Lag Time in Diffusion-Controlled Release Formulations Containing a Drug-Free Outer Layer

Theoretical considerations along with extensive Monte Carlo simulations are used to calculate the lag time before the initiation of diffusion-controlled drug release in multilayer planar devices with an outer layer containing no drug. The presented results are also relevant in formulations coated by a drug-free membrane as well as in other reservoir systems. The diffusion of drug molecules through the outer layer towards the release medium is considered, giving rise to the observed lag time. We have determined the dependence of lag time on the thickness and the diffusion coefficient of the drug-free outer layer, as well as on the initial drug concentration and the surface area of the planar device. A simple expression, obtained through an analytical solution of diffusion equation, provides an approximate estimate for the lag time that describes the numerical results reasonably well; according to this relation, the lag time is proportional to the squared thickness of the outer layer over the corresponding diffusion coefficient and inversely proportional to the logarithm of the linear number density of the drug that is initially loaded in the inner layer.