Minimizing the passive release of heparin-binding growth factors from an affinity-based delivery system.

We consider a mathematical model that describes the leakage of heparin-binding growth factors from an affinity-based delivery system. In the delivery system, heparin binds to a peptide which has been covalently cross-linked to a fibrin matrix. Growth factor in turn binds to the heparin, and growth factor release is governed by both binding and diffusion mechanisms, the purpose of the binding being to slow growth factor release. The governing mathematical model, which in its original formulation consists of six partial differential equations, is reduced to a system of just two equations. It is usually desirable that there be no passive release of growth factor from a device, with all of the growth factor being held in place via binding until such time as it is actively released by invading cells. However, there will inevitably be some passive release, and so it is of interest to identify conditions that will make this release as slow as possible. In this paper, we identify a parameter regime that ensures that at least a fraction of the growth factor will release slowly. It is found that slow release is assured if the matrix is prepared with the concentration of cross-linked peptide greatly exceeding the dissociation constant of heparin from the peptide, and with the concentration of heparin greatly exceeding the dissociation constant of the growth factor from heparin. Also, for the first time, in vitro experimental release data are directly compared with the theoretical release profiles generated by the model. We propose that the two stage release behaviour frequently seen in experiments is due to an initial rapid out-diffusion of free growth factor over a diffusion time scale (typically days), followed by a much slower release of the bound fraction over a time scale depending on both diffusion and binding parameters (frequently months).

A mathematical model for pulsatile release: controlled release of rhodamine B from UV-crosslinked thermoresponsive thin films.

A controlled drug delivery system fabricated from a thermoresponsive polymer was designed to obtain a pulsatile release profile which was triggered by altering the temperature of the dissolution medium. Two stages of release behaviour were found: fast release for a swollen state and slow (yet significant and non-negligible) release for a collapsed state. Six cycles of pulsatile release between 4 °C and 40 °C were obtained. The dosage of drug (rhodamine B) released in these cycles could be controlled to deliver approximately equal doses by altering the release time in the swollen state. However, for the first cycle, the swollen release rate was found to be large, and the release time could not be made short enough to prevent a larger dose than desired being delivered. A model was developed based on Fick's law which describes pulsatile release mathematically for the first time, and diffusion coefficients at different temperatures (including temperatures corresponding to both the fully swollen and collapsed states) were estimated by fitting the experimental data with the theoretical release profile given by this model. The effect of temperature on the diffusion coefficient was studied and it was found that in the range of the lower critical solution temperature (LCST), the diffusion coefficient increased with decreasing temperature. The model predicts that the effective lifetime of the system lies in the approximate range of 1-42 h (95% of drug released), depending on how long the system was kept at low temperature (below the LCST). Therefore this system can be used to obtain a controllable pulsatile release profile for small molecule drugs thereby enabling optimum therapeutic effects.