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.

Heterogeneous three-dimensional strain fields during unconfined cyclic compression in bovine articular cartilage explants

“…Important aspects and results of these analyses were that: (1) 2D cartilage strains were computed at equilibrium for both confined [29] and unconfined test protocols [23,36], (2) strains in the thickness direction varied as a function of depth, and (3) strains perpendicular to the thickness direction were either generally zero [23,29] or at least an order of magnitude smaller than strains in the thickness direction [34]. Based on these strain fields, it was possible to compute estimates for equilibrium moduli [28,33]. Also, all strain components changed nonlinearly with increasing load [34].…”

A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage

“…First, we require that the first-order constants {λ 11 , λ 22 , λ 33 } be continuous across the surfaces of discontinuity. The rationale for this requirement is that previous analyses suggested that material stability is difficult to ensure if the first-order constants jump, because eight stiffness matrices must be positive-definite (see, Klisch et al 2004;Wang et al 2003). Second, we neglect the secondorder terms associated with λ and μ [see Eqs.…”

“…The proteoglycans are negatively charged molecules that mainly resist compressive loads (Basser et al 1998;Lai et al 1991) while the collagen net work primarily resists tensile and shear loads (Mow and Ratcliffe 1997;Venn and Maroudas 1977). Due to this molecular structure, articular cartilage typically exhibits a mechanical response with marked anisotropy and tension-compression asymmetry (Akizuki et al 1986;Laasanen et al 2003;Soltz and Ateshian 2000;Wang et al 2003;Woo et al 1976Woo et al , 1979, and likely experiences finite, multi-dimensional strains due to typical in vitro and in vivo loads. Although MRI mea surements of in situ and in vivo joints have predicted that cartilage is subject to average strains of less than 10% under physiologic loading conditions (Eckstein et al 2000;Herberhold et al 1999), local strains may be much higher due to nonhomogeneous mechanical properties that depend on both anatomic location and depth from the articular surface (Schinagl et al 1997;Wang et al 2001).…”

“…For infinitesimal strains, Ateshian and colleagues (Soltz and Ateshian 2000;Wang et al 2003) have employed elastic and biphasic models with a bimodular stress constitutive equation that allows for different mechanical proper ties in tension and compression. Their model can describe the mechanical response in unconfined compression in three orthogonal directions while providing reasonable predictions for the other protocols (Wang et al 2003).…”

“…Their model can describe the mechanical response in unconfined compression in three orthogonal directions while providing reasonable predictions for the other protocols (Wang et al 2003). Those models were based on a bimodular theory for infinitesimal strains (Curnier et al 1995) in which the material constants may be discon tinuous (or jump) across a surface of discontinuity in strain space, provided that the stress continuity conditions are sat isfied at the surface.…”