William A. Grissom

Spatial Domain Method for the Design of RF Pulses in Multicoil Parallel Excitation

Parallel excitation has been introduced as a means of accelerating multidimensional, spatially‐selective excitation using multiple transmit coils, each driven by a unique RF pulse. Previous approaches to RF pulse design in parallel excitation were either formulated in the frequency domain or restricted to echo‐planar trajectories, or both. This paper presents an approach that is formulated as a quadratic optimization problem in the spatial domain and allows the use of arbitrary k‐space trajectories. Compared to frequency domain approaches, the new design method has some important advantages. It allows for the specification of a region of interest (ROI), which improves excitation accuracy at high speedup factors. It allows for magnetic field inhomogeneity compensation during excitation. Regularization may be used to control integrated and peak pulse power. The effects of Bloch equation nonlinearity on the large‐tip‐angle excitation error of RF pulses designed with the method are investigated, and the utility of Tikhonov regularization in mitigating this error is demonstrated. Magn Reson Med, 2006.

Reduction of transmitter B1 inhomogeneity with transmit SENSE slice‐select pulses

Parallel transmitter techniques are a promising approach for reducing transmitter B1 inhomogeneity due to the potential for adjusting the spatial excitation profile with independent RF pulses. These techniques may be further improved with transmit sensitivity encoding (SENSE) methods because the sensitivity information in pulse design provides an excitation that is inherently compensated for transmitter B1 inhomogeneity. This paper presents a proof of this concept using transmit SENSE 3D tailored RF pulses designed for small flip angles. An eight‐channel receiver coil was used to mimic parallel transmission for brain imaging at 3T. The transmit SENSE pulses were based on the fast‐kz design and produced 5‐mm‐thick slices at a flip angle of 30° with only a 4.3‐ms pulse length. It was found that the transmit SENSE pulses produced more homogeneous images than those obtained from the complex sum of images from all receivers excited with a standard RF pulse. Magn Reson Med 57:842–847, 2007.

Hybrid referenceless and multibaseline subtraction MR thermometry for monitoring thermal therapies in moving organs.

PURPOSE Magnetic resonance thermometry using the proton resonance frequency (PRF) shift is a promising technique for guiding thermal ablation. For temperature monitoring in moving organs, such as the liver and the heart, problems with motion must be addressed. Multi-baseline subtraction techniques have been proposed, which use a library of baseline images covering the respiratory and cardiac cycle. However, main field shifts due to lung and diaphragm motion can cause large inaccuracies in multi-baseline subtraction. Referenceless thermometry methods based on polynomial phase regression are immune to motion and susceptibility shifts. While referenceless methods can accurately estimate temperature within the organ, in general, the background phase at organ/tissue interfaces requires large polynomial orders to fit, leading to increased danger that the heated region itself will be fitted by the polynomial and thermal dose will be underestimated. In this paper, a hybrid method for PRF thermometry in moving organs is presented that combines the strengths of referenceless and multi-baseline thermometry. METHODS The hybrid image model assumes that three sources contribute to image phase during thermal treatment: Background anatomical phase, spatially smooth phase deviations, and focal, heat-induced phase shifts. The new model and temperature estimation algorithm were tested in the heart and liver of normal volunteers, in a moving phantom HIFU heating experiment, and in numerical simulations of thermal ablation. The results were compared to multi-baseline and referenceless methods alone. RESULTS The hybrid method allows for in vivo temperature estimation in the liver and the heart with lower temperature uncertainty compared to multi-baseline and referenceless methods. The moving phantom HIFU experiment showed that the method accurately estimates temperature during motion in the presence of smooth main field shifts. Numerical simulations illustrated the methods sensitivity to algorithm parameters and hot spot features. CONCLUSIONS This new hybrid method for MR thermometry in moving organs combines the strengths of both multi-baseline subtraction and referenceless thermometry and overcomes their fundamental weaknesses.

Additive angle method for fast large-tip-angle RF pulse design in parallel excitation

Current methods for parallel excitation RF pulse design are based on the small‐tip‐angle approximation, which provides a computationally efficient means of pulse calculation. In general, pulses designed with those methods are inaccurate when scaled to produce large‐tip angles, and methods for large‐tipangle pulse design are more computationally demanding. This paper introduces a fast iterative method for large‐tip‐angle parallel pulse design that is formulated as a small number of Bloch equation simulations and fast small‐tip‐angle pulse designs, the results of which add to produce large‐tip‐angle pulses. Simulations and a phantom experiment demonstrate that the method is effective in designingmultidimensional large‐tip‐angle pulses of high excitation accuracy, compared to pulses designed with small‐tip‐angle methods. Magn Reson Med 59:779–787, 2008.

