Designing multichannel, multidimensional, arbitrary flip angle RF pulses using an optimal control approach

Bilateral orthogonality generative acquisitions method for homogeneous T 2 * images using parallel transmission at 7 T

PURPOSE

The novel bilateral orthogonality generative acquisitions method has been developed for homogeneousT 2 * $$ {\mathrm{T}}_2^{\ast } $$ images without the effects of transmit field inhomogeneity using a parallel-transmission (pTx) system at 7 T.

THEORY AND METHODS

A new method has been introduced using four low-angle gradient-echo (GRE) acquisitions to obtain homogeneousT 2 * $$ {\mathrm{T}}_2^{\ast } $$ contrast by removing the effects of transmit field inhomogeneity in the pTx system. First, two input images are obtained in circularly polarized mode and another mode in which the first transmit channel or channel group have an additional transmit phase of π. The last two acquisitions are single-channel acquisitions for a dual-channel system or single-channel group acquisitions for more than two channels. The introduced method is demonstrated in dual-channel and eight-channel pTx systems using phantom and whole-brain in vivo experiments. Noise performance of the proposed method is also tested against the ratio of two GRE acquisitions and the TIAMO (time-interleaved acquisitions of modes) method.

RESULTS

Th new method results in more homogeneousT 2 * $$ {\mathrm{T}}_2^{\ast } $$ contrast in the final images than the compared methods, particularly in the low-intensity regions of circularly polarized-mode images for the images obtained via ratio of the two GRE acquisitions.

CONCLUSION

The introduced method is easy to implement, robust, and provides homogeneousT 2 * $$ {\mathrm{T}}_2^{\ast } $$ images of the whole brain using pTx systems with any number of channels, compared with the ratio of the two GRE images and the TIAMO method.

Robust dual-angle T 1 measurement in magnetization transfer spectroscopy by time-optimal control

Magnetization transfer spectroscopy relies heavily on the robust determination ofT 1 relaxation times of nuclei participating in metabolic exchange. Challenges arise due to the use of surface RF coils for transmission (highB 1 + variation) and the broad resonance band of most X nuclei. These challenges are particularly pronounced when fastT 1 mapping methods, such as the dual-angle method, are employed. Consequently, in this work, we develop resonance offset andB 1 + robust excitation RF pulses for 31P magnetization transfer spectroscopy at 7T through ensemble-based time-optimal control. In our approach, we introduce a cost functional for designing robust pulses, incorporating the full Bloch equations as constraints, which are solved using symmetric operator splitting techniques. The optimal control design of the RF pulses developed demonstrates improved accuracy, desired phase properties, and reduced RF power when applied to dual-angleT 1 mapping, thereby improving the precision of exchange-rate measurements, as demonstrated in a preclinical in vivo study quantifying brain creatine kinase activity.

The effect of and correction for through-slice dephasing on 2D gradient-echo double angle B 1 + mapping

PURPOSE

To show thatB 0 $$ {\mathrm{B}}_0 $$ variations through slice and slice profile effects are two major confounders affecting 2D dual angleB 1 + $$ {\mathrm{B}}_1^{+} $$ maps using gradient-echo signals and thus need to be corrected to obtain accurateB 1 + $$ {\mathrm{B}}_1^{+} $$ maps.

METHODS

The 2D gradient-echo transverse complex signal was Bloch-simulated and integrated across the slice dimension including nonlinear variations inB 0 $$ {\mathrm{B}}_0 $$ inhomogeneities through slice. A nonlinear least squares fit was used to find theB 1 + $$ {\mathrm{B}}_1^{+} $$ factor corresponding to the best match between the two gradient-echo signals experimental ratio and the Bloch-simulated ratio. The correction was validated in phantom and in vivo at 3T.

RESULTS

For our RF excitation pulse, the error in theB 1 + $$ {\mathrm{B}}_1^{+} $$ factor scales by approximately 3.8% for every 10 Hz/cm variation inB 0 $$ {\mathrm{B}}_0 $$ along the slice direction. Higher accuracy phantomB 1 + $$ {\mathrm{B}}_1^{+} $$ maps were obtained after applying the proposed correction; the root mean squareB 1 + $$ {\mathrm{B}}_1^{+} $$ error relative to the gold standardB 1 + $$ {\mathrm{B}}_1^{+} $$ decreased from 6.4% to 2.6%. In vivo whole-liverT 1 $$ {\mathrm{T}}_1 $$ maps using the correctedB 1 + $$ {\mathrm{B}}_1^{+} $$ map registered a significant decrease inT 1 $$ {\mathrm{T}}_1 $$ gradient through slice.

CONCLUSION

B 0 $$ {\mathrm{B}}_0 $$ inhomogeneities varying through slice were seen to have an impact on the accuracy of 2D double angleB 1 + $$ {\mathrm{B}}_1^{+} $$ maps using gradient-echo sequences. Consideration of this confounder is crucial for research relying on accurate knowledge of the true excitation flip angles, as is the case ofT 1 $$ {\mathrm{T}}_1 $$ mapping using a spoiled gradient recalled echo sequence.

Dynamic and rapid deep synthesis of chemical exchange saturation transfer and semisolid magnetization transfer MRI signals

Model-driven analysis of biophysical phenomena is gaining increased attention and utility for medical imaging applications. In magnetic resonance imaging (MRI), the availability of well-established models for describing the relations between the nuclear magnetization, tissue properties, and the externally applied magnetic fields has enabled the prediction of image contrast and served as a powerful tool for designing the imaging protocols that are now routinely used in the clinic. Recently, various advanced imaging techniques have relied on these models for image reconstruction, quantitative tissue parameter extraction, and automatic optimization of acquisition protocols. In molecular MRI, however, the increased complexity of the imaging scenario, where the signals from various chemical compounds and multiple proton pools must be accounted for, results in exceedingly long model simulation times, severely hindering the progress of this approach and its dissemination for various clinical applications. Here, we show that a deep-learning-based system can capture the nonlinear relations embedded in the molecular MRI Bloch-McConnell model, enabling a rapid and accurate generation of biologically realistic synthetic data. The applicability of this simulated data for in-silico, in-vitro, and in-vivo imaging applications is then demonstrated for chemical exchange saturation transfer (CEST) and semisolid macromolecule magnetization transfer (MT) analysis and quantification. The proposed approach yielded 63-99% acceleration in data synthesis time while retaining excellent agreement with the ground truth (Pearson's r > 0.99, p < 0.0001, normalized root mean square error < 3%).

