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 Parallel excitation was recently proposed (1,2) as a means of accelerating multidimensional selective excitation using multiple coils driven with independent waveforms. In a manner analogous to parallel imaging methods, such as sensitivity encoding (SENSE) (4) and generalized autocalibrating partially parallel acquisition (GRAPPA) (5), a reduced excitation k-space trajectory (6) can be used to achieve a desired excitation pattern by exploiting the blurring behavior of coil sensitivity patterns in the excitation k-space domain to deposit RF energy in regions that are not traversed by the trajectory. Accelerated selective excitation is useful for reducing specific absorption rate (SAR) (2), and shortening multidimensional RF pulses in such applications as compensation for B 1 and B 0 inhomogeneity (7-10). The feasibility of parallel excitation was also recently verified experimentally (11,12).Several methods currently exist for designing small-tipangle RF pulses in parallel excitation (1-3). The pioneering pulse design methods were introduced by Katscher et al. (1) and Zhu (2). The method introduced by Katscher et al. (1), dubbed transmit SENSE, is characterized by the explicit use of transmit sensitivity patterns in the pulse design process, and its formulation is based on a convolution in excitation k-space. It allows usage of arbitrary kspace trajectories. Zhu's (2) method makes explicit use of transmit sensitivity patterns, but is formulated as an optimization problem in the spatial domain, and, as described, is restricted to echo-planar k-space trajectories. Griswold et al. (3) proposed a k-space domain method that is analogous to GRAPPA imaging. It is unique in that it does not require prior determination of sensitivity patterns. Instead, it involves an extra calibration step in the pulse design process. It also appears to be restricted to echo-planar k-space trajectories.In this paper we propose an alternative RF pulse design method that is closely related to transmit SENSE (1), but is formulated in the spatial domain. It is a multicoil generalization of the iterative pulse design method proposed by Yip et al. (13), and is based on the minimization of a qua...

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.

Purpose: Magnetic resonance thermometry using the proton resonance frequency ͑PRF͒ 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 method's 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.

Parallel transmitter techniques are a promising approach for reducing transmitter B 1 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 B 1 inhomogeneity. This paper presents a proof of this concept using transmit SENSE 3D tailored RF pulses designed for small flip angles. An eightchannel receiver coil was used to mimic parallel transmission for brain imaging at 3T. The transmit SENSE pulses were based on the fast-k z 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.

Large-tip-angle multidimensional 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 non-uniform 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 non-idealities such as main field inhomogeneties.