Computational modeling of unsteady surfactant-laden liquid plug propagation in neonatal airways

Abstract

Surfactant-free and surfactant-laden liquid plug propagation in neonatal airways in various generations representing the upper and lower airways are investigated computationally using a finite-difference/front-tracking method. Emphasis is placed on the unsteady surfactant-laden plug propagation as a model for Surfactant Replacement Therapy (SRT) and airway reopening. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations. Available experimental data for surfactant Survanta are used to relate surface tension coefficient to surfactant concentration at the interface. It is found that, for the surfactant-free case, the trailing film thickness is in good agreement with Taylor's law for plugs with plug length greater than the airway width. Mechanical stresses that could be injurious to epithelial cells such as pressure and shear stress and their gradients are maximized on the front and rear menisci with increasing magnitudes in the lower generations. These mechanical stresses, especially pressure and pressure gradient, are diminished with the introduction of surfactants. Surfactant is absorbed onto the trailing film and thickens it, eventually leading to either plug rupture or, if totally consumed prior to rupture, to steadily propagating plug. In the upper airways, initially small plugs rupture rapidly and plugs with comparable initial plug length with the airway width persist and propagate steadily. For a more effective SRT treatment, we recommend utilization of plugs with initial plug length greater than the airway width. Increasing surfactant strength or increasing the initially instilled surfactant concentration is found to be ineffective.