Exact Analytical Relations for the Average Release Time in Diffusional Drug Release

Although analytical solutions for the problem of diffusion-controlled drug release from uniform formulations of simple geometries, like slabs, spheres, or cylinders, are well known, corresponding exact expressions for the average release times are not widely used. However, such exact analytical formulae are very simple and useful. When the drug is initially distributed homogeneously within the matrix, the average time of release from a sphere of radius R is tav=(1/15)R2/D and from a slab of thickness L is tav=(1/12)L2/D, where D is the corresponding drug diffusion coefficient. Regarding cylindrical tablets of height H and radius R, simple analytical expressions are obtained in the two opposite limits of either very long (H >> R) or very short (HMUCH LESS-THANR) cylinders. In the former case, of practically radial release, the average release time is tav=(1/8)R2/D, while in the latter case the same result as that of a slab with thickness H is recovered, tav=(1/12)H2/D, as expected. These simple and exact relations are useful not only for an estimate of the average release time from a drug carrier device when diffusion is the dominant mechanism of drug delivery, but also for the experimental determination of the drug diffusion coefficient in a release system of interest through the measured release profile, given the mean squared size of the formulation.