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

TL;DR

This paper introduces a lattice gas model to analyze drug release from porous membranes, revealing how release parameters relate linearly and through scaling to membrane porosity, supported by analytical and simulation results.

Contribution

It presents a novel statistical mechanical model linking drug release parameters to membrane porosity, with analytical solutions and Monte Carlo simulations elucidating their relationships.

Findings

Linear relation between release time parameter and inverse porosity

Scaling relation between Weibull shape parameter and porosity

Analytical and simulation results support the model's predictions

Abstract

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.