A 3D Model for Mechanistic Control of Drug Release

Abstract

A three-dimensional mathematical model for sorption/desorption by a cylindrical polymeric matrix with dispersed drug is proposed. The model is based on a system of partial differential equations coupled with boundary conditions over a moving boundary. We assume that the penetrant diffuses into a swelling matrix and causes a deformation, which induces a stressdriven diffusion and consequently a non-Fickian mass flux. A physically sound nonlinear dependence between strain and penetrant concentration is considered and introduced in a Boltzmann integral with a kernel computed from a Maxwell-Wiechert model. Numerical simulations show how the mechanistic behavior can have a role in drug delivery design. Introduction.In this paper we study a three-dimensional model of diffusion of a solvent into a cylindrical polymeric matrix containing drug and followed by the drug release. To describe drug release from a polymeric matrix, several models have been proposed [11,12,13,15,18,25,27]. However to the best of our knowledge, the influence of the mechanical properties of a swelling polymer in the sorption of a solvent and in the desorption of drug has not yet been considered in the literature. We propose a model where we combine non-Fickian sorption of the liquid agent, non-Fickian desorption, coupled with nonlinear dissolution and polymer swelling.It is well known that the diffusion of a liquid agent into a polymeric sample cannot be completely described by Fick's classical law. The liquid strains the polymeric matrix that, while swelling, exerts a stress that acts as a barrier to the incoming fluid. To explain these phenomena several authors [2,4,5,11,22,23,24] agree that a modified flux must be considered, that is

Modeling of non‐Fickian diffusion and dissolution from a thin polymeric coating: An application to drug‐eluting stents

“…The function σ( c ) stands for the stress. As shown in the works of Ferreira et al,() the viscoelastic diffusion coefficient D v is positive and has an exact physical interpretation.…”

“…The function σ(c) stands for the stress. As shown in the works of Ferreira et al, 23,24 the viscoelastic diffusion coefficient D v is positive and has an exact physical interpretation. The viscoelastic behavior of a polymer can be studied by means of mechanical models, where the elastic properties can be represented by springs and the viscous properties by dashpots.…”

“…We note that we are assuming that the fluid permeates the polymeric matrix instantaneously, making it fully wetted and relaxed. For models that take into consideration the effect of the incoming fluid, in the context of stents, we refer the reader to the work of Gudiño and Sequeira and, in a general setting, to the work of Ferreira et al…”

An iterative approach to solve a nonlinear moving boundary problem describing the solvent diffusion within glassy polymers

“…In this sense, a set of PDEs for the solvent and the drug including the non‐Fickian diffusion of the solvent induced by the viscoelastic properties of the polymer and a Fickian release of dissolved drug with respect to the cross‐link density and the concentration of the solvent has been investigated. As well as this, in Ferreira et al, the drug release from a cylinderical polymeric swelling system was explored as a system of PDEs. Recently, analyzing the complex drug release systems shows that the Fick's classical law encountered with some limitations to describe the diffusion process.…”

“…The studies subject to this are available in literature. [31][32][33] Ferreira et al 34 have considered a polymeric spherical closed release system containing a constant amount of solid dispersed drug that swells inside a sphere within a solvent fluid. In this sense, a set of PDEs for the solvent and the drug including the non-Fickian diffusion of the solvent induced by the viscoelastic properties of the polymer and a Fickian release of dissolved drug with respect to the cross-link density and the concentration of the solvent has been investigated.…”