Ultra-high field MRI: parallel-transmit arrays and RF pulse design

This paper reviews the field of multiple or parallel radiofrequency (RF) transmission for magnetic resonance imaging (MRI). Currently the use of ultra-high field (UHF) MRI at 7 tesla and above is gaining popularity, yet faces challenges with non-uniformity of the RF field and higher RF power deposition. Since its introduction in the early 2000s, parallel transmission (pTx) has been recognized as a powerful tool for accelerating spatially selective RF pulses and combating the challenges associated with RF inhomogeneity at UHF. We provide a survey of the types of dedicated RF coils used commonly for pTx and the important modeling of the coil behavior by electromagnetic (EM) field simulations. We also discuss the additional safety considerations involved with pTx such as the specific absorption rate (SAR) and how to manage them. We then describe the application of pTx with RF pulse design, including a practical guide to popular methods. Finally, we conclude with a description of the current and future prospects for pTx, particularly its potential for routine clinical use.

Advanced design of MRI inversion pulses for inhomogeneous field conditions by optimal control

Non-selective inversion pulses find widespread use in MRI applications, where requirements on them are increasingly demanding. With the use of high and ultra-high field strength systems, robustness to Δ B 0 and B 1 + inhomogeneities, while tackling SAR and hardware limitations, has rapidly become important. In this work, we propose a time-optimal control framework for the optimization of Δ B 0 - and B 1 + -robust inversion pulses. Robustness is addressed by means of ensemble formulations, while allowing inclusion of hardware and energy limitations. The framework is flexible and performs excellently for various optimization goals. The optimization results are analyzed extensively in numerical experiments. Furthermore, they are validated, and compared with adiabatic RF pulses, in various phantom and in vivo measurements on a 3 T MRI system.

High-fidelity control of spin ensemble dynamics via artificial intelligence: from quantum computing to NMR spectroscopy and imaging

High-fidelity control of spin ensemble dynamics is essential for many research areas, spanning from quantum computing and radio-frequency (RF) engineering to NMR spectroscopy and imaging. However, attaining robust and high-fidelity spin operations remains an unmet challenge. Using an evolutionary algorithm and artificial intelligence (AI), we designed new RF pulses with customizable spatial or temporal field inhomogeneity compensation. Compared with the standard RF shapes, the new AI-generated pulses show superior performance for bandwidth, robustness, and tolerance to field imperfections. As a benchmark, we constructed a spin entanglement operator for the weakly coupled two-spin-1/2 system of ¹³CHCl₃, achieving high-fidelity transformations under multiple inhomogeneity sources. We then generated band-selective and ultra-broadband RF pulses typical of biomolecular NMR spectroscopy. When implemented in multipulse NMR experiments, the AI-generated pulses significantly increased the sensitivity of medium-size and large protein spectra relative to standard pulse sequences. Finally, we applied the new pulses to typical imaging experiments, showing a remarkable tolerance to changes in the RF field. These AI-generated RF pulses can be directly implemented in quantum information, NMR spectroscopy of biomolecules, magnetic resonance imaging techniques for in vivo and materials sciences.

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).

Mitigating transmit‐B 1 artifacts by predicting parallel transmission images with deep learning: A feasibility study using high‐resolution whole‐brain diffusion at 7 Tesla

Purpose

To propose a novel deep learning (DL) approach to transmit‐B₁ (B₁⁺)‐artifact mitigation without direct use of parallel transmission (pTx), by predicting pTx images from single‐channel transmission (sTx) images.

Methods

A deep encoder–decoder convolutional neural network was constructed and trained to learn the mapping from sTx to pTx images. The feasibility was demonstrated using 7 T Human‐Connectome Project (HCP)‐style diffusion MRI. The training dataset comprised images acquired on 5 healthy subjects using commercial Nova RF coils. Relevant hyperparameters were tuned with a nested cross‐validation, and the generalization performance evaluated using a regular cross‐validation.

Results

Our DL method effectively improved the image quality for sTx images by restoring the signal dropout, with quality measures (including normalized root‐mean‐square error, peak SNR, and structural similarity index measure) improved in most brain regions. The improved image quality was translated into improved performances for diffusion tensor imaging analysis; our method improved accuracy for fractional anisotropy and mean diffusivity estimations, reduced the angular errors of principal eigenvectors, and improved the fiber orientation delineation relative to sTx images. Moreover, the final DL model trained on data of all 5 subjects was successfully used to predict pTx images for unseen new subjects (randomly selected from the 7 T HCP database), effectively recovering the signal dropout and improving color‐coded fractional anisotropy maps with largely reduced noise levels.

Conclusion

The proposed DL method has potential to provide images with reduced B1⁺ artifacts in healthy subjects even when pTx resources are inaccessible on the user side.

Selective RF excitation designs enabled by time-varying spatially non-linear ΔB0 fields with applications in fetal MRI

PURPOSE

To demonstrate, through numerical simulations, novel designs of spatially selective radiofrequency (RF) excitations of the fetal brain by both a restricted 2D slice and 3D inner-volume selection. These designs exploit a single-channel RF pulse, conventional gradient fields, and the spatially non-linear ΔB₀ fields of a multi-coil shim array, using an auto-differentiation optimization algorithm.

