Assessment of the aortic stress–strain relation in uniaxial tension

The passive elastic characteristics of the abdominal aorta were investigated in two experimental animal models, aiming at assessing the stress–strain relation of the aortic wall. Twenty porcine and 15 rabbit healthy abdominal aortas were subjected to uniaxial stress–strain analysis, performed on a tensile-testing device, while immersed in a physiologic saline bath at body temperature. Measured parameters included original length, width and thickness, as well as axial force and extension. Based on these data, Kirchhoff stress and Green–St.Venant strain were computed and one-dimensional constitutive equations were defined, comprising of a power function and two exponential ones, in turn, for the low, physiologic and high-stress regions. The stress–strain curves were plotted as elastic modulus versus stress, displaying nonlinear part I and linear parts II and III. These were regressed, yielding parameters k, q (part I), a, b (part II) and c, d (part III). A detailed comparison of these constitutive parameters was undertaken between the two species, demonstrating variations in d (p<0.05). No statistical differences were found in parameters a, b, c, k and q, implying that the two aortas were equally stiff under low and physiologic stresses, whereas the porcine aorta was stiffer at higher stresses. In conclusion, a bi-exponential in addition to a power law was established, relating stress and strain in the aorta, which is advantageous in comparison with previous constitutive equations. Under passive conditions, the nonlinear nature of this constitutive law may account for the low, part I, physiologic, part II, and high-stress, part III of the stress–strain relationship, supporting the concept of the aortic wall as a biphasic material.