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Research Papers

Importance of Collagen Orientation and Depth-Dependent Fixed Charge Densities of Cartilage on Mechanical Behavior of Chondrocytes

[+] Author and Article Information
Rami K. Korhonen1

Human Performance Laboratory, Faculty of Kinesiology, University of Calgary, Calgary, AB, T2N 1N4, Canada; Department of Physics,University of Kuopio, POB 1627, FI-70211 Kuopio, Finlandkorhonen@kin.ucalgary.ca, rami.korhonen@uku.fi

Petro Julkunen

Department of Physics, University of Kuopio, POB 1627, FI-70211 Kuopio, Finland; Department of Clinical Neurophysiology, Kuopio University Hospital, POB 1777, FI-70211 Kuopio, Finland

Wouter Wilson

Department of Biomedical Engineering, Eindhoven University of Technology, POB 513, 5600 MB Eindhoven, The Netherlands

Walter Herzog

Human Performance Laboratory, Faculty of Kinesiology, University of Calgary, Calgary, AB, T2N 1N4, Canada

It should be noted that cell shapes were dissimilar after free swelling for different collagen network moduli, inducing differences in cell strains (normalized cell height and width).

1

Corresponding author.

J Biomech Eng 130(2), 021003 (Mar 27, 2008) (11 pages) doi:10.1115/1.2898725 History: Received May 05, 2006; Revised June 19, 2007; Published March 27, 2008

The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 10

Normalized cell height (a) and width (b) as a function of time with zero FCD in the superficial, middle, and deep zone chondrocytes. Parameters were analyzed from the stress-relaxation stage of the loading protocol (Fig. 2).

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Figure 1

Schematic presentation of articular cartilage structure with typical tensile modulus in a depth-dependent manner. Tensile modulus was implemented in a fibril-reinforced finite element model.

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Figure 2

Finite element mesh in unconfined compression geometry with zoomed microscopic mesh of the chondrocytes and their environment. Three cells were implemented in the model: superficial, middle, and deep. Diameters of the cells and thicknesses of the PCMs varied throughout tissue depth (Table 1). Loading protocol with a free swelling, a 5% compression, and followed by 1200s relaxation is presented below.

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Figure 3

Chondrocyte shape in initial configuration, after free swelling and under static 5% compression. SZ=superficial zone, MZ=middle zone, and DZ=deep zone.

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Figure 4

Axial depth-dependent strain of the ECM and the chondrocytes under 5% (a), 10% (b), and 15% (c) static surface-to-surface strains. Local strains of the ECM were calculated as a mean value along the width of each layer in the depths of 5%, 30%, and 75% from the articular surface (from the two closest nodal points on the same vertical axis, Fig. 2). The results under 15% strain are presented with and without the effect of subchondral bone. The results by Wong (44) were done under 17% surface-to-surface strain. For the deep zone, ECM strains from Wong (44) are for upper and lower radial zones.

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Figure 5

Time dependent mechanical parameters of the superficial, middle, and deep zone chondrocytes, analyzed from the stress-relaxation stage of the loading protocol (Fig. 2). Normalized cell height (a) and width (b) as well as aspect ratio of the cells (c) as a function of time. Maximum von Mises stress (d), fluid pressure (e), and fluid velocity (f) of chondrocytes as a function of time.

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Figure 6

Aspect ratio (a) and fluid pressure (b) of the superficial, middle, and deep zone cells as a function of time, as assessed in the presence of subchondral bone. Parameters were analyzed from the stress-relaxation stage of the loading protocol (Fig. 2). The presence of subchondral bone was simulated by restricting lateral movement of the bottom nodes.

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Figure 7

Normalized cell height and width of the chondrocytes in the superficial, middle, and deep zones as a function of time, as assessed through homogeneous isotropic (a) and (b) and transversely isotropic (c) and (d) biphasic models. Parameters were analyzed from the stress-relaxation stage of the loading protocol (Fig. 2).

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Figure 8

Effect of collagen network modulus on the normalized cell height and width in the superficial, middle, and deep zones. Parameters were analyzed from the stress-relaxation stage of the loading protocol (Fig. 2). (a) and (b) Tensile modulus=1.7–4.5MPa (see Fig. 1); (c) and (d) tensile modulus=3.2–10.2MPa (see Fig. 1).

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Figure 9

Effect of collagen network modulus of the ECM (a), or FCD of the ECM (b), the pericellular matrices (c), or the chondrocytes (d) on the time-dependent aspect ratio of the superficial, middle, and deep zone chondrocytes. Parameters were analyzed from the stress-relaxation stage of the loading protocol (Fig. 2). Increasing the modulus for the collagen network by a factor of 10 from that of the reference configuration resulted in an aspect ratio of >1 for the deep chondrocyte.

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