Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres
McCue, Scott W., Hsieh, Mike, Moroney, Timothy J., & Nelson, Mark I. (2011) Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres. SIAM Journal on Applied Mathematics (SIAP), 71(6), pp. 2287-2311.
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 modelled 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 analyse 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 multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.
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