Investigation of alternative RF power limit control methods for 0.5T, 1.5T, and 3T parallel transmission cardiac imaging: A simulation study

To investigate safety and performance aspects of parallel‐transmit (pTx) RF control‐modes for a body coil at B0≤3T$$ {B}_0\le 3\mathrm{T} $$ .


INTRODUCTION
8][19][20][21][22][23][24][25] Two reasons have been given to explain why pTx with channel counts >2 never really became a standard at B 0 ≤ 3T.First, pTx is supposed to be costly.This argument has become less important, however, since today's RF power amplifiers (RFPA) are often based on a stack of ∼1-kW power MOSFETs, 26,27 which could be fed separately for pTx instead of stacking them for a single channel transmission.Second, its benefit at B 0 ≤ 3T might not outweigh the additional effort to ensure patients' safety. 16oday, (static) pTx is used in modern 3T systems with two Tx channels for body imaging to address spatial heterogeneities of the flip angle and, thus, the signal and image contrast. 16Cardiac 25 and quantitative MR have been shown to benefit particularly from pTx with more than two channels because of improved B + 1 homogeneity. 18,28,29][21][22][23][24][35][36][37][38] Because of this clinical potential, a thorough investigation of all pTx safety aspects at B 0 ≤ 3T is needed.RF safety in MRI is ensured by the IEC 60601-2-33 standard's 39 specific absorption rate (SAR) limits.PTx coils are treated like local transmit coils and thus have to adhere to strict local SAR limits, diminishing their performance, while single-channel driven body coils are not bound to local SAR limits and routinely violate them. 40,41n principle, it is possible to measure SAR in-vivo indirectly by electric properties tomography (EPT) [42][43][44][45] but necessary assumptions and limitations at tissue interfaces 44,46 make the results uncertain and model dependent.Local SAR assessments are commonly done in silico, therefore, by simulations on human voxel models. 37This approach relies on the availability of an exact digital model of the subject in the scanner. 37,47,481][52][53][54][55] Multiple sources of uncertainty exist in this process.In particular, uncertainties regarding the exact digital patient model, 50,[53][54][55][56] tissue parameters and geometries, 57,58 position [59][60][61] and state (e.g., breathing 62 ) need to be accounted for.It must be emphasized that almost identical uncertainties would occur for single-channel body coils if they had to obey local SAR limits, too.
Local SAR assessments are then performed with Q-matrices 2,63,64 compressed to virtual observation points 49 to reduce the number of required matrices by a factor ∼10 5 in exchange for a few percent SAR overestimation. 65For any complex RF shim vector (voltage amplitudes and phases applied to the different coil elements), the resulting peak spatial SAR can be calculated, and IEC compliance is ensured by rejecting all shim vectors generating excessive local SAR.This widely used safety approach will hereafter be referred to as 'SAR-controlled mode' (SCM).As it relies on exact phase information of each channel, SCM requires rather complex SAR-monitoring hardware. 66n this work, two alternative phase-agnostic RF safety control modes are compared to the established SCM in terms of their B + 1 performance when the patient's unknown anatomy and position in the scanner is mitigated with a safety factor. 67,68These are (i) a 'phase-agnostic SAR-controlled mode' (PASCM) where the phase information in SAR assessment is neglected 68 and (ii) the 'power-controlled mode' (PCM), where only the maximum amplitude of all channels is supervised. 69Next, the B + 1 performance of pTx and the CP mode are compared, i.e., the safely achievable amplitudes and homogeneity after all modeling uncertainties are properly accounted for.
An idealized body coil with fixed geometry, but configurable with 1, 2, 4, 8, or 16 independent channels at field strengths B 0 = 0.5T, 1.5T, and 3T, is used to investigate the effect of not exactly knowing the patient's digital body model or precise position.Multiple simulations are employed to determine the safe excitation limits, i.e., the conditions where the permissible SAR limits are reached.These are termed 'anchor simulations', they reflect the system manufacturer's safety assessment.The excitation limits are tested in subsequent 'target simulations' on previously unseen body models or positions.This step mimics the unknown patient in the scanner, it allows to assess the uncertainty and, hence, the necessary safety factor, of the previous anchor analysis.The analysis is performed for all three control modes and the best achievable image quality, assessed in terms of mean B + 1 and B + 1 -homogeneity, is used to quantify the efficiency of either mode.

