Finite element simulation of three dimensional residual stress in the aortic wall using an anisotropic tissue growth model

Abstract

Residual stress is believed to play a significant role in the in vivo stress state of the arterial wall, but quantifying residual stress in vivo is challenging. Based on the well-known assumptions that residual stress is a result of heterogeneous arterial growth and that it homogenizes the transmural distribution of arterial wall stress, we propose a new anisotropic tissue growth model for the aorta to recover the three-dimensional residual stress field in a bi-layer human aortic wall. Finite element simulations showed that the predicted residual stress magnitude with this method are within the documented range for human aorta. Particularly, the homeostatic inter-layer stress difference is identified as a key parameter to quantify the opening angle. To the authors' knowledge, this is the first finite element study employing anisotropic growth of aortic tissue in a bi-layer model to generate three-dimensional residual stress field, and the resultant opening angle can match with the experiments. A parametric study found that inter-layer stress homogeneity, arterial blood pressure, axial pre-stretch, and material stiffness strongly affect the residual stress field.

Keywords: Anisotropic growth; Artery; Finite element method; Residual stress.