Passive mechanical properties of porcine left circumflex artery and its mathematical description

Abstract 

The aim of this study was to analyze the pseudoelastic behavior of the coronary wall in vitro and to describe this behavior with three alternative strain energy functions frequently used in arterial mechanics.

Six tubular segments of artery were subjected to various levels of simultaneous transmural pressure and axial force encompassing the physiological range of loading. Measured data on force, pressure, stress-free geometry and vessel deformation were used to compute components of the Green strain tensor and to determine by least squares fit the values of constants appearing in the following strain energy functions: Fung's exponential function, a combined polynomial-exponential form and a neo-Hookean plus exponential expression.

The results obtained showed large biological variability. A comparison of the relative magnitude of the strain components did not reveal significant deviations from orthotropy under the given experimental conditions, hence shear terms were not included in the present constitutive formulations. The deformational behavior of the coronary artery displayed the high non-linearity typical for arteries of the muscular type. For states of equibiaxial stress the corresponding strains in the axial direction were larger than those in the circumferential direction, at least for loads in the upper and physiological range. All these aspects of coronary elasticity were mimicked fairly well by all three functions, although with slightly different degrees of accuracy.

Keywords: Porcine coronary artery, Elasticity, Anisotropy, Strain energy function, In vitro