Stochastic modeling of controlled-drug release

A drug release process by the oral route is random in nature and thus is subject to constant fluctuations. Moreover, individuals have varied tolerances to such fluctuations. The objective of this work is to characterize these fluctuations by a stochastic formalism. The system under consideration, i.e., the gastrointestinal tract consists of four consecutive compartments, i.e., stomach, duodenum, jejunum, and ileum. The master equation of the system as well as the governing equations for the means, variances, and covariances of the random variables, each representing the number of microspheres in an individual compartment, have been derived through the probabilistic population balance. These equations have been numerically solved to predict the total release fraction of drug and its internal fluctuations, and the dynamic statistics (means, variances, and covariances) of the amount of drug in each compartment at any time after administration. The dissolution-intensity functions in the model have been recovered from the available in vitro dissolution data from controlled-release pellets of isosorbide-5-nitrate (IS-5-N) by assuming that the rate of release is of the first order. The residence times and transition-intensity functions of drug in the individual compartments have been estimated from the available data generated by the gamma scintigraphies of IS-5-N pellets labeled by In-111. Based on these parameters, the total numbers of dissolved drug microspheres and their fluctuations at any instance have been calculated. The model is in accord with the existing in vivo dissolution data of the same drug independently obtained through plasma analysis. More important, the model predicts that fluctuations in terms of the standard deviations of the numbers of particles in the duodenum, jejunum, and ileum can be of the same orders of magnitude as the corresponding mean numbers when 100 microspheres are simultaneously administered orally; in practice, such fluctuations characterized by these deviations could result in an undesirable release profile. Discussion is given of the potential direct clinical application of the results obtained as well as the plausible indirect application of these results and the model derived to the analyses of chemical and biochemical reactors. (C) 1998 Elsevier Science S.A. All rights reserved.