Head‐and‐neck multichannel B1 + mapping and RF shimming of the carotid arteries using a 7T parallel‐transmit head coil

Abstract Purpose Neurovascular MRI suffers from a rapid drop in B1 + into the neck when using transmit head coils at 7 T. One solution to improving B1 + magnitude in the major feeding arteries in the neck is to use custom RF shims on parallel‐transmit head coils. However, calculating such shims requires robust multichannel B1 + maps in both the head and the neck, which is challenging due to low RF penetration into the neck, limited dynamic range of multichannel B1 + mapping techniques, and B0 sensitivity. We therefore sought a robust, large‐dynamic‐range, parallel‐transmit field mapping protocol and tested whether RF shimming can improve carotid artery B1 + magnitude in practice. Methods A pipeline is presented that combines B1 + mapping data acquired using circularly polarized (CP) and CP2‐mode RF shims at multiple voltages. The pipeline was evaluated by comparing the predicted and measured B1 + for multiple random transmit shims, and by assessing the ability of RF shimming to increase B1 + in the carotid arteries. Results The proposed method achieved good agreement between predicted and measured B1 + in both the head and the neck. The B1 + magnitude in the carotid arteries can be increased by 43% using tailored RF shims or by 37% using universal RF shims, while also improving the RF homogeneity compared with CP mode. Conclusion B1 + in the neck can be increased using RF shims calculated from multichannel B1 + maps in both the head and the neck. This can be achieved using universal phase‐only RF shims, facilitating easy implementation in existing sequences.


INTRODUCTION
Ultrahigh-field MRI offers increased SNR and longer T 1 relaxation time for both tissue and blood.At 7 T, these properties have the potential to improve the contrast, resolution, and imaging time of intracranial neurovascular modalities such as cerebral angiography and perfusion, as well as the visualization of vessel wall pathology.However, increasing B 0 also introduces limitations due to increased specific absorption rate (SAR) and reduced homogeneity and spatial extent of the transmit magnetic field (B 1 + ). 1 When using typical transmit head coils at 7 T, intracranial neurovascular imaging methods such as arterial spin labeling (ASL) [2][3][4][5][6] and intracranial vessel wall imaging 7,8 suffer from the rapid drop of B 1 + into the neck.4][5][6] For vessel wall imaging, it reduces the ability to suppress the signal in upstream arterial blood, which is required to provide sufficient black-blood contrast between the vessel wall and the inflowing arterial blood.Although higher nominal flip angles can be applied to increase the inversion or saturation efficiency of arterial blood in low-B 1 + areas, this is in practice constrained by a quadratic increase in SAR and by adverse effects on the magnetization of stationary spins within higher B 1 + imaging regions.Dielectric pads 9,10 can be positioned near the neck to increase both the transmit and receive sensitivity, 3,11 which has been found to increase the B 1 + efficiency in a slice just below the carotid siphon by 57%. 3 However, the use of dielectric pads increases experimental complexity and does not provide the ability to change the B 1 + field over time, such as between different acquisitions or between signal preparation and readout modules within a single acquisition.
Improved control over B 1 + in the neck can also be achieved using parallel transmission (pTx) 12 coils, which consist of multiple separate transmit channels.pTx provides improved control over the B 1 + field by manipulating the amplitude and/or phase of each of the individual transmit channels, known as RF shimming.This can be used to achieve improved spatial homogeneity of the B 1 + field, 13 to reduce the SAR, to achieve spatial 14,15 and spectral 16 selectivity, or to increase the B 1 + magnitude within a particular region of interest.Therefore, the use of pTx coils for neurovascular imaging could be used to improve the B 1 + in the feeding arteries in the neck, thereby allowing improved inversion or saturation of inflowing arterial blood.
Most conventional head pTx coils are designed for imaging the brain and lack transmit penetration into the neck.To improve the B 1 + coverage in the brainstem, the cerebellum, and the carotid arteries, previous work proposed custom pTx coil designs that consist of transmit elements surrounding both the brain and the neck (using fixed 17 or geometrically adjustable 18 transmit arrays).However, the use of such coil designs adds experimental complexity and expense relative to the use of conventional pTx coil designs.Therefore, this work focuses on the potential of improving B 1 + in the neck using conventional head pTx coils.
Before it is possible to calculate and optimize the achieved B 1 + field using pTx methods, the transmit field of all individual pTx channels must be characterized.Such multichannel B 1 + mapping 19 aims to measure the transmitted magnitude and relative phase of each transmit channel.Acquiring these data in both the head and the neck using pTx head coils can be challenging due to a combination of low RF penetration into the neck and the inherently limited dynamic range 19 of B 1 + mapping techniques.Using B 1 + mapping techniques with typical transmit voltages provides accurate data in the brain but does not provide useful information in the low-B 1 + areas in the neck.Conversely, using high transmit voltages can achieve improved B 1 + coverage in the neck, but is inaccurate for high-B 1 + regions in the head.
This paper proposes and validates an approach that combines B 1 + mapping data acquired at 7 T using two complementary RF shims (to ensure adequate overall coverage) and at multiple transmit voltages, to allow robust reconstruction of multichannel B1 + maps for both the head and the neck.Subsequently, data acquired using the proposed method are used to investigate how RF shimming can be used to improve the B 1 + magnitude in the major feeding arteries in the neck.
Parts of this work have previously been presented at the annual meeting of the International Society for Magnetic Resonance in Medicine. 20,21

