Regional and Layer Distribution of Residual Stresses in an Unloaded Aortic Medial Wall

The aorta is the largest artery in the human body, which is not merely a conduit tube of blood, but an organ that plays an important role in regulating the pulsatile flow originating from the left ventricle. Aortic mechanical and structural characteristics have profound effects on its physiology and pathophysiology. However, many aspects of the aortic tissue remain poorly understood, because even the assessment of the physiologic stress-stretch relation is particularly complicated by the layered wall structure and the regionally varying residual stresses. For instance, hypertensive aorta leads to the increase in a tensile stress in the circumferential direction due to chronic vascular dilation. Although an aortic wall globally (not locally) maintains a constant stress distribution by increasing its wall thickness, which is known as a biological adaptive mechanism of homeostasis, non-uniform deformation with a regional variation of residual stresses and strains would be inevitable. Thus, we assumed that the hypertensive aorta would be closely associated with an extraordinary stress distribution at anatomically specific sites in the aortic wall, i.e., some mechanical symptom of inhomogeneity related to hypertension can be detected readily and noninvasively even at an early stage when a in vivo-like numerical aorta model is available. In this sense, a finite element (FE) model is a powerful research tool to assist such a clinical investigation.

In our preceding work, we created a simplified unit FE model of the aortic media composed of elastic laminas (ELs) and smooth muscle layers (SMLs). In combination with the technique of Design of Experiments, we successfully reproduced EL buckling at an unloaded state and identified several key factors dominating a mechanical interaction between the buckled EL and the surrounding SML. In the present study, therefore, we aimed to reproduce a regional and layer distribution of residual stresses in the aortic medial wall in the in vitro condition. Our results demonstrated that a distribution of EL waviness across the aortic wall thickness was reasonable, i.e., the internal EL waviness was consistently greater than the external EL waviness, when a closed ring model was used, and the residual stress of SML fell within the range of reasonable values, ±1–10 kPa. We also found that the inner and outer layers of SML were under compressive and tensile residual stresses, respectively, at the unloaded state. However, it is still difficult to reproduce a reasonable stress distribution using a simplified unit FE model, suggesting that we should distinguish the zero-stress condition, which corresponds to the unloaded open sector with a radial cut, from the unloaded state of the closed aortic ring. This information will greatly help improve understanding of basic aortic physiology and pathophysiology, while providing the basis for comparison between normal and hypertensive aortas.