Assessment and Validation of a Hygroscopic Growth Model with Different Water Activity Estimation Methods

Hygroscopic growth models are currently of interest as aids for targeting the deposition of inhaled drug particles in preferred areas of the lung that will maximize their pharmaceutical effect. Mathematical models derived to estimate hygroscopic growth over time have been previously developed but have not been thoroughly validated. For this study, model validation involved a comparison of modeled values to measured values when the growing droplet had reached equilibrium. A second validation process utilized a novel system to measure the growth of a droplet on a microscope coverslip relative to modeled values when the droplet is undergoing the initial rapid growth phase. Various methods currently used to estimate the water activity of the growing droplet, which influences the droplet growth rate, were also compared. Results indicated that a form of the hygroscopic growth model that utilizes coupled-differential equations to estimate droplet diameter and temperature over time was valid throughout droplet growth until it reached its equilibrium size. Accuracy was enhanced with the use of a polynomial expression to estimate water activity relative to the use of a simplified estimate of water activity based on Raoult's Law. Model accuracy was also improved when constraining the film of salt solution surrounding the dissolving salt core at saturation.