (Figure S1).This variation in performance was also seen in CP adiabatic pulses, which is likely due to an unmet adiabatic condition due to SAR restrictions, as shown in some subjects in Figure 6.Therefore, we suspect that, if possible, it is more desirable to use a FOCUS approach with pulse optimization tailored to the individual.An interesting future comparison would be to compare the FOCUS method with another recent subject-specific technique, SUPs. 8he SAR supervision comparison studied the VOP approach derived from EMF simulations and fixed transmit channel power limits as a proxy for VOPs.The EMF-based VOPs are only used in the self-built 8-Tx coil in this study and are derived from simulations from 3 subjects at three different positions each with a VOP worst-case overestimation factor of 25% and additional safety factors.The per-channel power limit approach was used in the commercial 8-Tx coil and derived for the self-built coil as well.For the EMF-based case, there were 15 local SAR VOPs, and in the per-channel limit case, 8 local "VOP" checkpoints, resulting in the same order of magnitude complexity for SAR calculations online and SAR constraints or regularization in offline pulse design.The EMF-based VOP management led to consistently lower SAR values than the fixed transmit channel power limits method in both coils, while still maintaining reliable overestimation and computational feasibility.Although the coil model is not available for the commercial coil, the intermediate comparison of both SAR management methods in the self-built coil allowed for some separation of coil design/performance characteristics and SAR estimation differences.
Furthermore, using the EMF-based SAR supervision and pTx inversion pulses, a set of 1-mm 3 isotropic MPRAGE sequences and 0.5-mm 3 isotropic resolution sequences could be acquired within local SAR estimations below the IEC limits for head imaging in normal mode operation (10 W/kg).These sequences could only be acquired in first-level mode (up to 20 W/kg) when using the commercial coil's local SAR management.While the self-built coil only required scans to operate within normal mode for the pTx pulses designed, it is also possible that pulses with higher respective SED values could be calculated for better pulse performance in terms of NRMSE due to the inherent trade-off between pulse design accuracy and SED penalization during optimization.A comparison of the two SAR management methods both operating within first-level mode could further support the benefits of using EMF-based VOPs.Additionally, UP sb, EMF generated higher SED estimates than UP com and UP sb, ChPowLim when evaluated using per-channel power limits for estimation, but lower when using EMF-based VOPs.This indicates that using EMF-based VOPs in pTx pulse design may lead to a better distribution of local SAR exposure across the head.
Despite the SAR and performance advantages they offer, pTx inversion pulses in some cases show small B 0 -related artifacts at air-tissue interfaces near the nasal cavity or the inner ear.Furthermore, poor inversion was achieved in the center of the brain for some cases as well.These two types of artifacts did not match very well with the corresponding FA simulations and may be related to the limited accuracy of the B 1 + and B 0 maps or patient movement.In fact, a major limitation of the FOCUS approach in general is the requirement of fast but accurate B 1 + and B 0 mapping sequences, which is not the case for UPs.
To overcome these artifacts, several future adaptations could be implemented.7][28][29][30] Second, B 1 + maps could additionally be corrected with an estimation of motion-induced changes in the B 1 + field 31 during the measurement.Furthermore, pTx inversion pulses could be designed to be more robust to B 0 offsets, such as by introducing weighted B 0 uncertainties or offsets into the pulse calculation. 23Finally, a brain extraction algorithm (to remove scalp and other non-brain tissue) may be used for all field maps before performing any pulse design.This could potentially lead to lower SED values for the pulses because B 1 + intensity in non-brain tissues is likely to be lower on average, meaning it contributes to larger power deposition when included in a design.Another favorable result of such a brain extraction might be better homogeneity inside the brain tissue, yet the FA may consequently drop severely in non-brain tissues, rendering them invisible.Conversely, this could be problematic if these tissues were deemed clinically relevant for certain diagnoses.
Because FOCUS pulses are designed online, they impose certain SED limits to ensure predictable SAR values for any sequence that uses these pulses.These limits could therefore be set to the SED of a corresponding CP pulse, thereby guaranteeing that every sequence protocol that runs in CP mode will also run in pTx mode.3][34] On the other hand, using a fixed SPINS trajectory or k T -point trajectory with rectangular RF subpulse shapes have shown to serve as a rather simple solution, permitting individual optimization in real time.With additional degrees of freedom, more complex gradient and RF pulse shapes may introduce more local minima in the nonconvex joint optimization problem, placing heavier reliance on well-chosen starting values for an individual optimization.
Short calculation times become harder to maintain when sequences use several different pulses.For example, 2D sequences must mitigate different field distributions for slice-selective pulses.The application of 2D UPs has only yet been achieved for STA pulses with fixed slice configurations. 10"MetaPulse2D" is a recent customized approach that adapts slice-selective UPs created for rigid slice positions to arbitrary slice orientations and positions. 35Another recent approach replaces the UP with several cluster-specific pulses that are used as a warm start. 36From there, neural networks quickly choose the best fitting cluster for every slice online by predicting every pulse's potential FA distribution with FOCUS optimization.In combination with two-spoke excitation pulses designed with strict SAR constraints, short online calculation times were achieved on an external computer.Another example of sequences with many pulses are turbo spin echo (RARE/TSE/FSE) sequences. 37These sequences may benefit from a combination of FOCUS excitation pulses and a universal train of refocusing pulses optimized with the direct signal control with variable excitation and refocusing pulses (DiSCoVER) method, 38,39 where online customization to addresses protocol changes during the examination. 40While universal solutions have already been shown for 2D sequences with multiple RF pulses, these recent individual approaches still need evaluation in clinical populations.
The dependency on initialization values for FOCUS pulses was originally shown in Herrler et al. 9 but also in this paper when comparing FOCUS pulses across two RF coils.For excitation, the pTx pulse (UP or FOCUS pulse) designed for the RF coil was the better choice in almost every case, yet this was not always true for inversion pulses.In fact, the pTx inversion UP designed for the other coil would have been the better choice for a nonnegligible number of subjects (∼28%), which highlights the challenges of the LTA joint optimization and limitations of using a single UP as warm start for individual optimization.One potential solution might be to develop a clustering algorithm that selects the best choice for each subject among several previously generated pulses based on the previously acquired B 1 + and B 0 maps akin to what was presented in Herrler et al. 36 and Tomi-Tricot et al. 41

