Universal Pulses Research Articles

Design of calibration-free RF pulses for T -weighted single-slab 3D turbo-spin-echo sequences at 7T utilizing parallel transmission.

T -weighted turbo-spin-echo (TSE) sequences are a fundamental technique in brain imaging but suffer from field inhomogeneities at ultra-high fields. Several methods have been proposed to mitigate the problem, but were limited so far to nonselective three-dimensional (3D) measurements, making short acquisitions difficult to achieve when targeting very high resolution images, or needed additional calibration procedures, thus complicating their application. Slab-selective excitation pulses were designed for flexible placement utilizing the concept of k -spokes. Phase-coherent refocusing universal pulses were subsequently optimized with the Gradient Ascent Pulse Engineering algorithm and tested in vivo for improved signal homogeneity. Implemented within a 3D variable flip angle TSE sequence, these pulses led to a signal-to-noise ratio (SNR) improvement ranging from 10%to 30% compared to a two-dimensional (2D) T2w TSE sequence employing -shimmed pulses. field inhomogeneities could be mitigated and artifacts from deviations reduced. The concept of universal pulses was successfully applied. We present a pulse design method which provides a set of calibration-free universal pulses (UPs) for slab-selective excitation and phase-coherent refocusing in slab-selective TSE sequences.

Parallel-transmission spatial spectral pulse design with local specific absorption rate control: Demonstration for robust uniform water-selective excitation in the human brain at 7 T.

To propose a novel method for parallel-transmission (pTx) spatial-spectral pulse design and demonstrate its utility for robust uniform water-selective excitation (water excitation) across the entire brain. Our design problem is formulated as a magnitude-least-squares minimization with joint RF and k-space optimization under explicit specific-absorption-rate constraints. For improved robustness against off-resonance effects, the spectral component of the excitation target is prescribed to have a water passband and a fat stopband. A two-step algorithm was devised to solve our design problem, with Step 1 aiming to solve a reduced problem to find a sensible start point for Step 2 to solve the original problem. The efficacy of our pulse design was evaluated in simulation, phantom, and human experiments using the commercial Nova head coil. Universal pulses were also designed based on a 10-subject training data set to demonstrate the utility of our method for plug-and-play pTx. For kT-points and spiral nonselective parameterizations, our design method outperformed the pTx interleaved binomial approach, reducing RMS error by up to about 35% for water excitation and about 97% for fat suppression (over a 200-Hz bandwidth) while decreasing local specific absorption rate by about 30%. Both our subject-specific and universal pulses improved water excitation, restoring signal loss in the cerebellum while suppressing fat signal even in regions of large susceptibility-induced off-resonances. Demonstrated useful for 4D (3D spatial, one-dimensional spectral) pTx spatial-spectral pulse design, our proposed method provides an effective solution for robust volumetric uniform water excitation, holding a promise to many ultrahigh-field applications.

Calibration‐free whole‐brain CEST imaging at 7T with parallel transmit pulse design for saturation homogeneity utilizing universal pulses (PUSHUP)

Calibration‐free whole‐brain CEST imaging at 7T with parallel transmit pulse design for saturation homogeneity utilizing universal pulses (PUSHUP)

Accelerated mapping and robust parallel transmit pulse design for heart and prostate imaging at 7 T.

To investigate the impact of reduced k-space sampling on mapping and the resulting impact on phase shimming and dynamic/universal parallel transmit (pTx) RF pulse design. Channel-wise 3D maps were measured at 7 T in 35 and 23 healthy subjects for the heart and prostate region, respectively. With these maps, universal phase shims optimizing homogeneity and efficiency were designed for heart and prostate imaging. In addition, universal 4kT-point pulses were designed for the heart. Subsequently, individual phase shims and individual 4kT-pulses were designed based on maps with different acceleration factors and tested on the original maps. The performance of the pulses was compared by evaluating their coefficients of variation (CoV), efficiencies and specific energy doses (SED). Furthermore, validation measurements were carried out for one heart and one prostate subject. For both organs, the universal phase shims showed significantly higher efficiencies and lower CoVs compared to the vendor provided default shim, but could still be improved with individual phase shims based on accelerated maps (acquisition time = 30 s). In the heart, the universal 4kT-pulse achieved significantly lower CoVs than tailored phase shims. Tailored 4kT-pulses based on accelerated maps resulted in even further reduced CoVs or a 2.5-fold reduction in SED at the same CoVs as the universal 4kT-pulse. Accelerated maps can be used for the design of tailored pTx pulses for prostate and cardiac imaging at 7 T, which further improve homogeneity, efficiency, or SED compared to universal pulses.

