Development of a CFD boundary condition to model transient vapor absorption in the respiratory airways

The absorption of moderately and highly soluble vapors into the walls of the conducting airways was previously shown to be a transient process over the timescale of an inhalation cycle. However, a boundary condition to predict the transient wall absorption of vapors in CFD simulations does not exist. The objective of this study was to develop and test a boundary condition that can be used to predict the transient absorption of vapors in CFD simulations of transport in the respiratory airways. To develop the boundary condition, an analytical expression for the concentration of an absorbed vapor in an air-mucus-tissue-blood (AMTB) model of the respiratory wall was developed for transient and variable air-phase concentrations. Based on the analytical expression, a flux boundary condition was developed at the air-mucus interface as a function of the far-field air-phase concentration. The new transient boundary condition was then implemented to predict absorption in a realistic model of the extrathoracic nasal airways through the larynx (nasal-laryngeal geometry). The results of the AMTB wall model verified that absorption was highly time dependent over the timescale of an inhalation cycle (approximately 1-2 s). At 1 s, transient conditions resulted in approximately 2-3 times more uptake in tissue and 20-25 times less uptake in blood than steady state conditions for both acetaldehyde and benzene. Application of this boundary condition to computational fluid dynamics simulations of the nasal-laryngeal geometry showed, as expected, that transient absorption significantly affected total deposition fractions in the mucus, tissue, and blood. Moreover, transient absorption was also shown to significantly affect the local deposition patterns of acetaldehyde and benzene. In conclusion, it is recommended that future analyses of vapors in the conducting airways consider time-dependent wall absorption based on the transient flux boundary condition developed in this study. Alternatively, a steady state absorption condition may be applied in conjunction with correction factors determined from the AMTB wall model.