Modeling bronchial circulation with application to soluble gas exchange: description and sensitivity analysis

Abstract

The steady-state exchange of inert gases across an in situ canine trachea has recently been shown to be limited equally by diffusion and perfusion over a wide range (0.01–350) of blood solubilities (βblood; ml ⋅ ml−1 ⋅ atm−1). Hence, we hypothesize that the exchange of ethanol (βblood = 1,756 at 37°C) in the airways depends on the blood flow rate from the bronchial circulation. To test this hypothesis, the dynamics of the bronchial circulation were incorporated into an existing model that describes the simultaneous exchange of heat, water, and a soluble gas in the airways. A detailed sensitivity analysis of key model parameters was performed by using the method of Latin hypercube sampling. The model accurately predicted a previously reported experimental exhalation profile of ethanol ( R 2= 0.991) as well as the end-exhalation airstream temperature (34.6°C). The model predicts that 27, 29, and 44% of exhaled ethanol in a single exhalation are derived from the tissues of the mucosa and submucosa, the bronchial circulation, and the tissue exterior to the submucosa (which would include the pulmonary circulation), respectively. Although the concentration of ethanol in the bronchial capillary decreased during inspiration, the three key model outputs (end-exhaled ethanol concentration, the slope of phase III, and end-exhaled temperature) were all statistically insensitive ( P > 0.05) to the parameters describing the bronchial circulation. In contrast, the model outputs were all sensitive ( P < 0.05) to the thickness of tissue separating the core body conditions from the bronchial smooth muscle. We conclude that both the bronchial circulation and the pulmonary circulation impact soluble gas exchange when the entire conducting airway tree is considered.