Finite element simulation of fluid dynamics and CO$_2$ gas exchange in the alveolar sacs of the human lung

TL;DR

This paper develops a numerical framework using finite element methods and ALE techniques to simulate fluid flow and CO2 exchange in human lung alveolar sacs, accounting for geometric deformation during breathing.

Contribution

It introduces novel pressure-stabilisation formulations within the ALE framework for alveolar gas exchange modeling on anisotropic meshes.

Findings

Numerical results on a simplified alveolar geometry demonstrate the model's effectiveness.

Pressure stabilisation techniques influence simulation stability and accuracy.

Boundary conditions significantly affect gas exchange simulations.

Abstract

In this article we present a numerical framework based on continuum models for the fluid dynamics and the CO$_2$ gas distribution in the alveolar sacs of the human lung during expiration and inspiration, including the gas exchange to the cardiovascular system. We include the expansion and contraction of the geometry by means of the Arbitrary Lagrangian Eulerian (ALE) method. For discretisation, we use equal-order finite elements in combination with pressure-stabilisation techniques based on local projections or interior penalties. We derive formulations for both techniques that are suitable on arbitrarily anisotropic meshes. These formulations are novel within the ALE method. Moreover, we investigate the effect of different boundary conditions, that vary between inspiration and expiration. We present numerical results on a simplified two-dimensional alveolar sac geometry and investigate the influence of the pressure stabilisations as well as the boundary conditions