Finite element modeling of articular cartilage at different length scales

Abstract

The composition and structure of articular cartilage (AC) are inhomogeneous within the tissue and vary throughout its depth. Its extracellular matrix can be considered as a fiber-reinforced composite solid consisting of a dense stable network of collagen fibers embedded in a proteoglycan (PG) gel. Several studies have shown that this specialized structure plays a vital role in the mechanical function of AC. In pathological conditions, such as osteoarthritis (OA), degeneration of cartilage due to changes in mechanical properties is observed. Osteoarthritis is the most common cause of disability in the elderly and affects more than 20 million people in the USA alone. The focus of this work is to understand the mechanical response of AC using finite element models using ABAQUS, a commercial FEA package that is widely used in the field of cartilage mechanics. This is done at two different scales - the macroscale and the mesoscale. At the macroscale, AC is considered as a homogeneous isotropic poroviscoelastic (PVE) material saturated by the interstitial fluid (water). Indentation tests are performed on cartilage from the mouse tibia plateau using two different sized flat-ended conical indenters with flat-end diameters of 15 μm and 170 μm. A finite element (FE) model of the test is developed and the PVE parameters identified by using inverse methods to minimize the errors between FE simulated and test data. Data from the smaller indenter is first used to fit the viscoelastic (VE) parameters, on the basis that for this tip size the gel diffusion time (approximate time constant of the poroelastic (PE) response) is of the order of 0.1 s, so that the PE response is negligible. These parameters are then used to fit the data from the larger indenter for the PE parameters, using the VE parameters extracted from the data from the smaller indenter. At the mesoscale the inhomogeneities of AC need to be addressed to understand the microstructural behavior of AC. The problem of interest in this part of the work is to understand the mechanical role of interfibrillar cross-links (IFLs), if they exist, suspected in AC and most collagenous tissues. A 3D FE model of AC meso-structure motivated by the parallel fibril geometry of the mid and deep zones of the patella is developed consisting of a PE matrix, unidirectional, bilinear fibrils (different stiffness in tension and compression), and the IFLs. Parametric studies are then performed for the model in simulated compression tests along the fibril direction and the effect of the IFLs and matrix are predicted and compared. Results suggest presence of IFLs would increase the effective modulus in compression. This is due to maintaining organization of the fibrils into a network due to IFLs imparting stability to the network by preventing early bending of fibrils and effectively reducing the Poisson effect. Finally, with a set of literature based parameters, compression tests for AC using the mesomodel show that removing the cross-links results in a significant (43%) drop in the effective compressive modulus, suggesting resolution necessary to experimentally detect the IFLs. At the mesoscale, the IFLs would play the mechanical role of stabilizing the fibril network and enhancing its stiffness.