Journal
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
Volume 93, Issue 10-11, Pages 811-822Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/zamm.201200196
Keywords
Drug release; porous media; homogenization; evolving microstructure; numerical simulation; mixed finite element method
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Funding
- Deutsche Telekom Stiftung
- Office of Gender and Diversity of the University of Erlangen-Nuremberg
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Biodegradable collagen matrices have become a promising alternative to traditional drug delivery systems. The relevant mechanisms in controlled drug release are the diffusion of water into the collagen matrix, the swelling of the matrix coming along with drug release, and enzymatic degradation of the matrix with additional simultaneous drug release. These phenomena have been extensively studied in the past experimentally, via numerical simulations as well as analytically. However, a rigorous derivation of the macroscopic model description, which includes the evolving microstructure due to the degradation process, is still lacking. Since matrix degradation leads to the release of physically entrapped active agent, a good understanding of these phenomena is very important. We present such a derivation using formal twoscale asymptotic expansion in a level set framework and complete our results with numerical simulations in comparison with experimental data.
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