THEORY
Multichannel absolute B 1 + maps can be obtained through direct measurement of (linear combinations of) the absolute B , where the relative contribution of each transmit element is estimated.Using this, the absolute B 1 + field for the ith transmit element can be calculated based on its relative contribution to the combined absolute B 1 + field, as follows: where the calculated B1 + i values correspond to the shim configuration used for B1 + abs .Relative B 1 + maps are acquired based on the signal ratios of spoiled gradient echo (SPGR) images acquired from the individual transmit channels.In the low-flip-angle regime, SPGR signal levels are proportional to transmit field magnitudes.However, with large spatial variation of the transmit field strength (such as between the head and the neck at 7 T), this low-flip-angle assumption does not apply over the full FOV.Therefore, Padormo et al. 22 proposed combining SPGR data from different RF transmission voltages.For the th transmission voltage, the measured ratio between the steady-state SPGR signal S j and the applied transmission voltage d j can be expressed using the low-flip-angle approximations as where I prop ∝ B1 + rel is the desired B 1 + -proportional image intensity;  denotes the Gaussian noise contribution; and n  (which is always negative) corresponds to systematic errors due to the low-flip-angle approximation in the presence of saturation effects.Using this equation, the B 1 + -proportional image component of each individual voxel is calculated for each transmit channel using maximum likelihood estimation 23 across the data sets acquired at different transmission voltages.
We propose using a similar approach to increase the dynamic range of absolute B 1 + measurements by combining acquisitions using different transmit voltages (50, 100, and 175 V per channel).The B 1 + maps are acquired using a 3D B 1 + mapping method termed Sandwiched sat-TFL, 24 which has a reported dynamic range of 40 • to 120 • (at a per-channel voltage of 60 V).We increase this dynamic range by acquiring data at different transmit voltages with overlap in the dynamic range of the maps (Figure 1).We propose a series of consistency criteria to identify which voxels in each map are within the identified dynamic range.The individual reconstructions are first expressed in voltage-independent units of Hz/V.Then, on a voxel-by-voxel basis, measured values are excluded from the final (combined) B 1 + map: 1.If the satTFL reference image (S 0 ) signal is smaller than the noise SD; or 2. If the measured value at a given transmit voltage is outside the dynamic range (< 4.44 Hz/V at 50 V per channel, < 2.22 Hz/V or > 6.67 Hz/V at 100 V per channel, or > 3.81 Hz/V at 175 V per channel); or 3.If more than one value remains for a given voxel, the most appropriate value(s) is/are retained as follows: a.Some (< 1/1000) voxels gave values within the expected dynamic ranges at all three voltages, despite the valid dynamic ranges not overlapping.This generally occurred at air/tissue interfaces, and these voxels were therefore masked to prevent unreliable values.b.If either measurements at both 50 V and 100 V or both 100 V and 175 V are valid for a given voxel, this is the result of respective overlapping dynamic ranges.If the average value is in the higher half of the overlapping range, only the measurement at the higher transmit voltage is used to maintain higher SNR.Otherwise, both values are included in the calculation of the combined map.
If only one transmit voltage value remained for a given voxel after applying all three exclusion criteria, that value was used for the combined B 1 + map.If multiple transmit voltages remained (due to being within the lower half of the overlapping dynamic range), the average value of the B 1 + measurements was used.
Inaccuracies in absolute B 1 + data reconstructed from different transmit voltages can remain in locations with low B 1 + magnitudes due to destructive interference of the individual transmit channels.To provide increased coverage in areas with low B 1 + for any given shim, methods such as B 1 + time-interleaved acquisition of modes (B1TIAMO 25 ) can be used to combine B 1 + maps acquired using different RF shims.B1TIAMO combines acquisitions using different RF shims as a weighted average of the B 1 + based on the signal levels of the respective reference images to provide a single combined reconstruction with more consistent accuracy.Finally, additional B 0 correction can be required when RF pulses used in the B 1 + mapping sequence have a frequency dependence.For example, when using a 500-μs rectangular pulse for presaturation (as used in this paper), the frequency response is a sinc function with zero-crossings at ±2 kHz.However, if the frequency dependence of such an RF pulse is known, its effects can be corrected (at the cost of an SNR penalty proportional to the frequency dependence) by scaling the voxel-wise B 1 + estimates based on a separately acquired B 0 map.Note that, since this work, the sandwiched satTFL implementation has been proposed to use a B 0 -insensitive hyperbolic secant pulse. 24

