Probabilistic cellular automata modeling of intercellular interactions in airways: Complex pattern formation in patients with chronic obstructive pulmonary disease.

The chronic obstructive pulmonary disease (COPD) is a highly prevalent lung disease, in which unusual interactions between fibrocytes and CD8+ T lymphocytes in the peribronchial area could induce chronic inflammation and tissue remodeling. We considered a probabilistic cellular automata type model where the two types of cells follow simple local interaction rules taking into account cell death, proliferation, migration and infiltration. A rigorous mathematical analysis carried out within the framework of a streamlined model makes it possible to estimate with precision the parameters of the model using multiscale experimental data obtained in control and disease conditions. The simulation of the model is simple to be implemented. In simulations, two distinct patterns emerged, which can be analyzed quantitatively. In particular, we show that the change in fibrocyte density in the COPD condition is mainly the consequence of their infiltration into the lung during exacerbations, suggesting possible explanations for experimental observations in normal and COPD tissue. Our integrated approach combining probabilistic cellular automata type model and experimental findings will provide further insights into COPD in future studies.