Fast Large-Tip-Angle Multidimensional and Parallel RF Pulse Design in MRI

Large-tip-angle multidimensional radio-frequency (RF) pulse design is a difficult problem, due to the nonlinear response of magnetization to applied RF at large tip-angles. In parallel excitation, multidimensional RF pulse design is further complicated by the possibility for transmit field patterns to change between subjects, requiring pulses to be designed rapidly while a subject lies in the scanner. To accelerate pulse design, we introduce a fast version of the optimal control method for large-tip-angle parallel excitation. The new method is based on a novel approach to analytically linearizing the Bloch equation about a large-tip-angle RF pulse, which results in an approximate linear model for the perturbations created by adding a small-tip-angle pulse to a large-tip-angle pulse. The linear model can be evaluated rapidly using nonuniform fast Fourier transforms, and we apply it iteratively to produce a sequence of pulse updates that improve excitation accuracy. We achieve drastic reductions in design time and memory requirements compared to conventional optimal control, while producing pulses of similar accuracy. The new method can also compensate for nonidealities such as main field inhomogeneties.

Time-Optimal Design for Multidimensional and Parallel Transmit Variable-Rate Selective Excitation

Variable‐rate selective excitation (VERSE) is a radio frequency (RF) pulse reshaping technique. It is most commonly used to reduce the peak magnitude and specific absorption rate (SAR) of RF pulses by reshaping pulses and gradient waveforms to reduce RF magnitude while preserving excitation profiles. In this work, a general time‐optimal VERSE algorithm for multidimensional and parallel transmit pulses is presented. Time optimality is achieved by translating peak RF limits to gradient upper bounds in excitation k‐space. The limits are fed into a time‐optimal gradient waveform design technique. Effective SAR reduction is achieved by reducing peak RF subject to a fixed pulse length. The presented method is different from other VERSE techniques in that it provides a noniterative time‐optimal multidimensional solution, which drastically simplifies VERSE designs. Examples are given for 1D and 2D single channel and 2D parallel transmit pulses. Magn Reson Med, 61:1471–1479, 2009.

Small-tip-angle spokes pulse design using interleaved greedy and local optimization methods.

Current spokes pulse design methods can be grouped into methods based either on sparse approximation or on iterative local (gradient descent‐based) optimization of the transverse‐plane spatial frequency locations visited by the spokes. These two classes of methods have complementary strengths and weaknesses: sparse approximation‐based methods perform an efficient search over a large swath of candidate spatial frequency locations but most are incompatible with off‐resonance compensation, multifrequency designs, and target phase relaxation, while local methods can accommodate off‐resonance and target phase relaxation but are sensitive to initialization and suboptimal local cost function minima. This article introduces a method that interleaves local iterations, which optimize the radiofrequency pulses, target phase patterns, and spatial frequency locations, with a greedy method to choose new locations. Simulations and experiments at 3 and 7 T show that the method consistently produces single‐ and multifrequency spokes pulses with lower flip angle inhomogeneity compared to current methods. Magn Reson Med, 2012.

Joint design of trajectory and RF pulses for parallel excitation

We propose an alternating optimization framework for the joint design of excitation k‐space trajectory and RF pulses for small‐tip‐angle parallel excitation. Using Bloch simulations, we show that compared with conventional designs with predetermined trajectories, joint designs can often excite target patterns with improved accuracy and reduced total integrated pulse power, particularly at high reduction factors. These benefits come at a modest increase in computational time. Magn Reson Med 58:598–604, 2007.

Reweighted ℓ1 Referenceless PRF Shift Thermometry

Temperature estimation in proton resonance frequency (PRF) shift MR thermometry requires a reference, or pretreatment, phase image that is subtracted from image phase during thermal treatment to yield a phase difference image proportional to temperature change. Referenceless thermometry methods derive a reference phase image from the treatment image itself by assuming that in the absence of a hot spot, the image phase can be accurately represented in a smooth (usually low order polynomial) basis. By masking the hot spot out of a least squares (ℓ2) regression, the reference phase images coefficients on the polynomial basis are estimated and a reference image is derived by evaluating the polynomial inside the hot spot area. Referenceless methods are therefore insensitive to motion and bulk main field shifts, however, currently these methods require user interaction or sophisticated tracking to ensure that the hot spot is masked out of the polynomial regression. This article introduces an approach to reference PRF shift thermometry that uses reweighted ℓ1 regression, a form of robust regression, to obtain background phase coefficients without hot spot tracking and masking. The method is compared to conventional referenceless thermometry, and demonstrated experimentally in monitoring HIFU heating in a phantom and canine prostate, as well as in a healthy human liver. Magn Reson Med, 2010.

Spectral-spatial pulse design for through-plane phase precompensatory slice selection in T2*-weighted functional MRI.

T  2* ‐weighted functional MR images suffer from signal loss artifacts caused by the magnetic susceptibility differences between air cavities and brain tissues. We propose a novel spectral‐spatial pulse design that is slice‐selective and capable of mitigating the signal loss. The two‐dimensional spectral–spatial pulses create precompensatory phase variations that counteract through‐plane dephasing, relying on the assumption that resonance frequency offset and through‐plane field gradient are spatially correlated. The pulses can be precomputed before functional MRI experiments and used repeatedly for different slices in different subjects. Experiments with human subjects showed that the pulses were effective in slice selection and loss mitigation at different brain regions. Magn Reson Med 61:1137–1147, 2009.