Modelling Particle-Wall Interaction in Dry Powder Inhalers

Abstract

Dry powder inhalers deliver drugs in powdered form to the lungs. The drug is stored within the inhaler bound to an excipient. The drug-excipient conglomerate is broken apart in a vortex chamber by collisions with the walls and other conglomerates. During the initial doses, some drug adheres to the wall of the vortex chamber reducing the amount of drug delivered to the patient. We developed mathematical models for particle-wall adhesion to investigate why drug particles adhere to the wall of the vortex chamber. Two different models are developed to validate our results and a good agreement has been obtained. The first model describes the motion of particles in a turbulent flow field based on Stochastic Differential Equations (SDE). The second model is a continuum model of particle-wall adhesion based on Partial Differential Equations (PDE). This model focuses on the rate at which drug particles are captured by the wall and the time taken for drug particles to fill the wall area. Estimates of magnitudes of adhesive forces suggest that excipient particles do not adhere to the walls, while drug particles bind to the wall due to van der Waals forces when their velocity is below a critical value.