Random effects in drug dissolution

The deterministic models of dissolution are commonly used in pharmaceutical studies, however, experimental results point to stochastic nature of the dissolution processes. In this paper we present stochastic modifications of deterministic models using the concept of Wiener process. The models are given in form of stochastic differential equations and their properties are studied. Probability distributions of the dissolution data are derived for all the stochastic models. Variability of the dissolution data is discussed and sources of the random fluctuations are divided into two categories – the variability of the dissolution vessel environment and the measurement errors. Based on these considerations a function describing variability of the dissolution data at each time instant is proposed. Practical application of the stochastic approach based on experimental data is illustrated by finding maximum-likelihood estimation of model parameters and identification of noise sources and their levels in the system. Their influence on the estimates of the mean dissolution time is shown.