A two-dimensional hexagonal network model of alveolar mechanics

Pulmonary micromechanics (at the scale of alveoli) involves a delicate balance among tissue material properties, geometry, surface tension, pressure and stress distribution. To date, there is not a consensus among alveolar mechanics researchers about how these factors interact, in part because alveoli are so difficult to image and study in vivo. Here, we propose a basic mathematical model of a two-dimensional hexagonal network of mechanically coupled alveoli. We investigate equilibrium configurations of both dry and wet, internally pressurized elastic networks. Specifically, we compute pressure-area curves to quantify the differences among networks with different spring constants, internal pressures, network size and surface tensions. We conclude that a two-dimensional hexagonal network in force equilibrium is an appropriate first step in modeling the mechanics of the dynamic lung