Advanced three-dimensional tailored RF pulse design in volume selective parallel excitation

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).

Joint Design of RF and Gradient Waveforms via Auto-differentiation for 3D Tailored Excitation in MRI

This paper proposes a new method for joint design of radiofrequency (RF) and gradient waveforms in Magnetic Resonance Imaging (MRI), and applies it to the design of 3D spatially tailored saturation and inversion pulses. The joint design of both waveforms is characterized by the ODE Bloch equations, to which there is no known direct solution. Existing approaches therefore typically rely on simplified problem formulations based on, e.g., the small-tip approximation or constraining the gradient waveforms to particular shapes, and often apply only to specific objective functions for a narrow set of design goals (e.g., ignoring hardware constraints). This paper develops and exploits an auto-differentiable Bloch simulator to directly compute Jacobians of the (Bloch-simulated) excitation pattern with respect to RF and gradient waveforms. This approach is compatible with arbitrary sub-differentiable loss functions, and optimizes the RF and gradients directly without restricting the waveform shapes. For computational efficiency, we derive and implement explicit Bloch simulator Jacobians (approximately halving computation time and memory usage). To enforce hardware limits (peak RF, gradient, and slew rate), we use a change of variables that makes the 3D pulse design problem effectively unconstrained; we then optimize the resulting problem directly using the proposed auto-differentiation framework. We demonstrate our approach with two kinds of 3D excitation pulses that cannot be easily designed with conventional approaches: Outer-volume saturation (90° flip angle), and inner-volume inversion.

On the way to routine cardiac MRI at 7 Tesla - a pilot study on consecutive 84 examinations

INTRODUCTION

Cardiac magnetic resonance (CMR) at ultrahigh field (UHF) offers the potential of high resolution and fast image acquisition. Both technical and physiological challenges associated with CMR at 7T require specific hardware and pulse sequences. This study aimed to assess the current status and existing, publicly available technology regarding the potential of a clinical application of 7T CMR.

METHODS

Using a 7T MRI scanner and a commercially available radiofrequency coil, a total of 84 CMR examinations on 72 healthy volunteers (32 males, age 19-70 years, weight 50-103 kg) were obtained. Both electrocardiographic and acoustic triggering were employed. The data were analyzed regarding the diagnostic image quality and the influence of patient and hardware dependent factors. 50 complete short axis stacks and 35 four chamber CINE views were used for left ventricular (LV) and right ventricular (RV), mono-planar LV function, and RV fractional area change (FAC). Twenty-seven data sets included aortic flow measurements that were used to calculate stroke volumes. Subjective acceptance was obtained from all volunteers with a standardized questionnaire.

RESULTS

Functional analysis showed good functions of LV (mean EF 56%), RV (mean EF 59%) and RV FAC (mean FAC 52%). Flow measurements showed congruent results with both ECG and ACT triggering. No significant influence of experimental parameters on the image quality of the LV was detected. Small fractions of 5.4% of LV and 2.5% of RV segments showed a non-diagnostic image quality. The nominal flip angle significantly influenced the RV image quality.

CONCLUSION

The results demonstrate that already now a commercially available 7T MRI system, without major methods developments, allows for a solid morphological and functional analysis similar to the clinically established CMR routine approach. This opens the door towards combing routine CMR in patients with development of advanced 7T technology.

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.

SAR Simulations & Safety

At ultra-high fields, the assessment of radiofrequency (RF) safety presents several new challenges compared to low-field systems. Multi-channel RF transmit coils in combination with parallel transmit techniques produce time-dependent and spatially varying power loss densities in the tissue. Further, in ultra-high-field systems, localized field effects can be more pronounced due to a transition from the quasi stationary to the electromagnetic field regime. Consequently, local information on the RF field is required for reliable RF safety assessment as well as for monitoring of RF exposure during MR examinations. Numerical RF and thermal simulations for realistic exposure scenarios with anatomical body models are currently the only practical way to obtain the requisite local information on magnetic and electric field distributions as well as tissue temperature. In this article, safety regulations and the fundamental characteristics of RF field distributions in ultra-high-field systems are reviewed. Numerical methods for computation of RF fields as well as typical requirements for the analysis of realistic multi-channel RF exposure scenarios including anatomical body models are highlighted. In recent years, computation of the local tissue temperature has become of increasing interest, since a more accurate safety assessment is expected because temperature is directly related to tissue damage. Regarding thermal simulation, bio-heat transfer models and approaches for taking into account the physiological response of the human body to RF exposure are discussed. In addition, suitable methods are presented to validate calculated RF and thermal results with measurements. Finally, the concept of generalized simulation-based specific absorption rate (SAR) matrix models is discussed. These models can be incorporated into local SAR monitoring in multi-channel MR systems and allow the design of RF pulses under constraints for local SAR.

