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.

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kspace trajectory joint optimization of the ptx radiofrequency rf and gradient waveforms 34 62 normalized rootmeansquare error 412 error reduced field of view imaging cube shape brain shape clinical gradient system parameterization of kspace trajectories 3d optimized 3d cross shells trajectory 7t scanner small tip angle leastsquares rf pulse design excitation of arbitrary threedimensional 3d magnetization parallel transmission ptx pulses ptx channels reson med b0 robustness fat suppression in spectroscopy

Bastien Guérin, Lothar R. Schad, Lawrence L. Wald,Mathias Davids,.Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories. 76 (4),1182-1170.

Bastien Guérin, et al."Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories" 76

Bastien Guérin, Lothar R. Schad, Lawrence L. Wald,Mathias Davids,"Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories"