Modeling elastic lamina buckling in the unloaded aortic media

Abstract

Mathematical modeling of the thoracic aorta is important for detecting extraordinary and unusual stress or strain distributions of the hypertensive aortic wall, even in early stages, and for understanding the development and progression of various cardiovascular diseases. In a freshly isolated aortic media, which mainly comprises elastic laminas (ELs) and smooth muscle layers (SMLs), circumferential EL waviness and longitudinal EL undulation are often observed because of the buckling of ELs, which is closely associated with residual stresses of ELs and SMLs in the aortic wall. However, the mechanism underlying EL buckling or specific mechanical interactions between EL and SML remains unclear. We hypothesized that the longitudinal EL undulation is likely formed by the superposition of the circumferential EL waviness along the aortic axis. Hence, a series of numerical simulations were conducted based on a design of experiments approach by implementing residual stresses. We identified that the prestress initially administered to ELs in the circumferential and axial directions, and the predefined internodal gap, which couples the EL and SML, are essential mechanical parameters to computationally reconstruct the circumferential EL waviness and the longitudinal EL undulation at an unloaded state. In addition, a mechanical balance between the assigned prestresses along the circumferential and axial directions is crucial for successful representation of structural buckling of EL in the unloaded aortic media. Although further study is required, we have verified that our hypothesis is reasonable in the current work. Moreover, the information we obtained here will greatly help improve understanding the roles of EL and SML in the aortic medial wall at the in vitro and in vivo states, while simultaneously providing a basis for more sophisticated computational modeling of the aorta.