A mechanical analysis of conduit arteries accounting for longitudinal residual strains

Identification of an appropriate stress-free reference configuration is critically important in providing a reasonable prediction of the intramural stress distribution when performing biomechanical analyses on arteries. The stress-free state is commonly approximated as a radially cut ring that typically opens into a nearly circular sector, relieving much of the circumferential residual strains that exist in the traction-free configuration. An opening angle is often used to characterize this sector. In this study, we first present experimental results showing significant residual deformations in the longitudinal direction of two commonly studied arteries in the pig: the common carotid artery and the left anterior descending coronary artery. We concluded that a radially cut ring cannot completely describe the stress-free state of the arteries. Instead, we propose the use of a longitudinal opening angle, in conjunction with the traditional circumferential opening angle, to experimentally quantify the stress-free state of an artery. Secondly, we propose a new kinematic model to account for the addition of longitudinal residual strains through employing the longitudinal opening angle and performed a stress analysis. We found that with the inclusion of longitudinal residual strains in the stress analysis, the predicted circumferential stress gradient was decreased by 3-fold and the predicted longitudinal stress gradient was increased by 5.7-fold. Thus, inclusion of longitudinal residual strains has a significant effect on the predicted stress distribution in arteries.