Nanoscale Organisation and Dynamics Group, University of Western Sydney, Locked Bag 1797, Penrith, NSW 2751, Australia.
J Chem Phys. 2013 Mar 7;138(9):094202. doi: 10.1063/1.4793525.
Nuclear magnetic resonance (NMR) diffusion (including diffusion MRI) experiments are only as powerful as the models used to analyse the NMR diffusion data. A major problem, especially with measurements on biological systems, is that the existing models are only very poor approximations of cellular shape. Here, diffusion propagators and pulsed gradient spin-echo attenuation equations are derived in the short gradient pulse limit for diffusion within the annular region of a concentric cylinder of finite length and, similarly, within the annular region of a concentric sphere. The models include the possibility of relaxation at the boundaries and, in the case of the concentric cylinder, having the cylinder arbitrarily oriented with respect to the direction of the applied field gradient. The two models are also of interest due to their direct analogy to optical double slit diffraction. Also expressions for the mean square displacements, which are very useful information for determining the diffusion coefficient within these complex geometries, are obtained as well as for the limiting cases of diffusion on cylindrical and spherical shells and in a ring.
核磁共振（NMR）扩散（包括扩散 MRI）实验的威力取决于用于分析 NMR 扩散数据的模型。一个主要问题，特别是在对生物系统进行测量时，是现有的模型只是对细胞形状的非常粗略的近似。在这里，在短梯度脉冲极限下，为有限长度的同心圆柱的环形区域内的扩散以及类似地，在同心球的环形区域内推导了扩散传播器和脉冲梯度自旋回波衰减方程。这些模型包括在边界处弛豫的可能性，并且在同心圆柱的情况下，圆柱相对于施加的磁场梯度方向任意取向。这两个模型也很有趣，因为它们与光学双狭缝衍射有直接的类比。还得到了均方位移的表达式，这对于在这些复杂几何形状内确定扩散系数非常有用，以及对于圆柱壳和球形壳以及环上的扩散的极限情况也是如此。
