A Novel Approach Towards Modeling the Collagen Fibril Network for Use in Nonlinear Anisotropic Polyconvex Mixture Models of Articular Cartilage

Abstract

Despite distinct mechanical functions, biological soft tissues have a common microstructure in which a ground matrix is reinforced by a collagen (COL) fibril network. The highly anisotropic, heterogeneous, and asymmetric material properties caused by the microstructural nature of the COL fibril network suggest the importance, as well as the challenges, of accurately modeling soft tissue biomechanics. For soft fibrous tissues with multiple constituents, mathematical distribution functions have represented dispersed and continuous (i.e. non-discrete) fibrils oriented in all directions depending on the type of (and anatomical location in) the tissue under investigation [1–2]. These types of continuous fibril models have been used recently for articular cartilage [3–5]. The strain energy of the COL fibril network is calculated based on the response of individual fibrils in tension in different directions and integrated over a unit sphere at a material point. The specific aims of the current study were to: 1. introduce a novel approach to modeling a continuous distribution of COL fibrils in soft tissues; 2. develop a strain energy function for the COL network based on the proposed distribution function of COL fibrils; 3. derive the stress and material elasticity tensors for the COL network that may be “pre-stressed” in a stress-free natural configuration of the tissue; 4. propose a special model that may be appropriate for immature tissue and establish its suitability for use in a polyconvex tissue strain energy function.