Distribution of Stresses and of Strain-Energy Density through the Wall Thickness in a Canine Aortic Segment

Abstract

In this paper we presented a method for determining the distribution of circumferential (S_θ), longitudinal (S_z), and radial (S_r) stress and of strain-energy density (W) in canine aortic segments under physiological loading. Aortic segments from 13 dogs were studied in vitro. Intraluminal pressure and longitudinal force were varied over ranges of 25 to 200 cm H₂O and 0 to 100 g, respectively, and the external radius and the segment length were measured at each step. A nonlinear theory of large deformation of the aortic tissue based on the assumptions of incompressibility and curvilinear orthotropy was applied to the data. The 3, 7, or 12 constitutive constants of the theory were calculated without using the usual thin-wall assumption. These constants were then used to calculate the distribution of stresses and of W. The results indicated that (I) S_θ, S_z, S_r, and W were largest in magnitude at the endothelial surface and decreased toward the adventitial surface, (2) the decrease was most marked in the inner third of the vessel wall, (3) in general S_θ > S_z > W > S_r, and (4) at a given longitudinal stretch an increase in intraluminal pressure increased S_θ, S_z, |S_r|, and W, with the effect being most marked on S_θ.