A biphasic mathematical model for the release of polymer-drug conjugates from poly(vinyl alcohol) hydrogels

Background: Hydrogels are a popular vehicle for controlled drug release. In comparison with small-soluble drugs of simple diffusion, the release of large polymer-drug conjugates is more complex and could not be predicted by a simple diffusion model. This study was aimed at mathematical modeling of the release of polymer-drug conjugates to design controlled drug-release hydrogel systems. Methods: Fluorescein was used as a small model drug, whereas fluorescein isothiocyanate-dextran acted as a polymer-drug conjugates. The molecules were encapsulated in poly(vinyl alcohol)-based hydrogels with different concentrations and degrees of crosslinking. The release data were fitted using a one-diffusion coefficient (1DC) model and a two-diffusion coefficient (2DC) model, performed by Matlab. Significant findings: The simple 1DC model fitted the release data of small molecules (< 10 kDa) very well, while the more complex 2DC model was needed to predict the release of macromolecules (10-250 kDa) for a better fit. The 2DC model proposed that a hydrogel is a heterogeneous structure with dense and loose areas, and macromolecules diffuse through the two areas with different diffusivity. We further demonstrated that the biphasic model could be applied to design hydrogel systems for precision drug release profiles.