METHODS

The design algorithm jointly optimizes the RF pulse and the time-varying ΔB₀ fields, which is produced by a 64-channel multi-coil ΔB₀ body array to augment the RF and the linear gradient fields, using an auto-differentiation approach. Two design targets were specified, one a 4-mm thick slice with a limited in-slice extent in one dimension ("restricted slice"), and the other a 3D inner-volume selection encompassing the fetal brain ("inner volume"). The RF duration was limited to 2 ms for the restricted slice excitation and 6 ms for the inner-volume excitation.

RESULTS

Excitation profiles were achieved for both the restricted slice excitation task (one-minus-minimum magnitude, 8%) within the region of interest (ROI) and (maximum-minus-zero magnitude, 8%) in the suppressed regions and the fetal brain volume excitation task (13% and 9%, respectively).

CONCLUSIONS

The proposed joint design of RF and time-varying, spatially non-linear ΔB₀ fields achieves the target excitation profiles with short RF pulse durations and demonstrates the potential to enhance fetal MRI with multi-channel body shim arrays.

Optimal control gradient precision trade-offs: Application to fast generation of DeepControl libraries for MRI

We have recently demonstrated supervised deep learning methods for rapid generation of radiofrequency pulses in magnetic resonance imaging (https://doi.org/10.1002/mrm.27740, https://doi.org/10.1002/mrm.28667). Unlike the previous iterative optimization approaches, deep learning methods generate a pulse using a fixed number of floating-point operations - this is important in MRI, where patient-specific pulses preferably must be produced in real time. However, deep learning requires vast training libraries, which must be generated using the traditional methods, e.g., iterative quantum optimal control methods. Those methods are usually variations of gradient descent, and the calculation of the gradient of the performance metric with respect to the pulse waveform can be the most numerically intensive step. In this communication, we explore various ways in which the calculation of gradients in quantum optimal control theory may be accelerated. Four optimization avenues are explored: truncated commutator series expansions at zeroth and first order, a novel midpoint truncation scheme at first order, and the exact complex-step method. For the spin systems relevant to MRI, the first-order midpoint truncation is found to be sufficiently accurate, but also significantly faster than the machine precision gradient. This makes the generation of training databases for the machine learning methods considerably more realistic.

Accuracy and performance analysis for Bloch and Bloch-McConnell simulation methods

PURPOSE

To introduce new solution methods for the Bloch and Bloch-McConnell equations and compare them quantitatively to different known approaches.

THEORY AND METHODS

A new exact solution per time step is derived by means of eigenvalues and generalized eigenvectors. Fast numerical solution methods based on asymmetric and symmetric operator splitting, which are already known for the Bloch equations, are extended to the Bloch-McConnell equations. Those methods are compared to other numerical methods including spin domain, one-step and multi-step methods, and matrix exponential. Error metrics are introduced based on the exact solution method, which allows to assess the accuracy of each solution method quantitatively for arbitrary example data.

RESULTS

Accuracy and performance properties for nine different solution methods are analyzed and compared in extensive numerical experiments including various examples for non-selective and slice-selective MR imaging applications. The accuracy of the methods heavily varies, in particular for short relaxation times and long pulse durations.

CONCLUSION

In absence of relaxation effects, the numerical results confirm the rotation matrices approach as accurate and computationally efficient Bloch solution method. Otherwise, as well as for the Bloch-McConnell equations, symmetric operator splitting methods are recommended due to their excellent numerical accuracy paired with efficient run time.

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.

k-Space Domain Parallel Transmit Pulse Design

PURPOSE

To accelerate the design of (under- or oversampled) multidimensional parallel transmission pulses.

METHODS

A k-space domain parallel transmission pulse design algorithm was proposed that produces a sparse matrix relating a complex-valued target excitation pattern to the pulses that produce it, and can be finely parallelized. The algorithm was applied in simulations to the design of 3D SPINS pulses for inner volume excitation in the brain at 7 Tesla. It was characterized in terms of the dependence of computation time, excitation error, and required memory on algorithm parameters, and it was compared to an iterative spatial domain pulse design method in terms of computation time, excitation error, Gibbs ringing, and ability to compensate off-resonance.

RESULTS

The proposed algorithm achieved approximately 80% faster pulse design compared to the spatial domain method with the same number of parallel threads, with the tradeoff of increased excitation error and RMS RF amplitude. It reduced the memory required to store the design matrix by 99% compared to a full matrix solution. Even with a coarse design grid, the algorithm produced patterns that were free of Gibbs ringing. It was similarly sensitive to k-space undersampling as the spatial domain method, and was similarly capable of compensating for off-resonance.

CONCLUSIONS

The proposed k-space domain algorithm accelerates and finely parallelizes parallel transmission pulse design, with a modest tradeoff of excitation error and RMS RF amplitude.

Multi-task convolutional neural network-based design of radio frequency pulse and the accompanying gradients for magnetic resonance imaging

Modern MRI systems usually load the predesigned RFs and the accompanying gradients during clinical scans, with minimal adaption to the specific requirements of each scan. Here, we describe a neural network-based method for real-time design of excitation RF pulses and the accompanying gradients' waveforms to achieve spatially two-dimensional selectivity. Nine thousand sets of radio frequency (RF) and gradient waveforms with two-dimensional spatial selectivity were generated as the training dataset using the Shinnar-Le Roux (SLR) method. Neural networks were created and trained with five strategies (TS-1 to TS-5). The neural network-designed RF and gradients were compared with their SLR-designed counterparts and underwent Bloch simulation and phantom imaging to investigate their performances in spin manipulations. We demonstrate a convolutional neural network (TS-5) with multi-task learning to yield both the RF pulses and the accompanying two channels of gradient waveforms that comply with the SLR design, and these design results also provide excitation spatial profiles comparable with SLR pulses in both simulation (normalized root mean square error [NRMSE] of 0.0075 ± 0.0038 over the 400 sets of testing data between TS-5 and SLR) and phantom imaging. The output RF and gradient waveforms between the neural network and SLR methods were also compared, and the joint NRMSE, with both RF and the two channels of gradient waveforms considered, was 0.0098 ± 0.0024 between TS-5 and SLR. The RF and gradients were generated on a commercially available workstation, which took ~130 ms for TS-5. In conclusion, we present a convolutional neural network with multi-task learning, trained with SLR transformation pairs, that is capable of simultaneously generating RF and two channels of gradient waveforms, given the desired spatially two-dimensional excitation profiles.

