Joint design of kT-points trajectories and RF pulses under explicit SAR and power constraints in the large flip angle regime

Bayesian optimization of gradient trajectory for parallel-transmit pulse design

PURPOSE

Spoke pulses improve excitation homogeneity in parallel-transmit MRI. We propose an efficient global optimization algorithm, Bayesian optimization of gradient trajectory (BOGAT), for single-slice and simultaneous multislice imaging.

THEORY AND METHODS

BOGAT adds an outer loop to optimize kT-space positions. For each position, the RF coefficients are optimized (e.g., with magnitude least squares) and the cost function evaluated. Bayesian optimization progressively estimates the cost function. It automatically chooses the kT-space positions to sample, to achieve fast convergence, often coming close to the globally optimal spoke positions. We investigated the typical features of spokes cost functions by a grid search with field maps comprising 85 slabs from 14 volunteers. We tested BOGAT in this database, and prospectively in a phantom and in vivo. We compared the vendor-provided Fourier transform approach with the same magnitude least squares RF optimizer.

RESULTS

The cost function is nonconvex and seen empirically to be piecewise smooth with discontinuities where the underlying RF optimum changes sharply. BOGAT converged to within 10% of the global minimum cost within 30 iterations in 93% of slices in our database. BOGAT achieved up to 56% lower flip angle RMS error (RMSE) or 55% lower pulse energy in phantoms versus the Fourier transform approach, and up to 30% lower RMSE and 29% lower energy in vivo with 7.8 s extra computation.

CONCLUSION

BOGAT efficiently estimated near-global optimum spoke positions for the two-spoke tests, reducing flip-angle RMSE and/or pulse energy in a computation time (˜10 s), which is suitable for online optimization.

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

PURPOSE

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.

METHODS

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.

RESULTS

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.

CONCLUSION

Subpopulation UPs present an opportunity to improve theB 1 + $$ {\mathrm{B}}_1^{+} $$ homogeneity and reduce anatomical SAR safety margins at 7T without additional acquisition time for calibration.

Whole-liver flip-angle shimming at 7 T using parallel-transmit kT -point pulses and Fourier phase-encoded DREAM B 1 + mapping

PURPOSE

To obtain homogeneous signal throughout the human liver at 7 T. Flip angle (FA) shimming in 7T whole-liver imaging was performed through parallel-transmit kT -point pulses based on subject-specific multichannel absoluteB 1 + $$ {\mathrm{B}}_1^{+} $$ maps from Fourier phase-encoded dual refocusing echo acquisition mode (PE-DREAM).

METHODS

The optimal number of Fourier phase-encoding steps for PE-DREAMB 1 + $$ {\mathrm{B}}_1^{+} $$ mapping was determined for a 7T eight-channel parallel-transmission system. FA shimming experiments were performed in the liver of 7 healthy subjects with varying body mass index. In these subjects, firstB 0 $$ {\mathrm{B}}_0 $$ shimming and Fourier PE-DREAMB 1 + $$ {\mathrm{B}}_1^{+} $$ mapping were performed. Subsequently, three small-flip-angle 3D gradient-echo scans were acquired, comparing a circularly polarized (CP) mode, a phase shim, and a kT -point pulse. Resulting homogeneity was assessed and compared with estimated FA maps and distributions.

RESULTS

Fourier PE-DREAM with 13 phase-encoding steps resulted in a good tradeoff betweenB 1 + $$ {\mathrm{B}}_1^{+} $$ accuracy and scan time. Lower coefficient of variation values (average [min-max] across subjects) of the estimated FA in the volume of interest were observed using kT -points (7.4 [6.6%-8.0%]), compared with phase shimming (18.8 [12.9%-23.4%], p < 0.001) and CP (43.2 [39.4%-47.1%], p < 0.001). kT -points delivered whole-liver images with the nominal FA and the highest degree of homogeneity. CP and phase shimming resulted in either inaccurate or imprecise FA distributions. Here, locations having suboptimal FA in the estimated FA maps corresponded to liver areas suffering from inconsistent signal intensity and T1 -weighting in the gradient-echo scans.

