Quantifying parenchymal tethering in a finite element simulation of a human lung slice under bronchoconstriction

Airway hyper-responsiveness (AHR), a hallmark of asthma, is a highly complex phenomenon characterised by multiple processes manifesting over a large range of length and time scales. Multiscale computational models have been derived to embody the experimental understanding of AHR. While current models differ in their derivation, a common assumption is that the increase in parenchymal tethering pressure P(teth) during airway constriction can be described using the model proposed by Lai-Fook (1979), which is based on intact lung experimental data for elastic moduli over a range of inflation pressures. Here we reexamine this relationship for consistency with a nonlinear elastic material law that has been parameterised to the pressure-volume behaviour of the intact lung. We show that the nonlinear law and Lai-Fook's relationship are consistent for small constrictions, but diverge when the constriction becomes large.