Tailored and universal parallel transmit broadband pulses for homogeneous 3D excitation of the human heart at 7T

Purpose: To research and evaluate the performance of broadband tailored kT-point pulses (TP) and universal pulses (UP) for homogeneous excitation of the human heart at 7T. Methods: Relative 3D B + 1 -maps of the thorax were acquired from 29 healthy volunteers. TP and UP were designed using the small-tip-angle approximation for a different composition of up to seven resonance frequencies. TP were computed for each of the 29 B + 1 -maps, and UPs were calculated using 22 B + 1 -maps and tested in seven testcases. The performance of the pulses was analyzed using the coefficient of variation (CV) in the 3D heart volumes. The 3D gradient-echo (GRE) scans were acquired for the seven testcases to qualitatively validate the B + 1 -predictions. Results: Single-and double-frequency optimized pulses achieved homogeneity in flip angle (FA) for the frequencies they were optimized for, while the broadband pulses achieved uniformity in FA across a 1300 Hz frequency range. Conclusion:


INTRODUCTION
Ultra-high field (UHF) MRI has shown great promise in enabling high-resolution imaging and accurate quantification of human tissue. 1,24][5] Despite these promising advancements, UHF MRI, particularly in the context of cardiac fat/water imaging, also presents several challenges that require careful consideration and thoughtful approaches for successful implementation. 1,2ne such challenge is the inherent inhomogeneity of the transmit field (B + 1 ) at UHF, resulting in spatially varying flip angle (FA) and potential FA dropouts.This variability in FAs across the target region affects image contrast and, therefor compromises diagnostic accuracy.Although various approaches have been developed to address the inhomogeneous transmit field, 2,[6][7][8] the application of UHF MRI to the human body, which is usually larger in size than the human brain, requires specialized methodologies to tackle this issue effectively.][11][12][13][14] A range of innovative solutions has been proposed to address these challenges, encompassing the integration of multi-transmit RF coils and parallel transmission (pTx) techniques [15][16][17][18][19][20][21] using volunteer-specific B + 1 information alongside motion-robust non-Cartesian acquisition schemes and advanced reconstruction approaches. 11,22,23ynamic pTx employs, in contrast to static pTx, temporally changing RF and gradient waveforms.Such pulses are known to be susceptible to variations in the main magnetic field (ΔB 0 ). 8While dynamic pTx pulses can be designed with a short pulse duration to be less sensitive to ΔB 0 variations, 12,24 they can also be optimized to compensate for local ΔB 0 deviations by including measured ΔB 0 information, thereby mitigating their impact on image quality and diagnostic accuracy. 8,21,25,26 fundamental problem with designing such tailored pulses in the human body is the adjustment time of 10-15 min required to acquire volunteer specific B + 1 /ΔB 0 information, design, and apply the tailored pTx pulses.This issue has been successfully addressed using universal pulses (UP) in the human brain [27][28][29] and the human body targeting the heart. 30,31However, such UPs cannot be applied straightforwardly for fat/water separation techniques at 7T, 5 since the resonant frequencies of fat span a range of approximately 1300 Hz at 7T.Since both UP and TP are designed to excite a single frequency, typically water, they might result in reduced excitation fidelity for other frequencies, such as those within the fat spectrum.This limitation hinders, for example, successful fat/water separation using a Dixon approach, [32][33][34] a CSI technique that relies on the in-phase/out-of-phase cycling of fat and water signals.
Broadband pTx has been demonstrated to be effective for various applications, including slab-selective spokes pulses 35 or non-selective excitation and refocusing pulses using Gradient Ascent Pulse Engineering (GRAPE). 36,37In contrast to designing the pulse for a single resonance frequency, these techniques utilize pulses designed at multiple resonance frequencies to compensate for ΔB 0 field variations in specific target regions in the human brain, such as the sinuses and the left cerebellum. 37][34] Second, we introduce broadband TP and UP that eliminate the need for measured ΔB 0 information, as previously required in dynamic pTx approaches. 8,19,21,26Experimental data at 7T validate the B + 1 predictions and indicate the successful excitation of fat and water in the human heart at 7T.

