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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, $\exp [-(t/τ)^b ]$, also known as stretched exponential, 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.