A simple dynamical model of the oxygen uptake in the human pulmonary acinus

We have developed a mathematical model called a “machine acinus.” The machine acinus has the size and configuration of a real acinus and operates under realistic dynamics. All the complexity of O 2 trapping and blood saturation are merged into a parameter called the integrative permeability, Ω, whose value is linked to the alveolar pressure, P A,O2 , and the O 2 uptake, V O2 (Foucquier et al., Respir Physiol Neurobiol, 2013). Dynamic convection‐diffusion equations for the machine acinus are solved numerically for rest and peak exercise. Besides the adaptation at rest to the cardiac output, the results demonstrate the necessity of a hypoxic vasoconstriction adaptation to diffusion limitations. We show that a healthy adult's breathing can be predicted, at rest and exercise, with only two parameters: the threshold pressure for vasoconstriction (close to 100 mmHg) and Ω. If we model emphysema and pulmonary edema as a loss of acinar surface and a decrease in the permeability, respectively, we find that a safety margin against these diseases exists at rest. For instance, V O2 preserves 90% of its normal value under 50% surface reduction. In addition, our model predicts that the acinar region where the diseases take place is important. When the surface loss is concentrated in a distal region, V O2 is significantly reduced compared to that with the loss in the proximal region. This work was supported by Air Liquide Santé International.