Fundamentals of release mechanism interpretation in multiparticulate systems: the prediction of the commonly observed release equations from statistical population models for particle ensembles

The kinetics of release from a population of microparticles is determined by the distribution of a small number of parameters governing the release function in a heterogeneous population. A general model for treatment of the distribution is developed for any release pattern common to a whole population, which is shown to lead to a variety of different cumulative release equations, including those hitherto considered to govern the release mechanism from microcapsules. Thus, the main case, that of constant release rate from individuals differing in rate constant, is shown to yield, according to the statistical distribution of the parameters, ensemble kinetics following first-order, square-root of time (Higuchi's equation), cube-root law (Hixson-Crowell) or a combination of initial zero-order followed by square-root of time relationships, all of which have been used to describe experimental systems studied. It is demonstrated that the cumulative release kinetics observed in a multiparticle system, being a function of the statistical distribution of parameters, does not characterize the basic release mechanism, which can only be determined directly from studies on individuals. The treatment also shows that in the case of first-order release by individuals, the ensembles cannot also observe first-order kinetics, except in the rare case of homogeneity of the determining parameters in the population.