Modeling Prestress-Driven Buckling Behavior of Elastic Lamina in the Aortic Media

Abstract

Mathematical modeling of the thoracic aorta is important for understanding the development and progression of various cardiovascular diseases, helping to detect extraordinary stress distributions of the hypertensive aortic wall, even in early stages. However, it is difficult to ensure the biofidelity of biological materials in formulating a mathematical model. In a freshly isolated aortic media, composed mainly of smooth muscle cell layers (SMLs) and elastic laminae (ELs), circumferential EL waviness and longitudinal EL undulation are often observed because of the structural “buckling” of ELs. This is considered to be closely associated with residual stresses of SMLs and ELs in the aortic wall but the mechanism underlying such EL buckling behavior remains unclear. In the present study, a series of numerical simulations were designed to identify effective mechanical parameters to reproduce EL buckling in the aortic media. We found that prestress initially administered to ELs in the circumferential and axial directions, and the predefined internodal distance, which couples the SML and EL, are essential to computationally reconstruct the circumferential EL waviness and the longitudinal EL undulation in an unloaded state. We also proposed a set of equations based on the numerical results and successfully predicted EL buckling behaviors of the aorta in vitro.