DeepControl: 2DRF pulses facilitating B 1 + inhomogeneity and B0 off-resonance compensation in vivo at 7 T

PURPOSE

Rapid 2DRF pulse design with subject-specific B 1 + inhomogeneity and B₀ off-resonance compensation at 7 T predicted from convolutional neural networks is presented.

METHODS

The convolution neural network was trained on half a million single-channel transmit 2DRF pulses optimized with an optimal control method using artificial 2D targets, B 1 + and B₀ maps. Predicted pulses were tested in a phantom and in vivo at 7 T with measured B 1 + and B₀ maps from a high-resolution gradient echo sequence.

RESULTS

Pulse prediction by the trained convolutional neural network was done on the fly during the MR session in approximately 9 ms for multiple hand-drawn regions of interest and the measured B 1 + and B₀ maps. Compensation of B 1 + inhomogeneity and B₀ off-resonances has been confirmed in the phantom and in vivo experiments. The reconstructed image data agree well with the simulations using the acquired B 1 + and B₀ maps, and the 2DRF pulse predicted by the convolutional neural networks is as good as the conventional RF pulse obtained by optimal control.

CONCLUSION

The proposed convolutional neural network-based 2DRF pulse design method predicts 2DRF pulses with an excellent excitation pattern and compensated B 1 + and B₀ variations at 7 T. The rapid 2DRF pulse prediction (9 ms) enables subject-specific high-quality 2DRF pulses without the need to run lengthy optimizations.

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.

First in-vivo human imaging at 10.5T: Imaging the body at 447 MHz

PURPOSE

To investigate the feasibility of imaging the human torso and to evaluate the performance of several radiofrequency (RF) management strategies at 10.5T.

METHODS

Healthy volunteers were imaged on a 10.5T whole-body scanner in multiple target anatomies, including the prostate, hip, kidney, liver, and heart. Phase-only shimming and spoke pulses were used to demonstrate their performance in managing the B 1 + inhomogeneity present at 447 MHz. Imaging protocols included both qualitative and quantitative acquisitions to show the feasibility of imaging with different contrasts.

RESULTS

High-quality images were acquired and demonstrated excellent overall contrast and signal-to-noise ratio. The experimental results matched well with predictions and suggested good translational capabilities of the RF management strategies previously developed at 7T. Phase-only shimming provided increased efficiency, but showed pronounced limitations in homogeneity, demonstrating the need for the increased degrees of freedom made possible through single- and multispoke RF pulse design.

CONCLUSION

The first in-vivo human imaging was successfully performed at 10.5T using previously developed RF management strategies. Further improvement in RF coils, transmit chain, and full integration of parallel transmit functionality are needed to fully realize the benefits of 10.5T.

Multiple-Input Multiple-Output (MIMO) MRI: Combining Parallel Excitation and Parallel Reception for Enhanced Imaging

Magnetic resonance imaging (MRI) plays a critical role in visualizing the structure and functions of the human body. In order to accelerate imaging time and improve image quality, radio-frequency (RF) coil receive arrays are commonly employed to acquire the magnetic resonance (MR) signal. Similarly, multiple transmit coils have been shown to accelerate and refine RF excitation. In this work, we investigate the optimization of total imaging time and image accuracy when considering both the transmit and receive coil arrays; we term this strategy multiple-input multiple-output (MIMO) MRI. Our RF pulse design method is modeled by minimizing the excitation errors while simultaneously maximizing the signal-to-noise ratio (SNR) of the reconstructed MR image. It further allows a key tradeoff between the two optimizers. Additionally, multiple acceleration factors, varying numbers of receive coils used, maximum excitation error tolerance, and different excitation patterns are simulated and analyzed in this model. For a given excitation pattern, our method is shown to improve the SNR by 18-130% under certain acceleration schemes, as compared to conventional parallel transmission methods, while simultaneously controlling the excitation error within a desired scope (NRMSE ≤ 0.12).

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.

A simplified framework to optimize MRI contrast preparation

PURPOSE

This article proposes a rigorous optimal control framework for the design of preparation schemes that optimize MRI contrast based on relaxation time differences.

METHODS

Compared to previous optimal contrast preparation schemes, a drastic reduction of the optimization parameter number is performed. The preparation scheme is defined as a combination of several block pulses whose flip angles, phase terms and inter-pulse delays are optimized to control the magnetization evolution.

RESULTS

The proposed approach reduces the computation time of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:math> -robust preparation schemes to around a minute (whereas several hours were required with previous schemes), with negligible performance loss. The chosen parameterization allows to formulate the total preparation duration as a constraint, which improves the overall compromise between contrast performance and preparation time. Simulation, in vitro and in vivo results validate this improvement, illustrate the straightforward applicability of the proposed approach, and point out its flexibility in terms of achievable contrasts. Major improvement is especially achieved for short-T₂ enhancement, as shown by the acquisition of a non-trivial contrast on a rat brain, where a short-T₂ white matter structure (corpus callosum) is enhanced compared to surrounding gray matter tissues (hippocampus and neocortex).

CONCLUSIONS

This approach proposes key advances for the design of optimal contrast preparation sequences, that emphasize their ability to generate non-standard contrasts, their potential benefit in a clinical context, and their straightforward applicability on any MR system.

