Drug diffusion from polymeric delivery devices: a problem with two moving boundaries

Mike Hsieh, Scott W. McCue, Timothy J. Moroney, Mark I. Nelson


An existing model for solvent penetration and drug release from a spherically shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of the polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as non-Fickian or Case~II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.

  • G. Astarita and G. C. Sarti. A class of mathematical models for sorption of swelling solvents in glassy polymers. Polymer Engineering and Science., 18, 1978, 388--395. doi:10.1002/pen.760180510.
  • D. S. Cohen and T. Erneux. Free boundary problems in controlled release pharmaceuticals. I: Diffusion in glassy polymers. SIAM Journal on Applied Mathematics., 48, 1988, 1451--1465. http://www.jstor.org/stable/2101759.
  • D. S. Cohen and T. Erneux.. Free boundary problems in controlled release pharmaceuticals. II: Swelling-controlled release. SIAM Journal on Applied Mathematics., 48, 1988, 1466--1474. http://www.jstor.org/stable/2101760.
  • T. Higuchi. Mechanism of sustained-action medication: theoretical analysis of rate of release of solid drugs dispersed in solid matrices. Journal of Pharmaceutical Sciences., 52, 1963, 1145--1149. doi:10.1002/jps.2600521210.
  • J.-S. Lin, C.-C. Hwang, C.-M. Lin, and J.-Y. Lai. Solvent transport in spherical polymer-penetrant systems. Chemical Engineering Science., 56, 2001, 151--156. doi:10.1016/S0009-2509(00)00410-3.
  • J.-S. Lin and Y.-L. Peng. Swelling controlled release of drug in spherical polymer-penetrant systems. International Journal of Heat and Mass Transfer., 48, 2005, 1186--1194. doi:10.1016/j.ijheatmasstransfer.2004.08.031.
  • S. W. McCue, M. Hsieh, T. J. Moroney, and M. I. Nelson. Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres. Submitted.
  • B. Narasimhan and N. A. Peppas. Molecular analysis of drug delivery systems controlled by dissolution of the polymer carrier. Journal of Pharmaceutical Sciences., 86, 1997, 297--304. doi:10.1021/js960372z.
  • F. A. Radu, M. Bause, P. Knabner, G. W. Lee, and W. C. Friess. Modeling of drug release from collagen matrices. Journal of Pharmaceutical Sciences, 91, 2002, 964--972. doi:10.1002/jps.10098.
  • J. Siepmann, K. Podual, M. Sriwongjanya, N. A. Peppas and R. Bodmeier. A new model describing the swelling and drug release kinetics from hydroxypropyl methylcellulose tablets. Journal of Pharmaceutical Sciences., 88, 1999, 65--72. doi:10.1021/js9802291.
  • S. Kill and K. Dam-Johansen. Controlled drug delivery from swellable hydroxypropylmethylcellulose matrices: model-based analysis of observed radial front movements. Journal of Controlled Release., 90, 2003, 1--21. doi:10.1016/S0168-3659(03)00122-6.
  • N. Wu, L.-S. Wang, D. C.-W. Tan, S. M. Moochhala, and Y.-Y. Yang. Mathematical modeling and in vitro study of controlled drug release via a highly swellable and dissoluble polymer matrix: polyethylene oxide with high molecular weights. Journal of Controlled Release., 102, 2005, 569--581. doi:10.1016/j.jconrel.2004.11.002.

Full Text:


DOI: http://dx.doi.org/10.0000/anziamj.v52i0.3940

Remember, for most actions you have to record/upload into OJS
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.