Optical determination of anisotropic material properties of bovine articular cartilage in compression

Abstract

The precise nature of the material symmetry of articular cartilage in compression remains to be elucidated. The primary objective of this study was to determine the equilibrium compressive Young's moduli and Poisson's ratios of bovine cartilage along multiple directions (parallel and perpendicular to the split line direction, and normal to the articular surface) by loading small cubic specimens (0.9×0.9×0.8 mm, n=15) in unconfined compression, with the expectation that the material symmetry of cartilage could be determined more accurately with the help of a more complete set of material properties. The second objective was to investigate how the tension-compression nonlinearity of cartilage might alter the interpretation of material symmetry. Optimized digital image correlation was used to accurately determine the resultant strain fields within the specimens under loading. Experimental results demonstrated that neither the Young's moduli nor the Poisson's ratios exhibit the same values when measured along the three loading directions. The main findings of this study are that the framework of linear orthotropic elasticity (as well as higher symmetries of linear elasticity) is not suitable to describe the equilibrium response of articular cartilage nor characterize its material symmetry; a framework which accounts for the distinctly different responses of cartilage in tension and compression is more suitable for describing the equilibrium response of cartilage; within this framework, cartilage exhibits no lower than orthotropic symmetry.

Introduction

As the load-bearing material of diarthrodial joints, articular cartilage helps to absorb mechanical shocks and distribute high joint loads more evenly across the underlying bony structures, while maintaining minimal friction and wear (Mankin et al., 1994; Mow and Ateshian, 1997; Ateshian et al., 1998). Articular cartilage is a structurally and compositionally complex material. Most of the biochemical constituents of articular cartilage (e.g., glycosaminoglycans, collagen and water) are inhomogeneously distributed, giving the tissue a layered character (Weiss et al., 1968; Redler and Zimny, 1970; Bullough and Jagannath, 1983; Maroudas et al., 1969; Venn and Maroudas, 1977; Muir, 1980; Buckwalter et al., 1985; Hardingham and Fosang, 1992). These variations in the structure and composition of cartilage are closely related to the inhomogeneous and anisotropic mechanical and electrochemical properties of the tissue.

Despite the intensive study of articular cartilage in the field of biomechanics, the exact nature of cartilage as a material remains to be elucidated. There are still no established answers to some of the most basic questions such as the nature of the material's symmetry that are commonly asked for a classical material. As greater efforts have been placed on the study of tissue anisotropy in tension, it has been shown that the equilibrium tensile modulus of articular cartilage is significantly greater for specimens harvested parallel to the split-line directions than for those perpendicular to the split lines (Kempson et al (1968), Kempson et al. (1973); Woo et al (1976), Woo et al (1979); Roth and Mow, 1980; Huang et al., 1999); the tensile modulus has also been investigated along the depth-direction (Basser et al., 1998; Narmoneva et al., 1999), but has not yet been related to the other two directions. Nevertheless, since the tensile properties of cartilage have been found to differ along two of these three mutually perpendicular directions (Huang et al., 1999; Narmoneva et al., 1999; Korhonen et al., 2001), it is likely that the highest symmetry of cartilage is at best orthotropic, with its three planes of symmetry defined in situ by the split-line direction in a plane tangent to the surface (1-direction), the direction perpendicular to the split-line direction in the same tangent plane (2-direction), and the direction normal to this plane (3-direction), i.e. the “radial” (or depth) direction of the cartilage layer (Soltz and Ateshian, 2000). In further support of cartilage anisotropy in tension, several studies (Woo et al., 1979; Chang et al., 1999; Elliott et al., 1999; Huang et al., 1999) have demonstrated that Poisson's ratio for cartilage in uniaxial tension exceeds 0.5, which is permissible only for anisotropic materials (e.g., Lai et al., 1993). For human humeral head cartilage, Huang et al. (1999) reported an average Poisson's ratio value of ν₊₁₂=1.3 for uniaxial tension along the 1-direction and measurement of the contraction along the 2-direction, and a similar average of ν₊₂₁=1.3 for the converse configuration, in the superficial zone of cartilage; in the middle zone, these values reduced to ν₊₁₂=1.2 and ν₊₂₁=1.0. For human patellar cartilage, Chang et al. (1999) reported average values of ν₊₁₂=0.9 and ν₊₁₃=1.8 in the surface-to-middle zone, and ν₊₁₂=0.5 and ν₊₁₃=0.7 in the deep zone, whereas Elliott et al. (1999) reported ν₊₁₂=2.2 in the superficial zone and ν₊₁₂=0.6 in the middle zone.

In contrast to tensile measurements, there are only a few preliminary studies that have investigated the anisotropy of cartilage in compression. Jurvelin et al. (1996) have reported measurements of the compressive modulus of cartilage in unconfined compression, on cylindrical specimens whose axis was oriented either along the radial 3-direction (which is the most commonly tested direction in compression studies) or along a direction parallel to the cartilage surface (though no relation to the split-line direction was reported). They found the compressive modulus of human knee cartilage in the 3-direction to be smaller (0.58 MPa versus 0.85 MPa), suggesting that cartilage is also anisotropic in compression. However, in a study by Soltz et al. (1999) where immature bovine carpometacarpal joint cartilage cubes were tested in unconfined compression along the 1-, 2-, and 3-directions, no significant differences were found in the compressive moduli among the three direction (with mean values ranging from 0.41 MPa along the 1-direction to 0.47 MPa in the 3-direction). From compression experiments, Poisson's ratio at equilibrium has been found to be small in human and bovine articular cartilage (Jurvelin et al., 1997; Wang et al., 2000b; Wong et al., 1998; Wong, 1999). Optical measurements from unconfined compression have yielded an average equilibrium Poisson's ratio of 0.18 in bovine humeral head cartilage (Jurvelin et al., 1997) and 0.06 in bovine carpometacarpal joint cartilage (Wang et al., 2000b).

While these results suggest that cartilage does not exhibit the same anisotropy in compression as it does in tension, the nature of the anisotropy of cartilage in compression remains undetermined. The primary objective of this study, therefore, is to determine the equilibrium compressive Young's moduli and Poisson's ratios of bovine cartilage along multiple directions (1-, 2- and 3-directions) by loading cubic specimens in unconfined compression, with the expectation that the material symmetry of cartilage can be determined more accurately with the help of a more complete set of material properties. Optimized digital image correlation (DIC) is adopted to accurately determine the resultant strain fields within the specimens under loading. It is noted that the studies reported above on the tensile and compressive properties of articular cartilage confirm that the cartilage moduli and Poisson ratios can be very different in tension and compression. Thus, the second objective of this study is to investigate how the tension-compression nonlinearity of cartilage might alter the interpretation of material symmetry (Curnier et al., 1995; Soltz and Ateshian, 2000). Based on previous findings in the literature as reviewed above, it is hypothesized in the current study that the material symmetry of cartilage is no lower than orthotropic.