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, \(\exp [-(t/\tau)^b ]\), also known as stretched exponential, and the dependence of adjusted parameters \(b\) and \(\tau\) is usually associated, in the pharmaceutical literature, with physical mechanisms dominating the drug dynamics inside the capsule. The relation of parameters \(\tau\) and \(b\) with porosity \(\lambda\) are found to satisfy, a simple linear relation for between \(\tau\) and \(\lambda^{-1}\), which can be explained through simple physically based arguments, and a scaling relation between \(b\) and \(\lambda\), with the scaling coefficient proportional to the system dimension.