IEEE Trans Med Imaging. 2014 Mar;33(3):739-48. doi: 10.1109/TMI.2013.2295465.
Parallel transmission is a very promising candidate technology to mitigate the inevitable radio-frequency (RF) field inhomogeneity in magnetic resonance imaging at ultra-high field. For the first few years, pulse design utilizing this technique was expressed as a least squares problem with crude power regularizations aimed at controlling the specific absorption rate (SAR), hence the patient safety. This approach being suboptimal for many applications sensitive mostly to the magnitude of the spin excitation, and not its phase, the magnitude least squares (MLS) problem then was first formulated in 2007. Despite its importance and the availability of other powerful numerical optimization methods, the MLS problem yet has been faced almost exclusively by the pulse designer with the so-called variable exchange method. In this paper, we investigate various two-stage strategies consisting of different initializations and nonlinear programming approaches, and incorporate directly the strict SAR and hardware constraints. Several schemes such as sequential quadratic programming, interior point methods, semidefinite programming and magnitude squared least squares relaxations are studied both in the small and large tip angle regimes with RF and static field maps obtained in vivo on a human brain at 7T. Convergence and robustness of the different approaches are analyzed, and recommendations to tackle this specific problem are finally given. Small tip angle and inversion pulses are returned in a few seconds and in under a minute respectively while respecting the constraints, allowing the use of the proposed approach in routine.
并行传输是一种很有前途的候选技术，可以减轻超高场磁共振成像中不可避免的射频（RF）场不均匀性。在最初的几年中，利用该技术的脉冲设计表示为具有粗略功率正则化的最小二乘问题，旨在控制特定吸收率（SAR），从而保障患者安全。由于该方法对于大多数主要对自旋激发幅度而不是相位敏感的应用来说并不理想，因此 2007 年首次提出了幅度最小二乘（MLS）问题。尽管它很重要，并且有其他强大的数值优化方法可用，但 MLS 问题几乎完全由所谓的变量交换方法的脉冲设计师来解决。在本文中，我们研究了各种由不同初始化和非线性规划方法组成的两阶段策略，并直接纳入严格的 SAR 和硬件约束。在活体人脑 7T 上获得的 RF 和静态场图的小和大翻转角范围内研究了顺序二次规划、内点法、半定规划和幅度平方最小二乘松弛等几种方案。分析了不同方法的收敛性和鲁棒性，并最终给出了解决该特定问题的建议。小翻转角和反转脉冲分别在几秒钟和一分钟内返回，同时遵守约束条件，允许在常规中使用所提出的方法。
