Abstract
Ventilation is at the origin of a spending of energy coming from air circulation in the bronchial tree and from the mechanical resistance of the tissue to motion. Both amplitude and frequency of ventilation are submitted to a trade-off related to this energy, but they are also submitted to a constraint linked to the function of the lung: to transport enough oxygen and carbon dioxide in order to respect metabolism needs. We propose a model for oxygen and carbon dioxide transport in the lung that accounts for the core physical phenomena: lung's tree-like geometry, transport of gas by convection and diffusion, exchanges with blood and a sinusoidal ventilation. Then we optimize the power dissipated by the ventilation of our model relatively to ventilation amplitude and period under gas flow constraints. Our model is able to predict physiological ventilation properties and brings interesting insights on the robustness of different regimes. Hence, at rest, the power dissipated depends very little on the period near the optimal value. Whereas, at strong exercise any shift from the optimal has dramatic effect on the power. These results are fully coherent with the physiological observation and raises the question: how the control of ventilation could select for the optimal configuration? Also, interesting insights about pathologies affecting ventilation could be derived, and our model might give insights on therapeutical responses, with specific breathing strategies or for better driving mechanical ventilation.
Highlights
The respiratory system’s function consists in supplying the body with oxygen and in removing carbon dioxide
We propose a model for oxygen and carbon dioxide transport in the lung that accounts for the core physical phenomena: lung’s tree-like geometry, transport of gas by convection and diffusion, exchanges with blood and a sinusoidal ventilation
We propose a transversal approach for this problem, by developing a model based on the core physical phenomena involved in lung’s ventilation and function (Weibel, 1984)
Summary
The respiratory system’s function consists in supplying the body with oxygen and in removing carbon dioxide. Partial pressure in oxygen and carbon dioxide in blood are strongly regulated in mammals (Weibel, 1984). While oxygen directly affects the cells’ access to energy, carbon dioxide drives blood pH, whose allowed range for healthy cellular function is tight (Madshus, 1988). The transfer of these two species between lung and blood are driven by the amount of blood flow in pulmonary capillaries, the gradient of the partial pressure between alveoli and capillaries, the blood/alveoli membrane characteristics and the properties of the ventilation
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