Wide dynamic range multichannel B 1 + mapping
To obtain robust multichannel B 1 + maps, a three-step process was used, as summarized in Figure 2.
For the first step, sandwiched satTFL absolute B 1 + maps were acquired at three different transmit voltages (50, 100, and 175 V per channel) to achieve the required large dynamic range.Absolute B 1 + maps at all three voltages were acquired twice, using two complementary RF shim configurations (circular polarization or CP mode [defined by the coil manufacturer] and CP2-mode [defined as a 45 • phase increment per channel on top of CP mode]) and combined using the B1TIAMO 25 postprocessing approach.This approach calculates a weighted average of the B 1 + maps acquired using the two RF shims.For this, a B1TIAMO weighting factor m, as used in Eq. ( 4) of Brunheim et al., 25 of 3 was used based on preliminary results.A B 0 map was also acquired to correct for static field-inhomogeneity effects arising from the 500-μs rectangular preparation RF pulse used for presaturated TurboFLASH B 1 + mapping.All acquired absolute B 1 + maps and the B 0 map were combined to form a single absolute B 1 + map in Hz/V.Second, relative B 1 + maps were acquired at multiple voltages (50, 100, and 175 V per channel) and reconstructed using the previously described large dynamic range relative B 1 + mapping approach. 22The final step combined the absolute maps with the relative maps to form complex multichannel B 1 + field maps in both the head and neck (Eq.[1]; final step in Figure 2).

3.2
In vivo experiments Data were acquired on a Siemens (Erlangen, Germany) Magnetom 7T scanner using a Nova Medical (Wilmington, MA) 8Tx/32Rx head coil under an institutional ethics agreement.To ensure consistency in the acquired B 0 data, the tune-up B 0 shim was used for all acquisitions.Data reconstruction and shim calculation were performed using MATLAB (The MathWorks, Natick, MA, USA) on a system using an Intel (Santa Clara, CA, USA) Xeon CPU E5-2680 (v4) running at 2.40 GHz with 14 cores and 28 logical processors.
Using the approach outlined in Figure 2, large dynamic range B 1 + field maps were measured and reconstructed for all 10 volunteers.For 4 subjects (Subjects 1, 2, 9, and 10), additional absolute B 1 + maps were measured for validation purposes using two arbitrary RF shims (again acquired at reference voltages of 50, 100, and 175 V per channel to facilitate validation with full spatial coverage).