Volunteer information and MR scanner hardware
MRI data was acquired in adherence to an approved Institutional Review Board (IRB) protocol with a 7T MR system (Siemens Magnetom, Germany) using a commercial 32-element body coil array (MRI.TOOLS, Germany) operating in 8TX/32RX (transmit/receive) mode.Volunteers were divided into library (14 Male/8 Female, 21-66 years and 19-35 kg/m 2 ) and testcases (5 males/2 females, 22-40 years and 20-25 kg/m 2 ).The posterior coil half was centered on the volunteer's heart in head-foot direction, whereas the anterior coil half was placed based on anatomic landmarks and feedback from the volunteer with a 2 cm gap to the volunteer's chin.The safety limits were meticulously executed following established protocols and consistent with previous studies conducted in this field. 5,11,12,30,31,38

Adjustments and calibration scans
For each volunteer, 3D relative B + 1 -maps of the thorax were acquired using a radial phase-encoding (RPE) trajectory during shallow breathing conditions throughout the scanning process (TE/TR = 2.02 ms/5 ms, voxel-size = 4 x 4 x 4 mm 3 and FOV = 250 x 312 x 312 mm 3 , TA = 3 min 25 s). 11The acquired raw files were exported to a workstation (12 cores with 2.1 GHz, 128 GB RAM) and reconstructed in approximately 1 min with a non-respiratory resolved reconstruction with an isotropic spatial resolution of 4 mm.The resulting 3D channel-wise B + 1 -maps were subsequently employed in designing and evaluating TPs and UPs for this study.

Pulse design and evaluation
The pulse design was implemented in MATLAB using the small-tip-angle approximation with an interleaved greedy and local optimization 21,26 to achieve a target FA of 10 • in the heart volume.The heart region was manually selected covering the entire heart on a slice-by-slice basis based on the sum of B + 1 magnitudes over the TX channels for every volunteer.The kT-points pulses were optimized using the integrated RF power and the root mean squared error of the FA and were implemented using a power limit per TX channel.Each pulse consists of four 0.15 ms long square RF pulses and four 0.09 ms long 3D gradient blips, leading to a total pulse duration of 0.96 ms.The starting phases of the pulse design and the regularization parameters (4.64/107.97 for TP/UP) have been adopted from L-curve analysis with 200 random initial phase combinations from our previous work. 31The source code, the used parameters, and the 3D relative B + 1 datasets can be found at: https: //github.com/chaigner/FRobUP_body.
In this work, three distinct types of TP/UP were designed and evaluated relative to the Larmor frequency of water protons at 7T of 298 MHz: (i) TP S /UP S optimized for a single frequency at 0 Hz, (ii) TP D /UP D optimized for two frequency peaks (0 and 1010 Hz), and (iii) broadband TP BB /UP BB optimized for seven frequency peaks ranging from −178 to 1129 Hz.It is important to note that only the specified frequencies are explicitly considered during the optimization process.All other frequencies are treated as a "don't care" region, allowing for greater flexibility and control over the pulse design.The following symbols will be used to differentiate between the different frequencies in this work: f S (single-frequency; 0 Hz), f D (double-frequency; 1010 and 0 Hz), and f BB (broadband; 1129, 1010, 772, 576, 115, 0, and -178 Hz).
TP were computed individually for each B + 1 -dataset while UP were computed using all 22 B + 1 -maps. 31Both pulse types were designed to generate a homogenous FA distribution across the heart volume for different frequencies.ΔB 0 offsets were added to all spatial points in the optimization to incorporate up to seven frequencies, including water and six fat peaks. 39The measured B + 1 and synthetic uniform ΔB 0 maps at these frequencies were stacked and fed into the pulse design algorithm, following the same procedure as for the UP design.For instance, in the case of UP BB , the design library contains 22 B + 1 and 154 ΔB 0 datasets, resulting from 22 volunteers and seven ΔB 0 offsets.
The mean computation time required for generating a TP ranged between 20 s (TP S ) and 99 s (TP BB ), while the computation time for the UP ranged between 2 min (UP S ) and 10 min (UP BB ).The optimization time for individual volunteers varied from 14 to 32 s for TP S and 49 to 153 s for TP BB .This results in approximately 10 to 15 min of adjustment time for the whole pipeline to perform subject-tailored pTx of the human heart.This includes data acquisition (3 min 25 s), offline non-Cartesian reconstruction (1 min), manual 3D region of interest (ROI) placement (3 min), pulse design (1-2 min), and variable extra time for checking the results.
The performance of the pulses was assessed using the FA coefficient of variation (CV) within the 3D heart volumes and the integrated RF power.The RF amplitudes were scaled to achieve an average FA of 10 degrees at a ΔB 0 offset of 0 Hz.