CONCLUSIONS
We have presented universal and online-customized excitation and inversion pTx pulses for two 8-Tx head coils with distinct SAR management VOPs at 7 T. Using the MPRAGE sequence, we evaluated their benefit in terms of RF homogeneity and estimations of local SAR exposure using the two pTx coils.In addition to Ups, FOCUS

F I G U R E 2
Flip-angle (FA) normalized RMS error (NRMSE) (top row) and SED estimates (bottom row) of adiabatic HS4 pulses (circularly polarized [CP]) with a nominal voltage of 400 V (HS4 400V ), Ups, and FOCUS (parallel transmit [pTx]) inversion pulses.The UP and FOCUS pulses were derived from their own coil field map, and SAR data are colored green.The gain variation of the RF power amplifier was also taken into account, which led to a certain variation in SED among different subjects.(Left column) NRMSE and SED values using commercial coil data sets (N = 132) that use fixed channel power limits for SED estimation.(Center column) NRMSE and SED values using self-built coil data sets (N = 12) that use per-channel power limits for SED estimation.(Right column) NRMSE and SED values using self-built coil data sets (N = 12) that use VOPs for SED estimation.For data sets acquired with the commercial coil, FOCUS com achieves NRMSE values of < 12.45% in 95% of the volunteers, thereby showing the best robustness among all pulses.

VOPs % max local SAR ChPowLim limits % Max local SAR Ratio ChPowLim limits/ EMF-based VOPs
15222594, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/mrm.29569by University Of Glasgow, Wiley Online Library on [13/03/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 15222594, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/mrm.29569by University Of Glasgow, Wiley Online Library on [13/03/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License inversion pulses consist of relatively simple gradient and RF pulse shapes and may serve as a low-SAR alternative to the commonly used adiabatic pulses.When trained on a distinct coil from the coil that is used, FOCUS pulses achieve slightly better performance to Ups.FOCUS pulses for inversion generalize a bit better across different 8-Tx head coils than UPs.Furthermore, using EMF simulations to manage local SAR with VOPs can provide significant advantages in terms of local SAR estimation, while always providing an overestimation of the ground-truth local SAR for safety considerations.In the case of MPRAGE with pTx excitation and inversion used in this study, EMF-based local SAR management enables high-resolution sequences that still meet the IEC limits for head imaging in normal mode operation.