  We consider a mathematical model that describes the release 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 five partial
differential equations, is reduced to a system of just two equations. We
identify the governing non-dimensional parameters that can be varied to tune
the growth factor release rate. In particular, we identify a parameter regime
that ensures slow passive release (usually desirable) of at least a fraction of
the growth factor. 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 is
directly compared with 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).