F I G U R E 1
(A) Simulation setup with human voxel model 'Duke' in the coil.(B) The unwound schematic of the birdcage coil of panel (A) with 48 ports marked by circles.Five different port combinations were investigated, with the number of independent RF channels varying from 1 to 16. See Figure S16 for a representation with voltage phasors.(C) Front view of all tested human voxel models with coil location (black dot in coil center), effective volume of coil (here shown for 3T, dotted cyan rectangle), head (dark blue), and torso (purple).leg width, 50 mm end-ring thickness, material: perfect electric conductor [PEC]) surrounded by a concentric shield (1500 mm length, 376 mm radius, material: PEC) was used in all simulations.In total, the structure had 48 ports: one in the middle of each leg and one between each two legs on the end-rings, see Figure 1A.The coil was driven in five idealized configurations with channel counts N c = 1, 2, 4, 8, or 16, by combining ports accordingly, see Figure 1B.N c = 1 is the CP mode and serves as a reference, N c = 2 (two linearly polarized modes, independently fed at the 0 • and 90 • ports) is also available on many modern 3T scanners.
A realistic configuration, as investigated in Supporting Information A 70 for 3T and 16 channels, is required for any real-life implementation on a specific coil, but it might result different geometries for each channel count and field strength with less generality.From a risk management perspective, it is advantageous to monitor the current in the coil directly, for example with pickup coils, 66 as uncertainties from components in the previous signal path are avoided.We therefore focused this work on the idealized configurations, that assume the knowledge of the current at each coil port.
Eleven human voxel models (10 from the virtual population 71 plus the original XCAT model 72 ) were positioned for a cardiac exam (heart center at scanner coordinate z = 0, backs resting on the y = −170 mm plane), see Figure 1C.4][75] Such loop in model Glenn at 0.5T was masked, see Figures S19 and S20.While models XCAT and Eddie are based on the same male model of the visible human project, 76 the XCAT model is adjusted to conform to the 50% percentile of US adults. 72Different positions of one model (Duke) in the scanner were also investigated, the results are presented in Supporting Information B.
Finite-difference time-domain (FDTD) simulations, each with one active and 47 non-active ports (treated as Z 0 = 50 Ω resistors), were carried out on an Nvidia Quadro GV100 graphics card in Sim4Life 6.2 (ZMT ZurichMedTech AG, Zürich, Switzerland) (model Eddy: Sim4Life 7.0) at frequencies of 21.3 MHz (0.5T), 63.9 MHz (1.5T), or 127.7 MHz (3T), all with 2 mm isotropic voxel size and frequency-specific tissue properties from the IT'IS database 4.0. 77For virtual observation point (VOP) compression and auxiliary calculations an Intel Xeon Silver 4108 CPU was used.Total computation time for one configuration at 3T was ∼12 h.

Coil configurations
Only static, dimensionless RF shim vectors 7 u N c = ( u (1) , u (2) , … , u (Nc) ) T were analyzed in this work where The five port-to-channel-conversation-matrices u N c with sizes N c × 48 were derived with a simplified electromagnetic co-simulation, 78 see Supporting Information C.

Normalized SAR VOPs
were derived for all configuration combinations of the human voxel model, the position, the field strength and the channel count as described in Ref. 38 The VOPs were normalized to dimensionless matrices Ql by dividing each Q l by its respective IEC normal mode limit, 39 see Supporting Information D [79][80][81] for details.

Safety limits
Shim vectors u are considered safe in terms of the IEC normal mode, if the following conditions are fulfilled for all the N l Ql -matrices of a configuration.
In SAR-controlled mode (SCM), the requirement is 'the dimensionless normalized peak spatial SAR ps ŜAR is limited to 1'; formalized as In phase agnostic SAR-controlled mode (PASCM), the requirement is 'ps ŜAR of the worst-case phase combination is limited by 1'; formalized as where | ⋅ | denotes the element-wise absolute value as In power-controlled mode 69 (PCM), the requirement is 'the maximum single channel amplitude of each shim vector is limited by '; formalized as see Supporting Information E for details.Implementation and hardware supervision on a real scanner are easier for PASCM and PCM, since no phase information is needed.They are inherently less efficient, however, since the given limit must cover the worst case of all possible phase combinations.