Simulation studies
A simulation study examined the impact of pulse duration on TP and UP performance.Each pulse was simulated 19 times, using linearly scaled pulse durations from 0.384 ms to 3.840 ms, with RF adjustments to maintain the FA.FA simulations were conducted for all testcases with 201 ΔB 0 offsets (−2500 to 1500 Hz).It is important to note that re-optimizing the pulse for a longer or shorter pulse duration could necessitate a different number of kT points, potentially impacting pulse performance.The mean and SD of the FA in all heart volumes was calculated for each pulse type, pulse duration, and ΔB 0 offset.Based on the mean FA values for the different ΔB 0 offsets, the transmit bandwidth was determined where the pulses achieved a mean FA exceeding 9 • , corresponding to a maximal deviation of 10% from the target FA of 10 • .

Statistical analysis
To assess statistical significance, we employed the Mann-Whitney U-test, assuming independent samples FA predictions of tailored and universal pTx pulses (TP S /UP S ) optimized for water (f S = 0 Hz) and evaluated at 0 Hz (water) and 1010 Hz (main fat peak at 7T). (A) Sagittal views of the 3D volume illustrate the FA homogeneity at the water frequency and the spatial variations and dropouts observed at the fat frequency.(B) Quantitative assessment of predicted FA homogeneity across the entire target volumes of all datasets evaluated at 0 Hz and 1010 Hz.Statistically significant outcomes are denoted by a star (*), while non-statistically significant results are indicated as "NS".(C) Model fat and water spectrum indicating which frequencies have been optimized in the pulse design.Peak numbering (1), (2), etc. is taken from Hamilton et al. 40 from two groups with continuous distributions and equal medians.The significance level was set to 5%.

Experimental validation of optimized pulses
The 3D RPE gradient echo (GRE) scans were acquired in three phantoms (rapeseed oil, CuSu doped water, and polyvinylpyrrolidone [PVP]) and five testcases to validate the efficacy of TP S /TP BB using the following parameters: TE/TR = 1.58 ms/2.75 ms, FOV = 256 x 256 x 256 mm 3 , voxel-size = 4 x 4 x 4 mm, TA = 135 s.While the water/oil phantoms were used to demonstrate the performance of TP BB , a set of 10 PVP phantom scans were acquired by manually setting the resonance frequency from −2000 to 1000 Hz (w.r.t. the vendor supplied frequency scout) to test the broadband properties of TP S , TP D , and TP BB (see Figure S1).Additionally, in two additional testcases, higher resolution 3D RPE GRE scans were acquired with TP S , TP BB , and UP BB using the following parameters: TE/TR = 1.58 ms/3.38 ms, FOV = 250 x 250 x 250 mm 3 , voxel-size = 2 x 2 x 2 mm, TA = 221 s.Note that all RF pulses were implemented with the same peak RF voltage of 104 V to stay below the power-per-channel limits of our specific absorption rate (SAR) supervision using the minimal TE/TR combination for each sequence, resulting in potentially different FAs for the different pulses.

