Rapid convergence of optimal control in NMR using numerically-constructed toggling frames.
Rapid convergence of optimal control in NMR using numerically-constructed toggling frames.
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DOI：
10.1016/j.jmr.2017.05.011
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发表时间：
2017-08
期刊：
影响因子：
--
通讯作者：
Arthanari H
中科院分区：
文献类型：
--
作者：
Coote P;Anklin C;Massefski W;Wagner G;Arthanari H
本文提出了一种快速求解任意时变自旋1/2哈密顿量的Bloch方程的数值方法。该方法依赖于快速的向量化计算，如求和和四元数乘法，而不是缓慢的计算，如矩阵求幂。构造了一个切换框架，其中哈密顿量是时不变的，因此具有简单的解析解。关键的见解是，构建这个框架比在原始框架中求解系统动力学更快。快速求解任意哈密顿量的布洛赫方程在NMR最优控制的背景下特别有用。最优控制理论可用于设计NMR光谱中一系列任务的脉冲形状。然而，它需要在算法的每个阶段对布洛赫方程进行多次模拟，并针对每个相关参数集（例如化学位移频率）进行模拟。这通常是耗时的。我们证明，通过工作在一个适当的切换帧，最佳的控制脉冲可以产生得更快。我们提出了一种新的替代著名的GRAPE算法不断更新的切换帧的最佳脉冲的产生，并证明这种方法是非常快的。19 F片段筛选实验证明了快速最佳脉冲产生的用途和益处。
We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame. Rapidly solving the Bloch equations for an arbitrary Hamiltonian is particularly useful in the context of NMR optimal control. Optimal control theory can be used to design pulse shapes for a range of tasks in NMR spectroscopy. However, it requires multiple simulations of the Bloch equations at each stage of the algorithm, and for each relevant set of parameters (e.g. chemical shift frequencies). This is typically time consuming. We demonstrate that by working in an appropriate toggling frame, optimal control pulses can be generated much faster. We present a new alternative to the well-known GRAPE algorithm to continuously update the toggling-frame as the optimal pulse is generated, and demonstrate that this approach is extremely fast. The use and benefit of rapid optimal pulse generation is demonstrated for 19F fragment screening experiments.
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DOI：
10.1006/jmra.1996.0157
发表时间：
1996-08-01
期刊：
JOURNAL OF MAGNETIC RESONANCE SERIES A
影响因子：
--
作者：
Levante, TO;Bremi, T;Ernst, RR
通讯作者：
Ernst, RR
影响因子：
2.2
作者：
Luy, B;Kobzar, K;Glaser, SJ
通讯作者：
Glaser, SJ
影响因子：
2.2
作者：
Khaneja, N;Reiss, T;Glaser, SJ
通讯作者：
Glaser, SJ
影响因子：
15
作者：
GRZESIEK, S;BAX, A
通讯作者：
BAX, A
影响因子：
10.2
作者：
Higham, Nicholas J.
通讯作者：
Higham, Nicholas J.