The role of polymer matrix structure and interparticle interactions in diffusion-limited drug release.

A lattice random-walk model is used to simulate diffusion in a porous polymer. This model may be useful for the practical design of drug-release systems. Both interacting and noninteracting particles (random walkers) were allowed to diffuse through a pore with a single exit hole. It was found that the specific interactions among the diffusing particles have little influence on the overall release rate. Diffusion through more complicated structures was investigated by simulating the diffusion of particles through two pores connected by a constricted channel whose length and width were varied. The overall rate of release was found to be proportional to the width of the constricted channel. When the length of the channel was greater than or equal to the length of the pore, the rate of release was also inversely proportional to the channel length. From a practical standpoint, release rates can be decreased (and times for release increased) by one or two orders of magnitude by decreasing the width and expanding the length of the interconnecting channels in the polymer matrix.

Diffusion in lipid bilayers containing barriers.

In epithelial cells, a barrier or tight junction restricts the diffusion of lipid probes from the apical to the basolateral side of the outer membrane bilayer. This phenomenon is studied theoretically with the diffusion equation on planar and spherical surfaces. Two models for the tight junction are considered: a penetrable barrier embedded in a monolayer and an impenetrable obstacle in the outer membrane of a bilayer than must be bypassed by flip-flopping between inner and outer membranes. The rate of passing from one side of the cell to the other is calculated for each of these models under steady state conditions. The results are compared with recent fluorescent photobleaching recovery experiments. The theoretical interpretation indicates that it would be difficult to distinguish experimentally between the flip-flop case and the barrier crossing case. Assuming a flip-flop model, large differences in the magnitude of the flip-flop rates of probes are necessary to explain the experimental results as suggested by Dragsten et al. (Dragsten, P. R., R. Blumenthal, and J. S. Handler, 1981, Nature [Lond.], 294:718--722).