Joint design of spoke trajectories and RF pulses for parallel excitation

The spoke trajectory is often used in designing multidimensional RF pulses for applications requiring thin slice selection and in-slice modulation. Ideally, a full set of spokes covering the whole k-space are desired to generate a given excitation pattern. In practice, however, only a small number of spokes can be used due to the RF pulse length limitation. The spoke locations are, therefore, critical to the performance of the resulting RF pulse and should be in principle optimized jointly with the RF pulse for a given excitation pattern and transmit sensitivities. In this work, we formulate the joint design problem as an optimal spoke selection problem based on the small-tip-angle RF pulse design. A sequential selection based algorithm with recursive cost function evaluation is proposed to seek optimized spoke locations to minimize the excitation error. Bloch equation simulations and experimental results on a 3 Tesla scanner equipped with a two-channel parallel excitation system demonstrate that the proposed method can produce significantly smaller excitation error than conventional methods with high computational efficiency.