Designing multichannel, multidimensional, arbitrary flip angle RF pulses using an optimal control approach
Designing multichannel, multidimensional, arbitrary flip angle RF pulses using an optimal control approach
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DOI：
10.1002/mrm.21485
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发表时间：
2008-03-01
影响因子：
3.3
通讯作者：
Liang, Zhi-Pei
中科院分区：
文献类型：
--
作者：
Xu, Dan;King, Kevin F.;Liang, Zhi-Pei
迄今为止，绝大多数并行传输射频脉冲设计都是基于布洛赫方程的小尖端角 (STA) 近似。这些方法只能设计具有小翻转角（例如 30 度）的激励脉冲。当使用某些k空间轨迹时，线性类大尖端角（LCLTA）方法能够通过串联一系列小激励脉冲来设计大尖端角并行传输脉冲。然而，STA 和 LCLTA 都是非线性 Bloch 方程的线性近似。因此，由于高阶项而导致的与理想磁化分布的畸变可能出现在最终磁化分布中。这项工作通过将多维多通道射频脉冲设计公式化为直接基于布洛赫方程的多个控制的最优控制问题来解决这个问题。导出最优解的必要条件，并使用一阶梯度优化算法迭代求解最优控制问题，其中现有脉冲用作初始“猜测”。还提出了系统的设计流程。使用各种并行传输脉冲（激励、反转和重聚焦）的布洛赫模拟和模型实验结果说明了最优控制方法在改善磁化分布的空间定位或均匀性方面的有效性。
The vast majority of parallel transmission RF pulse designs so far are based on small-tip-angle (STA) approximation of the Bloch equation. These methods can design only excitation pulses with small flip angles (e.g., 30 degrees). The linear class largetip-angle (LCLTA) method is able to design large-tip-angle parallel transmission pulses through concatenating a sequence of small-excitation pulses when certain k-space trajectories are used. However, both STA and LCLTA are linear approximations of the nonlinear Bloch equation. Therefore, distortions from the ideal magnetization profiles due to the higher order terms can appear in the final magnetization profiles. This issue is addressed in this work by formulating the multidimensional multichannel RF pulse design as an optimal control problem with multiple controls based directly on the Bloch equation. Necessary conditions for the optimal solution are derived and a first-order gradient optimization algorithm is used to iteratively solve the optimal control problem, where an existing pulse is used as an initial "guess." A systematic design procedure is also presented. Bloch simulation and phantom experimental results using various parallel transmission pulses (excitation, inversion, and refocusing) are shown to illustrate the effectiveness of the optimal control method in improving the spatial localization or homogeneity of the magnetization profiles.