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Research Papers: Contact Mechanics

Quantifying Cartilage Contact Modulus, Tension Modulus, and Permeability With Hertzian Biphasic Creep

[+] Author and Article Information
A. C. Moore, J. F. DeLucca, D. M. Elliott

Department of Biomedical Engineering,
University of Delaware,
Newark, DE 19716

D. L. Burris

Department of Biomedical Engineering;Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716
e-mail: dlburris@udel.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received August 5, 2015; final manuscript received February 11, 2016; published online July 26, 2016. Assoc. Editor: Zhong Min Jin.

J. Tribol 138(4), 041405 (Jul 26, 2016) (7 pages) Paper No: TRIB-15-1288; doi: 10.1115/1.4032917 History: Received August 05, 2015; Revised February 11, 2016

This paper describes a new method, based on a recent analytical model (Hertzian biphasic theory (HBT)), to simultaneously quantify cartilage contact modulus, tension modulus, and permeability. Standard Hertzian creep measurements were performed on 13 osteochondral samples from three mature bovine stifles. Each creep dataset was fit for material properties using HBT. A subset of the dataset (N = 4) was also fit using Oyen's method and FEBio, an open-source finite element package designed for soft tissue mechanics. The HBT method demonstrated statistically significant sensitivity to differences between cartilage from the tibial plateau and cartilage from the femoral condyle. Based on the four samples used for comparison, no statistically significant differences were detected between properties from the HBT and FEBio methods. While the finite element method is considered the gold standard for analyzing this type of contact, the expertise and time required to setup and solve can be prohibitive, especially for large datasets. The HBT method agreed quantitatively with FEBio but also offers ease of use by nonexperts, rapid solutions, and exceptional fit quality (R2 = 0.999 ± 0.001, N = 13).

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Figures

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Fig. 1

Spherical indentation rig. A capacitance sensor measures beam deflection, which is proportional to force through the spring constant. As the cartilage exudes fluid and deforms the Z-stage piezo-actuates to maintain a constant load.

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Fig. 2

(a) Creep deformation versus time for sample 1 at a constant load of 120 mN. Sample #1a was the first test and #1c was the last repeat; each repeat was conducted after 20 mins of free swelling. (b) Comparisons of Ec, Ey+, M, and k0 for sample 1. Error bars represent the standard deviation of repeat measurements and fits.

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Fig. 4

Comparison of results from HBT fits to creep and creep relaxation. Creep relaxation is a hybrid of creep and stress relaxation.

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Fig. 5

Material properties for 13 samples from three bovine stifles as determined by HBT. Samples are grouped by their respective cartilage surface, femoral surface (light gray), or tibial surface (dark gray). Tibial samples were only obtained from joint 1. Femoral surfaces from different joints (1, 2, and 3) are shaded differently to highlight their differences. Error bars represent experimental uncertainty.

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Fig. 6

The percentage difference between FEBio and the HBT (light gray) and Oyen (dark gray) methods. Error bars represent the standard deviation for N = 4. Asterisks (*) represent significant differences from FEBio.

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Fig. 3

Additional tests were conducted to evaluate the HBT method. (a) Three different creep loads (35, 50, and 120 mN) were applied to the same location on sample 2 to determine the effect of creep load on tissue properties. (b) Sample 3 was used to test the assumption of an infinite biphasic layer. The sample was evaluated after sequentially reducing its diameter from 19 to 4.8 mm.

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