The effects of local fibre organization on the elastic and rupture behaviour of tissue engineered fibrous cap models

Abstract

Atherosclerosis is a cardiovascular disease in the arteries and a primary cause of death in the industrialized world. Most deaths due to atherosclerosis occur when the fibrous cap covering the necrotic core ruptures, leading to a blood clot. To determine whether an atherosclerotic plaque will rupture requires the development of accurate computational models. One of the key aspects for these models is the material model, in which collagen fibres play a major role. This study aims to contribute to the making of a numerical model which accurately represents atherosclerotic plaque by comparing the elastic and rupture behaviour of engineered collagenous micro tissues and their respective finite element models in ABAQUS. The Holzapfel-Gasser-Ogden material model of these computational models is based on a combination of global material parameters and local material parameters based on the local fibre organisation. A framework developed to measure the local fibre organisation using provided imagery of a nuclear stained tissue engineered sample shows the collagen fibres align along the loading direction and the edges of the geometry. The fibers are less dispersed along the edges of the geometry and on the left and right of a formed soft inclusion. A uniaxial tensile test was performed on four tissue engineered samples. The elastic and rupture behaviour of the samples during the uniaxial tensile tests is replicated in ABAQUS using both isotropic and homogeneous material parameters, and anisotropic heterogenous material parameters. The stresses measured in the simulations are highly dependent on both the material parameters and the geometry of the model. The strains are mostly dependent on the geometry, but are affected by the material model. Due to the higher stiffness at the edges of the geometry of the anisotropic samples, the stresses increased greatly, and the strains decreased slightly. The rupture behaviour of the cultured samples is replicated in the FEM simulations using extended finite element method (XFEM). The damage in the samples with isotropic material parameters initiates both from the soft inclusion as the left and right edges of the geometry. The damage in the samples with anisotropic material parameters initiates, similarly to the cultured samples, only from the sides of the soft inclusion. The damage in both the cultured and simulated samples propagate mostly horizontal and from the soft inclusion outward. In three out of four isotropic samples however, damage propagates to varying degrees from the edge of the geometry inward. Based on these findings it is concluded that implementing the local fibre organisation in the material model can improve the accuracy of finite element simulations of collagenous soft tissues, which includes atherosclerotic plaque, as the rupture behaviour of the simulations with anisotropic material parameters more accurately represents the rupture behaviour of the engineered fibrous tissues in comparison with simulations with isotropic material parameters.