Improved large tip angle parallel transmission pulse design through a perturbation analysis of the Bloch equation

Parallel transmission has emerged as an efficient means for implementing multidimensional spatially selective radiofrequency excitation pulses. To date, most theoretical and experimental work on parallel transmission radiofrequency (RF) pulse design is based on the small-tip-angle approximation to the Bloch equation. The small-tip-angle, while mathematically compact, is not an exact solution and leads to significant errors when large-tip-angle pulses are designed. Methods have been proposed to overcome the limitations of the small-tip-angle using regularized least-square optimization or optimal control algorithms. These methods, however, are based on further approximations to the Bloch equation or require the use of general purpose algorithms that do not capitalize fully on the dynamics of the physical model at hand. In this article, a novel algorithm for large-tip-angle parallel transmission pulse design is proposed. The algorithm relies on a perturbation analysis of the Bloch equation and it depicts the relationship between the excited magnetization, its deviation from the target pattern and the desired pulses. Simulations and experiments are used to validate the proposed method on a 7 T 8-channel transmit array. The results demonstrate that the perturbation analysis algorithm provides a fast and accurate approach for multidimensional large-tip-angle pulse design, especially when large acceleration factors and/or echo-planar trajectories are used.