Anchor-target analysis
Safety limits based on simulation always need a safety factor since neither the actual subject's anatomy nor its position are precisely known during the assessment.In the present work, this factor is determined by dividing the total number of N considered cases into n 'training' (termed: anchor) and N − n 'test' datasets (termed: target).Random shim vectors u r are selected and scaled to fully exploit the IEC head and local SAR limits in the anchor simulations, or the partial-body and whole-body SAR limits in the target simulation if this limit is stricter, see Figure 2. The SAR-type distinction reflects that (only) partial-body and whole-body SAR are normally known even for unknown subjects.All counts n ∈ {1, … , N − 1} and combinations of anchors were evaluated.For each control mode, coil configuration and B 0 , the safety factors are determined by the highest normalized local SAR (ps ŜAR) encountered in any target simulation.
In the general case of multiple configurations being used for anchoring, the maximum in Eqs.(1, 2) is evaluated over all Ql of all anchor simulations while in Eq. ( 3) the lowest single channel amplitude limit  of all anchor configurations is used.
Schematic flow chart of the anchor-target analysis to derive a safety factor.See text for further explanation.(A) Each possible target in a given set of N configurations is selected for further analysis.Selecting more than one target is equivalent to reducing the number of configurations in the overall set and subsequent multiple runs with the same anchors and different targets.(B) The non-target configurations are used as anchor.(C) The selected target configuration.(D) The following analysis is carried out for each RF-shim vector in a set of M random RF-shim vectors.(E) The RF-shim vector is scaled such that the local and head SAR limit of the anchors as well as the global whole-body and partial-body SAR limits of the target are fulfilled.(F) The maximum of normalized local SAR and normalized head SAR is evaluated for the scaled 'anchor-safe' RF-shim vector.(G) This process is repeated for all N possible targets and M random RF-shim vectors.The overall maximum normalized SAR is used as safety factor.hd, head; wb, whole body; pb, partial body; hd, head; wb, whole body; pb, partial body.
In subsequent target simulations, which are always performed for a single configuration, the ps ŜAR of these scaled shim vectors u M,r is calculated with the target's Ql : This process is repeated for 10 6 random shim vectors u M,r with r = 1 • • • 10 6 (50% with random phases but equal amplitudes, 50% with random phases and amplitudes) and if the target's maximum ps ŜAR exceeds unity it is used as safety factor s M : ) .
For PCM (only), a theoretical upper bound for ps ŜAR exists, as ps ŜAR PCM,max ≥ s ′ PCM can be calculated directly from the amplitude limits  a and  t , of anchor and target simulations, respectively: An example anchor-target analysis is demonstrated in Figure 3 for anchors Yoon-sun and Glenn and target Louis.
A global safety limit covering each conceivable patient configuration is not meaningful.A larger-bodied patient having a cardiac exam and a neonate having a brain exam require and deserve different limits to achieve both RF safety and performance.Appropriately selected patient groups are needed, therefore, and only the seven human models between 50 kg and 80 kg (Louis, Yoon-sun, Ella, Glenn, Jeduk, Duke, and XCAT, i.e., five males and two females) were used for this anchor-target analysis.Each possible combination of one to six anchors was evaluated on each of the remaining targets.For completeness, an analysis including all models despite their hugely different body masses, has also been performed.Predictably, this resulted in much higher safety factors > 6, see Figures S21  and S22.
It should be reasonable to expect that the generated safety limit covers additional, completely unknown patients within the given patient group.This must be ensured with an appropriate safety factor that covers the model variability.The choice of the safety factor is essential to ensure safety and high RF performance.A too high safety factor is conservative, but limits performance more than necessary while a too low safety factor can result in damage for the patient.This work is therefore aiming at the lowest safety factor that still ensures safety for all Schematic anchor-target analysis for the example of anchor models Yoon-sun and Glenn and target model Louis at 3T, eight channels with SAR-controlled mode.(A) Scaling of one example shim vector such that the local and head SAR limit of the anchors as well as the global whole-body and partial body SAR limits of the target are fulfilled.Anchors: Maximum intensity projections of normalized local SAR for one shim vector.The discrete steps between torso and extremities are caused by the different IEC limits.(B) Applying the same 'anchor-safe' shim vector to the target results in significant local SAR overshoots.(C) Distribution of ps ŜAR in the target for 10 6 shim vectors; please note the logit x-axis.The example shim vector marked by '×' is at the 1% percentile of the shim vectors with the highest ps ŜAR.hd, head; wb, whole body; pb, partial body.investigated models, if the most susceptible model would be unknown.The updated control-modes thus combine the safety factor of the leave-one-out anchor-target analysis with the VOPs of all configurations to ensure conservativeness.In the analyzed example, this corresponds to combining the safety factor of the anchor-target analysis with six anchors and one target with the VOPs of all seven models.
Once the safety factors are known, the safety limits are updated by multiplication of the cumulated Ql of all configurations with s M : In power-controlled mode, this is equal to dividing the lowest single channel amplitude limit  by (s PCM ) : Please note that PCM was treated like the SAR controlled modes in all mode comparisons, i.e., not the PCM-exclusive theoretical maximum but the highest actually encountered ps ŜAR value was used.
To assess the B + 1 performance for each control mode, the trade-off between best possible mean and coefficient of variation CV , both evaluated in the central imaging plane of the torso, was examined.To this end, shim vectors were optimized with the Nelder-Mead algorithm, 82 see Supporting Information F.

