Determination of the Poisson's ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration

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Abstract

Chondrocytes in articular cartilage are regularly subjected to compression and recovery due to dynamic loading of the joint. Previous studies have investigated the elastic and viscoelastic properties of chondrocytes using micropipette aspiration techniques, but in order to calculate cell properties, these studies have generally assumed that cells are incompressible with a Poisson's ratio of 0.5. The goal of this study was to measure the Poisson's ratio and recovery properties of the chondrocyte by combining theoretical modeling with experimental measures of complete cellular aspiration and release from a micropipette. Chondrocytes isolated from non-osteoarthritic and osteoarthritic cartilage were fully aspirated into a micropipette and allowed to reach mechanical equilibrium. Cells were then extruded from the micropipette and cell volume and morphology were measured throughout the experiment. This experimental procedure was simulated with finite element analysis, modeling the chondrocyte as either a compressible two-mode viscoelastic solid, or as a biphasic viscoelastic material. By fitting the experimental data to the theoretically predicted cell response, the Poisson's ratio and the viscoelastic recovery properties of the cell were determined. The Poisson's ratio of chondrocytes was found to be 0.38 for non-osteoarthritic cartilage and 0.36 for osteoarthritic chondrocytes (no significant difference). Osteoarthritic chondrocytes showed an increased recovery time following full aspiration. In contrast to previous assumptions, these findings suggest that chondrocytes are compressible, consistent with previous studies showing cell volume changes with compression of the extracellular matrix.

Introduction

Chondrocytes are the cells within articular cartilage responsible for the turnover and maintenance of extracellular matrix components. With osteoarthritis, this balance of anabolic and catabolic activities are altered (Poole, 1995), leading to progressive joint degeneration and loss of cartilage function (Guilak et al., 1994; Setton et al., 1994). Articular cartilage undergoes numerous cycles of compression and recovery repeatedly due to joint loading, and deformation of the cartilage layer is associated with significant changes in the shape and volume of the chondrocytes (Guilak, 1995; Buschmann et al., 1996; Wong et al., 1997) that fully recover with release of compression (Guilak et al., 1995). Such deformations are also associated with changes in the stress–strain and fluid flow environment of the cell that vary with time and location in the tissue Mow et al. (1994). These physical factors are believed to serve as signals that influence the biologic activity of the chondrocytes under both physiologic and pathologic conditions (Guilak et al., 1997). Previous studies have attempted to predict the mechanical environment within cartilaginous tissues using theoretical models of cell–matrix interactions (Bachrach et al., 1995; Wu et al., 1999; Baer and Setton, 2000; Guilak and Mow, 2000; Baer et al., 2003). Such models require information on the mechanical properties of chondrocytes under various loading conditions. A more thorough understanding of the chondrocyte's mechanical properties, and identification of potential differences in behavior in response to loading and release from load, would provide further insights into the role of mechanical factors in regulating matrix metabolism.

Previous studies have investigated the mechanical properties of chondrocytes or chondrocyte-like cells by compression in agarose (Freeman et al., 1994), with partial aspiration into a micropipette (Trickey et al., 2000, Trickey et al., 2004; Jones et al., 1999; Guilak et al., 2002), and with indentation (Hung et al., 2001; Koay et al., 2001, Koay et al., 2003). These studies have shown that the chondrocyte behaves as a viscoelastic solid material, and both the elastic and viscoelastic material properties of chondrocytes have been determined using theoretical analyses of these experiments. However, given the dynamic nature of the cytoskeleton, which is believed to play a major role in the chondrocyte's mechanical properties, (Trickey et al., 2004) it is not clear that these properties are equivalent under different loading conditions. Furthermore, the various analytical solutions (Sato et al., 1987, Sato et al., 1990; Theret et al., 1988) and numerical models (Haider and Guilak, 2000, Haider and Guilak, 2002) used to determine cell properties from the micropipette experiment have assumed that cells are incompressible and do not change volume in response to compression. However, previous studies have demonstrated a small loss of volume in both non-osteoarthritic and osteoarthritic chondrocytes in response to complete aspiration (Jones et al., 1999) as well as with compression of the extracellular matrix in situ (Guilak, 1995), suggesting that chondrocytes are in fact compressible.

The objective of this study was to determine the Poisson's ratio and the elastic and viscoelastic properties of non-osteoarthritic and osteoarthritic chondrocytes during recovery after release from compression. To investigate this behavior, chondrocytes were aspirated completely into a micropipette, and the recovery properties were determined after the cell was released from the micropipette through analysis with finite element simulations of the experiment using several different constitutive models of cell behavior.

Section snippets

Methods

Cartilage was obtained from human femoral heads removed as waste tissue during joint replacement surgeries in accordance with protocols approved by the Duke University Institutional Review Board. As described previously (Trickey et al., 2000, Trickey et al., 2004), cartilage was removed only from sections of the femoral head which looked macroscopically similar and was also examined by histology. A section of the cartilage and bone was fixed in formalin, paraffin embedded, sliced perpendicular

Results

The compressible properties of the cells, represented by the Poisson's ratio ν of the biphasic mixture, were determined fitting the experimental measurements of cell volume change to a finite element simulation of the full aspiration experiment (i.e., complete entry of the cell into the micropipette). The actual aspiration of the cell was not modeled, but was emulated by placing the cell inside a large tube whose diameter was reduced during the simulation. Although the transient behavior of

Discussion

By combining a theoretical model of micropipette aspiration and recovery with experimental measures of cell volume and dimensions, the Poisson's ratio and the compressible and viscoelastic properties of chondrocytes were determined. No significant differences were observed between the properties of non-osteoarthritic and osteoarthritic chondrocytes except for an increase in the relaxation time in the radial direction λr. The findings of this study indicate that the chondrocyte is not completely

Acknowledgements

This study was supported by grants from the National Science Foundation #DGE-9616283, the National Institutes of Health #AR50245, #AR48182, and #AG15768, and the Eindhoven University of Technology.

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