Constant gradient elastography with optimal control RF pulses

This article presents a new motion encoding strategy to perform magnetic resonance elastography (MRE). Instead of using standard motion encoding gradients, a tailored RF pulse is designed to simultaneously perform selective excitation and motion encoding in presence of a constant gradient. The RF pulse is designed with a numerical optimal control algorithm, in order to obtain a magnetization phase distribution that depends on the displacement characteristics inside each voxel. As a consequence, no post-excitation encoding gradients are required. This offers numerous advantages, such as reducing eddy current artifacts, and relaxing the constraint on the gradients maximum switch rate. It also allows to perform MRE with ultra-short TE acquisition schemes, which limits T₂ decay and optimizes signal-to-noise ratio. The pulse design strategy is developed and analytically analyzed to clarify the encoding mechanism. Finally, simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved when compared to standard MRE encoding strategies.

Phase-sensitive B1 mapping: Effects of relaxation and RF spoiling

PURPOSE

To develop a phase-based B₁ mapping technique accounting for the effects of imperfect RF spoiling and magnetization relaxation.

THEORY AND METHODS

The technique is based on a multi-gradient-echo sequence with 2 successive orthogonal radiofrequency (RF) excitation pulses followed by the train of gradient echoes measurements. We have derived a theoretical expression relating the MR signal phase produced by the 2 successive RF pulses to the B₁ field and B₀ -related frequency shift. The expression takes into account effects of imperfections of RF spoiling and T₁ and T2* relaxations.

RESULTS

Our computer simulations and experiments revealed that imperfections of RF spoiling cause significant errors in B₁ mapping if not accounted for. By accounting for these effects along with effects of magnetization relaxation and frequency shift, we demonstrated the high accuracy of our approach. The technique has been tested on spherical phantoms and a healthy volunteer.

CONCLUSION

In this paper, we have proposed, implemented, and demonstrated the accuracy of a new phase-based technique for fast and robust B₁ mapping based on the measured MR signal phase, frequency, and relaxation. Because imperfect RF spoiling effects are accounted for, this technique can be applied with short TRs and therefore substantially reduces the scan time. Magn Reson Med 80:101-111, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Rotation relaxation splitting for optimizing parallel RF excitation pulses with T1- and T2-relaxations in MRI

Exact solutions of the Bloch equations with T₁- and T₂-relaxation terms for piecewise constant magnetic fields are numerically challenging. We therefore investigate an approximation for the achieved magnetization in which rotations and relaxations are split into separate operations. We develop an estimate for its accuracy and explicit first and second order derivatives with respect to the complex excitation radio frequency voltages. In practice, the deviation between an exact solution of the Bloch equations and this rotation relaxation splitting approximation seems negligible. Its computation times are similar to exact solutions without relaxation terms. We apply the developed theory to numerically optimize radio frequency excitation waveforms with T₁- and T₂-relaxations in several examples.

Active control of the spatial MRI phase distribution with optimal control theory

This paper investigates the use of Optimal Control (OC) theory to design Radio-Frequency (RF) pulses that actively control the spatial distribution of the MRI magnetization phase. The RF pulses are generated through the application of the Pontryagin Maximum Principle and optimized so that the resulting transverse magnetization reproduces various non-trivial and spatial phase patterns. Two different phase patterns are defined and the resulting optimal pulses are tested both numerically with the ODIN MRI simulator and experimentally with an agar gel phantom on a 4.7T small-animal MR scanner. Phase images obtained in simulations and experiments are both consistent with the defined phase patterns. A practical application of phase control with OC-designed pulses is also presented, with the generation of RF pulses adapted for a Magnetic Resonance Elastography experiment. This study demonstrates the possibility to use OC-designed RF pulses to encode information in the magnetization phase and could have applications in MRI sequences using phase images.

Optimal control design of preparation pulses for contrast optimization in MRI

This work investigates the use of MRI radio-frequency (RF) pulses designed within the framework of optimal control theory for image contrast optimization. The magnetization evolution is modeled with Bloch equations, which defines a dynamic system that can be controlled via the application of the Pontryagin Maximum Principle (PMP). This framework allows the computation of optimal RF pulses that bring the magnetization to a given state to obtain the desired contrast after acquisition. Creating contrast through the optimal manipulation of Bloch equations is a new way of handling contrast in MRI, which can explore the theoretical limits of the system. Simulation experiments carried out on-resonance quantify the contrast improvement when compared to standard T₁ or T₂ weighting strategies. The use of optimal pulses is also validated for the first time in both in vitro and in vivo experiments on a small-animal 4.7T MR system. Results demonstrate their robustness to static field inhomogeneities as well as the fact that they can be embedded in standard imaging sequences without affecting standard parameters such as slice selection or echo type. In vivo results on rat and mouse brains illustrate the ability of optimal contrast pulses to create non-trivial contrasts on well-studied structures (white matter versus gray matter).

Local SAR, global SAR, and power-constrained large-flip-angle pulses with optimal control and virtual observation points

PURPOSE

To present a constrained optimal-control (OC) framework for designing large-flip-angle parallel-transmit (pTx) pulses satisfying hardware peak-power as well as regulatory local and global specific-absorption-rate (SAR) limits. The application is 2D and 3D spatial-selective 90° and 180° pulses.

THEORY AND METHODS

The OC gradient-ascent-pulse-engineering method with exact gradients and the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is proposed. Local SAR is constrained by the virtual-observation-points method. Two numerical models facilitated the optimizations, a torso at 3 T and a head at 7 T, both in eight-channel pTx coils and acceleration-factors up to 4.

RESULTS

The proposed approach yielded excellent flip-angle distributions. Enforcing the local-SAR constraint, as opposed to peak power alone, reduced the local SAR 7 and 5-fold with the 2D torso excitation and inversion pulse, respectively. The root-mean-square errors of the magnetization profiles increased less than 5% with the acceleration factor of 4.

CONCLUSION

A local and global SAR, and peak-power constrained OC large-flip-angle pTx pulse design was presented, and numerically validated for 2D and 3D spatial-selective 90° and 180° pulses at 3 T and 7 T. Magn Reson Med 77:374-384, 2017. © 2015 Wiley Periodicals, Inc.

