Direct Measurement of the Poisson’s Ratio of Human Patella Cartilage in Tension

Abstract

Articular cartilage has been shown to exhibit large transverse contractions when loaded in tension, suggesting the existence of large values for the Poisson’s ratio. Previous studies have suggested that this effect is dependent on amplitude of applied strain, so that a single Poisson’s ratio may not be sufficient to describe cartilage behavior. In this study, the Poisson’s ratio (ν), toe region modulus (Eo), and linear region modulus (E) of human patellar articular cartilage were calculated in simple tension tests from optical analysis of the two-dimensional strain fields at equilibrium. The Poisson’s ratio was found to be independent of strain due to the absence of viscoelastic effects during testing. The Poisson’s ratio was found to be significantly higher in the surface zone (1.87±1.11, p<0.01) than in the middle zone (0.62±0.23), with no significant correlation of ν with age of the cartilage. In general, values for Poisson’s ratio were greater than 0.5, suggesting cartilage behavior in tension deviates from isotropy. Reported values for the Poisson’s ratio of cartilage in compression have been much lower than values measured here in tension, reflecting a mechanical contribution of the collagen fibers to anisotropy in tension but not compression. The toe-region modulus (Eo) was significantly higher in the surface zone (4.51±2.78 MPa, n=8) compared to the middle zone (2.51±1.93 MPa, n=10). In addition, the linear-region modulus (E) in the surface zone, but not middle zone (3.42±2.17 MPa, n=10), was found to correlate with age (R=0.97, p<0.02) with values of surface zone E equal to 23.92±12.29 MPa (n=5) for subjects under 70 yr of age, and 4.27±2.89 MPa (n=3) for subjects over 70 yr. Moduli values and trends with depth were consistent with previous studies of human and animal cartilage. From direct measures of two independent material properties, ν and E, we calculated a shear modulus, G, which had not been previously reported for cartilage from tensile testing. Calculated values for surface zone G were 3.64±1.80 MPa for subjects under 70 yr old and 0.96±0.69 MPa for subjects over 70 yr old, and were significantly higher in the surface zone than in the middle zone (1.10±0.78 MPa). This study provides an intrinsic measure for the Poisson’s ratio of articular cartilage and its dependence on depth which will be important in understanding the nonlinear tension-compression and anisotropic behaviors of articular cartilage.