Accelerated multidimensional radiofrequency pulse design for parallel transmission using concurrent computation on multiple graphics processing units

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.

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.

Sparse parallel transmission on randomly perturbed spiral k-space trajectory

Combination of parallel transmission and sparse pulse is able to shorten the excitation by using both the coil sensitivity and sparse k-space, showing improved fast excitation capability over the use of parallel transmission alone. However, to design an optimal k-space trajectory for sparse parallel transmission is a challenging task. In this work, a randomly perturbed sparse k-space trajectory is designed by modifying the path of a spiral trajectory along the sparse k-space data, and the sparse parallel transmission RF pulses are subsequently designed based on this optimal trajectory. This method combines the parallel transmission and sparse spiral k-space trajectory, potentially to further reduce the RF transmission time. Bloch simulation of 90° excitation by using a four channel coil array is performed to demonstrate its feasibility. Excitation performance of the sparse parallel transmission technique at different reduction factors of 1, 2, and 4 is evaluated. For comparison, parallel excitation using regular spiral trajectory is performed. The passband errors of the excitation profiles of each transmission are calculated for quantitative assessment of the proposed excitation method.

Efficient method to design RF pulses for parallel excitation MRI using gridding and conjugate gradient

Parallel excitation (pTx) techniques with multiple transmit channels have been widely used in high field MRI imaging to shorten the RF pulse duration and/or reduce the specific absorption rate (SAR). However, the efficiency of pulse design still needs substantial improvement for practical real-time applications. In this paper, we present a detailed description of a fast pulse design method with Fourier domain gridding and a conjugate gradient method. Simulation results of the proposed method show that the proposed method can design pTx pulses at an efficiency 10 times higher than that of the conventional conjugate-gradient based method, without reducing the accuracy of the desirable excitation patterns.

Medical image processing on the GPU - past, present and future

Graphics processing units (GPUs) are used today in a wide range of applications, mainly because they can dramatically accelerate parallel computing, are affordable and energy efficient. In the field of medical imaging, GPUs are in some cases crucial for enabling practical use of computationally demanding algorithms. This review presents the past and present work on GPU accelerated medical image processing, and is meant to serve as an overview and introduction to existing GPU implementations. The review covers GPU acceleration of basic image processing operations (filtering, interpolation, histogram estimation and distance transforms), the most commonly used algorithms in medical imaging (image registration, image segmentation and image denoising) and algorithms that are specific to individual modalities (CT, PET, SPECT, MRI, fMRI, DTI, ultrasound, optical imaging and microscopy). The review ends by highlighting some future possibilities and challenges.

Multi-slice parallel transmission three-dimensional tailored RF (PTX 3DTRF) pulse design for signal recovery in ultra high field functional MRI

T(2)(∗) weighted fMRI at high and ultra high field (UHF) is often hampered by susceptibility-induced, through-plane, signal loss. Three-dimensional tailored RF (3DTRF) pulses have been shown to be an effective approach for mitigating through-plane signal loss at UHF. However, the required RF pulse lengths are too long for practical applications. Recently, parallel transmission (PTX) has emerged as a very effective means for shortening the RF pulse duration for 3DTRF without sacrificing the excitation performance. In this article, we demonstrate a RF pulse design strategy for 3DTRF based on the use of multi-slice PTX 3DTRF to simultaneously and precisely recover signal with whole-brain coverage. Phantom and human experiments are used to demonstrate the effectiveness and robustness of the proposed method on three subjects using an eight-channel whole body parallel transmission system.

A fast pulse design for parallel excitation with gridding conjugate gradient

Parallel excitation (pTx) is recognized as a crucial technique in high field MRI to address the transmit field inhomogeneity problem. However, it can be time consuming to design pTx pulses which is not desirable. In this work, we propose a pulse design with gridding conjugate gradient (CG) based on the small-tip-angle approximation. The two major time consuming matrix-vector multiplications are substituted by two operators which involves with FFT and gridding only. Simulation results have shown that the proposed method is 3 times faster than conventional method and the memory cost is reduced by 1000 times.

Inner-volume imaging in vivo using three-dimensional parallel spatially selective excitation

This work describes the first experimental realization of three-dimensional spatially selective excitation using parallel transmission in vivo. For the design of three-dimensional parallel excitation pulses with short durations and high excitation accuracy, the choice of a suitable transmit k-space trajectory is crucial. For this reason, the characteristics of a stack-of-spirals trajectory and of a concentric-shells trajectory were examined in an initial simulation study. It showed that, especially when undersampling the trajectories in combination with parallel transmission, experimental parameters such as transmit-coil geometry and off-resonance conditions have an essential impact on the suitability of the selected trajectory and undersampling scheme. Both trajectories were applied in MR inner-volume imaging experiments which demonstrate that acceptably short and robust three-dimensional selective pulses can be achieved if the trajectory is temporally optimized and its actual path is measured and considered during pulse calculation. Pulse durations as short as 3.2 ms were realized and such pulses were appropriate to accurately excite arbitrarily shaped volumes in a corn cob and in a rat in vivo. Reduced field-of-view imaging of these selectively excited targets allowed high spatial resolution and significantly reduced measurement times and furthermore demonstrates the feasibility of three-dimensional parallel excitation in realistic MRI applications in vivo.

A novel fast algorithm for parallel excitation: pulse design in MRI

Spatially selective excitations with parallel transmitters have been regarded as a key in solving several high field MRI problems such as inhomogeneity correction and reducing specific absorption rate. However, three-dimensional pulse design in general is very time consuming which may prevent it from real-time applications. In this work, we explore the sparsity in the pulse design system equation. The size of system equation is reduced after a sparse transform and therefore design speed can be significantly increased. Computer simulations in several common scenarios show that the proposed design method can achieve up to an order of magnitude speedup than the conventional design methods while maintaining similar excitation accuracy.