NMR中非线性梯度场下扩散行为的理论描述和蒙特卡罗模拟

摘要

利用传播子方法研究了在一般非线性场梯度下NMR信号的扩散衰减. 在自由扩散和平板间的限制扩散情况下获得了扩散衰减因子的理论表达式. 该表达式适用范围宽, 且具有较简单的数学形式和明确的物理意义. 文中还将理论预测与蒙特卡罗模拟结果进行了比较. 结果表明: 文中所采用的理论方法适合于表述自由扩散和短脉冲近似下的受限扩散; 蒙特卡罗模拟提供了一种定性研究MRI和NMR中非均匀场梯度扩散衰减的方法.%A propagator method was used to calculate diffusion attenuation of the NMR signal under general nonlinear field gradients. Theoretical expressions of the attenuation factor were obtained for free and restricted diffusion between two plates. Monte Carlo simulation was performed and the results were compared with the theory. It shows that the theoretical method is appropriate for the free diffusion, as well as the restricted diffusion under the short gradient pulse approximation. Monte Carlo simulation provides an alternate way to quantify the effects of inhomogeneous field gradients used in MRI and NMR.