SAR limiting factors
The SAR analysis based on normalized Q-matrices 38 allows to investigate local and non-local SAR limits simultaneously.The limiting factor for the selected group of seven models in the 50-80 kg weight group is local 10 g-averaged SAR; never head, partial or whole-body SAR.Only if vastly different body models are compared, whole-body SAR can become limiting, see Figure S23.A median local SAR violation of factor 2.7 is observed for the CP mode hitting the whole-body SAR limit, see Figure S24.

3.2.1
Power limits (only applicable to the power-controlled mode) In PCM, the maximum permissible total power P (N c , ) ∝ ((N c , )) 2 N c can be calculated directly.This was done for all 165 combinations of five channel counts N c , 11 human models  with total body mass m() and height h(), and three field strengths, see Figure S25.
Figure 4 illustrates P (N c , ) as a function of body-mass and body-height, for each B 0 , normalized to the mean across all channel counts and body models, i.e., each box shows the range across channel counts.
For B 0 = 0.5T and 1.5T, the normalized total permissible power decreases with increasing body mass or height.In contrast, no clear trend can be observed for B 0 = 3T.

Safety factors
For the anchor-target analysis with six anchor models and one target model, the ps ŜAR distribution, whose maximum defines the necessary safety factor, is shown in Figure 5.A hierarchy of models exists for N c = 1 where all control modes are identical by design.Only the one model with the highest 'SAR susceptibility' can reach ps ŜAR > 1 as it is included in the anchor group for all other models.For N c ≥ 2, PCM and PASCM always show lower ps ŜAR than SCM and this difference increases with channel count.For up to four channels, the PCM distributions extend to ≥ 99% of the theoretical ps ŜAR maximum (red stars) but for 16 channels the maximum is missed by Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with six anchor models and one target model (leave one out), where each violin represents 10 6 initial random shim vectors.Values > 1 mean that an anchor-safe excitation that also fulfills the target's partial and whole-body SAR limit exceeds the local SAR limit in the target model; the maximum value of each distribution defines the required safety factor.For the single-channel CP mode (circles) the three SAR modes become identical.Star symbols indicate the theoretical maximum (PCM only).For SCM, each tested shim vector must by construction produce ps ŜAR ≥ 1 in one target model.∼10 − 40%.This indicates that 10 6 random shim vectors are not sufficient to fully explore such high-dimensional parameter space, see Figure S26.
To investigate this aspect further, the optimization algorithm was used to find maximum ps ŜAR excitations for PCM and SCM for target Yoon-sun and the remaining 6 models as anchor, see Figure 6 and Supporting Information G.These 'optimized' vectors reach the PCM upper limit with error below 0.5% for all channel counts.The realized ps ŜAR of 10 6 random shim vectors falls below the optimized ps ŜAR for N c ≥ 16 (PCM) and N c ≥ 8 (SCM) with increasing differences for higher channel count.Since phases are irrelevant, the PCM vector space is effectively lower dimensional than its Maximum ps ŜAR as a function of channel count for 3T of an anchor-target analysis with model Yoon-sun as target and all six other models (Louis, Ella, Glenn, Jeduk, Duke, XCAT) as anchors.
SCM counterpart and requires less test vectors to be explored.
The maximum ps ŜAR of all random shim vectors for all combinations of anchor models and target model is shown in Figure 7 as a function of anchor count.
The maximum ps ŜAR decreases with rising anchor-model count by construction.While safety factors of up to 6 are needed if only a single anchor model is used (16 channels, 0.5T; factor 5 for 8 and 16 channels at 3T) for SCM, the usage of six anchor models reduces that factor to ∼2 for all SCM cases, see Table 1.For PCM and PASCM, the observed maximum ps ŜAR, i.e., the safety factors, are consistently lower compared to SCM, varying between ∼3.6 (PCM) and ∼ 4.8 (PASCM) for one anchor (both four channels, 0.5T), and ∼ 1.3 (PCM) and ∼ 1.6 (PASCM) for six anchor models (except for PCM at two channels and 3T).

