CEA, I2BM, NeuroSpin, LRMN, Gif sur Yvette, France.
Magn Reson Med. 2012 Feb;67(2):339-43. doi: 10.1002/mrm.23270. Epub 2011 Dec 2.
When designing a radio-frequency pulse to produce a desired dependence of magnetization on frequency or position, the small flip angle approximation is often used as a first step, and a Fourier relation between pulse and transverse magnetization is then invoked. However, common intuition often leads to linear scaling of the resulting pulse so as to produce a larger flip angle than the approximation warrants--with surprisingly good results. Starting from a modified version of the Bloch-Riccati equation, a differential equation in the flip angle itself, rather than in magnetization, is derived. As this equation has a substantial linear component that is an instance of Fourier's equation, the intuitive approach is seen to be justified. Examples of the accuracy of this higher tip angle approximation are given for both constant- and variable-phase pulses.
当设计射频脉冲以产生所需的磁化强度对频率或位置的依赖关系时，通常首先采用小翻转角近似，并随后调用脉冲和横向磁化强度之间的傅里叶关系。然而，常见的直觉通常会导致产生的脉冲呈线性比例缩放，从而产生比近似允许的更大的翻转角——结果却出人意料地好。从修改后的 Bloch-Riccati 方程出发，推导出一个在翻转角本身而不是磁化强度中的微分方程。由于这个方程有一个实质性的线性分量，它是傅里叶方程的一个实例，因此直观的方法被证明是合理的。给出了恒相和变相信号脉冲的这种更高翻转角近似的准确性示例。
