Modelling drug release from inert matrix systems: From moving-boundary to continuous-field descriptions

Abstract

The purpose of this review is to provide a comprehensive overview of mathematical procedures that can be used to describe the release of drugs from inert matrix systems. The review focuses on general principles rather than particular applications. The inherent multiscale nature of the drug-release process is pointed out and multiscale modelling is exemplified for inert porous matrices. Although effects of stagnant layers and finite volumes of release media are briefly discussed, the systematic analysis is restricted to systems under sink conditions. When the initial drug loading exceeds the drug solubility in the matrix, Higuchi-type moving-boundary descriptions continue to be highly valuable for obtaining approximate analytical solutions, especially when coupled with integralbalance methods. Continuous-field descriptions have decisive advantages when numerical solutions are sought. This is because the mathematical formulation reduces to a diffusion equation with a nonlinear source term, valid over the entire matrix domain. Solutions can thus be effortlessly determined for arbitrary geometries by using standard numerical packages.

Melt-Extruded Eudragit® FS-Based Granules for Colonic Drug Delivery

“…Tortuosity defines the ratio between the length of the channel connecting two points and the distance between two points. A higher tortuosity would result in longer the diffusion channels and a lower drug release rate (30). It was hypothesized that slower drug release from the melt-extruded granules was due to their less porous structure.…”

Oral Controlled‐Release Polymeric Drug Delivery Systems

“…In this section, the basic models are described. The interested reader is encouraged to consult the many reviews available in the literature for more detail [14,[19][20][21][23][24][25][26][27][28][29][30][31][32][33].…”

“…A porous network may also be formed upon dissolution of the drug when the drug loading is high. In such cases, the diffusivity is no longer unidirectional and an adjustment must be made for the tortuosity τ and porosity ε of the network [31]. The tortuosity and porosity may be analytically determined and used to determine an effective diffusion term for substitution into Eq.…”

A general model of coupled drug release and tissue absorption for drug delivery devices

“…Despite being the subject of intense theoretical and applied research over the past decades [7,8], it is still often unclear exactly what the mechanism of drug release from the DDD is and, as a consequence, even more difficult to predict the drug release kinetics. Nevertheless, countless models have been proposed.…”