mean (B + 1 ) performance
The potential and the limitations of pTx for image quality are illustrated in Figure 8A-C for the example of the Duke model and eight channels.In the trade-off curves between mean(B + 1 ) and the CV as a B + 1 -inhomogeneity surrogate, pTx excels if the subject model was exactly known and no safety factor is needed: the sweet spot of the pTx curve (here defined as shim vector with lowest cost C = −mean for  = 3; gray curve and symbols) offers 25% more mean(B + 1 ) and still improves CV (B + 1 ) by factors of up to 3, compared to the CP excitation.However, safety factors are normally needed and reduce the available power, and hence mean (B + 1 ), for any given mode (colored curves).This affects pTx stronger than the CP mode: threefold homogeneity improvements are still possible but cost B + 1 , particularly for PCM, where even at equal homogeneity the mean is reduced by 5 − 10%.SCM provides consistently 5% − 20% more mean than PCM for the same homogeneity.PASCM performs close to PCM for 0.5T and 1.5T and approaches SCM at 3T.
In Figure 8D-F, the mean(B + 1 ) performance of pTx shims compared to CP is shown for all control modes at image inhomogeneity CV ( B + 1 ) = 0.1, a typical value for CP excitation at 1.5T.Note that at 3T it takes N c ≥ 4 to achieve this homogeneity at least in some and N c = 16 to meet it for all voxel models.
Necessarily, SCM without safety factor, i.e., assuming that the exact patient model is known, is always performing best with a 20-30% gain in mean compared to CP, largely independent of the channel count.Normally, however, the patient model is not known, safety factors must be included, and the overall mean drops by factors of 1.5-2.Compared to the CP mode with safety factor, pTx again provides ∼20% more mean for SCM but ∼10% less for PCM.With one exception (four channels at 0.5T), these numbers vary little with channel count or field strength.Note that for either control mode, the inclusion of the safety factor and basing the SAR assessment on all models dramatically reduced the box sizes and, hence, the model dependence.As seen before, PASCM performs similar to PCM at 0.5T and 1.5T and approaches SCM for high channel counts at 3T.
A third comparison is shown in Figure 8G-I, where the cost function C = −mean is evaluated for  = 3 and the difference of the lowest shim vector cost to the respective CP-mode cost is plotted for each configuration.SCM always outperforms the CP mode, in this metric, while PASCM and PCM fall behind the CP mode at 0.5T and 1.5T and have a slight advantage at 3T.

Safety aspects
The employment of pTx to improve B + 1 homogeneity 4 or reduce implant heating 37 requires a solid framework to ensure patient safety even if no precise digital patient model is available.A method to assess RF safety for a given body coil but for an inherently unknown patient is presented in this work.Safety factors are derived from the highest ps ŜAR in target models, yielding shim vectors that can safely be applied to unknown subjects, as long as these are not too different with respect to body mass.This procedure is applied for three different RF control modes Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Values > 1 mean that an anchor-safe excitation exceeds permissible local SAR limits in the target model.See Figure S27 for more details.

