Short-term consolidation of articular cartilage in the long-term context of osteoarthritis

© 2015 Elsevier Ltd. Over ten percent of the population are afflicted by osteoarthritis, a chronic disease of diarthrodial joints such as the knees and hips, costing hundreds of billions of dollars every year. In this condition, the thin layers of articular cartilage on the bones degrade and weaken over years, causing pain, stiffness and eventual immobility. The biggest controllable risk factor is long-term mechanical overloading of the cartilage, but the disparity in time scales makes this process a challenge to model: loading events can take place every second, whereas degradation occurs over many months. Therefore, a suitable model must be sufficiently simple to permit evaluation over long periods of variable loading, yet must deliver results sufficiently accurate to be of clinical use, conditions unmet by existing models. To address this gap, we construct a two-component poroelastic model endowed with a new flow restricting boundary condition, which better represents the joint space environment compared to the typical free-flow condition. Under both static and cyclic loading, we explore the rate of gradual consolidation of the medium. In the static case, we analytically characterise the duration of consolidation, which governs the duration of effective fluid-assisted lubrication. In the oscillatory case, we identify a region of persistent strain oscillations in otherwise consolidated tissue, and derive estimates of its depth and magnitude. Finally, we link the two cases through the concept of an equivalent static stress, and discuss how our results help explain the inexorable cartilage degeneration of osteoarthritis.