Development of a mathematical model of the innate immune response to inhaled toxicants.

Lung inflammation due to inhalation of toxicants such as wood smoke is a feature of many respiratory diseases, including asthma, chronic obstructive pulmonary disease (COPD), interstitial lung diseases, and respiratory infections. We present a mathematical model of immune cell and cytokine interactions in the presence of inhaled toxicants. The model, focusing on interactions between epithelial cells, macrophages, and pro- and anti-inflammatory cytokines, is constructed by developing several submodels calibrated to fit both experimental in vitro data and our understanding of the transition from type I to type II immune responses. The model's predictions align with experimental observations, showing an initial pro-inflammatory (type I) response dominated by M1 macrophages transitioning to an anti-inflammatory/repair (type II) response characterized by M2 macrophages. Simulations of different exposure scenarios demonstrate that although a single exposure elicits a self-limiting inflammatory response, repeated exposures lead to persistent inflammation and elevated M2:M1 ratios consistent with chronic lung conditions. The model provides a novel mathematical framework that captures complex immune system transitions through a minimal set of equations, demonstrating how relatively simple mathematical structures can effectively represent sophisticated biological behavior while maintaining analytical tractability. Through stability analysis and careful parameter selection, we show that the model exhibits biologically relevant steady states that align with experimental observations. This framework enables the exploration of various exposure patterns and potential interventions on inflammatory dynamics, serving as a foundation for the future development of a virtual tissue model of macrophage-epithelial cell interactions.