Drug release from collagen matrices including an evolving microstructure

Abstract

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.

Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity

“…Frank (2013) considered several grain shapes in the fixed geometry case and applied circular grains for varying porosity. Numerical computations using MFEM on circular grains with varying radii were also considered by Ray et al (2013) for drug release from collagen matrices. Ray et al (2013) derived approximate solutions of the corresponding cell problems and found good correspondence with experimental results.…”

“…Numerical computations using MFEM on circular grains with varying radii were also considered by Ray et al (2013) for drug release from collagen matrices. Ray et al (2013) derived approximate solutions of the corresponding cell problems and found good correspondence with experimental results. van Noorden (2009a) implemented his upscaled pore scale equations for reactive transport on circular grains with altering grain radius, fitting the effective diffusion and permeability with a rational polynomial function.…”

“…Both Frank (2013) and van Noorden (2009a) consider incompressible flow, but extending to compressible flow should be straightforward by replacing the mass conservation equation. As the upscaled temperature equation has the same structure as the upscaled solute transport equation, it can be implemented using similar steps as performed by Frank (2013), Ray et al (2013) or van Noorden (2009a.…”

“…In these papers, the position of the interface between grain and void space is tracked, giving a problem with a free boundary. Similar models can also be obtained for biofilm growth (van Noorden et al 2010), for drug release from collagen matrices (Ray et al 2013), and on an evolving microstructure (Peter 2009). These models do not include any temperature dependence.…”

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

“…In these papers, the position of the interface between grain and void space is tracked, giving a problem with a free boundary. Similar models can also be obtained for biofilm growth (van Noorden et al 2010), for drug release from collagen matrices (Ray et al 2013), and on an evolving microstructure (Peter 2009). These models do not include any temperature dependence in the reaction rates nor any heat transfer.…”