Fast and robust design of time-optimal k-space trajectories in MRI

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).

T-Hex: Tilted hexagonal grids for rapid 3D imaging

PURPOSE

The purpose of this work is to devise and demonstrate an encoding strategy for 3D MRI that reconciles high speed with flexible segmentation, uniform k-space density, and benign T 2 ∗ effects.

METHODS

Fast sampling of a 3D k-space is typically accomplished by 2D readouts per shot using EPI trains or spiral readouts. Tilted hexagonal (T-Hex) sampling is a way of acquiring more k-space volume per excitation while maintaining uniform sampling density and a smooth T 2 ∗ filter. The k-space volume covered per shot is controlled by the tilting angle. Image reconstruction is performed with a 3D extension of the iterative SENSE approach, incorporating actual field dynamics and static off-resonance. T-Hex imaging is compared with established 3D schemes in terms of speed and noise performance.

RESULTS

Tilted hexagonal acquisition is found to achieve greater imaging speed than known alternatives, particularly in combination with spiral trajectories. The interplay of the proposed 3D trajectories, array detection, and off-resonance is successfully addressed by iterative inversion of the full signal model. Enhanced coverage per shot is of greatest utility for high speed in an intermediate resolution regime of 1 to 4 mm. T-Hex EPI combines the benefits of extended coverage per shot with increased robustness against off-resonance effects.

CONCLUSION

Sampling of tilted hexagonal grids is a feasible means of gaining 3D imaging speed with near-optimal SNR efficiency and benign depiction properties. It is a particularly promising technique for time-resolved applications such as fMRI.

Towards a general framework for fast and feasible k-space trajectories for MRI based on projection methods

The design of feasible trajectories to traverse the k-space for sampling in magnetic resonance imaging (MRI) is important while considering ways to reduce the scan time. Over the recent years, non-Cartesian trajectories have been observed to result in benign artifacts and being less sensitive to motion. In this paper, we propose a generalized framework that encompasses projection-based methods to generate feasible non-Cartesian k-space trajectories. This framework allows to construct feasible trajectories from both random or structured initial trajectories, e.g., based on the traveling salesman problem (TSP). We evaluate the performance of the proposed methods by simulating the reconstruction of 128 × 128 and 256 × 256 phantom and brain MRI images in terms of structural similarity (SSIM) index and peak signal-to-noise ratio (PSNR) using compressed sensing techniques. It is observed that the TSP-based trajectories from the proposed projection method with constant acceleration parameterization (CAP) result in better reconstruction compared to the projection method with constant velocity parameterization (CVP) and this for a similar read-out time. Further, random-like trajectories are observed to be better than TSP-based trajectories as they reduce the read-out time while providing better reconstruction quality. A reduction in read-out time by upto 67% is achieved using the proposed projection with permutation (PP) method.

Time-domain principal component reconstruction (tPCR): A more efficient and stable iterative reconstruction framework for non-Cartesian functional MRI

PURPOSE

To improve the reconstruction efficiency (i.e., computational load) and stability of iterative reconstruction for non-Cartesian fMRI when using high undersampling rates and/or in the presence of strong off-resonance effects.

THEORY AND METHODS

The magnetic resonance encephalography (MREG) sequence with 3D non-Cartesian trajectory and 0.1s repetition time (TR) was applied to acquire fMRI datasets. Different from a conventional time-point-by-time-point sequential reconstruction (SR), the proposed time-domain principal component reconstruction (tPCR) performs three steps: (1) decomposing the k-t-space fMRI datasets into time-domain principal component space using singular value decomposition, (2) reconstructing each principal component with redistributed computation power according to their weights, and (3) combining the reconstructed principal components back to image-t-space. The comparison of reconstruction accuracy was performed by simulation experiments and then verified in real fMRI data.

RESULTS

The simulation experiments showed that the proposed tPCR was able to significantly reduce reconstruction errors, and subsequent functional activation errors, relative to SR at identical computational cost. Alternatively, at fixed reconstruction accuracy, computation time was greatly reduced. The improved performance was particularly obvious for L1-norm nonlinear reconstructions relative to L2-norm linear reconstructions and robust to different regularization strength, undersampling rates, and off-resonance effects intensity. By examining activation maps, tPCR was also found to give similar improvements in real fMRI experiments.

CONCLUSION

The proposed proof-of-concept tPCR framework could improve (1) the reconstruction efficiency of iterative reconstruction, and (2) the reconstruction stability especially for nonlinear reconstructions. As a practical consideration, the improved reconstruction speed promotes the application of highly undersampled non-Cartesian fast fMRI.