RESULTS
Figure 1 presents the FA predictions of single-frequency optimized TP S /UP S with a fixed pulse duration of 0.96 ms FA predictions of broadband tailored (TP BB ) and universal (UP BB ) pulses evaluated at 0 Hz (water) and 1010 Hz (fat).(A) Sagittal views of the same slices as in Figure 1, demonstrating FA homogeneity at both water and fat frequencies.(B) Quantitative assessment of predicted FA homogeneity across all target volumes (shown in Figure 1) assessed at 0 Hz and 1010 Hz revealing low CV values of below 23% for TP BB and UP BB .Statistically significant outcomes are denoted by a star (*), while non-statistically significant results are indicated as "NS".(C)Model fat and water spectrum indicating which frequencies have been optimized in the pulse design.Peak numbering (1), (2), etc. is taken from Hamilton et al. 40 evaluated at 0 Hz and 1010 Hz (main fat peak at 7T). Figure 1A displays sagittal views of the 3D volume, highlighting the FA homogeneity at the water frequency but also the significant spatial variations and dropouts at the fat frequency.Figure 1B provides a quantitative assessment of FA homogeneity across the heart volumes of all datasets.Across the 29 datasets, the evaluation at 0 Hz yielded low CV values, with a mean of 6.4%/12.8%for TP S /UP S and 38%/49% at 1010 Hz. Figure 1C provides a schematic model fat and water spectrum (the signal amplitude is for illustrative purposes only and was not considered in the pulse design) indicating which frequencies were used in the optimization. 40igure 2 presents the FA predictions of broadband optimized TP BB /UP BB with a fixed pulse duration of 0.96 ms evaluated at 0 and 1010 Hz. Figure 2A displays sagittal views of the 3D volume, highlighting the FA homogeneity at the water and fat frequency.Figure 2B provides a quantitative assessment of FA homogeneity across the entire target volumes of all datasets.The TP BB /UP BB evaluation at 0 Hz yielded low CV values, with a mean of 10%/15.4%.In contrast to the results shown in Figure 1, low CV values were also observed when evaluating the TP BB /UP BB at 1010 Hz, with a mean of 10.4%/15.3%. Figure 2C provides a model fat and water spectrum indicating which frequencies were used in the optimization.The spatial phase profile evaluated at 0 Hz and 1010 Hz after the application of TP BB is shown in Figure S2.
Figure 3 illustrates the performance of various TP/UP optimized for different resonance frequencies (f S /f D /f BB ) with pulse durations ranging from 0.384 to 3.840 ms. Figure 3A displays a representative sagittal slice of testcase #2, showcasing the TP/UP evaluations with fixed pulse duration of 0.96 ms at three resonance frequencies (0, 576, Performance analysis of tailored and universal pTx pulses (TP/UP) with different pulse durations optimized for specific frequencies (f S , f D and f BB ).(A) The sagittal slice of testcase #2 shows the evaluation of TP/UP pulses with fixed pulse duration of 0.96 ms at three frequencies (0, 576, and 1010 Hz).TP S /UP S and TP D /UP D exhibit inhomogeneous FA predictions for frequencies not included in the optimization.Broadband pulses demonstrate consistent FA predictions across all frequencies.(B) Mean FA and SD within the target volume for all five testcases, focusing on a ΔB 0 interval from −500 to 1500 Hz (small circles mark the evaluated frequency).Broadband pulses yield a FA distribution with minimal deviations within the 1307 Hz frequency range.(C) Transmit bandwidth where TP/UP pulses, with pulse durations (the entire kT-points train) ranging from 0.384 to 3.84 ms, achieve a mean FA exceeding 9 • within the heart region.Broadband pulses demonstrate the broadest bandwidth, thus outperforming TP S /UP S regarding off-resonance variations.and 1010 Hz).As expected, TP S /UP S and TP D /UP D achieve FA homogeneity only at those frequencies they were optimized for, while the broadband pulses result in consistent and homogeneous FA predictions across all frequencies.Figure S3 shows the evaluation for all seven frequencies, while S4 exhibits three orthogonal planes for two frequencies supporting the summarized findings in Figure 3A.
