Parallel-transmission-enabled three-dimensional T2-weighted imaging of the human brain at 7 Tesla

Parallel transmit (pTx) with online pulse design for task-based fMRI at 7 T

PURPOSE

Parallel transmission (pTx) is an approach to improve image uniformity for ultra-high field imaging. In this study, we modified an echo planar imaging (EPI) sequence to design subject-specific pTx pulses online. We compared its performance against EPI with conventional circularly polarised (CP) pulses.

METHODS

We compared the pTx-EPI and CP-EPI sequences in a short EPI acquisition protocol and for two different functional paradigms in six healthy volunteers (2 female, aged 23-36 years, mean age 29.2 years). We chose two paradigms that are typically affected by signal dropout at 7 T: a visual objects localiser to determine face/scene selective brain regions and a semantic-processing task.

RESULTS

Across all subjects, pTx-EPI improved whole-brain mean temporal signal-to-noise ratio (tSNR) by 11.0% compared to CP-EPI. We also compared the ability of pTx-EPI and CP-EPI to detect functional activation for three contrasts over the two paradigms: face > object and scene > object for the visual objects localiser and semantic association > pattern matching for the semantic-processing paradigm. Across all three contrasts, pTx-EPI showed higher median z-scores and detected more active voxels in relevant areas, as determined from previous 3 T studies.

CONCLUSION

We have demonstrated a workflow for EPI acquisitions with online per-subject pulse calculations. We saw improved performance in both tSNR and functional acquisitions from pTx-EPI. Thus, we believe that online calculation pTx-EPI is robust enough for future fMRI studies, especially where activation is expected in brain areas liable to significant signal dropout.

Parallel transmission 2D RARE imaging at 7T with transmit field inhomogeneity mitigation and local SAR control

PURPOSE

We develop and test a parallel transmit (pTx) pulse design framework to mitigate transmit field inhomogeneity with control of local specific absorption rate (SAR) in 2D rapid acquisition with relaxation enhancement (RARE) imaging at 7T.

METHODS

We design large flip angle RF pulses with explicit local SAR constraints by numerical simulation of the Bloch equations. Parallel computation and analytical expressions for the Jacobian and the Hessian matrices are employed to reduce pulse design time. The refocusing-excitation "spokes" pulse pairs are designed to satisfy the Carr-Purcell-Meiboom-Gill (CPMG) condition using a combined magnitude least squares-least squares approach.

RESULTS

In a simulated dataset, the proposed approach reduced peak local SAR by up to 56% for the same level of refocusing uniformity error and reduced refocusing uniformity error by up to 59% (from 32% to 7%) for the same level of peak local SAR compared to the circularly polarized birdcage mode of the pTx array. Using explicit local SAR constraints also reduced peak local SAR by up to 46% compared to an RF peak power constrained design. The excitation and refocusing uniformity error were reduced from 20%-33% to 4%-6% in single slice phantom experiments. Phantom experiments demonstrated good agreement between the simulated excitation and refocusing uniformity profiles and experimental image shading.

CONCLUSION

PTx-designed excitation and refocusing CPMG pulse pairs can mitigate transmit field inhomogeneity in the 2D RARE sequence. Moreover, local SAR can be decreased significantly using pTx, potentially leading to better slice coverage, enabling larger flip angles or faster imaging.

