Modeling of elastic lamina buckling coupled with smooth muscle layer deformation in the aortic media: technique for readily implementing residual stresses

Abstract

In vivo aortic wall thickening is a mechanical adaptation to the prolonged increase in intravascular pressure resulting from hypertension, which is mainly regulated by primary components of the aortic media, the elastic lamina (EL) and the smooth muscle-rich layer (SML). This study built a simplified finite element (FE) model of the aortic medial wall comprising the EL and SML, and simulated EL undulation or buckling at a no-load condition, i.e., (in the in vitro) unloaded state, by releasing a set of compressive prestresses initially given to the EL. Using the design of experiments approach (Graeco-Latin square method), we identified specific mechanical boundary conditions to computationally reconstruct EL buckling in the circumferential direction of the aorta. Additionally, it was shown that EL waviness almost vanished when ~20% strain (mimicking a circumferential stretch due to intravascular pressure) was applied to the buckled FE model obtained in the in vitro unloaded state. This feature is beneficial for numerical modeling of the detailed aortic wall structure, because the entire process is computationally efficient and can be readily implemented in a commercially available FE solver. Although further study is required, our findings will help clarify the roles of the EL and SML in the aortic wall and promote the understanding of the mechanisms of the medial tissue stress response. In addition, we expect this modeling technique to serve as a useful tool in the future for interpreting stress distribution relevant to vascular physiology at normal and pathological states.