Investigation of role of cartilage surface polymer brush border in lubrication of biological joints

Although experimental evidence has suggested that the polymer brush border (PBB) on the cartilage surface is important in regulating fluid permeability in the contact gap, the current theoretical understanding of joint lubrication is still limited. To address this research gap, a multiscale cartilage contact model that includes PBB, in particular its effect on the fluid permeability of the contact gap, is developed in this study. Microscale modeling is employed to estimate the permeability of the contact gap. This permeability is classified into two categories: For a gap size > 1 µm, the flow resistance is assumed to be dominated by the cartilage roughness; for gap size < 1 µm, flow resistance is assumed to be dominated by the surface polymers extending beyond the collagen network of the articular cartilage. For gap sizes of less than 1 µm, the gap permeability decreases exponentially with increasing aggrecan concentration, whereas the aggrecan concentration varies inversely with the gap size. Subsequently, the gap permeability is employed in a macroscale cartilage contact model, in which both the contact gap space and articular cartilage are modeled as two interacting poroelastic systems. The fluid exchange between these two media is achieved by imposing pressure and normal flux continuity boundary conditions. The model results suggest that PBB can substantially enhance cartilage lubrication by increasing the gap fluid load support (e.g., by 26 times after a 20-min indentation compared with the test model without a PBB). Additionally, the fluid flow resistance of PBB sustains the cartilage interstitial fluid pressure for a relatively long period, and hence reduces the vertical deformation of the tissue. Furthermore, it can be inferred that a reduction in the PBB thickness impairs cartilage lubrication ability.