A new mathematical approach modeling surfactant transport in pulmonary airways

The goal of this paper is to describe a bulk-phase convection - diffusion transport of pulmonary surfactant in two-phase free surface flow. Transport in this system can be very complex because of interactions between surfactant and mechanical properties of the system (physicochemical hydrodynamics). Once adsorbed to the air - liquid interface with a surface concentration, surfactant alters an interfacial surface tension. As an interfacial stress balance, which governs the fluid mechanics, is a function of surface tension, a strong coupling exists between the surfactant transport dynamics and the fluid mechanics. Motivation for this study was the development of an understanding of surfactant transport dynamics during respiratory distress syndrome (RDS) of premature infants, where the primary pathology is due to a low bulk surfactant concentration. In this physiologically significant case, the true physicochemical dynamics cannot be adequately understood without accounting for the bulk transport processes. To model this problem, we consider the mechanics of a semi-infinite gas bubble progression in a liquid-filled rigid-walled, axisymmetric tube with radius R under steady-state conditions. The presented model extends beyond previous models of surfactant transport in the systems that may relate to airway reopening. First, the adsorption kinetics and the equation of state are described using the non-linear Langmuir adsorption model. Most previous studies used a linear relationship between the surfactant concentration and the local surface tension. Linear models are valid only for the small departures from equilibrium.