Role of Deep Vertical and Superficial Horizontal Collagen Fibrils Networks in Mechanics of Articular Cartilage

Introduction: Integrity and function of articular cartilage depends directly on networks of collagen fibrils that resist tension and embed the water and matrix resulting in a nonlinear, nonhomogeneous and anisotropic tissue. At the superficial zone, the fibrils are parallel to the articular surface whereas they are rather random in the transitional zone and perpendicular in the deep zone anchoring the tissue firmly to the subchondral bone [1]. To investigate tissue mechanics, fibril-reinforced composite models are commonly employed [2]. Despite numerous investigations, the mechanical role of vertical fibrils (VF) in the deep zone has often been either neglected or overlooked. The current work aims to investigate the role of deep VF and superficial horizontal fibrils (HF) in cartilage mechanics using a nonlinear fibril-reinforced finite element model of cartilage incorporating the tissue fibrils networks. The role of changes in fibrils volume fractions and loading rate are investigated under both relaxation and creep loading conditions. Materials and Methods: In the indentation model, a cylinder with radius R=17 mm and height H=2.5 mm is considered which roughly represents the cartilage geometry at the medial tibial plateau [3]. The indenter is assumed rigid and impermeable with a profile identical to that of the femoral medial condyle at the sagittal plane [3]. The subchondral bone at the base is taken rigid. The fibrillar networks are simulated either by membrane or continuum elements. In the superficial zone, the collagen fibrils are uniformly distributed in membrane elements [4]. In the transitional zone with no dominant orientation, continuum elements that take the principal strain directions as the material principal axes represent collagen fibrils. In the deep zone, VF are represented with vertical membrane elements offering no resistance in circumferential direction. Based on earlier measurements, total volume fraction of 15%, 10.5% and 9% are estimated for the superficial, transitional and deep zones, respectively. The matrix drained moduli and water content are taken depth dependent. Two loading protocols of stress relaxation and creep are used. In the former, 20% nominal strain is applied in 0.5 s whereas in creep a 500 N load is applied in 0.5 s remaining constant to 60 minutes. The cartilage surface is impermeable only at the areas in contact with the indenter. To examine the role of fibril networks, the volume fraction of VF is varied from the reference 9% to 0, 3 and 15% while that of HF is changed from 15% to 0, 7.5 and 20%. The effect of changes in the strain rate is also investigated. Results: The VF significantly increased the cartilage transient (t=0.5 s) stiffness, an effect that disappeared at equilibrium (Fig. 1). This stiffening effect was due to the pore pressure that dramatically increased as VF volume fraction increased. Despite considerable increase in the axial reaction force and pore pressure, the maximum principal strain in the solid matrix and the VF markedly dropped as higher VF volume fractions were considered (Fig. 2). The HF also increased the transient axial stiffness but to a lesser extent (Fig. 1). The location of maximum strain in solid matrix shifted from the subchondral junction in absence of VF to the articular surface in absence of HF. The transient response was similar in creep and relaxation. With time in relaxation test, the maximum strains substantially diminished everywhere to <4% in all cases. In creep, however, large strains in the solid matrix and superficial HF network persisted with time and the chevron pattern of VF network became more evident (Fig. 3). Discussion: Commonly used confined and unconfined (when with no underlying bone) testing configurations cannot capture the mechanical role of deep VF network. The VF network demonstrated crucial roles at the transient period in dramatically increasing the tissue stiffness and in protecting the solid matrix against large distortions at the subchondral junction. The transient maximum principal strain diminished from 51.3% to 22.8% in presence of 9% VF content and that despite a concurrent three-fold increase in the reaction force. The HF network also demonstrated similar effects but to a lesser extent. The foregoing stiffening effects, however, disappeared both with time and at loading rates slower than those expected in physiological activities such as walking. The role of VF and HF diminished with time in creep test leaving the solid matrix at the deep zones prone to greater shear strains. Results of creep and relaxation indentation models were equivalent in the transient period but diverged in post-transient periods. In contrast to the relaxation model in which the chevron deformation pattern of VF disappeared with time, in creep this pattern, in agreement with observations on post-transient micro-deformation of cartilage in creep [5], was accentuated with time. Damages to deep VF network or their anchorage to the bone, in bone bruises for example, would weaken the transient stiffness and place the tissue at higher risk of failure particularly at the deep zone. Proper modelling of fibrils networks is essential for reliable predictions. References: 1. Kaab et al, J Anat 193:23-34, 1998. 2. Li et al, 14:673-682, 1999. 3. Bendjaballah et al, The Knee 2:69-79, 1995. 4. Shirazi & Shirazi-Adl, Med Eng Phys 27:827-835, 2005. 5. Thambyah & Broom, J Anat 209:611-622, 2006. Acknowledgements: Supported by CIHR and NSERC-Canada.