Abstract
Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.
Highlights
Articular cartilage (AC) is a biphasic tissue covering the ends of bones in diarthrodial joints
The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage
Where μf is the fluid pressure, I is the unit tensor, ns,0 is initial solid volume fraction, J is the determinant of the deformation tensor F, totf is the number of fibril orientations considered at each location, ρc is the volume fraction of the collagen fibrils in the ith direction with respect to the total volume of the solid matrix, σnf is the stress in the non-fibrillar matrix, σf iso is the stress in the collagen fiber network, and π is the osmotic swelling pressure
Summary
Articular cartilage (AC) is a biphasic tissue covering the ends of bones in diarthrodial joints. Common understanding is that the applied load is initially supported by the pressurized interstitial fluid (Ateshian 2009; Ateshian and Wang 1995; Oloyede and Broom 1993). This can be explained because of AC’s low permeability, which traps the fluid in the collagen-PG network becoming pressurized when the tissue is loaded. The exact relative contribution of the viscoelastic collagen compared to the hydraulic fluid pressure under various strain rates has not yet been elucidated Because of their negative charges, proteoglycans create an osmotic pressure that participates in load sharing (Maroudas and Thomas 1970). Osmotic swelling has been incorporated by several groups in computational models of cartilage (Lai et al 1991; Huyghe and Janssen 1997; Sun et al 1999; Van Loon et al 2003), understanding the nonlinear and time-dependent contribution of osmotic pressure to the mechanical behavior of cartilage is challenging (Olsen et al 2004)
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