Modelling of self-diffusion and relaxation time NMR in multicompartment systems with cylindrical geometry

Multicompartment characteristics of relaxation and diffusion in a model for (plant) cells and tissues have been simulated as a means to test separating the signal into a set of these compartments. A numerical model of restricted diffusion and magnetization relaxation behavior in PFG-CPMG NMR experiments, based on Fick's second law of diffusion, has been extended for two-dimensional diffusion in systems with concentric cylindrical compartments separated by permeable walls. This model is applicable to a wide range of (cellular) systems and allows the exploration of temporal and spatial behavior of the magnetization with and without the influence of gradient pulses. Numerical simulations have been performed to show the correspondence between the obtained results and previously reported studies and to investigate the behavior of the apparent diffusion coefficients for the multicompartment systems with planar and cylindrical geometry. The results clearly demonstrate the importance of modelling two-dimensional diffusion in relation to the effect of restrictions, permeability of the membranes, and the bulk relaxation within the compartments. In addition, the consequences of analysis by multiexponential curve fitting are investigated.