Carotid artery RF shimming
To assess the theoretical upper limit for the boost in B 1 + in the neck that can be achieved using pTx RF shims, the total (theoretically) available B 1 + was evaluated in vivo on a voxel-by-voxel basis by summing the B 1 + magnitudes across the transmit channels.
For shim calculations and evaluation, hand-drawn vessel masks, comprising the internal carotid arteries (ICAs) and the circle of Willis, were drawn for each subject from the MPRAGE images.These regions of interest were down-sampled to the resolution of the B 1 + and B 0 data and used as masks for the RF shim calculations.Where needed, the regions of interest were reduced to the areas corresponding to the carotid arteries.
Both phase-and-magnitude and phase-only RF shim combinations were calculated to assess any potential benefit of the extra degrees of freedom.Shims were calculated using cost functions that aim to maximize either B 1 + magnitude, B 1 + homogeneity, or a combination of both.The cost function min } was used to maximize the magnitude, where a quadratic term is used to ensure simultaneous minimization of the required energy (as a surrogate for global SAR) to achieve a certain effective flip angle.The coefficient of variation (CoV) was used to maximize the B 1 + homogeneity: min , where std denotes the SD.Finally, the combination of the magnitude and homogeneity was optimized using where  is a regularization parameter.
To assess the prospect of deploying a universal shim in the neck, the convergence properties of universal neck RF shims were assessed using the data from the 10 volunteers.To test the results when calculating a universal RF shim for N (≤ 10) subjects, a candidate RF shim was calculated for the first N subjects, and its performance was evaluated using the multichannel B 1 + data of all 10 subjects.The first N subjects were selected chronologically by acquisition date.For each comparison, tailored RF shims (where the shim is optimized for each subject separately) were included as an indication of the theoretical upper limit of the universal shim.

4.1
Wide dynamic range multichannel B 1 + mapping Figure 3 shows an example of combining absolute CP-mode B 1 + maps acquired using different transmit voltages when using the proposed exclusion criteria.Figure 3B-D shows the original CP-mode B 1 + maps acquired using transmit voltages of 50, 100, and 175 V per channel, respectively, and the resulting combined B 1 + map is shown in Figure 3E.The masks of which voxel values were used to calculate the combined B 1 + map (after application of the exclusion criteria) can be seen in Figure 3F-H, along with the number of values used to calculate the final combined B 1 + map in Figure 3I. Figure 4 shows an example MPRAGE image along with B 1 + maps from the first step in the B 1 + mapping pipeline.B 0 off-resonance of up to −1.2 kHz in the neck results in a B 1 + underestimation of up to 49% if not corrected, as seen in Figure 4B. Figure 4C-E demonstrates the utility of B1TIAMO to increase the spatial coverage in areas with low CP-mode B 1 + .Figure 4E,F shows the changes caused by B 0 correction of the absolute B 1 + data based on the acquired B 0 maps.
An overview of the data acquired from the 10 healthy volunteers is shown in Figure 5.For each subject, a coronal slice of the MPRAGE data, a coronal projection of the hand-drawn vessel masks, and the reconstructed CP-mode B 1 + map are shown.These data were acquired using a commonly used head pTx coil, so they could also be useful for other research centers for the calculation of universal pTx shims or pulses, or for simulation purposes.Therefore, the multichannel B 1 + data and the B 0 data are made openly available online (doi: 10.5287/ora-pvzkkddda).
For Subjects 1, 2, 9, and 10, additional absolute B 1 + maps were measured using two arbitrary RF shims.Figure 6 compares the measured (using the shim settings on the scanner) and predicted (combined multichannel B 1 + maps using the corresponding shim coefficients) B 1 + maps for those validation shims.Visually good agreement is found for all four comparisons, with a RMS error of 0.25 Hz/V across all comparisons and a median B 1 + magnitude error of 3.8%.

