Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling

Abstract

In this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusion process which follows Fick’s second law while considering the convective phenomena from the polymer matrix to the liquid where the drug is delivered and the polymer–liquid drug distribution equilibrium. The resulting model is solved using Laplace transformation for two scenarios: (1) a constant initial condition for a single drug delivery experiment; and (2) a recursive delivery process where the liquid medium is replaced with fresh liquid after a fixed period of time, causing a stepped delivery rate. Finally, the proposed model is validated with experimental data.