Neuroimaging at 7 Tesla: a pictorial narrative review

Neuroimaging using the 7-Tesla (7T) human magnetic resonance (MR) system is rapidly gaining popularity after being approved for clinical use in the European Union and the USA. This trend is the same for functional MR imaging (MRI). The primary advantages of 7T over lower magnetic fields are its higher signal-to-noise and contrast-to-noise ratios, which provide high-resolution acquisitions and better contrast, making it easier to detect lesions and structural changes in brain disorders. Another advantage is the capability to measure a greater number of neurochemicals by virtue of the increased spectral resolution. Many structural and functional studies using 7T have been conducted to visualize details in the white matter and layers of the cortex and hippocampus, the subnucleus or regions of the putamen, the globus pallidus, thalamus and substantia nigra, and in small structures, such as the subthalamic nucleus, habenula, perforating arteries, and the perivascular space, that are difficult to observe at lower magnetic field strengths. The target disorders for 7T neuroimaging range from tumoral diseases to vascular, neurodegenerative, and psychiatric disorders, including Alzheimer's disease, Parkinson's disease, multiple sclerosis, epilepsy, major depressive disorder, and schizophrenia. MR spectroscopy has also been used for research because of its increased chemical shift that separates overlapping peaks and resolves neurochemicals more effectively at 7T than a lower magnetic field. This paper presents a narrative review of these topics and an illustrative presentation of images obtained at 7T. We expect 7T neuroimaging to provide a new imaging biomarker of various brain disorders.

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.

Improved 7 Tesla transmit field homogeneity with reduced electromagnetic power deposition using coupled Tic Tac Toe antennas

Recently cleared by the FDA, 7 Tesla (7 T) MRI is a rapidly growing technology that can provide higher resolution and enhanced contrast in human MRI images. However, the increased operational frequency (~ 297 MHz) hinders its full potential since it causes inhomogeneities in the images and increases the power deposition in the tissues. This work describes the optimization of an innovative radiofrequency (RF) head coil coupled design, named Tic Tac Toe, currently used in large scale human MRI scanning at 7 T; to date, this device was used in more than 1,300 neuro 7 T MRI scans. Electromagnetic simulations of the coil were performed using the finite-difference time-domain method. Numerical optimizations were used to combine the calculated electromagnetic fields produced by these antennas, based on the superposition principle, resulting in homogeneous magnetic field distributions at low levels of power deposition in the tissues. The simulations were validated in-vivo using the Tic Tac Toe RF head coil system on a 7 T MRI scanner.

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.

IMPULSE: A scalable algorithm for design of minimum specific absorption rate parallel transmit RF pulses

PURPOSE

Managing local specific absorption rate (SAR) in parallel transmission requires ensuring that the peak SAR over a large number of voxels (> 10 5 ) is below the regulatory limit. The safety risk to the patient depends on cumulative (not instantaneous) SAR thus making a joint design of all RF pulses in a sequence desirable. We propose the Iterative Minimization Procedure with Uncompressed Local SAR Estimate (IMPULSE), an efficient optimization formulation and algorithm that can handle uncompressed SAR matrices and optimize pulses for all slices jointly within a practical time frame.

THEORY AND METHODS

IMPULSE optimizes parallel transmit pulses for small-tip-angle slice selective excitation to minimize a single cost function incorporating multiple quantities (local SAR, global SAR, and per-channel power) averaged over the entire multislice scan subject to a strict constraint on excitation accuracy. Pulses for an 8-channel 7T head coil were designed with IMPULSE and compared with pulses designed using generic optimization algorithms and VOPs to assess the computation time and SAR performance benefits.

RESULTS

IMPULSE achieves lower SAR and shorter computation time compared with a VOP approach. Compared with the generic sequential quadratic programming algorithm, computation time is reduced by a factor of 5-6 by using IMPULSE. Using as many as 6 million local SAR terms, up to 120 slices can be designed jointly with IMPULSE within 45 s.

CONCLUSIONS

IMPULSE can handle significantly larger number of SAR matrices and slices than conventional optimization algorithms, enabling the use of uncompressed or partially compressed SAR matrices to design pulses for a multislice scan in a practical time frame.

