Elsevier

Journal of Biomechanics

Volume 41, Issue 11, 7 August 2008, Pages 2430-2437
Journal of Biomechanics

Mapping the depth dependence of shear properties in articular cartilage

https://doi.org/10.1016/j.jbiomech.2008.05.021Get rights and content

Abstract

Determining the depth dependence of the shear properties of articular cartilage is essential for understanding the structure–function relation in this tissue. Here, we measured spatial variations in the shear modulus G of bovine articular cartilage using a novel technique that combines shear testing, confocal imaging and force measurement. We found that G varied by up to two orders of magnitude across a single sample, exhibited a global minimum 50–250 μm below the articular surface in a region just below the superficial zone and was roughly constant at depths >1000 μm (the “plateau region”). For plateau strains γplateau≈0.75% and overall compressive strains ε≈5%, Gmin and Gplateau were ≈70 and ≈650 kPa, respectively. In addition, we found that the shear modulus profile depended strongly on the applied shear and axial strains. The greatest change in G occurred at the global minimum where the tissue was highly nonlinear, stiffening under increased shear strain, and weakening under increased compressive strain. Our results can be explained through a simple thought model describing the observed nonlinear behavior in terms of localized buckling of collagen fibers and suggest that compression may decrease the vulnerability of articular cartilage to shear-induced damage by lowering the effective strain on individual collagen fibrils.

Introduction

Articular cartilage is a specialized connective tissue that covers bones in diathroidal joints and transmits load across them. Its complex and inhomogeneous structure endows it with a specific mechanical response that enables it to remain effective for 6–9 decades, or most of a human lifetime. However, diseases of cartilage like osteoarthritis (OA) are common, affecting 46 million people and representing the leading cause of disability in the United States (Verbrugge, 1995). Damage to the structure of articular cartilage gives rise to disease by compromising proper functionality. Consequently, determining the complicated relationship between structure and function in this tissue is critical to understand the origin of cartilage diseases.

Articular cartilage is comprised mainly of water, type II collagen, chondrocytes and proteoglycans. These constituents are not distributed uniformly throughout the tissue. For example, collagen fibrils form a porous network with a pore density and predominant fibril orientation that vary with depth. In adult tissue, fibrils in the superficial zone tend to align parallel to the articular surface, those in the middle zone are randomly oriented and those in the deep zone are thicker and typically align perpendicular to the underlying bone (Bullough and Goodfellow, 1968). Like its structure and composition, many of the mechanical properties of articular cartilage have been shown to exhibit strong spatial variations. The depth dependence of the compressive and tensile properties of this tissue was first measured using partial thickness sectioning (Kempson et al., 1968). This technique involves cutting a full-thickness specimen of tissue into three or four pieces and testing each piece individually. It has been used, for example, to demonstrate that the strain-dependent mechanical properties of articular cartilage are manifestations of its strain- and depth-dependent properties (Chen et al., 2001). To improve spatial resolution, individual chondrocyte and local tissue deformations were measured by imaging fluorescently stained cells in cartilage samples before and after compression with a confocal microscope (Guilak et al., 1995). More recently, by using fluorescently stained chondrocyte nuclei imaged by video microscopy as markers to track tissue deformation, fine variations in the axial strain of full-thickness samples of articular cartilage were measured (Schinagl et al., 1996). In addition to adult tissue, this method was also applied to fetal and newborn bovine articular cartilage (Klein et al., 2007). These studies revealed that the compressive stiffness of articular cartilage at all stages of growth increases with depth.

On the other hand, few attempts have been made at determining spatial variations in the shear properties of articular cartilage. Bulk measurements of the complex shear modulus G* of articular cartilage were performed for the case of simple shear (Hayes and Bodine, 1978) and torsional shear (Zhu et al., 1993). But these studies did not determine the dependence of G* on depth d from the articular surface. In another study (Eliot et al., 2002), the depth-dependent shear modulus G(d) was inferred from measurements of the tensile modulus and Poisson's ratio in three 500-μm-thick partial thickness samples using the assumption of structural isotropy within each section. However, the structure of articular cartilage can vary over length scales much smaller than 500 μm. Furthermore, measurements of the physical properties of partial thickness sections of this tissue are often inconsistent with similar measurements performed on full-thickness specimens (Dumont et al., 1999). As a result, a more complete understanding of the relationship between structure and function in articular cartilage requires a more detailed measurement of the depth-dependent shear modulus.

To address this need, in this paper, we determine the dependence of the zero-frequency (i.e., equilibrium) shear modulus G on depth d from the articular surface with a high spatial resolution using a novel method that builds on previously demonstrated fluorescence-tracking techniques (Schinagl et al., 1996; Sveen, 2004). We then test how the shear modulus profile G(d) depends on the applied axial strain and shear strain. We find that our results can be explained by a simple thought model that takes into account known variations in collagen fibril alignment within articular cartilage.

Section snippets

Sample preparation

Seven full thickness, 6 mm diameter explants were harvested sterilely from the patellofemoral groove of six 1–3-day-old calves (Gold Medal Packing, Oriskany, NY). The harvesting procedure produces cylinders with an undamaged articular surface. After dissection, samples were soaked in phosphate-buffered saline (PBS) supplemented with U/mL penicillin and 100 μ/mL streptomycin for 30 min. Each cylinder was then cut along its long axis into two hemi-cylinders, and a small section (1–3 mm) of the deep

Results

The slope of the displacement map for a typical sample of articular cartilage under a compressive strain of 2.5% and a plateau shear strain of 2.3% (Fig. 3A) was constant over a significant range of depths (d>500 μm), indicative of constant shear strain. However, near the surface, the slope varied significantly. Similarly, the shear strain (Fig. 3B) and shear modulus (Fig. 3C) profiles exhibited significant spatial variations. In particular, the shear modulus exhibited a global minimum (Gmin) at

Discussion

The results in this study establish that articular cartilage exhibits complex and highly inhomogeneous shear properties. G exhibited a global minimum at the deep edge of the superficial zone that was significantly smaller than the shear modulus in the plateau region. In addition, the data presented above demonstrate that the shear modulus profile of articular cartilage was highly sensitive to the applied axial strain and the plateau shear strain. In particular, the region of tissue between the

Conflict of interest statement

There are no conflicts of interest to declare.

Acknowledgments

We thank L. Mahadevan, M. van der Meulen, S. Baker and L. Estroff for the valuable discussion. We also thank Harrick Scientific for their help in constructing an improved version of the tissue deformation device that was used for some of the measurements in the paper. This work was supported by NIH R21AR054867, NASA GSRP NNG-04GN57 H and CCMR MRSEC SEED DMR-0079992.

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