Sensitivity and optimality analysis of breathing scenarios for 1D or 0D models of gas diffusion in the lung
Résumé
In the present work we propose a new nonlinear coupled 1D model to describe lung ventilation and the transport and diffusion of both oxygen and carbon dioxide in the bronchial tree through the blood. It takes into account the so called Bohr-Haldane effect and is driven by the applied pleural pressure. The ability of this model to recover standard acknowledged values in healthy situations is provided. One key aspect is that, contrary to its 0D counterpart, it naturally takes into account mixing of gases along the tree and a time delay as the gases have to be transported before reaching the alveoli. We further investigate the sensitivity of both the 1D model and its 0D counterpart with respect to the breathing pattern by considering two types of pleural applied pressure: a piecewise constant one and a piecewise exponential one for various values of the breathing period, inspiratory ratio and pressure amplitude. We finally explore which cost functions the observed stereotypical breathing scenario may optimize, underlying the fact that it should be a combination of several criteria: low effort and small lung distension while maintaining carbon dioxide arterial partial pressure at a given level.
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