CONCLUSION

Homogeneous whole-liver 3D gradient-echo acquisitions at 7 T can be obtained with eight-channel kT -point pulses calculated based on subject-specific multichannel absolute Fourier PE-DREAMB 1 + $$ {\mathrm{B}}_1^{+} $$ maps.

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

PURPOSE

To optimize transmit k-space trajectories for a wide range of excitation targets and to design "universal pTx RF pulses" based on these trajectories.

METHODS

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.

RESULTS

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.

CONCLUSIONS

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).

Parallel transmit optimized 3D composite adiabatic spectral-spatial pulse for spectroscopy

PURPOSE

To develop a 3D composite adiabatic spectral-spatial pulse for refocusing in spin-echo spectroscopy acquisitions and to compare its performance against standard acquisition methods.

METHODS

A 3D composite adiabatic pulse was designed by modulating a train of parallel transmit-optimized 2D subpulses with an adiabatic envelope. The spatial and spectral profiles were simulated and validated by experiments to demonstrate the feasibility of the design in both single and double spin-echo spectroscopy acquisitions. Phantom and in vivo studies were performed to evaluate the pulse performance and compared with semi-LASER with respect to localization performance, sequence timing, signal suppression, and specific absorption rate.

RESULTS

Simultaneous 2D spatial localization with water and lipid suppression was achieved with the designed refocusing pulse, allowing high-quality spectra to be acquired with shorter minimum TE/TR, reduced SAR, as well as adaptation to spatially varying B0 and B 1 + field inhomogeneities in both prostate and brain studies.

CONCLUSION

The proposed composite pulse can serve as a more SAR efficient alternative to conventional localization methods such as semi-LASER at ultrahigh field for spin echo-based spectroscopy studies. Subpulse parallel-transmit optimization provides the flexibility to manage the tradeoff among multiple design criteria to accommodate different field strengths and applications.

Local excitation universal parallel transmit pulses at 9.4T

PURPOSE

To demonstrate that the concept of "universal pTx pulses" is applicable to local excitation applications.

METHODS

A database of B₀ / B 1 + 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 B 1 + mapping sequence.

RESULTS

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.

CONCLUSIONS

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 / B 1 + mapping and pTx-pulse calculation during the scan session.

Simultaneous optimization of radio frequency and gradient waveforms with exact Hessians and slew rate constraints applied to kT-points excitation

We consider an excitation pulse with piecewise constant gradient trajectories and radio frequency (RF) waveforms such that the solution of the Bloch equations without relaxation terms can be represented by rotations. Based on this analytic solution we formulate a non-linear program for finding sub-pulse durations, gradient strengths, and complex RF voltages which minimize the deviation between the achieved and desired magnetization. We develop explicit expressions for the first and second order derivatives of the objective function. We extend the non-linear program to precisely account for gradient slew rate constraints. Using an interior point solver we apply the developed theory to simultaneously optimize the positions of k_T-points, their associated RF voltages and durations.

Three-dimensional static and dynamic parallel transmission of the human heart at 7 T

Three-dimensional (3D) human heart imaging at ultra-high fields is highly challenging due to respiratory and cardiac motion-induced artifacts as well as spatially heterogeneous B1+ profiles. In this study, we investigate the feasibility of applying 3D flip angle (FA) homogenization targeting the whole heart via static phase-only and dynamic kT-point in vivo parallel transmission at 7 T. 3D B1+ maps of the thorax were acquired under free breathing in eight subjects to compute parallel transmission pulses that improve excitation homogeneity in the human heart. To analyze the number of kT-points required, excitation homogeneity and radiofrequency (RF) power were compared using different regions of interest in six subjects with different body mass index (BMI) values of 20-34 kg/m² for a wide range of regularization parameters. One subset of the optimized subject-specific pulses was applied in vivo on a 7 T scanner for six subjects in Cartesian 3D breath-hold scans as well as in two subjects in a radial phase-encoded 3D free-breathing scan. Across all subjects, 3-4 kT-points achieved a good tradeoff between RF power and nominal FA homogeneity. For subjects with a BMI in the normal range, the 4 kT-point pulses reliably improved the coefficient of variation by less than 10% compared with less than 25% achieved by static phase-only parallel transmission. in vivo measurements on a 7 T scanner validated the B1+ estimations and the pulse design, despite neglecting ΔB₀ in the optimizations and Bloch simulations. This study demonstrates in vivo that kT-point pTx pulses are highly suitable for mitigating nominal FA heterogeneities across the entire 3D heart volume at 7 T. Furthermore, 3-4 kT-points demonstrate a practical tradeoff between nominal FA heterogeneity mitigation and RF power.

