Effect of the anisotropic permeability in the frequency dependent properties of the superficial layer of articular cartilage

Articular cartilage is a tissue of fundamental importance for the mechanics of joints, since it provides a smooth and lubricated surface for the proper transfer of loads. From a mechanical point of view, this tissue is an anisotropic poroviscoelastic material: its characteristics at the macroscopic level depend on the complex microscopic architecture. With the ability to probe the local microscopic features, dynamic nanoindentation test is a powerful tool to investigate cartilage mechanics. In this work we focus on a length scale where the time dependent behaviour is regulated by poroelasticity more than viscoelasticity and we aim to understand the effect of the anisotropic permeability on the mechanics of the superficial layer of the articular cartilage. In a previous work, a finite element model for the dynamic nanoindentation test has been presented. In this work, we improve the model by considering the presence of an anisotropic permeability tensor that depends on the collagen fibers distribution. Our sensitivity analysis highlights that the permeability decreases with increasing indentation, thus making the tissue stiffer than the case of isotropic permeability, when solicited at the same frequency. With this improved model, a revised identification of the mechanical and physical parameters for articular cartilage is provided. To this purpose the model was used to simulate experimental data from tests performed on bovine tissue, giving a better estimation of the anisotropy in the elastic properties. A relation between the identified macroscopic anisotropic permeability properties and the microscopic rearrangement of the fiber/matrix structure during indentation is also provided.