Nonlinear Tensile Properties of Bovine Articular Cartilage and Their Variation With Age and Depth

[+] Author and Article Information
Mathieu Charlebois

Institute of Biomedical Engineering Ecole Polytechnique, Montreal, Quebec, Canada

Marc D. McKee

Faculty of Dentistry, and Dept of Anatomy and Cell Biology, McGill University, Montreal, Quebec, Canada

Michael D. Buschmann

Institute of Biomedical EngineeringDepartment of Chemical Engineering, Ecole Polytechnique, Montreal, Quebec, Canada

J Biomech Eng 126(2), 129-137 (May 04, 2004) (9 pages) doi:10.1115/1.1688771 History: Received October 17, 2002; Revised October 22, 2003; Online May 04, 2004
Copyright © 2004 by ASME
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a) Schematic of the apparatus used to cut parallel to the articular surface. The cartilage was placed articular surface down onto the styrofoam stage of the holder, which was fixed to the Vibratome. The weight ensured flat contact and cuts parallel to the articular surface. b) Schematic drawing of the mechanical tester. The upper clamp is fixed to the U support, which is fixed to the crossbeam, and the lower clamp is fixed to the pieces that move with the actuator (ring, load cell, piston of the actuator). The actuator is fixed to the crossbeam. c) Schematic representation of the cartilage strip installed in the clamps, showing the captured images and locations of cell fiducial markers (Pkij) used to evaluate deformation.
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a) Photograph of the tensile mechanical tester with the sample installed and ready to start a test. A plastic film encloses the bath in order to prevent evaporation because of the long duration of the testing protocol. The bath is made of glass and aquarium silicone sealant. b) Photograph of the unit for stretching under light microscopy.
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Photomicrographs of histological sections made on samples that were chemically fixed between the clamps. The left parts of the samples are the region between the clamps. a) Sample installed in sandpaper with 1500 grain size. b) Sample installed in sandpaper with 400 grain size. c) Sample installed in sandpaper with 150 grain size.
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Typical data of tensile stress relaxation tests of strips of cartilage that include the articular surface. The adult cartilage is stiffer then the adolescent, which in turn is stiffer than young cartilage. The ratio of equilibrium modulus to peak modulus was also greatly age-dependent, with values near zero for the young cartilage, about ∼20% for adolescent and ∼60% for the adult cartilage.
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a) The average peak modulus for young, adolescent and adult cartilage. The average peak modulus and its non-linearity increase with age. For the last deformation (8% to 10%) peak modulus values were 10.1±3.3 MPa (young), 18.7±5.9 MPa (adolescent), and 28.3±16.6 MPa (adult) (p=0.0169 with ANOVA when comparing the three groups). Non-linear dependence of peak modulus with strain was evident with best fits providing 0.8±0.4 MPa/% (young), 1.8±0.4 MPa/% (adolescent), and 3.1±1.7 MPa/% (adult) (p=0.0033 with ANOVA). b) The average equilibrium modulus for the young, adolescent and adult cartilage. The equilibrium modulus and its non-linearity increase with age with average values, for the last deformation (8% to 10%), of −0.1±0.5 MPa (young), 4.4±2.6 MPa (adolescent), and 15.4±9.6 MPa (adult) (p=0.0006 with ANOVA). Nonlinear increases of equilibrium modulus with strain was found for adolescent and adult cartilage, with values of 0.3±0.2 MPa/% (adolescent), and 1.7±1.0 MPa/% (adult) (p=0.0001 with ANOVA when comparing the three groups).
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Equilibrium modulus for all samples and all strains versus the corresponding peak modulus. The average slope of the linear fit represents the ratio of equilibrium modulus to peak modulus and increases with age.
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The computed longitudinal deformation as a function of the approximate position along the length of the sample where m=1 and 4 are near the clamps and m=2 and 3 are in the middle of the sample (in between the 6 longitudinal fiducial markers in Fig. 1c). Longitudinal deformation is constant throughout the length of the cartilage. The overall computed deformation was 7.7±0.6% even though a 10% deformation was applied grip to grip, possibly due to deformation occurring between the upper and lower clamp surfaces.
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The computed transverse deformation as a function of the approximate position along the length of the sample where j=1 and j=6 are near the grips and j=2 to 5 are more central (corresponding to the 6 longitudinal positions in Fig. 1c). Transverse deformation is higher in the center of the sample. There is also an increase in incremental transverse deformation at all positions along the sample after the first step (Table 1). The overall deformation in the center is 16.5±4.2%, while near the clamps the overall deformation is −4.7±3.0% and −4.6±1.6%, respectively, on both side of the sample.
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Pictures of slices from the different layers taken from the same adult sample. AS: articular surface of ∼300 microns thickness. MZ: median zone of ∼330 microns thickness. DZ: deep zone of ∼320 microns thickness. The top left panel shows the samples after they had just been cut, while images on the right show the curvature of the sample once installed in the clamps. The bottom left panel shows images of the same samples once removed from the clamps, clearly indicating differences between zones.



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