A method is presented for obtaining simple approximate solutions for the problem of self-diffusion in an ordered array of obstacles. Our results are compared with some previous exact and approximate solutions, and we find that our method agrees well with the exact results over a large range of the volume fraction of the obstructions. It is shown that there is an important distinction between measurements of the diffusion coefficient by the capillary flow method and the spin-echo method. The modifications for the spin-echo case are given and applied to recent measurements on the anisotropy of the self-diffusion of water in striated muscle and to measurements on cysts of the brine shrimp. The analysis shows that very large volume fractions of obstructive barriers are required in order to account for the reduction in the diffusion coefficient in biological systems. Thus this model analysis leads to the supposition that a substantial fraction (20- 40%) of the cell water is hydration water, or that the diffusion coefficient of the cytoplasmic water is reduced substantially from the free water value. In either case, the conclusion that a substantial fraction of cell water has diffusive properties that are altered by the macromolecules of the cytoplasm seems inescapable. In the case of NMR methodology, the measuring times are such that the values for diffusion are often influenced by the presence of macromolecular structures (obstructions) within the cells. This suggests that obstructions make a significant contribution to the value of the NMR diffusion coefficient and that NMR may have practical value for the evaluation of obstruction effects.
Rorschach, H. E.; Lin, C.; and Hazlewood, C. F.
"Diffusion of Water in Biological Tissues,"
Scanning Microscopy: Vol. 1991
, Article 1.
Available at: https://digitalcommons.usu.edu/microscopy/vol1991/iss5/1