Carotid artery RF shimming
The data from the 10 subjects shown in Figure 5 were used to study the potential B 1 + benefits in the carotid arteries when using RF shims versus standard CP mode.
Figure 7 shows the CP-mode absolute B 1 + , the total (theoretically) available B 1 + , and the resultant CP-mode B 1 + efficiency for two slices.Figure 7C shows that the theoretical upper limit of B 1 + in the neck is (as expected) low compared with the central head region.In addition, Figure 7D shows that CP mode only uses 57% ± 5% of the theoretically available maximum B 1 + , resulting in an average B 1 + magnitude in the neck for CP mode of 2.5 ± 1.0 Hz/V.This suggests that using pTx should be able to improve this very low B 1 + penetration, albeit never realizing the theoretical maximum over a large region.A universal RF shim can be used to increase the average B 1 + magnitude in the carotid arteries (as shown in Figure S1).However, the theoretical voxel-by-voxel upper limit indicated by the available maximum B 1 + is unachievable using a standard RF shimming approach.
Maximizing only the B 1 + magnitude without including a CoV constraint can result in B 1 + inhomogeneity and large inferior-superior variation in the B 1 + profile.Figure 8 shows the neck RF shim performance within the vessel mask when the CoV is included in the cost function using Eq. ( 3).Both magnitude-and-phase, and phase-only B 1 + shimming conditions were considered.Figure 8B shows that phase-only shimming performs almost as well as magnitude-and-phase shimming, with nearly identical The use of B results (differences < 1%) when using a regularization parameter λ > 1.5.Based on the L-curve in Figure 8B, a regularization parameter λ of 1.7 is found to produce a reasonable trade-off between B 1 + efficiency and minimizing the CoV. Figure 9 evaluates the number of subjects required to generate a universal shim.Good results can already be achieved when universal shims are calculated based on a single subject, and (when using λ = 1.7) no further improvement is observed when including more than 4 subjects.For all shim targets (B 1 + magnitude optimized, CoV optimized, and optimized using Eq.[3]), universal shims perform only slightly worse than fully per-subject tailored shims, and substantially better than CP mode.Additional leave-one-out comparisons, in which for each of the 10 subjects a universal phase-only neck shim is calculated based on the other 9 subjects, provide an average increase in B 1 + of 36% ± 14% relative to CP mode.The highest mean B 1 + increase in the leave-one-out comparisons is 62% (Subject 2), and the lowest mean increase is 8% (Subject 6, which already had the highest average B 1 + in CP mode).
The final RF shim, calculated as a phase-only universal shim based on all 10 subjects and using λ = 1.7, is shown in Figure 10.Over the full carotid artery masks, this universal RF shim achieves an average increase in B 1 + magnitude of 37% ± 16% relative to CP mode, while Central coronal slices of the 10-subject database (doi: 10.5287/ora-pvzkkddda) that was acquired using the proposed method.All data were acquired using the same FOV in coil coordinates.Left column, MPRAGE data (root sum of squares of circularly polarized [CP] mode and CP2 mode to improve structural visibility in the neck); middle column, coronal projections of the arterial vessel masks corresponding to the MPRAGE data; and right column, the CP-mode B 1 + map for each subject.The CP-mode B 1 + maps shown here are synthetic maps generated from the multichannel B 1 + data.
reducing the CoV by 26% ± 20%.When using tailored RF shims, the corresponding improvements relative to CP mode are a B 1 + magnitude increase of 43% ± 20% with a 31% ± 20% reduction in CoV.

Wide dynamic range multichannel B 1 + mapping
When combining B 1 + maps acquired using CP mode and CP2 mode and with different transmit voltages using the proposed pipeline, a robust B 1 + measurement can be obtained in the neck without compromising the B 1 + accuracy in the head.Figure 5 shows that this increased coverage is consistently achieved, independent of subject size and position within the coil.
Figures 3 and 4 show that both the combination of multiple transmit voltages and B1TIAMO contribute to increasing the coverage of the final B 1 + into the neck.The inclusion masks in Figure 3F-H show that data reconstructed from low-voltage acquisitions are used primarily for the high-B 1 + areas in the center of the brain and close to the transmit elements, whereas high-voltage data contribute primarily accurate information in the neck.These observations are consistent with the assumptions that motivated the use of multiple transmit voltages.Furthermore, they indicate that the exclusion criteria in Section 2, which do not make use of the spatial location of voxels, can accurately determine which transmit values to include at different spatial locations.

