A model for diffusive transport through a spherical interface probed by pulsed-field gradient NMR

In biological systems, because of higher intracellular viscosity and/or the restriction of the diffusion space inside cells, the (apparent) diffusion coefficient of an intracellular species (e.g., water) is generally smaller than when it is in the extracellular medium. This difference affects the spin-echo signal attenuation in the pulsed field gradient NMR experiment and thus affords a means of separating the intracellular from the extracellular species, thereby providing a basis for studying transmembrane transport. Such experiments have commonly been analyzed using the macroscopic model of Kärger (see Adv. Magn. Reson. 21:1-89 (1988)). In our previous study, we considered a microscopic model of diffusive transport through a spherical interface using the short gradient pulse approximation (J. Magn. Reson. A114:39-46 (1995)). The spins in the external medium were modeled with the "partially absorbing wall" condition or as having a small but finite lifetime. In the present paper, we extend our treatment to the case in which there is no limitation upon the lifetime in either medium. We also consider a simple modification of Kärger's model that more properly accounts for the restricted intracellular diffusion. Importantly, it was found that the exact solution within the short gradient pulse approximation developed here and the modified Kärger model are in close agreement in the (experimentally relevant) long-time limit. The results of this study show that when there is no limitation upon the lifetime of the transported species in either phase, the spin-echo attenuation curve is very sensitive to transport.