Squeezed Trajectory Design for Peak RF and Integrated RF Power Reduction in Parallel Transmission MRI

High peak RF amplitude and excessive specific absorption rate (SAR) are two critical concerns for hardware implementation and patient safety in scientific and clinical research for high field MRI using parallel transmissions (pTX). In this paper, we introduce a squeezing strategy to reduce peak RF amplitude and integrated RF power via direct reshaping of the k-space trajectory. In the existing peak RF / integrated RF power optimization methods gradient amplitude or slew rate is reduced, but the k-space trajectory remains unchanged. Unlike these traditional methods, we worked directly in the excitation k-space to reshape k-space traversal by a squeezing vector in order to achieve peak RF and total RF power optimization, using a particle swarm optimization algorithm. The squeezing strategy was applied to the conventional variable density spiral (CVDS) and the variable rate selective excitation (VERSE) trajectories, dubbed SVDS (squeezed variable density spiral) and SVERSE (squeezing trajectory with VERSE), respectively, for different excitation profiles of small or large tip angles. Pulse acceleration and off-resonance effects were evaluated for an 8-ch pTX via Bloch simulation. CVDS, VERSE, SVDS, and SVERSE pulses were implemented on a 3T scanner with a 2-ch pTX. Phantom and in vivo experiments were performed for reduced FOV (rFOV) imaging. The results show that SVDS pulses simultaneously reduce integrated RF power and peak RF by about 30% on average compared to CVDS pulses for a square pattern ( $80\times80$ mm2) with flip angles of 30°, 90°, and 180°. Compared with the VERSE method under the same peak RF constraints, the SVDS method reduces integrated RF power by an average of 20% for small tip excitations for profiles of slice, rectangular, square, and circle, and has slightly reduced excitation accuracy slightly (about 0.6%, from 6.8% to 7.4%). The SVERSE method shortens the duration of the VERSE pulse by 12.8% at large ti p angle (180°). Feasibility for rFOV imaging was demonstrated with phantom and in vivo experiments with squeezed pulses.

Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories

PURPOSE

To design short parallel transmission (pTx) pulses for excitation of arbitrary three-dimensional (3D) magnetization patterns.

METHODS

We propose a joint optimization of the pTx radiofrequency (RF) and gradient waveforms for excitation of arbitrary 3D magnetization patterns. Our optimization of the gradient waveforms is based on the parameterization of k-space trajectories (3D shells, stack-of-spirals, and cross) using a small number of shape parameters that are well-suited for optimization. The resulting trajectories are smooth and sample k-space efficiently with few turns while using the gradient system at maximum performance. Within each iteration of the k-space trajectory optimization, we solve a small tip angle least-squares RF pulse design problem. Our RF pulse optimization framework was evaluated both in Bloch simulations and experiments on a 7T scanner with eight transmit channels.

RESULTS

Using an optimized 3D cross (shells) trajectory, we were able to excite a cube shape (brain shape) with 3.4% (6.2%) normalized root-mean-square error in less than 5 ms using eight pTx channels and a clinical gradient system (Gmax  = 40 mT/m, Smax  = 150 T/m/s). This compared with 4.7% (41.2%) error for the unoptimized 3D cross (shells) trajectory. Incorporation of B0 robustness in the pulse design significantly altered the k-space trajectory solutions.

CONCLUSION

Our joint gradient and RF optimization approach yields excellent excitation of 3D cube and brain shapes in less than 5 ms, which can be used for reduced field of view imaging and fat suppression in spectroscopy by excitation of the brain only. Magn Reson Med 76:1170-1182, 2016. © 2015 Wiley Periodicals, Inc.

A Projection Algorithm for Gradient Waveforms Design in Magnetic Resonance Imaging

Collecting the maximal amount of information in a given scanning time is a major concern in magnetic resonance imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate, etc.), physical distortions (e.g., off-resonance effects) and sampling theorems (Shannon, compressed sensing) must be taken into account simultaneously, which makes this problem extremely challenging. To date, the main approach to design gradient waveform has consisted of selecting an initial shape (e.g., spiral, radial lines, etc.) and then traversing it as fast as possible using optimal control. In this paper, we propose an alternative solution which first consists of defining a desired parameterization of the trajectory and then of optimizing for minimal deviation of the sampling points within gradient constraints. This method has various advantages. First, it better preserves the density of the input curve which is critical in sampling theory. Second, it allows to smooth high curvature areas making the acquisition time shorter in some cases. Third, it can be used both in the Shannon and CS sampling theories. Last, the optimized trajectory is computed as the solution of an efficient iterative algorithm based on convex programming. For piecewise linear trajectories, as compared to optimal control reparameterization, our approach generates a gain in scanning time of 10% in echo planar imaging while improving image quality in terms of signal-to-noise ratio (SNR) by more than 6 dB. We also investigate original trajectories relying on traveling salesman problem solutions. In this context, the sampling patterns obtained using the proposed projection algorithm are shown to provide significantly better reconstructions (more than 6 dB) while lasting the same scanning time.

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.