Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression

Abstract

Articular cartilage exhibits complex mechanical properties such as anisotropy, inhomogeneity and tension–compression nonlinearity. This study proposes and demonstrates that the application of compressive loading in the presence of osmotic swelling can be used to acquire a spectrum of incremental cartilage moduli ( E Yi ) and Poisson's ratios ( ν ij ) from tension to compression. Furthermore, the anisotropy of the tissue can be characterized in both tension and compression by conducting these experiments along three mutually perpendicular loading directions: parallel to split-line (1-direction), perpendicular to split-line (2-direction) and along the depth direction (3-direction, perpendicular to articular surface), accounting for tissue inhomogeneity between the surface and deep layers in the latter direction. Tensile moduli were found to be strain-dependent while compressive moduli were nearly constant. The peak tensile (+) Young's moduli in 0.15 M NaCl were E + Y1 =3.1±2.3, E + Y2 =1.3±0.3, E + Y3 Surface=0.65±0.29 and E + Y3 Deep=2.1±1.2 MPa. The corresponding compressive (−) Young's moduli were E − Y1 =0.23±0.07, E − Y2 =0.22±0.07, E − Y3 Surface=0.18±0.07 and E − Y3 Deep=0.35±0.11 MPa. Peak tensile Poisson's ratios were ν +12=0.22±0.06, ν +21=0.13±0.07, ν +31 Surface=0.10±0.03 and ν +31 Deep=0.20±0.05 while compressive Poisson's ratios were ν −12=0.027±0.012, ν −21=0.017±0.007, ν −31 Surface=0.034±0.009 and ν −31 Deep=0.065±0.024 . Similar measurements were also performed at 0.015 M and 2 M NaCl, showing strong variations with ionic strength. Results indicate that (a) a smooth transition occurs in the stress–strain and modulus–strain responses between the tensile and compressive regimes, and (b) cartilage exhibits orthotropic symmetry within the framework of tension–compression nonlinearity. The strain-softening behavior of cartilage (the initial decrease in E Yi with increasing compressive strain) can be interpreted in the context of osmotic swelling and tension–compression nonlinearity.