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

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. Relative 3D -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 -maps, and UPs were calculated using 22 -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 -predictions. 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. Broadband TP and UP can be used for homogeneous excitation of the heart volume across a 1300 Hz frequency range, including the water and the main six fat peaks, or with longer pulse durations and higher FAs for a smaller transmit bandwidth. Moreover, despite large inter-volunteer variations, broadband UP can be used for calibration-free 3D heart FA homogenization in time-critical situations.

What can we gain from subpopulation universal pulses? A simulation-based study.

The aim of the study was to explore a novel methodology for designing universal pulses (UPs) that balances the benefits of a calibration-free approach with subject-specific online pulse design. The proposed method involves segmenting the population into subpopulations with variability in anatomical shapes and positions reduced to 75%, 50%, and 25% of their original values while keeping the mean values unchanged. An additional 25% extreme case with a large volume of interest and shifted position was included. For each group, a 5kT-points universal inversion pulse was designed and assessed by the normalized root mean square error (NRMSE) on the target longitudinal magnetization profile. The performance was compared to the conventional one-size-fits-all approach. A total of 132 electromagnetic simulations were executed to generate representative anatomies and specific absorption rate (SAR) distributions in a three-dimensional parameter space comprised of head breadth, head length, and Y-shift. The 99.9th percentile on the peak local SAR distribution was utilized to establish an intersubject variability safety margin. UPs designed for subpopulations with decreased head shape and position variability reduced the anatomical safety margin by up to 20%. Furthermore, when a head was significantly different to the average case, the proposed approach improved the inversion homogeneity by up to 24%, compared to the conventional one-size-fits-all approach. Subpopulation UPs present an opportunity to improve the homogeneity and reduce anatomical SAR safety margins at 7T without additional acquisition time for calibration.

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

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

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

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

Band-selective universal 90° and 180° rotation pulses covering the aliphatic carbon chemical shift range for triple resonance experiments on 1.2 GHz spectrometers

Biomolecular NMR spectroscopy requires large magnetic field strengths for high spectral resolution. Today’s highest fields comprise proton Larmor frequencies of 1.2 GHz and even larger field strengths are to be expected in the future. In protein triple resonance experiments, various carbon bandwidths need to be excited by selective pulses including the large aliphatic chemical shift range. When the spectrometer field strength is increased, the length of these pulses has to be decreased by the same factor, resulting in higher rf-amplitudes being necessary in order to cover the required frequency region. Currently available band-selective pulses like Q3/Q5 excite a narrow bandwidth compared to the necessary rf-amplitude. Because the maximum rf-power allowed in probeheads is limited, none of the selective universal rotation pulses reported so far is able to cover the full ^{13}C aliphatic region on 1.2 GHz spectrometers. In this work, we present band-selective 90° and 180° universal rotation pulses (SURBOP90 and SURBOP180) that have a higher ratio of selective bandwidth to maximum rf-amplitude than standard pulses. Simulations show that these pulses perform better than standard pulses, e. g. Q3/Q5, especially when rf-inhomogeneity is taken into account. The theoretical and experimental performance is demonstrated in offset profiles and by implementing the SURBOP pulses in an HNCACB experiment at 1.2 GHz.

Experimental Demonstration of Composite Pulses on IBM’s Quantum Computer

We perform comprehensive experimental tests of various composite pulse sequences using one of the open-access IBM quantum processors, based on superconducting transmon qubits. We implement explicit pulse control of the qubit by making use of the opportunity of low-level access to the backend, provided by IBM Quantum. We obtain the excitation profiles for a huge variety of broadband, narrowband, and passband composite pulses, producing any prechosen target probabilities, ranging from zero to one. We also test universal composite pulses that compensate errors in any experimental parameter. In all experiments, we find excellent agreement between theoretical and experimental excitation profiles. This proves both the composite pulses as a very efficient and flexible quantum control tool and the high quality of the IBM quantum processor. As an extreme example, we test and observe a pronounced narrowband excitation profile for a composite sequence of as many as 1001 pulses.

