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

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


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.


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.


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.

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