F I G U R E 6
Evaluation of the agreement between predicted (first row, calculated from reconstructed multichannel B 1 + maps) and measured (second row, acquired on the scanner using the same shim coefficients) B 1 + magnitude maps for two arbitrary RF shims.The third and fourth rows show the absolute difference (using a 5-fold boosted color scale) between the images in the first two rows, and the difference between the predicted (B 1 A single sandwiched satTFL acquisition using a transmit reference voltage of 60 V and using the same RF coil as this study has previously reported a dynamic range of a factor of 3 (ranging from 40 • to 120 • ). 24Therefore, using transmit voltages of 50, 100, and 175 V per channel, the multivoltage approach used here can provide accurate results over a dynamic range of B 1 + of a factor of 10.5, as the highest voltage of 175 V will enable B 1 + regions that are as low as 13.7 • at 60 V to be characterized accurately (60 V∕175 V × 40 • at the lower end of the linear range of the method), and the lowest voltage of 50 V will enable B 1 + regions that are as high as 144 • at 60 V to be characterized accurately (60 V∕50 V × 120 • at the upper end of the linear region of the method).
Despite the increased effective dynamic range when using multiple transmit voltages, even with a single shim (e.g., CP mode) no accurate B 1 + information can be acquired in locations that have very low B 1 + values due to destructive interference of the transmit fields.In such cases, Figure 4 confirms that including a CP2-mode acquisition and B1TIAMO combination of CP-mode and CP2-mode data provides complementary information and therefore yields an improved spatial extent of the B 1 + maps.However, further improvements might be possible using different calibration RF shims than CP mode and CP2 mode (such as designated neck shims) or additional RF shims in the B1TIAMO computation.
Although combining data acquired using different RF shims and transmit voltages provides B 1 + information with a larger spatial extent, B 0 off-resonance effects can reduce the accuracy of the measured B 1 + values.In this work, we used rectangular pulses that required an additional B 0 correction step (Figure 4) to obtain accurate values in areas with high B 0 off-resonance (up to −1.2 kHz were observed).Alternatively, nonadiabatic broadband full-passage hyperbolic secant pulses 27 can be used for the presaturated TurboFLASH acquisitions 24 to reduce the B 0 dependence of the B 1 + estimates.When comparing predicted B 1 + maps (reconstructed using the proposed pipeline) and measured B 1 + maps (acquired directly on the scanner) for arbitrary RF shims (Figure 6), excellent agreement can be observed throughout the imaging volume, including the neck.The mean RMS error of 0.25 Hz/V indicates that some differences remain between the predicted and acquired maps.However, some of this remaining disagreement may be caused by inaccuracies in the measured B 1 + maps rather than the predicted B 1 + maps.For example, in the low B 1 + regions in the middle of the head for Validation Shim 2, discontinuities that do not typically appear in B 1 + maps are visible in the measured B 1 + maps, whereas the predicted B 1 + maps remain spatially smooth.This is also visible in the scatter plots in Figure 5, where some higher errors are observed for voxels with low predicted B 1 + values.
The proposed multichannel B 1 + mapping method requires a total of 10 separate acquisitions (six absolute B 1 + maps, three sets of relative B 1 + maps, and one B 0 map) with a total scan time of 6:45 min for the reconstruction of a single set of multichannel B 1 + maps.This additional scan time would be a limiting factor if acquiring subject-specific field maps at the start of a clinical exam.However, this is not a limitation if using the method to acquire a B 1 + database for the calculation of universal RF shims or pulses.

