Xing Haoyang, Lin Fang, Wu Qizhu, Gong Qiyong
Huaxi MR Research Center, West China Hospital of Sichuan University, Chengdu, Sichuan, China; School of Physical Science and Technology, Sichuan University, Chengdu, Sichuan, China.
Magn Reson Med. 2013 Oct;70(4):1167-72. doi: 10.1002/mrm.24551. Epub 2012 Nov 20.
To enrich and develop more convenient and effective boundary treatment method in Monte-Carlo simulation of restricted diffusion nuclear magnetic resonance.
The conventional approach used in treating boundary behaviors of restricted diffusion is the elastic boundary reflection. Because random walk is not dynamic process, other boundary treatments such as inelastic reflection are acceptable and probably simplify the programming of diffusion nuclear magnetic resonance simulation. The present study simulated the pulse gradient spin echo nuclear magnetic resonance by employing three boundary models, i.e., the elastic boundary reflection, the non-elastic boundary reflection, and the equal-step-length random leap. Their effects on precision, convergence, and calculation efficiency were investigated, as well as the effects of non-fixed boundary reflection step-length drawn from a Gaussian distribution in barrier-crossing steps.
The results show no obvious difference in convergences and precisions for different methods when the relative step-length is sufficiently small. Compared with the traditional approach, the required computation time of the latter two was reduced in some degree.
Boundary treatments based on inelastic reflection are a feasible choice in Monte-Carlo simulation of nuclear magnetic resonance, and in comparison with the conventional approach, it not only renders programming more convenience but also possibly lead to higher calculating efficiency.
在受限扩散核磁共振的蒙特卡罗模拟中丰富和开发更便捷有效的边界处理方法。
处理受限扩散边界行为的传统方法是弹性边界反射。由于随机游走不是动态过程，其他边界处理方法如非弹性反射是可以接受的，并且可能会简化扩散核磁共振模拟的编程。本研究采用三种边界模型模拟脉冲梯度自旋回波核磁共振，即弹性边界反射、非弹性边界反射和等步长随机跳跃。研究了它们对精度、收敛性和计算效率的影响，以及在穿越势垒步骤中从高斯分布得出的非固定边界反射步长的影响。
结果表明，当相对步长足够小时，不同方法的收敛性和精度没有明显差异。与传统方法相比，后两种方法所需的计算时间在一定程度上有所减少。
基于非弹性反射的边界处理是核磁共振蒙特卡罗模拟中的一种可行选择，与传统方法相比，它不仅使编程更方便，而且可能导致更高的计算效率。