Pros and cons of ultra-high-field MRI/MRS for human application

Magnetic resonance imaging and spectroscopic techniques are widely used in humans both for clinical diagnostic applications and in basic research areas such as cognitive neuroimaging. In recent years, new human MR systems have become available operating at static magnetic fields of 7 T or higher (≥300 MHz proton frequency). Imaging human-sized objects at such high frequencies presents several challenges including non-uniform radiofrequency fields, enhanced susceptibility artifacts, and higher radiofrequency energy deposition in the tissue. On the other side of the scale are gains in signal-to-noise or contrast-to-noise ratio that allow finer structures to be visualized and smaller physiological effects to be detected. This review presents an overview of some of the latest methodological developments in human ultra-high field MRI/MRS as well as associated clinical and scientific applications. Emphasis is given to techniques that particularly benefit from the changing physical characteristics at high magnetic fields, including susceptibility-weighted imaging and phase-contrast techniques, imaging with X-nuclei, MR spectroscopy, CEST imaging, as well as functional MRI. In addition, more general methodological developments such as parallel transmission and motion correction will be discussed that are required to leverage the full potential of higher magnetic fields, and an overview of relevant physiological considerations of human high magnetic field exposure is provided.

Human Connectome Project-style resting-state functional MRI at 7 Tesla using radiofrequency parallel transmission

We investigate the utility of radiofrequency (RF) parallel transmission (pTx) for whole-brain resting-state functional MRI (rfMRI) acquisition at 7 Tesla (7T). To this end, Human Connectome Project (HCP)-style data acquisitions were chosen as a showcase example. Five healthy subjects were scanned in pTx and single-channel transmit (1Tx) modes. The pTx data were acquired using a prototype 16-channel transmit system and a commercially available Nova 8-channel transmit 32-channel receive RF head coil. Additionally, pTx single-spoke multiband (MB) pulses were designed to image sagittal slices. HCP-style 7T rfMRI data (1.6-mm isotropic resolution, 5-fold slice and 2-fold in-plane acceleration, 3600 image volumes and ∼ 1-h scan) were acquired with pTx and the results were compared to those acquired with the original 7T HCP rfMRI protocol. The use of pTx significantly improved flip-angle uniformity across the brain, with coefficient of variation (i.e., std/mean) of whole-brain flip-angle distribution reduced on average by ∼39%. This in turn yielded ∼17% increase in group temporal SNR (tSNR) as averaged across the entire brain and ∼10% increase in group functional contrast-to-noise ratio (fCNR) as averaged across the grayordinate space (including cortical surfaces and subcortical voxels). Furthermore, when placing a seed in either the posterior parietal lobe or putamen to estimate seed-based dense connectome, the increase in fCNR was observed to translate into stronger correlation of the seed with the rest of the grayordinate space. We have demonstrated the utility of pTx for slice-accelerated high-resolution whole-brain rfMRI at 7T; as compared to current state-of-the-art, the use of pTx improves flip-angle uniformity, increases tSNR, enhances fCNR and strengthens functional connectivity estimation.

Whole-brain 3D FLAIR at 7T using direct signal control

Purpose

Image quality obtained for brain imaging at 7T can be hampered by inhomogeneities in the static magnetic field, B₀, and the RF electromagnetic field, B₁. In imaging sequences such as fluid‐attenuated inversion recovery (FLAIR), which is used to assess neurological disorders, these inhomogeneities cause spatial variations in signal that can reduce clinical efficacy. In this work, we aim to correct for signal inhomogeneities to ensure whole‐brain coverage with 3D FLAIR at 7T.

Methods

The direct signal control (DSC) framework was used to optimize channel weightings applied to the 8 transmit channels used in this work on a pulse‐by‐pulse basis through the echo train in the FLAIR sequences. 3D FLAIR brain images were acquired on 5 different subjects and compared with imaging using a quadrature‐like mode of the transmit array. Precomputed “universal” DSC solutions calculated from a separate set of 5 subjects were also explored.

Results

DSC consistently enabled improved imaging across all subjects, with no dropouts in signal seen over the entire brain volume, which contrasted with imaging in quadrature mode. Further, the universal DSC solutions also consistently improved imaging despite not being optimized specifically for the subject being imaged.

