Constitutive descriptions of active stress in blood vessels leading to contractile instability

To model the contraction of blood vessels, an active stress component can be added to the (passive) Cauchy stress tensor. Different constitutive formulations have been used to describe this active stress component with varying parameterisations. In this work, we examine formulations for use with limited experimental contraction data as well as those developed to capture more comprehensive data sets. We show that a subset of these formulations exhibits unstable behaviour (i.e., a non-unique diameter solution for a given pressure) in certain parameter ranges, particularly when contractile deformations are large. Our work shows how limited contraction data complicates the selection of an appropriate active stress model for vascular applications.