A, Model for Tracheobronchial Clearance of Inhaled Particles in Man and a Comparison with Data

We report the development of a mathematical model for the mucociliary clearance of inhaled particles in the normal human lung. The model assumes Weibel's symmetric dichotomously branching system of airways in the lung. The model is formulated by assuming that the particles residing on the surface of the mucus blanket behave as a fluid and that their concentration is governed by the continuity equation. The concentration of particles in each airway generation of the lung is found to depend on the initial deposition pattern and the transport rate of mucus in each airway generation. The distribution of particles is determined by a model calculation which takes into account inertial impaction, gravitational sedimentation, and Brownian diffusion as the principal mechanisms of particle deposition. The mucus transport rates are found by first assuming that the mucus blanket which lines the airways is uniformly thick throughout the entire lung and that there is no net absorption or secretion of mucus in a given airway generation. The only mucociliary transport rate which has been well measured experimentally is in the trachea. We adjust the trachael transport rate in the model until a good agreement between predicted and observed clearance of 7.9μaerodynamic diameter particles from the lung is obtained. The tracheal transport rate necessary to achieve a good fit is 5.5 mm/min which agrees with measured values. With an established trachael transport rate we are then able to calculate transport rates in distal airways.