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.

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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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13 citations in Web of Science®

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ID Code: 43864
Item Type: Journal Article
Refereed: Yes
Keywords: controlled drug release, solvent penetration, glassy-rubbery polymer transition, mathematical modelling, moving boundary problem, Stefan problem, formal asymptotics, kinetic undercooling, numerical solution
DOI: 10.1137/110821688
ISSN: 0036-1399
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Approximation Theory and Asymptotic Methods (010201)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > PHARMACOLOGY AND PHARMACEUTICAL SCIENCES (111500) > Basic Pharmacology (111501)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2011 Society for Industrial and Applied Mathematics
Deposited On: 11 Aug 2011 22:29
Last Modified: 18 Jan 2012 22:48

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