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TECHNICAL PAPERS: Soft Tissue

# Compressive Properties of Mouse Articular Cartilage Determined in a Novel Micro-Indentation Test Method and Biphasic Finite Element Model

[+] Author and Article Information
Li Cao

Department of Biomedical Engineering,  Duke University, Box 90281, Durham, NC 27708

Inchan Youn

Division of Orthopaedic Surgery, Department of Surgery,  Duke University Medical Center, DUMC Box 3093, Durham, NC 27710

Farshid Guilak

Department of Biomedical Engineering,  Duke University, Box 90281, Durham, NC 27708 and Division of Orthopaedic Surgery, Department of Surgery,  Duke University Medical Center, DUMC Box 3093, Durham, NC 27710

Lori A Setton

Department of Biomedical Engineering,  Duke University, Box 90281, Durham, NC 27708 and Division of Orthopaedic Surgery, Department of Surgery,  Duke University Medical Center, DUMC Box 3093, Durham, NC 27710setton@duke.edu

J Biomech Eng 128(5), 766-771 (Apr 19, 2006) (6 pages) doi:10.1115/1.2246237 History: Received August 30, 2005; Revised April 19, 2006

## Abstract

The mechanical properties of articular cartilage serve as important measures of tissue function or degeneration, and are known to change significantly with osteoarthritis. Interest in small animal and mouse models of osteoarthritis has increased as studies reveal the importance of genetic background in determining predisposition to osteoarthritis. While indentation testing provides a method of determining cartilage mechanical properties in situ, it has been of limited value in studying mouse joints due to the relatively small size of the joint and thickness of the cartilage layer. In this study, we developed a micro-indentation testing system to determine the compressive and biphasic mechanical properties of cartilage in the small joints of the mouse. A nonlinear optimization program employing a genetic algorithm for parameter estimation, combined with a biphasic finite element model of the micro-indentation test, was developed to obtain the biphasic, compressive material properties of articular cartilage. The creep response and material properties of lateral tibial plateau cartilage were obtained for wild-type mouse knee joints, by the micro-indentation testing and optimization algorithm. The newly developed genetic algorithm was found to be efficient and accurate when used with the finite element simulations for nonlinear optimization to the experimental creep data. The biphasic mechanical properties of mouse cartilage in compression (average values: Young’s modulus, $2.0MPa$; Poisson’s ratio, 0.20; and hydraulic permeability, $1.1×10−16m4∕N‐s$) were found to be of similar orders of magnitude as previous findings for other animal cartilages, including human, bovine, rat, and rabbit and demonstrate the utility of the new test methods. This study provides the first available data for biphasic compressive properties in mouse cartilage and suggests a promising method for detecting altered cartilage mechanics in small animal models of osteoarthritis.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 8

A typical creep response on both linear (left) and logarithm (right) scales for the lateral tibial plateau uncovered by meniscus with a corresponding curve fit from the optimization

Figure 1

Schematic of specimen preparation. The testing spot was in the cartilage-cartilage contact area uncovered by meniscus on the lateral tibial plateau. The notch was made from top view under a stereomicroscope. The indenting site was decided by both posterior view and lateral view through a digital camera system.

Figure 2

Schematic of micro-indentation testing system (A: Extensometer; B: Load Cell; C: Specimen Chamber; D: Goniometers; E: Linear Stagers; F: Digital Camera; G: Glass Fiber Indenter). The double angle goniometer and three linear stagers under the specimen chamber allow five DOF of position control of the specimen. A digital camera system captures images from two different angles, assuring the normal surface contact between the indenter and cartilage surface.

Figure 3

Lateral view of a flat-ended glass fiber indenter on lateral tibial plateau. An indenter with a smaller diameter gives better surface contact, especially for highly curvy cartilage surface in mouse knee joints.

Figure 4

Photomicrograph of mouse cartilage section stained with Safranin-O∕Fast Green. Estimate of thickness measurement is shown.

Figure 5

Finite element mesh and boundary condition (u‐p formulation) for an axisymmetric micro-indentation configuration. The indenter height is the same as cartilage thickness. The meshed cartilage region is three times the size of glass fiber indenter. Rt and Rind are the radii of meshed cartilage and the indenter, respectively. F(t) is the applied constant force. ur and uz are radial displacement and axial displacement, respectively, and p is the pressure.

Figure 6

Sensitivity test of optimization. Known target parameters are used to generate calibration creep data by FEM. Estimated parameters are optimized for the calibration data with different initial populations (n=7).

Figure 7

Effects of thickness measurement errors on parameter estimates. Measurement errors on the order of 0–20% of average thickness values were incorporated in the optimization of the model to experimental data to estimate an uncertainty in parameter values. Parameters are shown for optimized values of Es and k against the introduced variation in measurement plotted on the x axis. The deviation in the parameter estimate from the “true” value is given at the top of each bar, to illustrate the range of parameter values as an estimate of the uncertainty. Overall, the error associated with variability in parameter estimation is less than the corresponding thickness measurement error. Note that values for the Poisson ratio varied by less than 10% in all optimization procedures. An asterisk indicates the baseline case in which the “true” thickness was used for optimization.

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