A statistical mechanical model for drug release: Relations between release parameters and porosity

A lattice gas model is proposed for investigating the release of drug molecules on devices with semi-permeable, porous membranes in two and three dimensions. The kinetic of this model was obtained through the analytical solution of the three-dimension diffusion equation for systems without membrane and with Monte Carlo simulations. Pharmaceutical data from drug release is usually adjusted to the Weibull function, exp[−(t∕τ)b], and the dependence of adjusted parameters b and τ is usually associated, in the pharmaceutical literature, with physical mechanisms dominating the drug dynamics inside the capsule. The relation of parameters τ and b with porosity λ are found to satisfy, a simple linear relation for between τ and λ−1, which can be explained through simple physically based arguments, and a scaling relation between b and λ, with the scaling coefficient proportional to the system dimension.