Improvement in imaging common temporal bone pathologies at 3 T MRI: small structures benefit from a small field of view

AIM

To compare image quality and evaluate its clinical importance in common temporal bone pathologies of a pTX-SPACE (parallel transmit [pTX] three-dimensional turbo spin-echo with variable flip angle [SPACE]) magnetic resonance imaging (MRI) sequence improved for spatial resolution to a standard-SPACE sequence exhibiting the same scan time at 3 T.

MATERIALS AND METHODS

Thirty-four patients were examined using a standard-SPACE and resolution improved pTX-SPACE sequence at 3 T MRI. The signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and image quality were assessed. Diseases investigated were vestibular schwannoma (VS), intralabyrinthine schwannoma (ILS), inner ear malformations, labyrinthitis, temporal bone fractures, and situation after VS resection.

RESULTS

Edge definition, intratumoural pattern, discrimination of VS from the modiolus and edge definition of ILS, separability from the spiral lamina, and detectability within cochlear turns were improved on the pTX-SPACE sequence. Detectability of malformations, post-traumatic changes, and discrimination of the cochlear and facial nerve after VS resection was improved on the pTX-SPACE sequence. In labyrinthitis, pTX-SPACE was not superior to standard-SPACE. The SNR and CNR were significantly reduced for pTX-SPACE.

CONCLUSIONS

pTX-SPACE significantly improves the detectability of temporal bone diseases, in particular, VS, ILS, and post-VS resection.

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.

Parallel-transmit-accelerated 2D Selective RF Excitation MR of the Temporal Bone: Enhanced Resolution of Labyrinthine and IAC Structures

RATIONALE AND OBJECTIVES

The purpose of this study was to compare a standard T2 SPACE sequence (standard-SPACE) used in temporal bone imaging at 3 T with a new parallel-transmit-accelerated 2D-selective radio frequency excitation technique for SPACE which was either time-improved or resolution-improved.

MATERIALS AND METHODS

Thirty-two consecutive patients were examined in this IRB-approved study using a standard T2 SPACE sequence, and then a time-improved zoomed SPACE sequence (short z-SPACE) with identical resolution but accelerated image acquisition and a resolution-improved zoomed SPACE sequence (high-resolution z-SPACE) with identical acquisition time but higher resolution at a 3-T magnetic resonance imaging system. Signal-to-noise ratio (SNR) was measured within selected regions of interest. Image quality of anatomic temporal bone structures was determined by two independent readers using a four-point visual scale.

RESULTS

Significant image quality improvement (p < 0.05) was observed in short z-SPACE and high-resolution z-SPACE, especially in structures of the cochlea and also regarding the delineation of the cranial nerves within the internal auditory canal. SNR measurements showed a lower SNR in the short z-SPACE and high-resolution z-SPACE sequences compared with standard-SPACE.

CONCLUSION

At 3 T parallel transmission using the zoomed SPACE sequences improves the delineation of small anatomical structures within the temporal bone significantly. It is especially helpful in depicting cochlear and internal auditory canal anatomy and can therefore improve imaging in patients with temporal bone pathologies.

Joint Design of Excitation k-Space Trajectory and RF Pulse for Small-Tip 3D Tailored Excitation in MRI

We propose a new method for the joint design of k-space trajectory and RF pulse in 3D small-tip tailored excitation. Designing time-varying RF and gradient waveforms for a desired 3D target excitation pattern in MRI poses a non-linear, non-convex, constrained optimization problem with relatively large problem size that is difficult to solve directly. Existing joint pulse design approaches are therefore typically restricted to predefined trajectory types such as EPI or stack-of-spirals that intrinsically satisfy the gradient maximum and slew rate constraints and reduce the problem size (dimensionality) dramatically, but lead to suboptimal excitation accuracy for a given pulse duration. Here we use a 2nd-order B-spline basis that can be fitted to an arbitrary k-space trajectory, and allows the gradient constraints to be implemented efficiently. We show that this allows the joint optimization problem to be solved with quite general k-space trajectories. Starting from an arbitrary initial trajectory, we first approximate the trajectory using B-spline basis, and then optimize the corresponding coefficients. We evaluate our method in simulation using four different k-space initializations: stack-of-spirals, SPINS, KT-points, and a new method based on KT-points. In all cases, our approach leads to substantial improvement in excitation accuracy for a given pulse duration. We also validated our method for inner-volume excitation using phantom experiments. The computation is fast enough for online applications.

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.