Mathematical modeling of the retention and clearance of low-toxicity particles in the lung

A mathematical model has been formulated to describe the mechanisms that determine the retention or clearance of insoluble inhaled particles in the rat lung. The hypotheses underlying the model are described – for example, the phagocytosis of free particles by macrophages, the transport of particles in macrophages from the alveolar region, the effect of the life cycle of macrophages leading to the eventual release of phagocytosed particles, the effect of lung burden on the macrophage activity, the transport of particles into the interstitium, the role of interstitial macrophages, the formation of granulomata, and transport of interstitialized particles to the thoracic lymph nodes. With these hypotheses, the fate of particles is described mechanistically via the cellular response of the lung. The mathematical model expresses these particle transitions as differential equations quantifying the transport of particles from one compartment to another, where the compartments represent the alveolar surface, the alveolar macrophages, overloaded alveolar macrophages, the interstitium, interstitial macrophages, and the thoracic lymph nodes. A companion article describes the application of the model to a data set from rats exposed to a low-toxicity dust at several concentrations and for a range of exposure times.