A Generalized Integral Method for Solving the Design Equations of Dissolution-Diffusion Controlled Drug Release from Planar, Cylindrical and Spherical Matrix Devices

Abstract

A versatile approach for solving the design equations of dissolution/diffusion-controlled drug release from planar, cylindrical and spherical matrix systems is provided, as an extension of a previously validated approach for planar geometry. The original set of differential mass balance equations is cast into an equivalent system of integral equations by generating appropriate Green’s functions. Mathematical features common to the matrix geometry, drug diffusion process, and boundary layer resistance are imbedded in Green’s functions, and thus separated from specific aspects arising from the drug dissolution process. This avoids repetitive computational effort when analyzing different drug dissolution rates. The solution for the perfect sink condition is given as a special case. Another singular feature is related to the friendly manipulation of a broad variety of spatially non-uniform drug loading, including size distribution of solid drug particles. Composite matrices consisting of multi-layers of equal diffusivity, including membranes, can be numerically simulated solving a concise dissolution–diffusion integral equation, coupled to the integral equations governing the variable surface area of the dissolving drug particles. This is made within a unique framework and without introducing extra difficulties or adjustments in the programming from one matrix architecture to another. The reliability of the approach presented is ascertained by comparing the results with existing analytical and numerical solutions for special cases, and also by matching, as asymptotic case, the numerical solution of the diffusion equation with a continuum dissolution source described by the Noyes–Whitney equation. An iterative routine, combined with the topological concept of homotopy, is used to improve the numerical performance.