A numerical framework for drug transport in a multi-layer system with discontinuous interlayer condition

Discontinuous boundary conditions arise naturally when describing various physical phenomena and numerically modelling such conditions can prove difficult. In the field of pharmaceutical sciences, two such cases are the partitioning of a compound between different materials and a flux rate membrane controlling mass transfer between materials which both result in a discontinuous jump in concentration across adjacent materials. In this study, we introduce a general one-dimensional finite element drug delivery framework, which along with diffusion, reversible binding and dissolution within material layers, incorporates the partitioning and mass transfer conditions between layers of material. We apply the framework to construct models of experiments, which along with experimental data, allow us to infer pharmacokinetic properties of potential material for drug delivery. Understanding such material properties is the key to optimising the therepeutic effect of a targeted drug delivery system.