Pulmonary epithelial wound healing and the immune system. Mathematical modeling and bifurcation analysis of a bistable system

Respiratory diseases such as asthma, acute respiratory distress syndrome (ARDS), influenza or COVID-19 often directly target the epithelium. Elevated immune levels and a ‘cytokine storm’ are directly associated with defective healing dynamics of lung diseases such as COVID-19 or ARDS. The infected cells leave wounded regions in the epithelium which must be healed for the lung to return to a healthy state and carry out its main function of gas-exchange. Due to the complexity of the various interactions between cells of the lung epithelium and surrounding tissue, it is necessary to develop models that can complement experiments to fully understand the healing dynamics. In this mathematical study we model the mechanism of epithelial regeneration. We assume that healing is exclusively driven by progenitor cell proliferation, induced by a chemical activator such as epithelial growth factor (EGF) and cytokines such as interleukin-22 (IL22). Contrary to previous studies of wound healing, we consider the immune system, specifically the T effector cells TH1, TH17, TH22 and Treg to strongly contribute to the healing process, by producing IL22 or regulating the immune response. We therefore obtain a coupled system of two ordinary differential equations for the epithelial and immune cell densities and two functions for the levels of chemicals that either induce epithelial proliferation or recruit immune cells. These functions link the two cell equations. We find that to allow the epithelium to regenerate to a healthy state, the immune system must not exceed a threshold value at the onset of the healing phase. This immune threshold is supported experimentally but was not explicitly built into our equations. Our assumptions are therefore sufficient to reproduce experimental results concerning the ratio TH17/Treg cells as a threshold to predict higher mortality rates in patients. This immune threshold can be controlled by parameters of the model, specifically the base-level growth factor concentration. This conclusion is based on a mathematical bifurcation analysis and linearization of the model equations. Our results suggest treatment of severe cases of lung injury by reducing or suppressing the immune response, in an individual patient, assessed by their disease parameters such as course of lung injury and immune response levels.