Instability in computational models of vascular smooth muscle cell contraction

Purpose Through their contractile and synthetic capacity, vascular smooth muscle cells play a key role in regulating the stiffness and resistance of the circulation. 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 proposed to describe this active stress component. Notably, however, the ex vivo measurement of the biomechanical behaviour of contacted blood vessels presents several experimental challenges, which complicate the acquisition of comprehensive data sets to inform complex active stress models. In this work, we examine formulations for use with limited experimental contraction data as well as those developed to capture more comprehensive data sets. Methods We prove analytically that a subset of these formulations exhibits unstable behaviours (i.e., a non-unique diameter solution for a given pressure) in certain parameter ranges, particularly when contractile deformations are large. Furthermore, using experimental literature data, we present two case studies where these active stress models are used to capture the contractile response of vascular smooth muscle cells in the presence of 1) limited and 2) extensive contraction data. Results Our work shows how limited contraction data complicates the selection of an appropriate active stress model for vascular applications, potentially resulting in unrealistic modelled behaviours. Conclusion As such, the data presented herein provide a useful reference for the selection of an active stress model which balances the trade-off between accuracy and the available biomechanical information.