General gradient delay correction method in bipolar multispoke RF pulses using trim blips

PURPOSE

To correct with gradient trim blips for gradient delays in bipolar-spoke RF pulses in slice-selective and slab-selective excitations, compatible with tilted acquisitions and anisotropic delays.

THEORY

The effect of small gradient delays with respect to RF pulses results in a dephasing of the second RF spoke, proportional to the slab-selection gradient amplitude and the distance of the slice center from the magnet isocenter. Accordingly, adding a trim blip along the corresponding logical gradient axis between the two spokes compensates for the same dephasing, and therefore cancels the gradient delay effects, regardless of position and orientation.

METHODS

Gradient delays on different axes were first measured on a 7T system based on an imaging method. Parallel transmission universal bipolar spokes were designed offline to mitigate the RF field inhomogeneity problem in the human brain. Trim blips were used to compensate for the known delays, which was validated with flip angle and temporal SNR measurements on two different volunteers at 7 T.

RESULTS

Pulses corrected with trim blips greatly reduced gradient delay effects. Acquisitions made with corrected and noncorrected pulses showed good fidelity with simulations.

CONCLUSIONS

Unlike time or phase-shifting approaches, trim blip-based methods apply to all possible bipolar spoke scenarios such as slice excitations, slab excitations, and anisotropy in the gradient delays.

Universal nonselective excitation and refocusing pulses with improved robustness to off-resonance for Magnetic Resonance Imaging at 7 Tesla with parallel transmission

PURPOSE

In MRI at ultra-high field, the k T -point and spiral nonselective (SPINS) pulse design techniques can be advantageously combined with the parallel transmission (pTX) and universal pulse techniques to create uniform excitation in a calibration-free manner. However, in these approaches, pulse duration is typically increased as compared to standard hard pulses, and excitation quality in regions exhibiting large resonance frequency offsets often suffer. This limitation is inherent to structure of k T -point or SPINS pulse, and likely can be mitigated using parameterization-free pulse design approaches.

METHODS

The Gradient Ascent Pulse Engineering (GRAPE) algorithm was used to design parameterization-free RF and magnetic field gradient (MFG) waveforms for creating 8 ∘ excitation, up to 105 ∘ scalable refocusing and inversion, nonselectively across the brain. Simulations were performed to provide flip angle normalized root-mean-squares error (FA-NRMSE) estimations for the 8 ∘ and the 180 ∘ k T -point, SPINS, and GRAPE pulses. GRAPE pulses were tested experimentally with anatomical head scans at 7T.

RESULTS

As compared to k T -points and SPINS, GRAPE provided substantial improvement of excitation, refocusing, and inversion quality at off-resonance while at least preserving the same global FA-NRMSE performance. As compared to k T -points, GRAPE allowed for a substantial reduction of the pulse duration for the 8 ∘ excitation and the 105 ∘ refocusing.

CONCLUSIONS

Parameterization-free universal nonselective pTX-pulses were successfully computed using GRAPE. Performance gains as compared to k T -points were validated numerically and experimentally for three imaging protocols. In its current implementation, the computational burden of GRAPE limits its use to applications where pulse computations are not subject to time constraints.

Comparison of SMS-EPI and 3D-EPI at 7T in an fMRI localizer study with matched spatiotemporal resolution and homogenized excitation profiles

