A stochastic differential equation model for drug dissolution and its parameters.

A stochastic differential equation describing the process of drug dissolution is presented. This approach generalizes the classical deterministic first-order model. Instead of assuming a constant fractional dissolution rate, it is considered here that the rate is corrupted by a white noise. The half-dissolution time is investigated for the model. The maximum likelihood and Bayes methods for the estimation of the parameters of the model are developed. The method is illustrated on experimental data. As expected, due to the nonlinear relationship between the fractional dissolution rate and the dissolution time, the estimates of the dissolution rate obtained from this stochastic model are systematically lower than the rate calculated from the deterministic model.