Parallel transmission for ultrahigh-field imaging

The development of MRI systems operating at or above 7 T has provided researchers with a new window into the human body, yielding improved imaging speed, resolution and signal-to-noise ratio. In order to fully realise the potential of ultrahigh-field MRI, a range of technical hurdles must be overcome. The non-uniformity of the transmit field is one of such issues, as it leads to non-uniform images with spatially varying contrast. Parallel transmission (i.e. the use of multiple independent transmission channels) provides previously unavailable degrees of freedom that allow full spatial and temporal control of the radiofrequency (RF) fields. This review discusses the many ways in which these degrees of freedom can be used, ranging from making more uniform transmit fields to the design of subject-tailored RF pulses for both uniform excitation and spatial selection, and also the control of the specific absorption rate. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

Application of the limited-memory quasi-Newton algorithm for multi-dimensional, large flip-angle RF pulses at 7T

OBJECTIVE

Ultrahigh field MRI provides great opportunities for medical diagnostics and research. However, ultrahigh field MRI also brings challenges, such as larger magnetic susceptibility induced field changes. Parallel-transmit radio-frequency pulses can ameliorate these complications while performing advanced tasks in routine applications. To address one class of such pulses, we propose an optimal-control algorithm as a tool for designing advanced multi-dimensional, large flip-angle, radio-frequency pulses. We contrast initial conditions, constraints, and field correction abilities against increasing pulse trajectory acceleration factors.

MATERIALS AND METHODS

On an 8-channel 7T system, we demonstrate the quasi-Newton algorithm with pulse designs for reduced field-of-view imaging with an oil phantom and in vivo with scans of the human brain stem. We used echo-planar imaging with 2D spatial-selective pulses. Pulses are computed sufficiently rapid for routine applications.

RESULTS

Our dataset was quantitatively analyzed with the conventional mean-square-error metric and the structural-similarity index from image processing. Analysis of both full and reduced field-of-view scans benefit from utilizing both complementary measures.

CONCLUSION

We obtained excellent outer-volume suppression with our proposed method, thus enabling reduced field-of-view imaging using pulse trajectory acceleration factors up to 4.

A new sequence for shaped voxel spectroscopy in the human brain using 2D spatially selective excitation and parallel transmission

Spatially selective excitation in two dimensions (2D-SSE) utilizing parallel transmission was applied as a means to acquire signal from voxels adapted to the anatomy of interest for in vivo (1) H MR spectroscopy. A novel method to select spectroscopy voxels with arbitrary shapes in two dimensions was investigated. An on-off scheme with an adiabatic slice selective inversion pulse preceding a 2D-SSE pulse together with a segmented inward spiral excitation k-space trajectory enabled rapid free induction decay acquisitions. Performance of the sequence was evaluated in simulations, phantom experiments, and in vivo measurements at 3 T. High spatial fidelity of the excitation profile was achieved for different target shapes and with little off-resonance deterioration. Metabolite concentrations in human brain determined with the new sequence were quantified with Cramér-Rao lower bounds less than 20%. They were in the physiological range and did not deviate systematically from results acquired with a conventional SPECIAL sequence. In conclusion, a new approach for shaped voxel MRS in the human brain is presented, which complements existing sequences. Simulations show that 2D-SSE pulses yield reduced chemical shift artifact when compared with conventional localization methods. Copyright © 2016 John Wiley & Sons, Ltd.

Distributing coil elements in three dimensions enhances parallel transmission multiband RF performance: A simulation study in the human brain at 7 Tesla

PURPOSE

We explore the advantages of using a double-ring radiofrequency (RF) array and slice orientation to design parallel transmission (pTx) multiband (MB) pulses for simultaneous multislice (SMS) imaging with whole-brain coverage at 7 Tesla (T).

METHODS

A double-ring head array with 16 elements split evenly in two rings stacked in the z-direction was modeled and compared with two single-ring arrays consisting of 8 or 16 elements. The array performance was evaluated by designing band-specific pTx MB pulses with local specific absorption rate (SAR) control. The impact of slice orientations was also investigated.

RESULTS

The double-ring array consistently and significantly outperformed the other two single-ring arrays, with peak local SAR reduced by up to 40% at a fixed excitation error of 0.024. For all three arrays, exciting sagittal or coronal slices yielded better RF performance than exciting axial or oblique slices.

CONCLUSIONS

A double-ring RF array can be used to drastically improve SAR versus excitation fidelity tradeoff for pTx MB pulse design for brain imaging at 7 T; therefore, it is preferable against single-ring RF array designs when pursuing various biomedical applications of pTx SMS imaging. In comparing the stripline arrays, coronal and sagittal slices are more advantageous than axial and oblique slices for pTx MB pulses. Magn Reson Med 75:2464-2472, 2016. © 2016 Wiley Periodicals, Inc.

Joint design of large-tip-angle parallel RF pulses and blipped gradient trajectories

PURPOSE

To design multichannel large-tip-angle kT-points and spokes radiofrequency (RF) pulses and gradient waveforms for transmit field inhomogeneity compensation in high field magnetic resonance imaging.

THEORY AND METHODS

An algorithm to design RF subpulse weights and gradient blip areas is proposed to minimize a magnitude least-squares cost function that measures the difference between realized and desired state parameters in the spin domain, and penalizes integrated RF power. The minimization problem is solved iteratively with interleaved target phase updates, RF subpulse weights updates using the conjugate gradient method with optimal control-based derivatives, and gradient blip area updates using the conjugate gradient method. Two-channel parallel transmit simulations and experiments were conducted in phantoms and human subjects at 7 T to demonstrate the method and compare it to small-tip-angle-designed pulses and circularly polarized excitations.

RESULTS

The proposed algorithm designed more homogeneous and accurate 180° inversion and refocusing pulses than other methods. It also designed large-tip-angle pulses on multiple frequency bands with independent and joint phase relaxation. Pulses designed by the method improved specificity and contrast-to-noise ratio in a finger-tapping spin echo blood oxygen level dependent functional magnetic resonance imaging study, compared with circularly polarized mode refocusing.