The simultaneous multi-slice EPI (SMS-EPI, a.k.a. MB-EPI) sequence has met immense popularity recently in functional neuroimaging. A still less common alternative is the use of 3D-EPI, which offers similar acceleration capabilities. The aim of this work was to compare the SMS-EPI and the 3D-EPI sequences in terms of sampling strategies for the detection of task-evoked activations at 7T using detection theory. To this end, the spatial and temporal resolutions of the sequences were matched (1.6 mm isotropic resolution, TR = 1200 ms) and their excitation profiles were homogenized by means of calibration-free parallel-transmission (Universal Pulses). We used a fast-event “localizer” paradigm of 5:20 min in order to probe sensorimotor functions (visual, auditory and motor tasks) as well as higher level functions (language comprehension, mental calculation), where results from a previous large-scale study at 3T (N = 81) served as ground-truth reference for the brain areas implicated in each cognitive function. In the current study, ten subjects were scanned while their activation maps were generated for each cognitive function with the GLM analysis. The SMS-EPI and 3D-EPI sequences were compared in terms of raw tSNR, t-score testing for the mean signal, activation strength and accuracy of the robust sensorimotor functions. To this end, the sensitivity and specificity of these contrasts were computed by comparing their activation maps to the reference brain areas obtained in the 3T study. Estimated flip angle distributions in the brain reported a normalized root mean square deviation from the target value below 10% for both sequences. The analysis of the t-score testing for the mean signal revealed temporal noise correlations, suggesting the use of this metric instead of the traditional tSNR for testing fMRI sequences. The SMS-EPI and 3D-EPI thereby yielded similar performance from a detection theory perspective.

Parallel Transmission for Ultrahigh Field MRI

Magnetic resonance imaging (MRI) has been driven toward ultrahigh magnetic fields (UHF) in order to benefit from correspondingly higher signal-to-noise ratio and spectral resolution. Technological challenges associated with UHF, such as increased radiofrequency (RF) energy deposition and RF excitation inhomogeneity, limit realization of the full potential of these benefits. Parallel RF transmission (pTx) enables decreases in the inhomogeneity of RF excitations and in RF energy deposition by using multiple-transmit RF coils driven independently and operating simultaneously. pTx plays a fundamental role in UHF MRI by bringing the potential applications of UHF into reality. In this review article, we review the recent developments in pTx pulse design and RF safety in pTx. Simultaneous multislice imaging and inner volume imaging using pTx are reviewed with a focus on UHF applications. Emerging pTx design approaches using improved pTx design frameworks and calibrations are reviewed together with calibration-free approaches that remove the necessity of time-consuming calibrations necessary for successful pTx. Lastly, we focus on the safety of pTx that is improved by using intersubject variability analysis, proactively managing pTx and temperature-based pTx approaches.

Design of universal parallel-transmit refocusing kT -point pulses and application to 3D T2 -weighted imaging at 7T

PURPOSE

T₂ -weighted sequences are particularly sensitive to the radiofrequency (RF) field inhomogeneity problem at ultra-high-field because of the errors accumulated by the imperfections of the train of refocusing pulses. As parallel transmission (pTx) has proved particularly useful to counteract RF heterogeneities, universal pulses were recently demonstrated to save precious time and computational efforts by skipping B₁ calibration and online RF pulse tailoring. Here, we report a universal RF pulse design for non-selective refocusing pulses to mitigate the RF inhomogeneity problem at 7T in turbo spin-echo sequences with variable flip angles.

METHOD

Average Hamiltonian theory was used to synthetize a single non-selective refocusing pulse with pTx while optimizing its scaling properties in the presence of static field offsets. The design was performed under explicit power and specific absorption rate constraints on a database of 10 subjects using a 8Tx-32Rx commercial coil at 7T. To validate the proposed design, the RF pulses were tested in simulation and applied in vivo on 5 additional test subjects.

RESULTS

The root-mean-square rotation angle error (RA-NRMSE) evaluation and experimental data demonstrated great improvement with the proposed universal pulses (RA-NRMSE ∼8%) compared to the standard circularly polarized mode of excitation (RA-NRMSE ∼26%).