T A B L E 1
Resulting safety factors for the anchor-target analysis with six anchors, cf. Figure 7.
SCM, PASCM, and PCM, to investigate their mutual performance and robustness differences.In the Supporting Information B 83 it is further demonstrated how the same approach can be applied to uncertainties of the subject's position.
A central result of the present work is the model dependence condensed in Figure 4-7.For B 0 ≤ 1.5T, the permissible power to meet local SAR limits tends to decrease with either patient mass or height (Figure 4) while the commonly applied whole-body SAR limits generously allow even more power to be applied for heavier patients.Also, we find for all coil configurations, field strengths, voxel models, or positions, that local SAR limits are inevitably vastly exceeded (by factors of ∼2.5, see Figure S24) if the whole-body SAR limit is fully exploited.This result indicates a need for a revision of IEC 60601-2-33. 39ven in the limited weight range of 50-80 kg, we observe a pronounced model dependence of maximum ps ŜAR values but no single 'most critical' model: the highest SAR for a shim vector which is safe for all other models is found in the XCAT model at 0.5T, Jeduk at 1.5T, and Yoon-sun at 3T, see Figure 5.In consequence, any attempt to derive safety limits from simulating just one or two voxel models must fail, as clearly shown in Figure 7, unless safety factors up to s ≈ 6 are applied.For high channel counts N c ≥ 8, SCM requires s > 2 even for the best case of six known anchor and only one unknown target model.This is the result of (i) the many degrees of freedom pTx offers, in conjunction with (ii) the requirement that the worst case of all tested shim vectors, rather than, e.g., the most probable one, defines the safety factor.A safety factor of 6 can be observed for all 11 human voxel models when using 10 anchor models, see Figure S21.This indicates the need to preselect a suitable model group for a safety assessment: extrapolations across large mass differences are unsafe, while a too wide model group produces prohibitively over-conservative safety factors.
Figure 5 displays the difficulty to fully explore the excitation space with random vectors for N c ≥ 8. PCM offers the elegant solution of the theoretical SAR maximum, while for (PA)SCM the proposed active search for high-SAR vectors may be the best option for higher channel counts.Alternatively, one might question the worst-case paradigm: do we really need to safeguard for excitations with a < 10 −6 probability to occur?
It must be noted that the pTx degrees of freedom are only one part of the problem, the other one is the variability of local SAR itself: the seemingly unsuspicious case of a single-channel CP coil at 1.5T requires safety factor 1.3, even for six anchor models.

4.2
Performance aspects

Comparison of SCM, PASCM, and PCM
By construction, all three control modes permit only excitations that are safe for all considered voxel models for all modes once the correct safety factor is applied.Differences exist, however, in terms of performance and robustness.SCM is the control mode of choice if mean(B + 1 ) is crucial.Sacrificing the phase information, as PCM and PASCM do, costs performance, initially, but provides higher robustness and therefore lower safety factors with respect to unknown patient models or positional uncertainties, see Figures 5-7, S10-S15.The phase agnostic supervision modes are also easier to implement technically, e.g., by integrating calibrated root-mean-square detectors directly into the coil. 66ASCM approaches SCM in performance for higher channel counts that are advantageous for pTx applications like implant heating mitigation, 22,36 see Supporting Information H. PCM's unique property to provide an easily calculable upper SAR limit for any given voxel model, without VOPs or iterating shim vectors, makes it the most robust control mode.This advantage must be evaluated against the accompanying performance loss and the outcome of that comparison will likely be situation dependent.

B 0 and channel-count dependence
No clear statement can be made about the field dependence of the SAR results (Figures 4-8).The variability of ps ŜAR across voxel models and channel counts or its dependence on the number of anchor models is similar for all B 0 , and no clear trend is observed.No field strength had a particular advantage or disadvantage in terms of safety parameters.Also, with respect to mean(B + 1 ) the relative performance gain of pTx vs. CP excitation varies surprisingly little with B 0 .The best pTx inhomogeneity is always a factor of ∼ 2 − 3 smaller than for CP and for specific, homogeneity-demanding applications like quantitative MRI, pTx may be worthwhile even at 1.5T or below.If the CP homogeneity at 1.5T of CV ( B + 1 ) = 0.1 is regarded sufficient, however, static pTx provides no significant benefit in mean (Figure 8), once the safety factor is considered.On an absolute scale, the present results confirm the common knowledge that B + 1 inhomogeneity increases with field strength; the need to do better than CP becomes most pressing at 3T. 16,18 Concerning the channel count N c , the variability of ps ŜAR tends to increase with N c (the violins in Figure 5 get larger), similarly as the number of anchor models needed to get the SCM safety factor down (Figure 7).Both dependences reflect the increasing dimensionality of the excitation vector space.Noteworthy is that this trend is absent or even weakly reversed, in the phase agnostic modes, since by design only the shim-vector phase-combinations that result in the highest SAR are considered.