CONCLUSION

A joint RF and gradient waveform design algorithm was proposed and validated to improve large-tip-angle inversion and refocusing at ultrahigh field.

Radiofrequency pulse design with numerical optimization in the Fourier domain

OBJECTIVE AND METHODS

A radiofrequency (RF) pulse design technique is presented that uses iterative constrained minimization to determine Fourier domain coefficients for an optimal time domain RF pulse. The design of new RF pulses is especially beneficial for field strengths of 7.0 T and above, where challenges pertaining to specific absorption rate (SAR) are exacerbated.

RESULTS AND CONCLUSION

A pair of 90° and 180° spin-echo pulses was designed to lower SAR without the need for a variable slice gradient. The optimized pulses were deployed to a 7.0 T human scanner to demonstrate a reduction in SAR while retaining signal-to-noise (SNR) ratio.

Efficient high-resolution RF pulse design applied to simultaneous multi-slice excitation

RF pulse design via optimal control is typically based on gradient and quasi-Newton approaches and therefore suffers from slow convergence. We present a flexible and highly efficient method that uses exact second-order information within a globally convergent trust-region CG-Newton method to yield an improved convergence rate. The approach is applied to the design of RF pulses for single- and simultaneous multi-slice (SMS) excitation and validated using phantom and in vivo experiments on a 3T scanner using a modified gradient echo sequence.

Optimal control design of turbo spin-echo sequences with applications to parallel-transmit systems

Purpose

The design of turbo spin‐echo sequences is modeled as a dynamic optimization problem which includes the case of inhomogeneous transmit radiofrequency fields. This problem is efficiently solved by optimal control techniques making it possible to design patient‐specific sequences online.

Theory and Methods

The extended phase graph formalism is employed to model the signal evolution. The design problem is cast as an optimal control problem and an efficient numerical procedure for its solution is given. The numerical and experimental tests address standard multiecho sequences and pTx configurations.

Results

Standard, analytically derived flip angle trains are recovered by the numerical optimal control approach. New sequences are designed where constraints on radiofrequency total and peak power are included. In the case of parallel transmit application, the method is able to calculate the optimal echo train for two‐dimensional and three‐dimensional turbo spin echo sequences in the order of 10 s with a single central processing unit (CPU) implementation. The image contrast is maintained through the whole field of view despite inhomogeneities of the radiofrequency fields.

Conclusion

The optimal control design sheds new light on the sequence design process and makes it possible to design sequences in an online, patient‐specific fashion. Magn Reson Med 77:361–373, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine

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

In Magnetic Resonance Imaging at ultra-high field, kT-points radiofrequency pulses combined with parallel transmission are a promising technique to mitigate the B1 field inhomogeneity in 3D imaging applications. The optimization of the corresponding k-space trajectory for its slice-selective counterpart, i.e. the spokes method, has been shown in various studies to be very valuable but also dependent on the hardware and specific absorption rate constraints. Due to the larger number of degrees of freedom than for spokes excitations, joint design techniques based on the fine discretization (gridding) of the parameter space become hardly tractable for kT-points pulses. In this article, we thus investigate the simultaneous optimization of the 3D blipped k-space trajectory and of the kT-points RF pulses, using a magnitude least squares cost-function, with explicit constraints and in the large flip angle regime. A second-order active-set algorithm is employed due to its demonstrated success and robustness in similar problems. An analysis of global optimality and of the structure of the returned trajectories is proposed. The improvement provided by the k-space trajectory optimization is validated experimentally by measuring the flip angle on a spherical water phantom at 7T and via Quantum Process Tomography.

Improving the time efficiency of the Fourier synthesis method for slice selection in magnetic resonance imaging

The design of slice selective pulses for magnetic resonance imaging can be cast as an optimal control problem. The Fourier synthesis method is an existing approach to solve these optimal control problems. In this method the gradient field as well as the excitation field are switched rapidly and their amplitudes are calculated based on a Fourier series expansion. Here, we provide a novel insight into the Fourier synthesis method via representing the Bloch equation in spherical coordinates. Based on the spherical Bloch equation, we propose an alternative sequence of pulses that can be used for slice selection which is more time efficient compared to the original method. Simulation results demonstrate that while the performance of both methods is approximately the same, the required time for the proposed sequence of pulses is half of the original sequence of pulses. Furthermore, the slice selectivity of both sequences of pulses changes with radio frequency field inhomogeneities in a similar way. We also introduce a measure, referred to as gradient complexity, to compare the performance of both sequences of pulses. This measure indicates that for a desired level of uniformity in the excited slice, the gradient complexity for the proposed sequence of pulses is less than the original sequence.

First and second order derivatives for optimizing parallel RF excitation waveforms

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

Multichannel compressive sensing MRI using noiselet encoding

The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI. Based on an empirical RIP analysis that compares the multichannel noiselet and multichannel Fourier measurement matrices in CS-MRI, we propose a multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, a pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain. The results indicate that noislet encoding preserves image resolution better than Fouirer encoding.

Design of multidimensional Shinnar-Le Roux radiofrequency pulses

PURPOSE

To generalize the conventional Shinnar-Le Roux method for the design of multidimensional radiofrequency pulses.

METHODS

Using echo-planar gradients, the multidimensional radiofrequency pulse design problem was converted into a series of one-dimensional polynomial design problems. Each of the one-dimensional polynomial design problems was solved efficiently. B0 inhomogeneity compensation and design of spatial-spectral pulses were also considered.

RESULTS

The proposed method was used to design two-dimensional excitation and refocusing pulses. The results were validated through Bloch equation simulation and experiments on a 3.0 T scanner. Large-tip-angle, equiripple-error, multidimensional excitation was achieved with ripple levels closely matching the design specifications.