CONCLUSION

This work further completes the spectrum of 3D universal pulses to mitigate RF field inhomogeneity throughout all 3D MRI sequences without any pTx calibration. The approach returns a single pulse that can be scaled to match the desired flip angle train, thereby increasing the modularity of the proposed plug and play approach. Magn Reson Med 80:53-65, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Homogeneous non-selective and slice-selective parallel-transmit excitations at 7 Tesla with universal pulses: A validation study on two commercial RF coils

Parallel transmission (pTx) technology, despite its great potential to mitigate the transmit field inhomogeneity problem in magnetic resonance imaging at ultra-high field (UHF), suffers from a cumbersome calibration procedure, thereby making the approach problematic for routine use. The purpose of this work is to demonstrate on two different 7T systems respectively equipped with 8-transmit-channel RF coils from two different suppliers (Rapid-Biomed and Nova Medical), the benefit of so-called universal pulses (UP), optimized to produce uniform excitations in the brain in a population of adults and making unnecessary the calibration procedures mentioned above. Non-selective and slice-selective UPs were designed to return homogeneous excitation profiles throughout the brain simultaneously on a group of ten subjects, which then were subsequently tested on ten additional volunteers in magnetization prepared rapid gradient echo (MPRAGE) and multi-slice gradient echo (2D GRE) protocols. The results were additionally compared experimentally with the standard non-pTx circularly-polarized (CP) mode, and in simulation with subject-specific tailored excitations. For both pulse types and both coils, the UP mode returned a better signal and contrast homogeneity than the CP mode. Retrospective analysis of the flip angle (FA) suggests that the FA deviation from the nominal FA on average over a healthy adult population does not exceed 11% with the calibration-free parallel-transmit pulses whereas it goes beyond 25% with the CP mode. As a result the universal pulses designed in this work confirm their relevance in 3D and 2D protocols with commercially available equipment. Plug-and-play pTx implementations henceforth become accessible to exploit with more flexibility the potential of UHF for brain imaging.

In vivo demonstration of whole-brain multislice multispoke parallel transmit radiofrequency pulse design in the small and large flip angle regimes at 7 Tesla

PURPOSE

A multispoke specific absorption rate (SAR) -aware pulse design approach for homogeneous multiple-slice small and large flip angle (FA) excitations with parallel transmission is proposed. The approach aims at optimizing in a slice-specific manner the spokes locations and radiofrequency pulses.

METHODS

The problem is posed as a set of slice-specific magnitude-least-squares problems, linked together by hardware and SAR constraints, and solved jointly using an active-set algorithm. Average Hamiltonian theory is exploited in the large FA case to greatly reduce the computational burden. The approach is validated numerically by means of simulations and experimentally on two volunteers at 7 Tesla through application of a high-resolution T2*-weighted brain imaging protocol.

RESULTS

The optimization of up to 1300 variables under 745 explicit constraints could be performed in less than 1 and 4 min for the small and large FA cases, respectively. The joint design proves valuable for SAR demanding protocols. Compared with the conventional circularly polarized mode, the designed pulses increased the signal by more than 40% in 70% of the voxels.

CONCLUSION

The B1+ inhomogeneity problem was mitigated efficiently in a multislice near whole-brain coverage protocol in the small and large FA regimes using a rapid slice-specific pulse design algorithm where the pulses were optimized jointly. Magn Reson Med 78:1009-1019, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Universal pulses: A new concept for calibration-free parallel transmission

PURPOSE

A calibration-free parallel transmission method is investigated to mitigate the radiofrequency (RF) field inhomogeneity problem in brain imaging at 7 Tesla (T).

THEORY AND METHODS

Six volunteers were scanned to build a representative database of RF and static field maps at 7T. Small-tip-angle and inversion pulses were designed with joint k_T -points trajectory optimization to work robustly on all six subjects. The returned "universal" pulses were then inserted in an MPRAGE sequence implemented on six additional volunteers without further field measurements and pulse optimizations. Similar acquisitions were performed in the circularly polarized mode and with subject-based optimizations for comparison. Performance of the different approaches was evaluated by means of image analysis and computation of the flip angle normalized root mean square errors (NRMSE).

RESULTS

For both the excitation and inversion, the universal pulses (NRMSE∼11%) outperformed the circularly polarized (NRMSE∼28%) and RF shim modes (NRMSE∼20%) across all volunteers and returned slightly worse results than for subject-based optimized pulses (NRMSE∼7%).

CONCLUSION

RF pulses can be designed to robustly mitigate the RF field inhomogeneity problem over a population class. This appears as a first step toward another plug and play parallel transmission solution where the pulse design can be done offline and without measuring subject-specific field maps. Magn Reson Med 77:635-643, 2017. © 2016 International Society for Magnetic Resonance in Medicine.