Hyperelastic behavior of porcine aorta segment under extension-inflation tests fitted with various phenomenological models.

Most of hyperelastic models for the constitutive modeling of the typical mechanical behaviour of the arterial wall tissue in literature are based on the test data from different animals and arteries. This paper is concerned with the material parameter identification of several phenomenological hyperelastic models by fitting the data from five extension-inflation tests of the porcine aorta segment, carried out in our laboratory. A membrane approximation is used to compute stresses and strains achieved during experiments, with usual assumption of material incompressibility. Three orthotropic two-dimensional strain-energy functions, based on use of the Green-Lagrange strains, are fitted to the test data: the well-known Fung's exponential model; the classical polynomial model with seven constants; and the logarithmic model; and also, two three-dimensional models are employed: polyconvex anisotropic exponential hyperelastic model and the convex isotropic exponential rubber-like hyperelastic constitutive law depending on the first invariant of the right Cauchy-Green deformation tensor. It has been found that isotropic model overestimates values of stresses in axial, and underestimates values of stresses in circumferential direction of artery segment, due to pronounced tissue anisotropy. Also, all two-dimensional models considered give good and similar prediction, while the polyconvex model demonstrates slightly lower performance in the axial direction of artery.

ARTreat Project: three-dimensional numerical simulation of plaque formation and development in the arteries.

Atherosclerosis is a progressive disease characterized by the accumulation of lipids and fibrous elements in arteries. It is characterized by dysfunction of endothelium and vasculitis, and accumulation of lipid, cholesterol, and cell elements inside blood vessel wall. In this study, a continuum-based approach for plaque formation and development in 3-D is presented. The blood flow is simulated by the 3-D Navier-Stokes equations, together with the continuity equation while low-density lipoprotein (LDL) transport in lumen of the vessel is coupled with Kedem-Katchalsky equations. The inflammatory process was solved using three additional reaction-diffusion partial differential equations. Transport of labeled LDL was fitted with our experiment on the rabbit animal model. Matching with histological data for LDL localization was achieved. Also, 3-D model of the straight artery with initial mild constriction of 30% plaque for formation and development is presented.