CONCLUSION

The conventional Shinnar-Le Roux method can be extended to design multidimensional radiofrequency pulses. The proposed method achieves almost equiripple excitation errors, allows easy control of the tradeoff among design parameters, and is computationally efficient.

Four dimensional spectral-spatial fat saturation pulse design

PURPOSE

The conventional spectrally selective fat saturation pulse may perform poorly with inhomogeneous amplitude of static (polarizing) field (B0 ) and/or amplitude of (excitation) radiofrequency field (B1 ) fields. We propose a four dimensional spectral-spatial fat saturation pulse that is more robust to B0/B1 inhomogeneity and also shorter than the conventional fat saturation pulse.

THEORY

The proposed pulse is tailored for local B0 inhomogeneity, which avoids the need of a sharp transition band in the spectral domain, so it improves both performance and pulse length. Furthermore, it can also compensate for B1 inhomogeneity. The pulse is designed sequentially by small-tip-angle approximation design and an automatic rescaling procedure.

METHODS

The proposed method is compared to the conventional fat saturation in phantom experiments and in vivo knee imaging at 3 T for both single-channel and parallel excitation versions.

RESULTS

Compared to the conventional method, the proposed method produces superior fat suppression in the presence of B0 and B1 inhomogeneity and reduces pulse length by up to half of the standard length.

CONCLUSION

The proposed four dimensional spectral-spatial fat saturation suppresses fat more robustly with shorter pulse length than the conventional fat saturation in the presence of B0 and B1 inhomogeneity.

Designing dipolar recoupling and decoupling experiments for biological solid-state NMR using interleaved continuous wave and RF pulse irradiation

Rapid developments in solid-state NMR methodology have boosted this technique into a highly versatile tool for structural biology. The invention of increasingly advanced rf pulse sequences that take advantage of better hardware and sample preparation have played an important part in these advances. In the development of these new pulse sequences, researchers have taken advantage of analytical tools, such as average Hamiltonian theory or lately numerical methods based on optimal control theory. In this Account, we focus on the interplay between these strategies in the systematic development of simple pulse sequences that combines continuous wave (CW) irradiation with short pulses to obtain improved rf pulse, recoupling, sampling, and decoupling performance. Our initial work on this problem focused on the challenges associated with the increasing use of fully or partly deuterated proteins to obtain high-resolution, liquid-state-like solid-state NMR spectra. Here we exploit the overwhelming presence of (2)H in such samples as a source of polarization and to gain structural information. The (2)H nuclei possess dominant quadrupolar couplings which complicate even the simplest operations, such as rf pulses and polarization transfer to surrounding nuclei. Using optimal control and easy analytical adaptations, we demonstrate that a series of rotor synchronized short pulses may form the basis for essentially ideal rf pulse performance. Using similar approaches, we design (2)H to (13)C polarization transfer experiments that increase the efficiency by one order of magnitude over standard cross polarization experiments. We demonstrate how we can translate advanced optimal control waveforms into simple interleaved CW and rf pulse methods that form a new cross polarization experiment. This experiment significantly improves (1)H-(15)N and (15)N-(13)C transfers, which are key elements in the vast majority of biological solid-state NMR experiments. In addition, we demonstrate how interleaved sampling of spectra exploiting polarization from (1)H and (2)H nuclei can substantially enhance the sensitivity of such experiments. Finally, we present systematic development of (1)H decoupling methods where CW irradiation of moderate amplitude is interleaved with strong rotor-synchronized refocusing pulses. We show that these sequences remove residual cross terms between dipolar coupling and chemical shielding anisotropy more effectively and improve the spectral resolution over that observed in current state-of-the-art methods.

A statistical analysis of the Bloch-Siegert B1 mapping technique

A number of B1 mapping methods have been introduced. A model to facilitate choice among these methods is valuable, as the performance of each technique is affected by a variety of factors, including acquisition signal-to-noise ratio (SNR). The Bloch-Siegert shift B1 mapping method has recently garnered significant interest. In this paper, we present a statistical model suitable for analysis of the Bloch-Siegert shift method. Unlike previously presented models, the analysis is valid in both low SNR and high SNR regimes. We present a detailed analysis of the performance of the Bloch-Siegert shift B1 mapping method across a broad range of acquisition scenarios, and compare it to two other B1 mapping techniques (the dual angle method and the phase sensitive method). Further validation of the model is presented through both Monte Carlo simulations and experimental results. The simulations and experimental results match the model well, lending confidence to its accuracy. Each technique is found to perform well with high acquisition SNR. However, our results suggest that the dual angle method is not reliable in low SNR environments. Furthermore, the phase sensitive method appears to outperform the Bloch-Siegert shift method in these low-SNR cases, although variations of the Bloch-Siegert method may be possible that improve its performance at low SNR.

Simultaneous multislice multiband parallel radiofrequency excitation with independent slice-specific transmit B1 homogenization

PURPOSE

To develop a new parallel transmit (pTx) pulse design for simultaneous multiband (MB) excitation in order to tackle simultaneously the problems of transmit B1 (B1+) inhomogeneity and total radiofrequency (RF) power, so as to allow for optimal RF excitation when using MB pulses for slice acceleration for high and ultrahigh field MRI.

METHODS

With the proposed approach, each of the bands that are simultaneously excited is subject to a band-specific set of B1 complex shim weights. The method was validated in the human brain at 7T using a 16-channel pTx system and was compared to conventional MB pulses operating in the circularly polarized (CP) mode. Further numerical simulations based on measured B1 maps were conducted.

RESULTS

The new method improved B1+ homogeneity by 60% when keeping the total RF power constant and reduced total RF power by 72% when keeping the excitation fidelity constant, as compared to the conventional CP mode.

CONCLUSION

A new pTx pulse design formalism is introduced targeting slice-specific B1+ homogenization in MB excitation while constraining total RF power. These pulses lead to significantly improved slice-wise B1+ uniformity and/or largely reduced total RF power, as compared to the conventionally employed MB pulses applied in the CP mode.