Drug polymer conjugates: Average release time from thin films

The reaction-diffusion problem describing the release of drugs conjugated through labile bonds to polymeric thin films has a known analytical solution, when the reaction kinetics is of first order. Using this solution, an exact formula is derived for the average release time of the system. This simple expression provides the characteristic time of release t_av as the sum of the corresponding average diffusion time plus the inverse reaction rate constant: t_av=(1/12)⋅(L²/D)+(1/k), where L is the slab thickness, D the diffusion coefficient, and k the reaction rate constant. The former term dominates in a diffusion-controlled release, while the latter one in a reaction-controlled delivery. The crossover regime is exactly described by their sum. The obtained result for the average release time is verified by direct numerical integration through the drug release profiles of the analytical solution. The value of fractional drug release at the characteristic average time is between 60-64%. These results can be used for the design of polymer-drug conjugates with a desired delivery time scale, as well as for the experimental determination of the values of microscopic parameters D and k in a conjugated system of interest.