Parenchymal tethering, airway wall stiffness, and the dynamics of bronchoconstriction.

We do not yet have a good quantitative understanding of how the force-velocity properties of airway smooth muscle interact with the opposing loads of parenchymal tethering and airway wall stiffness to produce the dynamics of bronchoconstriction. We therefore developed a two-dimensional computational model of a dynamically narrowing airway embedded in uniformly elastic lung parenchyma and compared the predictions of the model to published measurements of airway resistance made in rats and rabbits during the development of bronchoconstriction following a bolus injection of methacholine. The model accurately reproduced the experimental time-courses of airway resistance as a function of both lung inflation pressure and tidal volume. The model also showed that the stiffness of the airway wall is similar in rats and rabbits, and significantly greater than that of the lung parenchyma. Our results indicate that the main features of the dynamical nature of bronchoconstriction in vivo can be understood in terms of the classic Hill force-velocity relationship operating against elastic loads provided by the surrounding lung parenchyma and an airway wall that is stiffer than the parenchyma.