Mathematical modelling of drug permeation through a swollen membrane

This work proposes two different mathematical models (linear and numerical) able to simulate the drug permeation through a swollen membrane sandwiched by two external layers (trilaminate system). Moreover, a solid drug dissolution phenomenon in the donor compartment may be accounted for. Indeed, this is a situation that may often occur in permeation experiments. An insufficient stirring of the donor and of the receiver volume may give rise to two sandwiching layers and the target of a constant drug concentration in the donor compartment may be accomplished by putting a solid drug amount in the saturated donor solution. The linear model shows the advantage of having an analytical expression which extremely simplifies the calculation of the drug diffusion coefficient D inside the membrane. Its main drawback lies in the fact that it works only for thin trilaminate systems. The numerical model is more general than the linear one, as it works for all kind of trilaminate thickness and it may account for a solid powder dissolution in the donor compartment. Of course, it does not have an analytical solution and, thus, the D determination is less easy to perform as the numerical model is more time consuming than the linear one. These two models are then compared with the classical approach developed by Flynn and Barrie in order to better define its validity limits.