Numerical solutions to the time-dependent Bloch equations revisited
Numerical solutions to the time-dependent Bloch equations revisited
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DOI：
10.1016/j.mri.2010.07.003
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发表时间：
2011-01-01
影响因子：
2.5
通讯作者：
Tanki, Nobuyoshi
中科院分区：
文献类型：
--
作者：
Murase, Kenya;Tanki, Nobuyoshi
本研究的目的是展示一种简单快速的方法来求解瞬态布洛赫方程。首先，将与时间相关的Bloch方程简化为齐次线性微分方程，然后导出一个简单的方程并使用矩阵运算对其进行求解。通过与恒定射频照射情况下的解析解进行比较，考察了该方法的有效性。他们之间有很好的一致性，表明该方法的有效性。作为进一步的例子，该方法应用于化学交换饱和转移（CEST）或酰胺质子转移（APT）磁共振成像（MRI）的双池交换模型中的时间相关布洛赫方程，并从它们的解计算Z谱和不对称谱。还使用四阶/五阶龙格-库塔-菲尔伯格（RKF）方法计算它们以进行比较。他们之间也有很好的一致性，而且这种方法比 RKF 方法快得多。总之，该方法将有助于分析复杂的 CEST 或 APT 对比机制和/或研究 CEST 或 APT MRI 的最佳条件。 (C) 2011 Elsevier Inc. 保留所有权利。
The purpose of this study was to demonstrate a simple and fast method for solving the time-dependent Bloch equations. First, the time-dependent Bloch equations were reduced to a homogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. The validity of this method was investigated by comparing with the analytical solutions in the case of constant radiofrequency irradiation. There was a good agreement between them, indicating the validity of this method. As a further example, this method was applied to the time-dependent Bloch equations in the two-pool exchange model for chemical exchange saturation transfer (CEST) or amide proton transfer (APT) magnetic resonance imaging (MRI), and the Z-spectra and asymmetry spectra were calculated from their solutions. They were also calculated using the fourth/fifth-order Runge-Kutta-Fehlberg (RKF) method for comparison. There was also a good agreement between them, and this method was much faster than the RKF method. In conclusion, this method will be useful for analyzing the complex CEST or APT contrast mechanism and/or investigating the optimal conditions for CEST or APT MRI. (C) 2011 Elsevier Inc. All rights reserved.