Reduced biomechanical models for precision-cut lung-slice stretching experiments

Precision-cut lung-slices (PCLS), in which viable airways embedded within lung parenchyma are stretched or induced to contract, are a widely used ex vivo assay to investigate bronchoconstriction and, more recently, mechanical activation of pro-remodelling cytokines in asthmatic airways. We develop a nonlinear fibre-reinforced biomechanical model accounting for smooth muscle contraction and extracellular matrix strain-stiffening. Through numerical simulation, we describe the stresses and contractile responses of an airway within a PCLS of finite thickness, exposing the importance of smooth muscle contraction on the local stress state within the airway. We then consider two simplifying limits of the model (a membrane representation and an asymptotic reduction in the thin-PCLS-limit), that permit analytical progress. Comparison against numerical solution of the full problem shows that the asymptotic reduction successfully captures the key elements of the full model behaviour. The more tractable reduced model that we develop is suitable to be employed in investigations to elucidate the time-dependent feedback mechanisms linking airway mechanics and cytokine activation in asthma.