Potential and constraints for the application of CFD combined with Lagrangian particle tracking to dry powder inhalers
For about 15 years the performance of dry powder inhalers (DPIs) has been numerically analysed through CFD (computational fluid dynamics) approaches with the objective of understanding the evolving flow structures and the resulting transport of drug particles. Naturally the main interest is the numerical prediction of the emitted fine particle fraction (FPF) which is able to penetrate the lung airways. Due to the mostly used drug formulations (i.e. carrier-based or agglomerated drug powder) and the complex elementary processes occurring during the transport of such particles through inhalers this is not an easy task. Essential for a good and efficient performance of DPI is the drug particle detachment from a carrier or the aerosolisation of agglomerated drug powder. Mostly the motion of particulate matter through an inhaler is described in a Lagrangian way using either a discrete particle method (DPM) or a discrete element method (DEM).
This paper reviews the major published contributions related to the numerical calculations of dry powder inhalers by considering particles which may be coarse carrier or fine drug particles or even clusters including agglomerated fine particles or carriers covered with many drug particles. This review also considers simulations on the behaviour of single clusters interacting with flows or colliding with rigid walls.
Following that, the potentials and constraints of the DPM and DEM are critically assessed with regard to inhaler applications. As a result, the DPM is most suitable since the clusters (i.e. carrier with drug or agglomerated drugs) are considered and tracked as single entities. On the other hand, in DEM all individual primary particles within clusters are tracked accounting for the acting fluid forces and multiple contact interactions between particles. In most applications published so far, the fluid dynamic interactions between these primary particles are not adequately accounted for. Hence, both approaches need further modelling activities for realistically capturing all relevant elementary processes, such as, flow induced drug detachment from clusters, cluster-wall collisions and recollection of drug particles on clusters.
Moreover, recent calculations on the motion of carrier particles through an inhaler for statistically analysing the experienced flow stresses are presented. Also, carrier-wall collisions were evaluated with regard to number and intensity. The flow simulations were conducted for steady-state conditions based on RANS (Reynolds-averaged Navier-Stokes) in connection with the k-ω-SST (shear-stress transport) turbulence model. Carrier particle tracking was done considering all relevant forces, especially transverse lift forces.
Based on this information, fully resolved simulations of the flow over particle clusters (i.e. carrier particle coated with thousands of drug particles) using the Lattice-Boltzmann method (LBM) are introduced. Therefrom, the detachment probabilities by lift-off, as well as sliding and rolling stripping of fine drug particles are evaluated. For that purpose, laminar and turbulent plug flows, as well as shear flows, were assumed to interact with the fixed cluster in a cubic domain. Even at the highest relative velocities typically found in an inhaler, lift-off in a laminar flow was not possible when considering experimentally determined adhesion forces. However, turbulence is very effective in drug powder detachment from a carrier.
Finally results are presented using a novel carrier-wall collision model for describing drug detachment in Euler/Lagrange simulations. The results for two inhalers (i.e. Cyclohaler and Unihaler, a modular inhaler developed at the University of Kiel) revealed that carrier-wall collisions are very effective for inertia-induced drug detachment. Hence, the predicted fine particle fraction was found to be close to 100% for both inhalers.
As a conclusion of this study, it has become clear that the wall deposition of fine drug particles is an important mechanism during carrier or agglomerate wall collisions, which are responsible for the low emitted fine particle fraction (FPF) observed experimentally. It is hoped that this article provides requirements and guidelines for the further development of Euler/Lagrange simulations applied to dry powder inhaler devices.
Keywords: Dry powder inhaler, Numerical calculation CFD, Euler/Lagrange approach, Discrete element method, Discrete particle method, Drug formulations, Drug detachment,