Conclusion

3D FLAIR brain imaging at 7T is substantially improved using DSC and is able to recover regions of low signal without increasing imaging time or interecho spacing.

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.

Toward imaging the body at 10.5 tesla

PURPOSE

To explore the potential of performing body imaging at 10.5 Tesla (T) compared with 7.0T through evaluating the transmit/receive performance of similarly configured dipole antenna arrays.

METHODS

Fractionated dipole antenna elements for 10.5T body imaging were designed and evaluated using numerical simulations. Transmit performance of antenna arrays inside the prostate, kidneys and heart were investigated and compared with those at 7.0T using both phase-only radiofrequency (RF) shimming and multi-spoke pulses. Signal-to-noise ratio (SNR) comparisons were also performed. A 10-channel antenna array was constructed to image the abdomen of a swine at 10.5T. Numerical methods were validated with phantom studies at both field strengths.

RESULTS

Similar power efficiencies were observed inside target organs with phase-only shimming, but RF nonuniformity was significantly higher at 10.5T. Spokes RF pulses allowed similar transmit performance with accompanying local specific absorption rate increases of 25-90% compared with 7.0T. Relative SNR gains inside the target anatomies were calculated to be >two-fold higher at 10.5T, and 2.2-fold SNR gain was measured in a phantom. Gradient echo and fast spin echo imaging demonstrated the feasibility of body imaging at 10.5T with the designed array.

CONCLUSION

While comparable power efficiencies can be achieved using dipole antenna arrays with static shimming at 10.5T; increasing RF nonuniformities underscore the need for efficient, robust, and safe parallel transmission methods. Magn Reson Med 77:434-443, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Seven-Tesla MRI and neuroimaging biomarkers for Alzheimer's disease

The goal of this paper was to review the effectiveness of using 7-T MRI to study neuroimaging biomarkers for Alzheimer's disease (AD). The authors reviewed the literature for articles published to date on the use of 7-T MRI to study AD. Thus far, there are 3 neuroimaging biomarkers for AD that have been studied using 7-T MRI in AD tissue: 1) neuroanatomical atrophy; 2) molecular characterization of hypointensities; and 3) microinfarcts. Seven-Tesla MRI has had mixed results when used to study the 3 aforementioned neuroimaging biomarkers for AD. First, in the detection of neuroanatomical atrophy, 7-T MRI has exciting potential. Historically, noninvasive imaging of neuroanatomical atrophy during AD has been limited by suboptimal resolution. However, now there is compelling evidence that the high resolution of 7-T MRI may help overcome this hurdle. Second, in detecting the characterization of hypointensities, 7-T MRI has had varied success. PET scans will most likely continue to lead in the noninvasive imaging of amyloid plaques; however, there is emerging evidence that 7-T MRI can accurately detect iron deposits within activated microglia, which may help shed light on the role of the immune system in AD pathogenesis. Finally, in the detection of microinfarcts, 7-T MRI may also play a promising role, which may help further elucidate the relationship between cerebrovascular health and AD progression.

Recent applications of UHF-MRI in the study of human brain function and structure: a review

The increased availability of ultra-high-field (UHF) MRI has led to its application in a wide range of neuroimaging studies, which are showing promise in transforming fundamental approaches to human neuroscience. This review presents recent work on structural and functional brain imaging, at 7 T and higher field strengths. After a short outline of the effects of high field strength on MR images, the rapidly expanding literature on UHF applications of blood-oxygenation-level-dependent-based functional MRI is reviewed. Structural imaging is then discussed, divided into sections on imaging weighted by relaxation time, including quantitative relaxation time mapping, phase imaging and quantitative susceptibility mapping, angiography, diffusion-weighted imaging, and finally magnetization-transfer imaging. The final section discusses studies using the high spatial resolution available at UHF to identify explicit links between structure and function. Copyright © 2015 John Wiley & Sons, Ltd.

