A three-dimensional model of tracheobronchial particle distribution during mucociliary clearance in the human respiratory tract.

Although theoretical approaches to tracheobronchial (TB) clearance have been continuously refined during the past decades, questions concerning the exact course of particle removal from the TB tree have been largely remained unsolved. In order to clarify this problem, three-dimensional patterns of mucociliary particle clearance have to be generated at pre-defined time points after particle exposure. Here, we present a mathematical method for the generation of respective clearance patterns. Three-dimensional transport paths of inhaled particles as well as spatial deposition patterns were generated by determining spatial information of all airway tubes passed by the particles and the particle deposition sites. Three-dimensional data were converted to a coordinate system, within which the trachea represented the z-axis. Visualization of stored data was realized with the help of a freely available program code that is specialized in processing huge data sets. Mucociliary clearance of deposited particular mass was computed by assuming (1) an interrelationship between mucus velocity and airway caliber and (2) an average tracheal mucus velocity of 5.5mm min(-1). Position of cleared particles within the spatial TB tree was determined at t=0 h (immediately after exposure), t=12 h and t=24 h. Spatial patterns of mucociliary clearance were computed for particles with a uniform geometric diameter of 5μm and a density of 1g cm(-3). Inhalation of the aerosol loaded with those particles took place under sitting breathing conditions (breathing frequency: 15min(-1), tidal volume: 750 ml). As demonstrated by the generated clearance patterns, mucociliary transport of 5μm particles is completed after 30 h. Within the first 12 h following aerosol exposure, about 75% of the initially deposited particular mass is removed from the TB tree. After 24 h, 95% of the particles have been cleared. Clearance patterns are characterized by a successive transition of maximal particle concentrations towards more proximal airway generations. For 0.1μm particles and 1μm particles clearance times are significantly prolonged, whilst 10μm particles are even faster removed from the TB tree than the 5μm particles. Based on the results of this study the time span between initial deposition of particular matter and complete evacuation of deposited particles ranges from several hours to some days and depends on (1) the preferential deposition site of the inhaled material and (2) the mean mucus velocities in the bronchial airway generations.