Modeling the Delivery of Drugs from a Water-Soluble Gel

Abstract

The rate at which a drug is released into the bloodstream can be controlled by synthesizing the drug inside of a water-soluble gel. The gel slows the rate of release, which is determined by the diffusivity of the drug and the thickness of the gel. This paper describes a mathematical model for release based on diffusivity and thickness data collected from a flattened gel. The one-dimensional diffusion equation is used to model the release of the drug, and numerical methods are used to approximate this release. In this research, splines are used to approximate the thickness and diffusivity data, and a joint optimization problem is later devised to validate the model.