  In diffusion-controlled drug delivery, it is possible for drug molecules to
bind to the carrier material and never be released. A common way to incorporate
this phenomenon into the governing mechanistic model is to include an
irreversible first-order reaction term, where drug molecules become permanently
immobilised once bound. For diffusion-only models, all the drug initially
loaded into the device is released, while for reaction-diffusion models only a
fraction of the drug is ultimately released. In this short paper, we show how
to calculate this fraction for several common diffusion-controlled delivery
systems. Easy-to-evaluate analytical expressions for the fraction of drug
released are developed for monolithic and core-shell systems of slab, cylinder
or sphere geometry. The developed formulas provide analytical insight into the
effect that system parameters (e.g. diffusivity, binding rate, core radius)
have on the total fraction of drug released, which may be helpful for
practitioners designing drug delivery systems.
