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)], 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 A 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 A, with the scaling coefficient proportional to the system dimension. (C) 2019 Elsevier B.V. All rights reserved.