A coupled model for the dynamics of gas exchanges in the human lung with Haldane and Bohr's effects

We propose an integrated dynamical model for oxygen and carbon dioxide transfer from the lung into the blood, coupled with a lumped mechanical model for the ventilation process, for healthy patients as well as in pathological cases. In particular, we take into account the nonlinear interaction between oxygen and carbon dioxide in the blood volume, referred to as the Bohr and Haldane effects. We also propose a definition of the physiological dead space volume (the lung volume that does not contribute to gas exchange) which depends on the pathological state and the breathing scenario. This coupled ventilation-gas diffusion model is driven by the sole action of the respiratory muscles. We analyse its sensitivity with respect to characteristic parameters: the resistance of the bronchial tree, the elastance of the lung tissue and the oxygen and carbon dioxide diffusion coefficients of the alveolo-capillary membrane. Idealized pathological situations are also numerically investigated. We obtain realistic qualitative tendencies, which represent a first step towards classification of the pathological behaviours with respect to the considered input parameters.