A non-destructive approach to identify the stress-free state and material properties of arteries

Abstract

Residual strains and stresses in arteries play a significant role in homogenizing the stress field in the arterial wall and make arteries more compliant. The stress-free state of the artery needs to be identified in order to determine the residual stresses or strains in the unloaded and loaded states of the artery. The stress-free state of an artery can be characterized by two geometric parameters of the open sector achieved after a short artery segment is cut open radially, i.e., the inner radius and the opening angle. A traditional method to determine the stress-free state of arteries is to cut a short artery segment radially and measure the inner radius and the opening angle of the open sector, which is destructive by nature. In this paper, we propose a novel non-destructive method to identify the stress-free state of arteries, i.e., its inner radius and the opening angle, without the need to make the physical cut to the artery. The essence of this method is an inverse problem to identify the inner radius and the opening angle of the stress-free state by applying optimization algorithms based on a series of loaded states of the artery under different intraluminal pressures. Numerical simulations were conducted to generate a series of deformed states of an artery from which the inner radius and the opening angle of the stress-free state were identified thereafter. In addition, the effect of experimental error was investigated, and a method to modify the experimental data with error based on the pressure-radius relation of the artery was proposed. Furthermore, a non-destructive method was proposed to identify the material parameters in Fung’s constitutive model by applying the notion of average stretch ratios and stresses, from which the stress-free state can be further identified.