Figure 3B presents the mean and SD of the FA within the target volume for all seven testcases.The target FAs for each pulse type are shown by black crosses.Notably, TP D and UP D shows an overshoot for ΔB 0 values between 0 Hz and 1010 Hz.In contrast, TP BB /UP BB yield low FA variations across all target FAs, with maximum absolute deviations of less than 0.5 • .
Figure 3C depicts the computed transmit bandwidth where TP/UP, with pulse durations ranging from 0.384 to 3.840 ms, achieve a mean FA exceeding 9 • .For example, at a pulse duration of 0.96 ms, the mean transmit bandwidth (A) Quantitative evaluation of FA predictions in target regions using TP and UP with a fixed pulse duration of T = 0.96 ms.Results across 27 volunteers demonstrate poor FA homogeneity for frequencies other than the optimized frequency.Similarly, UPs exhibit higher CV values but follow the same trend.Robustness across all frequencies is achieved with pulses optimized for all seven frequencies.These findings highlight the importance of broadband pulse optimization for consistent FA predictions across different frequencies.(B) Relative RF power and RF peak amplitude overview for different pulse types, revealing increased requirements for UP compared to TP. Statistically significant outcomes are denoted by a star (*), while non-statistically significant results are indicated as "NS".was 925 Hz for TP S and 591 Hz for UP S .In contrast, the TP BB /UP BB yielded a much higher transmit bandwidth of 1625/1768 Hz.Please note that TP D /UP D can exhibit superior performance in terms of transmit bandwidth.However, the FA homogeneity of TP D /UP D consistently fell short of that achieved by TP BB /UP BB (as depicted in Figure 3B).
Figure 4 presents the quantitative evaluation of FA predictions in the target regions of TP/UP with a fixed pulse duration of 0.96 ms.Arrows and dashed boxes indicate cases where the frequencies of the evaluation match the optimization.In summary, robustness across all frequencies (f BB ) was only achieved with pulses optimized for all seven frequencies, resulting in mean CV values of 10.8% (TP BB ) and 15.6% (UP BB ).Consequently, TP BB /UP BB demonstrate favorable performance for f S /f D /f BB , while TP S /UP S perform well only for f S and exhibit increased CVs for f D /f BB .Figure 4B provides an overview of the relative RF power and peak RF amplitude requirements for the different TP/UP.The RF and gradient The 3D GRE images during free breathing, showcasing the improved signal homogeneity of the broadband TP bb in areas with potentially fatty tissue and strong ΔB 0 variations (indicated by arrows and zoomed regions).
waveforms are shown in Figure S5.There is no significant disparity in RF power between the different TP, but UP consistently seems to require more power than TP.For instance, UP BB requires approximately 2.3-times (2.0-times) more RF power compared to TP S (TP BB ), respectively.
Figure 5 displays the 3D GRE images acquired during free breathing for three of the testcases utilizing TP S , TP BB , and UP BB using the same peak RF voltage of 103.9 V.The lower RF efficiency of UP BB contributes to reduced signal, but it also offers the advantage of being calibration-free, eliminating the need for approximately 15 min of adjustment time.Notably, compared to the single-frequency optimized TP S , TP BB and UP BB exhibit a more homogeneous signal in volunteers with potentially fatty tissue surrounding the heart (indicated by arrows) and in areas with strong ΔB 0 variations.

