Three-dimensional model for aerosol transport and deposition in expanding and contracting alveoli

Particle transport and deposition within a model alveolus, represented by a rhythmically expanding and contracting hemisphere, was modeled by a three-dimensional analytical model for the time-dependent air velocity field as a superposition of uniform and radial flow components, satisfying both the mass and momentum conservation equations. Trajectories of particles entrained in the airflow were calculated by a numerical particle trajectory code to compute simultaneously deposition by inertial impaction, gravitational sedimentation, Brownian diffusion, and interception. Five different orientations of the orifice of the alveolus relative to the direction of gravity were selected. Deposition was calculated for particles from 1 nm to 10 mu m, for 3 breathing conditions, and for 5 different entrance times relative to the onset of inspiration. For the analyzed cases, the spatial orientation of the orifice of an alveolus has practically no effect on deposition for particles below about 0.1 mu m, where deposition is dominated by Brownian motion. Above about 1 m, where deposition is governed primarily by gravitational settling, deposition can vary from 0 to 100%, depending on the spatial orientation, while deposition of particles 0.1-1 mu m falls between these two extreme cases. Due to the isotropic nature of Brownian motion, deposition of the 10-nm particles is practically uniform for all spatial orientations. However, for larger particles, deposition can be quite inhomogeneous, consistent with the direction of gravity. While nearly all particles are exhaled during the successive expiration phase, there are a few cases where particles still leave the alveolus even after many breathing cycles.