Carotid artery RF shimming
Figure 7 shows that the B 1 + efficiency of CP mode is low in the neck (57% ± 5% along the carotid arteries), meaning that there is substantial opportunity for improvement using (universal) RF shims.Figure S1 confirms that a universal shim can substantially improve the carotid B 1 + , while showing a reduction in B 1 + in the circle of Willis (which, depending on the application, may be an advantage or a disadvantage).However, there is also substantial B 1 + variation along the vessel, suggesting that the shim performance can be improved by adding a B 1 + homogeneity constraint.The results in Figure 8 show that combining B 1 + homogeneity optimization with B 1 + magnitude optimization (using Eq. [3]) can improve the average homogeneity with a minimal reduction in B 1 + magnitude.When using a regularization parameter, λ, of 1.7, the CoV is reduced by 25% while the average B 1 + magnitude is reduced by only 5%. Figure 8B indicates that the results using phase-only shims are nearly equal to those of magnitude-and-phase shims when using λ > 1.5, indicating an inherent requirement for high B1 + use from all channels to achieve sufficient B 1 + in the neck.
The universal shim convergence comparison in Figure 9 shows that a universal shim for the vessels in the neck can easily be found (even based on a single subject), with no further improvement in shim performance when including more than 4 subjects in the shim calculation.Furthermore, Figure 9 shows that universal RF shims perform almost as effectively as fully tailored per-subject RF shims, while consistently outperforming CP mode in terms of both B 1 + magnitude and CoV.The results in Figure 10 show that both tailored and universal shims result in similar B 1 + profiles, explaining why the results in Figure 9 indicate that a shim calculated from a single subject can already provide reasonable results when used as a universal shim for all other subjects.Figure 10 also shows that, using a universal RF shim and λ = 1.7, the B 1 + magnitude in the vessels in the neck can be increased by 37%, while reducing the coefficient of variation by 26%.This can be achieved using phase-only RF shimming and does not require magnitude-and-phase RF shimming.These results are based on optimization of the B 1 + over the entire region of the carotid arteries in the vessel masks in Figure 5.For some applications, in particular for ASL, excitation targets can consist of a smaller portion of these vessels, such as when only labeling in a certain plane or when using vessel-selective ASL. 28n such cases, the optimization is less constrained, allowing for larger improvements in RF shim performance.For example, when only including the left internal carotid artery as a shim target, a phase-only universal RF shim can simultaneously achieve a 43% increase in B 1 + magnitude and a 42% decrease in CoV relative to CP mode (data not shown).When optimizing for a shim target consisting of the vessels within a single slice just below the carotid siphon (as used for pseudo-continuous ASL), the increase in B 1 + magnitude using a phase-only universal RF shim improves to 62% (with a 55% reduction in CoV).This indicates a slightly larger improvement than the increase in B 1 + magnitude in the same area when using dielectric pads instead of RF shimming, which were previously found to result in a 57% B 1 + increase. 3Using this single-slice shim, the minimum B 1 + in the labeling plane across the 10 subjects increases from 1.7 to 2.9 Hz/V.When using 0.3-ms pseudo-continuous ASL labeling pulses of 15 • , 5 this corresponds to a reduction in the peak transmit voltage from 165 V to 96 V, thereby reducing the need to increase the TR 4,5 or use VERSE-shimming 4 to remain within SAR limits. 6t should be noted that the vessel masks used in this study were drawn based on the vasculature of healthy volunteers.Although the results presented here indicate consistently improved B 1 + in the carotid arteries for subjects with typical (vascular) anatomy, both the B 1 + fields and the locations of the vessels in the neck might be different for patients with nonstandard anatomies.Figure 10 shows a consistent increase in B 1 + across both the left and the right side of the neck when using the proposed shim, with a decrease in B 1 + in the center of the neck.Although morphological variations in the shape of the internal carotid arteries increases with age, 29 a patient study into the variability of the medial location of the ICAs 30 found that the ICAs of most (96.1%)patients are located within the lateral half on each side of the neck and would therefore be expected to achieve substantial B 1 + improvements even for the universal RF shim.A total of 3.6% of the ICAs were found in the medial half of the lateral mass, where the B 1 + in CP mode is similar to the B 1 + using the proposed shim.The B 1 + reduction in Figure 10 would only correspond to the location of the ICAs in the remaining 0.3% of patients, who had ICAs located medial to the lateral mass.
Furthermore, the results presented here are all based on simple RF shims that are constrained to the superposition patterns that can be achieved using the available transmit channels.Because the average B 1 + efficiency of the proposed universal RF shim is 74% ± 3%, it is expected that further improvements can be achieved when using more advanced dynamic pTx pulses, where additional degrees of freedom are introduced by continuously changing the pTx coefficients in combination with the gradient waveforms and pulse amplitudes.Dynamic pTx can be used to further achieve improved B 1 + homogeneity and/or localization.However, an advantage of using RF shims is that they can directly be implemented into existing sequences without requiring further pulse design or introducing sequence timing restrictions, thereby not increasing experimental complexity for existing sequences while still achieving substantially improved B 1 + efficiency and homogeneity.
Finally, a combination of dielectric pads and pTx shimming could provide modest further improvements to the B 1 + performance in the neck.Preliminary B 1 + data (in a single volunteer), acquired both with and without dielectric pads, indicate that while RF shims provide better B 1 + results than dielectric pads, a combination of dielectric pads and pTx shimming provides further improvements to the resulting B 1 + in the neck.However, further work would be required to fully assess the performance of RF shims and the potential of using universal shims in combination with dielectric pads.

