IEEE Trans Med Imaging. 2018 Feb;37(2):461-472. doi: 10.1109/TMI.2017.2758391. Epub 2017 Oct 2.
Optimal control approaches have proved useful in designing RF pulses for large tip-angle applications. A typical challenge for optimal control design is the inclusion of constraints resulting from physiological or technical limitations that assure the realizability of the optimized pulses. In this paper, we show how to treat such inequality constraints, in particular, amplitude constraints on the B1 field, the slice-selective gradient, and its slew rate, as well as constraints on the slice profile accuracy. For the latter, a pointwise profile error and additional phase constraints are prescribed. Here, a penalization method is introduced that corresponds to a higher order tracking instead of the common quadratic tracking. The order is driven to infinity in the course of the optimization. We jointly optimize for the RF and slice-selective gradient waveform. The amplitude constraints on these control variables are treated efficiently by semismooth Newton or quasi-Newton methods. The method is flexible, adapting to many optimization goals. As an application, we reduce the power of refocusing pulses, which is important for spin echo-based applications with a short echo spacing. Here, the optimization method is tested in numerical experiments for reducing the pulse power of simultaneous multislice refocusing pulses. The results are validated by phantom and in-vivo experiments.
最优控制方法已被证明在设计大角度射频脉冲时非常有用。最优控制设计的一个典型挑战是包含由于生理或技术限制而产生的约束，以确保优化脉冲的可实现性。在本文中，我们展示了如何处理这些不等式约束，特别是 B1 场、切片选择梯度及其斜率以及切片轮廓精度的约束。对于后者，规定了逐点轮廓误差和附加相位约束。在这里，引入了一种惩罚方法，对应于高阶跟踪而不是常见的二次跟踪。在优化过程中，阶数被驱动到无穷大。我们联合优化 RF 和切片选择梯度波形。这些控制变量的幅度约束可以通过半光滑牛顿或拟牛顿方法有效地处理。该方法灵活，适用于许多优化目标。作为应用，我们降低了重聚焦脉冲的功率，这对于具有短回波间隔的基于自旋回波的应用非常重要。在这里，通过数值实验测试了该优化方法在降低同时多切片重聚焦脉冲功率方面的应用。结果通过体模和体内实验进行了验证。
