Effect of Indenter Size on Elastic Modulus of Cartilage Measured by Indentation

Our preliminary indentation experiments showed that the equilibrium elastic modulus of murine tibial cartilage increased with decreasing indenter size: flat-ended $60deg$ conical tips with end diameters of $15μm$ and $90μm$ gave $1.50±0.82MPa$ (⁠$mean±standard$ deviation) and $0.55±0.11MPa$⁠, respectively $(p<0.01)$⁠. The goal of this paper is to determine if the dependence on tip size is an inherent feature of the equilibrium elastic modulus of cartilage as measured by indentation. Since modulus values from nonindentation tests are not available for comparison for murine cartilage, bovine cartilage was used. Flat-ended conical or cylindrical tips with end diameters ranging from $5μmto4mm$ were used to measure the equilibrium elastic modulus of bovine patellar cartilage. The same tips were used to test urethane rubber for comparison. The equilibrium modulus of the bovine patellar cartilage increased monotonically with decreasing tip size. The modulus obtained from the $2mm$ and $4mm$ tips $(0.63±0.21MPa)$ agreed with values reported in the literature; however, the modulus measured by the $90μm$ tip was over two and a half times larger than the value obtained from the $1000μm$ tip. In contrast, the elastic modulus of urethane rubber obtained using the same $5μm–4mm$ tips was independent of tip size. The equilibrium elastic modulus of bovine patellar cartilage measured by indentation depends on tip size. This appears to be an inherent feature of indentation of cartilage, perhaps due to its inhomogeneous structure.