Rotation operator propagators for time-varying radiofrequency pulses in NMR spectroscopy: Applications to shaped pulses and pulse trains
Rotation operator propagators for time-varying radiofrequency pulses in NMR spectroscopy: Applications to shaped pulses and pulse trains
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DOI：
10.1016/j.jmr.2014.09.001
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发表时间：
2014-11-01
影响因子：
2.2
通讯作者：
Palmer, Arthur G., III
中科院分区：
文献类型：
--
作者：
Li, Ying;Rance, Mark;Palmer, Arthur G., III
射频脉冲串的传播器可以直接进行数值积分或通过平均汉密尔顿方法进行近似。前者提供了高精度和后者，在有利的情况下，方便的解析公式。传播算子的欧拉角旋转算子因式分解提供了对性能的深入了解，这些性能不容易从这些传统技术中的任何一种中辨别出来。这种方法在确定整形脉冲是否可以在某个带宽上由序列τ（1）-R-phi（beta）-τ（2）表示时是有用的，其中R-phi（beta）是在横向平面中围绕具有相位0的轴旋转角度β，τ（1）和τ（2）是时间延迟，允许通过调节脉冲之前或之后的时间周期来补偿脉冲期间的相位演变。微扰理论建立了τ（1）和τ（2）的显式公式，其与整形脉冲期间产生的平均横向磁化成比例。传播子的欧拉角表示在脉冲中断自由进动方案的迭代约简中也是有用的。应用到Carr-Purcell-Meiboom-Gill序列确定了一个八脉冲相位交替方案，该方案生成的传播算子几乎等于恒等算子。(C)2014爱思唯尔公司All rights reserved.
The propagator for trains of radiofrequency pulses can be directly integrated numerically or approximated by average Hamiltonian approaches. The former provides high accuracy and the latter, in favorable cases, convenient analytical formula. The Euler-angle rotation operator factorization of the propagator provides insights into performance that are not as easily discerned from either of these conventional techniques. This approach is useful in determining whether a shaped pulse can be represented over some bandwidth by a sequence tau(1)-R-phi(beta)-tau(2), in which R-phi(beta) is a rotation by an angle beta around an axis with phase 0 in the transverse plane and tau(1) and tau(2) are time delays, allowing phase evolution during the pulse to be compensated by adjusting time periods prior or subsequent to the pulse. Perturbation theory establishes explicit formulas for tau(1) and tau(2) as proportional to the average transverse magnetization generated during the shaped pulse. The Euler-angle representation of the propagator also is useful in iterative reduction of pulse-interrupted-free precession schemes. Application to Carr-Purcell-Meiboom-Gill sequences identifies an eight-pulse phase alternating scheme that generates a propagator nearly equal to the identity operator. (C) 2014 Elsevier Inc. All rights reserved.