A mathematical model of pulmonary gas exchange under inflammatory stress

During a severe local or systemic inflammatory response, immune mediators target lung tissue. This process may lead to acute lung injury and impaired diffusion of gas molecules. Although several mathematical models of gas exchange have been described, none simulate acute lung injury following inflammatory stress. In view of recent laboratory and clinical progress in the understanding of the pathophysiology of acute lung injury, such a mathematical model would be useful. We first derived a partial differential equations model of gas exchange on a small physiological unit of the lung ( approximately 25 alveoli), which we refer to as a respiratory unit (RU). We next developed a simple model of the acute inflammatory response and implemented its effects within a RU, creating a single RU model. Linking multiple RUs with various ventilation/perfusion ratios and taking into account pulmonary venous blood remixing yielded our lung-scale model. Using the lung-scale model, we explored the predicted effects of inflammation on ventilation/perfusion distribution and the resulting pulmonary venous partial pressure oxygen level during systemic inflammatory stresses. This model represents a first step towards the development of anatomically faithful models of gas exchange and ventilation under a broad range of local and systemic inflammatory stimuli resulting in acute lung injury, such as infection and mechanical strain of lung tissue.