Universal pulses for homogeneous excitation using single channel coils

PurposeUniversal Pulses (UPs) are excitation pulses that reduce the flip angle inhomogeneity in high field MRI systems without subject-specific optimization, originally developed for parallel transmit (PTX) systems at 7 T. We investigated the potential benefits of UPs for single channel (SC) transmit systems at 3 T, which are widely used for clinical and research imaging, and for which flip angle inhomogeneity can still be problematic. MethodsSC-UPs were designed using a spiral nonselective k-space trajectory for brain imaging at 3 T using transmit field maps (B1+) and off-resonance maps (B0) acquired on two different scanner types: a ‘standard’ single channel transmit system and a system with a PTX body coil.The effect of training group size was investigated using data (200 subjects) from the standard system. The PTX system was used to compare SC-UPs to PTX-UPs (15 subjects). In two additional subjects, prospective imaging using SC-UP was studied. ResultsAverage flip angle homogeneity error fell from 9.5 ± 0.5 % for ‘default’ excitation to 3.0 ± 0.6 % using SC-UPs trained over 50 subjects. Performance of the UPs was found to steadily improve as training group size increased, but stabilized after ~15 subjects.On the PTX-enabled system, SC-UPs again outperformed default excitation in simulations (4.8 ± 0.6 % error versus 10.6 ± 0.8 % respectively) though greater homogenization could be achieved with PTX-UPs (3.9 ± 0.6 %) and personalized pulses (SC-PP 3.6 ± 1.0 %, PTX-PP 2.9 ± 0.6 %).MP-RAGE imaging using SC-UP resulted in greater separation between grey and white matter signal intensities than default excitation. ConclusionsSC-UPs can improve excitation homogeneity in standard 3 T systems without further calibration and could be used instead of a default excitation pulse for nonselective neuroimaging at 3 T.

OTUP workflow: target specific optimization of the transmit k-space trajectory for flexible universal parallel transmit RF pulse design.

To optimize transmit k-space trajectories for a wide range of excitation targets and to design "universal pTx RF pulses" based on these trajectories. Transmit k-space trajectories (stack of spirals and SPINS) were optimized to best match different excitation targets using the parameters of the analytical equations of spirals and SPINS. The performances of RF pulses designed based on optimized and non-optimized trajectories were compared. The optimized trajectories were utilized for universal pulse design. The universal pulse performances were compared with subject specific tailored pulse performances. The OTUP workflow (optimization of transmit k-space trajectories and universal pulse calculation) was tested on three test target excitation patterns. For one target (local excitation of a central area in the human brain) the pulses were tested in vivo at 9.4 T. The workflow produced appropriate transmit k-space trajectories for each test target. Utilization of an optimized trajectory was crucial for the pulse performance. Using unsuited trajectories diminished the performance. It was possible to create target specific universal pulses. However, not every test target is equally well suited for universal pulse design. There was no significant difference in the in vivo performance between subject specific tailored pulses and a universal pulse at 9.4 T. The proposed workflow further exploited and improved the universal pulse concept by combining it with gradient trajectory optimization for stack of spirals and SPINS. It emphasized the importance of a well suited trajectory for pTx RF pulse design. Universal and tailored pulses performed with a sufficient degree of similarity in simulations and a high degree of similarity in vivo. The implemented OTUP workflow and the B0 /B1+ map data from 18 subjects measured at 9.4 T are available as open source (https://github.com/ole1965/workflow_OTUP.git).

Respiration induced changes and their impact on universal and tailored 3D kT-point parallel transmission pulses for 7T cardiac imaging.