DISCUSSION
This study aimed to investigate the impact of resonance frequency differences on dynamic kT-points TP/UP and to research and evaluate a broadband TP/UP design more robust to chemical and ΔB 0 shifts in a cohort of 29 volunteers.The findings revealed that pulses designed based on the water frequency exhibited favorable performance only for water-like tissue, i.e., for 500 Hz around the water resonance frequency for 0.96 ms long pulses.Notably, the proposed broadband pulses effectively compensated for the differences in the FA homogeneity for resonance covering an extensive frequency range of 1307 Hz.While TP BB requires similar RF power requirements to TP S or TP D , universal pulses required more RF power than TP.For instance, UP BB requires approximately twice the RF power compared to TP BB .
This study utilized a 3D B + 1 -mapping method to acquire relative and channel-specific B + 1 -maps, taking advantage of the RPE's short acquisition time and motion robustness.However, the resulting B + 1 -maps are biased due to the assumption of equal magnitudes between transmit and receive channels. 11Despite this limitation, the mapping method proved effective and has been successfully applied in various pTx applications at 7T, including calibration-free pTx via 3D UP for shallow breathing 31 and respiration robust TP/UP of the human heart at 7T 30 and high-resolution fat/water imaging in the heart using static pTx. 5 Tailored pTx in the human body can be challenging and time-consuming, particularly for the excitation of different respiration states or multiple resonance frequencies, due to increased computational demands and potential motion between B + 1 -mapping and pTx data acquisition. 8,12,30The proposed broadband UP BB provides a robust alternative to TP BB for a 1307 Hz frequency range, including all six primary fat and the water peak, with acceptable FA homogeneity.On average, the broadband UP approach saves roughly 10-15 min of adjustment times for B + 1 -acquisition (3:35 min), non-Cartesian reconstruction (1 min), manual ROI drawing (3 min), and pulse design and quality checks (up to 5 min).
In our previous works, 12,41 relatively short pulse durations of 0.96 ms for dynamic pTx pulses effectively circumvented the impact of ΔB 0 off-resonance effects in the human heart of up to 350 Hz.This eliminates the need for additional time-consuming calibration processes, such as prolonged measurements of volunteer-specific ΔB 0 maps.However, covering the 1307 Hz frequency range required for simultaneous fat and water excitation proved impractical due to FA limitations, necessitating the research and development of the proposed broadband dynamic pTx pulse design.
A potential extension of this work would be to use GRAPE optimization instead of kT-points and focusing the ΔB 0 robustness target region specifically to human heart, as demonstrated in broadband GRAPE UPs for the human brain. 37This could further reduce RF pulse duration, energy requirements, and/or improve homogeneity.
An unexpected yet consistent finding emerged across all testcases.The results of the two-frequency pulses exhibited an overshoot in FA predictions.While this trend was consistently observed in all testcases, drawing a broad conclusion regarding this effect would necessitate a more comprehensive range of testcases, exceeding the scope of this study.This work has two major limitations.First, the absence of fat-water separated in vivo images limited our assessment of the observed excitation performance of broadband pulses.Second, the lack of absolute B + 1 information in the experimental scans restricted our approach to penalize the integrated relative RF power instead of the integrated actual RF power or the RF peak voltage.While the performed experiments primarily aimed at qualitatively validating relative B + 1 predictions, absolute B + 1 measurements are crucial for accurate FA quantification or designing large FA pulses.Therefore, it is essential to acknowledge that exact FA values remain unknown despite our understanding of the spatial B + 1 patterns that can be scaled in the small tip angle regime.Future analyses will thus focus on integrating kT-point pulses into time-resolved 3D sequences, with specific attention given to techniques to achieve high-quality cardiac images at 7T. 5

CONCLUSIONS
This study presents two novel advancements in tailored and universal pulse design: simultaneous fat/water excitation for future fat/water imaging (e.g., Dixon) and broadband pulses robust to ΔB 0 inhomogeneities without requiring measured ΔB 0 information.