Purpose: Non-volatile agents such as glycerol are being introduced into solution-based pMDI formulations in order to control mean precipitant droplet size. To assess their biopharmaceutical efficacy, both microscopic and macroscopic characteristics of the plume must be known, including the effects of external factors such as the flow generated by the patient's inhalation. We test the hypothesis that the macroscopic properties (e.g. spray geometry) of a pMDI spray can be predicted using a self-similarity model, avoiding the need for repeated testing.
Methods: Glycerol-containing and glycerol-free pMDI formulations with matched mass median aerodynamic diameters are investigated. High-speed schlieren imaging is used to extract time-resolved velocity, penetration and spreading angle measurements of the pMDI spray plume. The experimental data are used to validate the analytical model.
Results: The pMDI spray develops in a manner characteristic of a fully-developed steady turbulent jet, supporting the hypothesis. Equivalent glycerol-containing and non glycerol-containing formulations exhibit similar non-dimensional growth rates and follow a self-similar scaling behaviour over a range of physiologically relevant co-flow rates.
Conclusions: Using the proposed model, the mean leading edge penetration, velocity and spreading rate of a pMDI spray may be estimated a priori for any co-flow conditions. The effects of different formulations are captured in two scaling constants. This allows formulators to predict the effects of variation between pMDIs without the need for repeated testing. Ultimately, this approach will allow pharmaceutical scientists to rapidly test a number of variables during pMDI development.