CONCLUSION
Combining B 1 + data acquired using different voltages with CP-mode and CP2-mode RF shims allows the reconstruction of accurate multichannel head-and-neck B 1 + maps for pTx head coils at 7 T. Using this, universal RF shims can be designed that increase the B 1 + magnitude in the arteries in the neck by 37%, while also improving the homogeneity.This is possible using phase-only universal RF shims, facilitating easy implementation in existing sequences at 7 T.

F I G U R E 1
Schematic representation of the measured absolute B 1 + values for acquisitions with different transmit voltages.Each single acquisition has a linear response within its dynamic range.Higher B 1 + magnitudes result in underestimation of the B 1 + ; lower values result in either overestimated or noise-dominated B 1 + values.Subplots show a single acquisition using a transmit voltage of 60 V (A) and the larger combined dynamic range when using three separate acquisitions at 50, 100, and 175 V (B).

F I G U R E 2
Schematic of the proposed B 1 + map acquisition and processing pipeline.In total, 10 different data sets are acquired (blue: six flip angle [FA] maps, one B 0 map, and three sets of relative maps) to reconstruct a single set of multichannel B 1 + maps.B1TIAMO, B 1 + time-interleaved acquisition of modes; CP, circularly polarized; pTx, parallel transmission.

F I G U R E 3
Absolute B 1 + maps acquired at different voltages (B-D) are combined to obtain a single map with an increased combined dynamic range (E).Voxel values from individual scans were included or excluded based on the signal levels in the reference images and exclusion criteria to impose consistency in the acquired values relative to the other acquired data sets, resulting in inclusion masks for each data set (F-H).(I) The total number of included values for each voxel in the slice.CP, circularly polarized.

+ pred ) and measured (B 1 +
meas ) voxel-wise values within the overlapping region.Dashed black lines indicate the mean errors, with dashed red lines indicating the means ±95%.Printed values indicate the RMS errors (RMSEs, black) and 95% confidence intervals (CI 95% , red).

F I G U R E 7 1 +F I G U R E 8
Two coronal slices from an example subject (Subject 1), showing a central slice (top row) and a more posterior slice (bottom row).Column B shows the B 1 + map (Hz/V) in circularly polarized (CP) mode.Column C shows the maximum possible B 1 + for each voxel (calculated as the sum of magnitude B 1 + per channel).Column D shows the CP-mode efficiency, calculated as the ratio of CP-mode B divided by total available B 1 + , indicating the loss of potential B 1 + arising when using CP mode.Plots investigating the trade-off between the coefficient of variation (CoV) of B 1 + within the vessel mask versus the achieved B 1 + magnitude (expressed as 1/B 1 + ).The desired regularization value, λ, that reduces CoV while retaining a strong B 1 + is found at approximately  = 1.7 (green region).(A) Universal shims that allow both phase and magnitude to change per channel.(B) Universal shims that allow only phase to change per channel.The dashed black line in (B) shows the data from (A) overlaid as a guide to the eye.The black dot indicates circularly polarized (CP) mode.

F I G U R E 9
Plots showing the number of subjects needed to generate a universal neck shim (based on phase-only RF shims).For each plot, the circularly polarized (CP) mode mean B 1 + and coefficient of variation (CoV) are shown for reference, followed by the relevant metrics for universal neck shims generated from increasing numbers of subjects.The final column for each plot shows the result when per-subject tailored shims are used (denoted as "Tail").The different columns show the results for three different cost functions: (A) minimizing {1/B 1 2 }; (B) minimizing {CoV}; and (C) minimizing the optimum combination of {1/B 1 2 } and {CoV} with regularization value λ = 1.7.

F I G U R E 10 1 +
An example RF shim for the carotid arteries, shown for Subjects 1-3.Columns show an MPRAGE slice containing a superior segment of the internal carotid arteries (A); the circularly polarized (CP) mode B 1 + in the same slice (B); the corresponding B fields when using a phase-only universal shim calculated using regularization  = 1.7 (C); and the B 1 + fields when using phase-only tailored shims that are optimized for each individual subject, again calculated using regularization  = 1.7 (D).The red outlines in (B) to (D) show in-slice portions of the carotid masks used for shim calculation (at their original resolution corresponding to the MPRAGE data).
1 + fields of the individual transmit elements.