Limitations
][9] Only static RF shimming is considered in this work, since it can be immediately applied to all existing pulse sequences and is thus the natural first step for pTx in the clinical market.More advanced techniques such as spokes 91,92 and kT-points 93 are known to provide superior image quality and are ultimately needed to harvest pTx' full performance potential.
In this study, the same IEC SAR limits are applied to all coil configurations, even though the local 10 g-averaged SAR limits are not formally required for the single-channel CP coil. 39This is a purely regulatory difference, however, while here we are aiming at a physics-based comparison of different coil configurations.
Only the cardiac imaging position was simulated for the model uncertainty analysis in this study.We assume pTx to be less relevant for head scanning at B 0 ≤ 3T and expect the results for abdominal scanning to be qualitatively similar to the investigated cardiac case.The aim of this work was to investigate the feasibility and limits of the safety factor concept.For an actual safety assessment by a manufacturer, more human models and positions have to be examined.Also, a more detailed coil model, including the tuning/matching network would be needed.On the other hand, only a single field strength and channel configuration would need to be considered unless a manufacturer aims at a flexibly reconfigurable coil.
SAR assessments based on a measured patient model 50,94 need no additional safety margins for model uncertainties and thus deliver, in principle, the highest mean B + 1 .This approach requires extra time and additional effort, however.An important step towards patient-specific local SAR assessment are deep learning methods, that can rapidly generate body models from MR images, [95][96][97] or directly generate local SAR maps from B + 1 maps 98 or even directly from MR images 99,100 and thus eliminate the time problematic.A large amount of sufficiently detailed 101 digital human models for training is required on the flip side.The measured tissue distributions, however, also contain uncertainties, and scans at different positions may need to be acquired and combined, because the model is typically larger than the coil's field of view.
With our own computational resources, we estimate 500 days of computing time and 50 TB of raw data for a safety assessment of a given 3T body-coil.This is not negligible but should be manageable for an MR system manufacturer.

CONCLUSIONS
The use of a pTx body coil at B 0 ≤ 3T is not limited by general safety concerns.Uncertainties in patient anatomy and position must be accounted for, however; either by simulating a large number of models and geometries or by imposing high safety factors.This allows for ∼3 times lower inhomogeneity even at 0.5T, compared to CP excitation, but largely eliminates the potential advantage of pTx in terms of mean(B + 1 ).An alternative second safety supervision mode, the 'power-controlled mode' PCM, sacrifices some performance but appears to be more reliable and robust in its SAR limits and can easily be implemented and supervised in real-time.A third mode, the 'phase-agnostic SAR controlled mode' PASCM, ranges in between SCM and PCM in terms of both simplicity and performance.

SUPPORTING INFORMATION
Additional supporting information may be found in the online version of the article at the publisher's website.
is the complex voltage amplitude of channel c and N c is the channel count.For a given u N c , the electromagnetic fields F (F = E or H) at position r = (x, y, z) are calculated as superposition of N c channel fields F(c)    N c which are themselves superpositions of the 48 port fields F(d)   48 by

F I G U R E 4
Maximum permissible relative total power P (N c , m) ∝ (N c , m) 2 N c as a function of human voxel model mass m (A-C) or height h (D-F), normalized to the mean value of each channel count N c and model for the given field strength.Each boxplot represents one model and contains the values of all five channel counts.The values are not comparable across different field strengths.