Human heart imaging at ultra-high fields is highly challenging because of respiratory motion-induced artefacts and spatially heterogeneous profiles. This work demonstrates that respiration resolved 3D -maps can be used with a dedicated tailored and universal parallel transmission (pTx) pulse design to compensate respiration related changes in subjects performing shallow and deep breathing (SB/DB). Three-dimensional (3D) -maps of the thorax were acquired in 31 subjects under SB and in 15 subjects under SB and DB. Different universal and tailored non-selective pTx pulses were designed from non-respiration resolved (NRR) and respiration resolved (RR) reconstructions of the SB/DB -maps. The performance of all pulses was tested with RR-SB/DB -maps. Respiration-robust tailored and universal pulses were applied in vivo in 5 subjects at 7T in 3D gradient-echo free-breathing scans. All optimized pTx pulses performed well for SB. For DB, however, only the universal and the tailored respiration-robust pulses achieved homogeneous flip angles (FAs) in all subjects and across all respiration states, whereas the tailored respiration-specific pulses resulted in a higher FA variation. The respiration-robust universal pulse resulted in an average coefficient of variation in the FA maps of 12.6% compared to 8.2% achieved by tailored respiration-robust pulses. In vivo measurements at 7T demonstrate the benefits of using respiration-robust pulses for DB. Universal and tailored respiration-robust pTx pulses based on RR -maps are highly preferred to achieve 3D heart FA homogenization at 7T when subjects perform DB, whereas universal and tailored pulses based on NRR -maps are sufficient when subjects perform SB.

Standardized universal pulse: A fast RF calibration approach to improve flip angle accuracy in parallel transmission.

In parallel transmission (pTX), subject-tailored RF pulses allow achieving excellent flip angle (FA) accuracy but often require computationally extensive online optimizations, precise characterization of the static field ( ), and the transmit RF field ( ) distributions. This costs time and requires expertise from the MR user. Universal pulses (UPs) have been proposed to reduce this burden, yet, with a penalty in FA accuracy. This study introduces the concept of standardized universal pulses (SUPs), where pulses are designed offline and adjusted to the subject through a fast online calibration scan. A SUP is designed offline using a so-called standardized database, wherein each map has been normalized to a reference transmit RF field distribution. When scanning a new subject, a 3-slice acquisition (scan time s) is performed and used to adjust the SUP to the subject through a linear transform. SUP performance was assessed at 7T with simulations by computing the FA-normalized root mean square error (FA-NRMSE) and the FA pattern stability as measured by the average and coefficient of variation of the FA across 15 control subjects, along with in vivo experiments using an MP2RAGE sequence implementing the SUP variant for the FLASH readout. Adjusted SUP improved the FA-NRMSE (8.8 for UP vs. 7.1 for adjusted SUP). Experimentally in vivo, this translated in an improved signal homogeneity and more accurate quantification using MP2RAGE. The proposed SUP approach improves excitation accuracy (FA-NRMSE) while preserving the same offline pulse design principle as offered by UPs.

Calibration-free pTx of the human heart at 7T via 3D universal pulses.

MRI at ultra-high fields in the human body is highly challenging and requires lengthy calibration times to compensate for spatially heterogeneous profiles. This study investigates the feasibility of using pre-computed universal pulses for calibration-free homogeneous 3D flip angle distribution in the human heart at 7T. Twenty-two channel-wise 3D data sets were acquired under free-breathing in 19 subjects to generate a library for an offline universal pulse (UP) design (group 1: 12 males [M] and 7 females [F], 21-66 years, 19.8-28.3 kg/m2 ). Three of these subjects (2M/1F, 21-33 years, 20.8-23.6 kg/m2 ) were re-scanned on different days. A 4kT-points UP optimized for the 22 channel-wise 3D data sets in group 1 (UP22-4kT) is proposed and applied at 7T in 9 new and unseen subjects (group 2: 4M/5F, 25-56 years, 19.5-35.3 kg/m2 ). Multiple tailored and universal static and dynamic parallel-transmit (pTx) pulses were designed and evaluated for different permutations of the data sets in group 1 and 2. The proposed UP22-4kT provides low variation in all subjects, seen and unseen, without severe signal drops. Experimental data at 7T acquired with UP22-4kT shows comparable image quality as data acquired with tailored-4kT pulses and demonstrates successful calibration-free pTx of the human heart. UP22-4kT allows for calibration-free homogeneous flip angle distributions across the human heart at 7T. Large inter-subject variations because of sex, age, and body mass index are well tolerated. The proposed universal pulse removes the need for lengthy (10-15 min) calibration scans and therefore has the potential to bring body imaging at 7T closer to the clinical application.

Can 7T MPRAGE match MP2RAGE for gray-white matter contrast?

