A mathematical model of phagocytosis and inflammation after the inhalation of quartz at different concentrations

A mathematical model was developed with several distinctive features to represent the various processes leading to silicosis. It assures the phagocytosis of quartz by the resident alveolar macrophages. It then models the necrosis of macrophages caused by the ingestion of quartz particles and the subsequent release of these clusters onto alveolar surfaces. The inflammatory recruitment of alveolar macrophages and neutrophils in response to the cell necrosis caused by the ingestion of quartz particles is described in a functional form and is included in the model. The model also describes the pathological and other biological reactions to quartz particles in the interstitium. Specifically, once the quartz particles arrive at the interstitium, they can be phagocytozed by interstitial macrophages. The pathological interaction between quartz and interstitial macrophages may lead to quartz particles being sequestered in silicotic nodules, and also cleared to the efferent lymph nodes.