Gas transport in branched airways during high-frequency ventilation

Abstract

A theoretical model of high-frequency ventilation (HFV) is presented based on the physical convective exchange process that occurs due to the irreversibility of gas velocity profiles in oscillatory flow through the bronchial airways. Mass transport during the convective exchange process can be characterized by a convective exchange length, LE, which depends only on the irreversibility of bronchial velocity profiles and can be measured by the experimental technique of photographic flow visualization in bronchial tree models. Using the exchange length and the molecular diffusivity, a simple model of overall bronchial mass transfer is developed. The model allows a prediction of the mean gas concentration profiles along the airways, the site of maximum mass transfer resistance, and overall flow rate of the gas of interest in or out of the lung as functions of the parameters of HFV. The results predicted by the model agree with the limited experimental data available for animals and humans. For normal unassisted ventilation, total bronchial cross-sectional area around the 15th Weibel bronchial generation is predicted to be the single most important parameter in controlling the total gas transport rate along the airways. For the breathing of room air, values of the respiratory quotient around 0.78 are predicted, which are insensitive to VT and f. The model represents a fruitful combination of fluid mechanical theory and experiment with physiologic data to yield new and deeper insight into the operation of the human respiratory system during HFV and normal breathing.