Ultra-High Field (UHF) MRI provides a significant increase in Signal-to-Noise Ratio (SNR) and gains in contrast weighting in several functional and structural acquisitions. Unfortunately, an increase in field strength also induces non-uniformities in the transmit field (B1+) that can compromise image contrast non-uniformly. The MPRAGE is one of the most common T1 weighted (T1w) image acquisitions for structural imaging. It provides excellent contrast between gray and white matter and is widely used for brain segmentation. At 7T, the signal non-uniformities tend to complicate this and therefore, the self-bias-field corrected MP2RAGE is often used there. In both MPRAGE and MP2RAGE, more homogeneous image contrast can be achieved with adiabatic pulses, like the TR-FOCI inversion pulse, or special pulse design on parallel transmission systems, like Universal Pulses (UP). In the present study, we investigate different strategies to improve the bias-field for MPRAGE at 7T, comparing the contrast and GM/WM segmentability against MP2RAGE. The higher temporal efficiency of MPRAGE combined with the potential of the user-friendly UPs was the primary motivation for this MPRAGE-MP2RAGE comparison. We acquired MPRAGE data in six volunteers, adding a k-space shutter to reduce scan time, a kt-point UP approach for homogeneous signal excitation, and a TR-FOCI pulse for homogeneous inversion. Our results show remarkable signal contrast improvement throughout the brain, including regions of low B1+ such as the cerebellum. The improvements in the MPRAGE were largest following the introduction of the UPs. In addition to the CNR, both SNR and GM/WM segmentability were also assessed. Among the MPRAGEs, the combined strategy (UP + TR-FOCI) yielded highest SNR and showed highest spatial similarity between GM segments to the MP2RAGE. Interestingly, the distance between gray and white matter peaks in the intensity histograms did not increase, as better pulses and higher SNR especially benefitted the (cerebellar) gray matter. Overall, the gray-white matter contrast from MP2RAGE is higher, with higher CNR and higher intensity peak distances, even when scaled to scan time. Hence, the extra acquisition time for MP2RAGE is justified by the improved segmentability.

Local excitation universal parallel transmit pulses at 9.4T.

To demonstrate that the concept of "universal pTx pulses" is applicable to local excitation applications. A database of B0 / maps from eight different subjects was acquired at 9.4T. Based on these maps, universal pulses that aim at local excitation of the visual cortex area in the human brain (with a flip angle of 90° or 7°) were calculated. The remaining brain regions should not experience any excitation. The pulses were designed with an extension of the "spatial domain method." A 2D and a 3D target excitation pattern were tested, respectively. The pulse performance was examined on non-database subjects by Bloch simulations and in vivo at 9.4T using a GRE anatomical MRI and a presaturated TurboFLASH mapping sequence. The calculated universal pulses show excellent performance in simulations and in vivo on subjects that were not contained in the design database. The visual cortex region is excited, while the desired non-excitation areas produce the only minimal signal. In simulations, the pulses with 3D target pattern show a lack of excitation uniformity in the visual cortex region; however, in vivo, this inhomogeneity can be deemed acceptable. A reduced field of view application of the universal pulse design concept was performed successfully. The proposed design approach creates universal local excitation pulses for a flip angle of 7° and 90°, respectively. Providing universal pTx pulses for local excitation applications prospectively abandons the need for time-consuming subject-specific B0 / mapping and pTx-pulse calculation during the scan session.

Coherent control techniques for two-state quantum systems: A comparative study

We evaluate various sources of errors that occur when attempting to produce a specified coherent change of a two-state quantum system using six popular coherent control techniques: resonant excitation, adiabatic following, composite adiabatic passage, universal composite pulses, shortcut to adiabaticity, and single-shot shaped pulses. As error sources, we consider spatial intensity distribution, transit time variation, inhomogeneous broadening, Doppler broadening, unwanted chirp, and shape errors, as well as errors generated by counter-rotating terms. For the various error types, different techniques emerge as the best performers, but overall we find that universal composite pulses perform most consistently and are most resilient to errors compared to all other procedures.

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

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

Second order phase dispersion by optimized rotation pulses

We show that the duration of broadband universal control pulses can be halved by choosing control targets with a quadratic function of phase dispersion. This class of control pulses perform a broadband universal rotation around an axis, in the Bloch sphere representation of two-level systems, given by this phase dispersion function. We present an effective optimal control method to avoid the problem of convergence to local extrema traps.