Modeling Coating Flow and Surfactant Dynamics inside the Alveolar Compartment

TL;DR

This paper develops a mathematical model for alveolar coating flow incorporating surfactant dynamics, using lubrication theory to simulate thin film behavior and surfactant effects in lung alveoli.

Contribution

It introduces a new coupled PDE model for alveolar coating and surfactant dynamics, derived under lubrication approximation, with numerical simulations based on experimental parameters.

Findings

Model captures the interaction between coating flow and surfactant concentration.

Numerical simulations demonstrate the model's ability to replicate alveolar behavior.

Provides a foundation for studying lung surfactant therapies and alveolar stability.

Abstract

We derive a new model for the coating flow inside the alveolar compartment, taking into account pulmonary surfactant production and recycling by Type 2 cells as well as its degradation. As the thickness of alveolar coating is much smaller than the average radius of the alveoli, we employ the classical lubrication approximation to describe the thin liquid film dynamics in the presence of pulmonary surfactant, which is a surface tension reducing agent and thus prevents the lungs from collapse. In the lubrication limit, we derive a degenerate system of two coupled parabolic partial differential equations that describe the time evolution of the thickness of the coating film inside the alveoli together with that of the surfactant concentration at the interface. We present numerical simulations using parameter values consistent with experimental measurements.