F I G U R E 8 (+ 1 ) 1 )+ 1 )
A-C) Trade-off between mean(B + 1 ) and B + 1 inhomogeneity measured by CV(B + 1 ) ('L-curves') for target model Duke with 8 channels.The VOPs of all seven models and the safety factors of Table 1 were used for SCM, PASCM and PCM (colored case).For comparison, the hypothetical case of an exactly known model (gray curve and symbols), SCM without safety factor and only the targets VOPs were used.The mean(B + 1 ) for a realistic target CV ( B = 0.1 is marked by a square, the shim vector with lowest cost C = −mean ( with  = 3 is marked with a triangle.(D-F) Relative mean(B + 1 ) at CV ( B = 0.1 of all safety limits and reference 'model known' as a function of B 0 field strength and channel count.All data are normalized to the CP mode value at the respective field strength.Higher values are better.At 3T, the desired target homogeneity is only achievable with higher channel counts.(G-H): Relative cost difference ΔC = k(C l − C CP ) of the lowest cost of all limits C l relative to the CP mode C CP with scalar constant k(B 0 ) depending on B 0 .The curves are therefore not comparable across different B 0 .Cost function C = −mean ( B + 1 ∕

Figure S1 .
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.

Figure S7 .
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.

Figure S8 .
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.

Figure S9 .
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.

Figure S11 .
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.

Figure S12 .
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.

Figure S13 .
Figure S1.Comparison of the absolute amplitudes between the ideal configuration and a realistic configuration.Figure S2.Positions of the ports in the coil model with human model Duke. Figure S3.Comparison of the CP mode B + 1 distribution of realistic configuration and ideal configuration.Figure S4.B + 1 maps of all 16 channels of the realistic configuration.Figure S5.B + 1 maps of all 16 channels of the ideal configuration.Figure S6.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Duke.Figure S7.Comparison of the 1-norm Q matrix values of realistic configuration and ideal configuration for model Ella. Figure S8.Anchor-target analysis with Ella and Duke for the ideal configuration and the realistic configuration.Figure S9.Coil center positions of simulations with human voxel model 'Duke' to investigate position uncertainty.Figure S10.Anchor-target analysis for small z-shifts.Figure S11.Safety factors needed for 1D positional bilateral inference or unilateral inference.Figure S12.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the SAR-controlled mode. Figure S13.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the phase agnostic SAR-controlled mode.

Figure S14 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S16 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S17 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S18 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S19 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S20 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S22 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S23 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S24 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S25 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.

Figure S27 .
Figure S14.Boxplots of the maximum ps ŜAR of all anchor-target runs of model Duke for a given z-shift for the power-controlled mode.Figure S15.3D inference from the 8 corners of a rectangular cuboid to the central point for 3 T and 8 channels.Figure S16.The unwound schematic of the birdcage coil with the voltage phasors for each channel configuration.Figure S17.Determination of the effective volume of the used RF coil.Figure S18.Trade-off between mean (B + 1 ) and CV(B + 1 ) for model Duke with a spinal cord dummy implant.Figure S19.Maximum intensity projections of point SAR in models Jeduk and Glenn.Figure S20.Maximum intensity projections of 10 g averaged SAR in models Jeduk and Glenn.Figure S21.Violin plots of ps ŜAR for all field strengths, channel counts and target models in an anchor-target analysis with 10 anchor models and 1 target model (leave one out).Figure S22.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.Figure S23.Maximum intensity projections of normalized local SAR for one shim vector for anchor model Dizzy and target model Fats.Figure S24.Boxplots of the maximum normalized 10g-averaged local SAR, partial-body SAR and head SAR.Figure S25.Maximum permissible total power P(N c , m) ∝ (N c , m) 2 N c as function of channel count and human voxel model mass for B 0 = 0.5 T, 1.5 T, and 3 T. Figure S26.Distribution of ps ŜAR for an anchor-target analysis with anchors Glenn and Yoon-sun and target Louis.Figure S27.Maximum ps ŜAR as a function of anchor model count, channel count and B 0 field strength.
This work has received funding from the EMPIR programme, co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme under grant number 17IND01 MIMAS and from the European Partnership of Metrology, co-financed by the Participating States and from the European Union's Horizon Europe research and innovation programme under grant number 21NRM05 STASIS.We thank ZMT for providing us the virtual family human body models within the MIMAS project.Open Access funding enabled and organized by Projekt DEAL. the head for parallel transmission at 7 T. Magn Reson Med.2023;90:2524-2538.doi:10.1002/mrm.29797101.Carluccio G, Akgun C, Vaughan JT, Collins C. Temperature-based MRI safety simulations with a limited number of tissues.Magn Reson Med.2021;86:543-550.doi:10.1002/mrm.28693