Cylindrical matrix device with a circular release area with inhomogeneous diffusivity

Abstract

A cylindrical matrix device with a circular release area with inhomogeneous diffusivity was analyzed using a Laplace transform–based method, using Bromwich integral and residue theorem. The two-dimensional model represented a pharmaceutical agent uniformly distributed in a polymeric matrix with a diffusivity spatially modulated, surrounded by an impermeable layer. The pharmaceutical agent could be transferred only through a small hole centered at the top surface of the cylinder. A closed-form solution was obtained in terms of Bessel functions with the aim to help study the effects of design parameters and geometries on the cumulative amount of pharmaceutical agent released. The cumulative flux of pharmaceutical agent increased with the mass transfer and diffusion coefficients and decreased with any increment in the device’s length and variations of the diffusivity coefficients. The delivery rate was described by an effective time constant calculated from Laplace transforms and using Bessel functions and their zeros. Reducing the orifice diameter or fabricating a longer system would delay transport of the medication. Simplified expressions for the release profile and the time constant were derived for special design cases.