Propagation of uncertainty in nasal spray in vitro performance models using Monte Carlo simulation: part I. Model prediction using Monte Carlo simulation.

Design of experiment (DOE) methodology can provide a complete evaluation of the influences of nasal spray activation and formulation properties on delivery performance which makes it a powerful tool for product design purposes. Product performance models are computed from complex expressions containing multiple factor terms and response terms. Uncertainty in the regression model can be propagated using Monte Carlo simulation. In this study, four input factors, actuation stroke length, actuation velocity, concentration of gelling agent, and concentration of surfactant were investigated for their influences on measured responses of spray pattern, plume width, droplet size distribution (DSD), and impaction force. Quadratic models were calculated and optimized using a Box-Behnken experimental design to describe the relationship between factors and responses. Assuming that the models perfectly represent the relationship between input variables and the measured responses, the propagation of uncertainty in both input variables and response measurements on model prediction was performed using Monte Carlo simulations. The Monte Carlo simulations presented in this article illustrate the propagation of uncertainty in model predictions. The most influential input variable variances on the product performance variance were identified, which could help prioritize input variables in terms of importance during continuous improvement of nasal spray product design. This work extends recent Monte Carlo simulations of process models to the realm of product development models.