Multiparametric imaging with heterogeneous radiofrequency fields

Magnetic resonance imaging (MRI) has become an unrivalled medical diagnostic technique able to map tissue anatomy and physiology non-invasively. MRI measurements are meticulously engineered to control experimental conditions across the sample. However, residual radiofrequency (RF) field inhomogeneities are often unavoidable, leading to artefacts that degrade the diagnostic and scientific value of the images. Here we show that, paradoxically, these artefacts can be eliminated by deliberately interweaving freely varying heterogeneous RF fields into a magnetic resonance fingerprinting data-acquisition process. Observations made based on simulations are experimentally confirmed at 7 Tesla (T), and the clinical implications of this new paradigm are illustrated with in vivo measurements near an orthopaedic implant at 3T. These results show that it is possible to perform quantitative multiparametric imaging with heterogeneous RF fields, and to liberate MRI from the traditional struggle for control over the RF field uniformity.

Magnetic resonance fingerprinting (MRF) requires a uniform B₁⁺ radiofrequency field. Here the authors present plug-n-play MRF, a technique that enables multiparametric imaging with heterogeneous B₁⁺ fields, and demonstrate its utility in the presence of RF distortion caused by a metallic orthopaedic implant.

Robust imaging of hippocampal inner structure at 7T: in vivo acquisition protocol and methodological choices

OBJECTIVE

Motion-robust multi-slab imaging of hippocampal inner structure in vivo at 7T.

MATERIALS AND METHODS

Motion is a crucial issue for ultra-high resolution imaging, such as can be achieved with 7T MRI. An acquisition protocol was designed for imaging hippocampal inner structure at 7T. It relies on a compromise between anatomical details visibility and robustness to motion. In order to reduce acquisition time and motion artifacts, the full slab covering the hippocampus was split into separate slabs with lower acquisition time. A robust registration approach was implemented to combine the acquired slabs within a final 3D-consistent high-resolution slab covering the whole hippocampus. Evaluation was performed on 50 subjects overall, made of three groups of subjects acquired using three acquisition settings; it focused on three issues: visibility of hippocampal inner structure, robustness to motion artifacts and registration procedure performance.

RESULTS

Overall, T2-weighted acquisitions with interleaved slabs proved robust. Multi-slab registration yielded high quality datasets in 96 % of the subjects, thus compatible with further analyses of hippocampal inner structure.

CONCLUSION

Multi-slab acquisition and registration setting is efficient for reducing acquisition time and consequently motion artifacts for ultra-high resolution imaging of the inner structure of the hippocampus.

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.

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.

Two-spoke placement optimization under explicit specific absorption rate and power constraints in parallel transmission at ultra-high field

The spokes method combined with parallel transmission is a promising technique to mitigate the B1(+) inhomogeneity at ultra-high field in 2D imaging. To date however, the spokes placement optimization combined with the magnitude least squares pulse design has never been done in direct conjunction with the explicit Specific Absorption Rate (SAR) and hardware constraints. In this work, the joint optimization of 2-spoke trajectories and RF subpulse weights is performed under these constraints explicitly and in the small tip angle regime. The problem is first considerably simplified by making the observation that only the vector between the 2 spokes is relevant in the magnitude least squares cost-function, thereby reducing the size of the parameter space and allowing a more exhaustive search. The algorithm starts from a set of initial k-space candidates and performs in parallel for all of them optimizations of the RF subpulse weights and the k-space locations simultaneously, under explicit SAR and power constraints, using an active-set algorithm. The dimensionality of the spoke placement parameter space being low, the RF pulse performance is computed for every location in k-space to study the robustness of the proposed approach with respect to initialization, by looking at the probability to converge towards a possible global minimum. Moreover, the optimization of the spoke placement is repeated with an increased pulse bandwidth in order to investigate the impact of the constraints on the result. Bloch simulations and in vivo T2(∗)-weighted images acquired at 7 T validate the approach. The algorithm returns simulated normalized root mean square errors systematically smaller than 5% in 10 s.