Theoretical analysis of inward hemispheric release above and below drug solubility

A detailed analysis of inward diffusional drug release from devices with hemispheric and related geometries is presented. When drug is loaded below its solubility, an infinite series describes drug concentration profiles and release kinetics, with an excellent approximation resulting when only one term of this series is retained. A connection between this geometric setting and diffusion in constricted porous domains is pointed out, as is the utility of mean first passage times and mean residence times derived for this model. For the case of drug loaded above its solubility, the pseudosteady state (PSS) approximation of Béchard and McMullen [J. Pharm. Sci. 77 (1988) 222] is compared against numerical results calculated for the full model in which the PSS assumption is removed. A close match is observed. Asymptotic analysis of the PSS expressions shows that the previously used zero-order release assumption is not quite correct, even at later times, and this affects parameter estimation procedures. A comparison between the model of Béchard and McMullen and earlier obtained experimental data [J. Pharm. Sci. 72 (1983) 17] reveals some qualitative discrepancies that are yet to be explained.