A recruitment model of quasi-linear power-law stress adaptation in lung tissue

When lung tissue is subjected to a step in strain, it exhibits a stress adaptation profile that is a power function of time. Furthermore, this power function is independent of the strain, even though the quasi-static stress-strain relationship of the tissue is highly nonlinear. Such behavior is known as quasi-linear viscoelasticity, but its mechanistic basis is unknown. We describe a model of soft tissue rheology based on the sequential recruitment of Maxwell bodies. The model is homogeneous in its elemental constitutive properties, yet predicts both power-law stress relaxation and quasi-linear viscoelasticity even when the stress-strain behavior of the model is nonlinear. The model suggests that stress relaxation in lung tissue could occur via a sequence of micro-rips that cause stresses to be passed from one local stress bearing region to another.