A novel constitutive model considering the role of elastic lamellae' structural heterogeneity in homogenizing transmural stress distribution in arteries.

Understanding how the homeostatic stress state can be reached in arterial tissues can provide new insights into vascular physiology. Even though the function of maintaining homeostasis is often linked to the concentric layers of medial elastic lamellae, how the lamellae are capable of evenly distributing the stress transmurally remains to be understood. The recent microstructural study by Yu et al. (2018 J. R. Soc. Interface 15, 20180492) revealed that, circumferentially, lamellar layers closer to the lumen are wavier than the ones further away from it and, thus, experience more unfolding when subjected to blood pressure. Motivated by this peculiar finding, the current study, for the first time, proposes a novel approach to model elastic lamellae and such structural heterogeneity using the extensible worm-like chain model. When implemented into the material description of the conventional two-layer artery model, in which adventitial collagen is modelled using the inextensible worm-like chain model, it is demonstrated that structural heterogeneity in elastic lamellae plays an important role in dictating transmural stress distribution and, therefore, the homeostasis of the arterial wall.