ASYMPTOTIC AND NUMERICAL RESULTS FOR A MODEL OF SOLVENT-DEPENDENT DRUG DIFFUSION THROUGH POLYMERIC SPHERES

• Published in: SIAM journal on applied mathematics Vol. 71; no. 6; pp. 2287 - 2311
• Main Authors: MCCUE, SCOTT W., HSIEH, MIKE, MORONEY, TIMOTHY J., NELSON, MARK I.
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01-01-2011
• Subjects: Applied mathematics; Diffusion coefficient; Drug delivery systems; Drug design; Kinetics; Mathematical models; Mathematics; Melting; Polymers; Solvents; Special Section; Spheres; Supercooling; Swelling
• ISSN: 0036-1399; 1095-712X
• DOI: 10.1137/110821688

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modeled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyze the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multilayered drug delivery device is suggested, which allows for more flexible control of drug release.