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TECHNICAL PAPERS: Soft Tissue

# Extraction of Mechanical Properties of Articular Cartilage From Osmotic Swelling Behavior Monitored Using High Frequency Ultrasound

[+] Author and Article Information
Q. Wang, A. F. Mak

Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hong Kong, China

Y. P. Zheng1

Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hong Kong, Chinaypzheng@ieee.org

H. J. Niu

Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hong Kong, China and Department of Biomedical Engineering,The Beihang University

1

Corresponding author.

J Biomech Eng 129(3), 413-422 (Nov 17, 2006) (10 pages) doi:10.1115/1.2720919 History: Received November 20, 2005; Revised November 17, 2006

## Abstract

Articular cartilage is a biological weight-bearing tissue covering the bony ends of articulating joints. Negatively charged proteoglycan (PG) in articular cartilage is one of the main factors that govern its compressive mechanical behavior and swelling phenomenon. PG is nonuniformly distributed throughout the depth direction, and its amount or distribution may change in the degenerated articular cartilage such as osteoarthritis. In this paper, we used a $50MHz$ ultrasound system to study the depth-dependent strain of articular cartilage under the osmotic loading induced by the decrease of the bathing saline concentration. The swelling-induced strains under the osmotic loading were used to determine the layered material properties of articular cartilage based on a triphasic model of the free-swelling. Fourteen cylindrical cartilage-bone samples prepared from fresh normal bovine patellae were tested in situ in this study. A layered triphasic model was proposed to describe the depth distribution of the swelling strain for the cartilage and to determine its aggregate modulus $Ha$ at two different layers, within which $Ha$ was assumed to be linearly dependent on the depth. The results showed that $Ha$ was $3.0±3.2$, $7.0±7.4$, $24.5±11.1MPa$ at the cartilage surface, layer interface, and deep region, respectively. They are significantly different $(p<0.01)$. The layer interface located at $70%±20%$ of the overall thickness from the uncalcified-calcified cartilage interface. Parametric analysis demonstrated that the depth-dependent distribution of the water fraction had a significant effect on the modeling results but not the fixed charge density. This study showed that high-frequency ultrasound measurement together with triphasic modeling is practical for quantifying the layered mechanical properties of articular cartilage nondestructively and has the potential for providing useful information for the detection of the early signs of osteoarthritis.

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## Figures

Figure 1

Specimen preparation: (a) bovine patella; (b) excised cylindrical cartilage-bone plug with a diameter of 6.35mm

Figure 2

Experimental setup of the noncontact ultrasound swelling measurement system. (a) The overall setup. A: computer with A∕D card and signal processing software; B: computer monitor with the software interface; C: 3D translating platform; D: ultrasound pulser∕receiver; E: humidity thermometer; F: probe thermometer; G: container filled with the saline solution; and H: ultrasound transducer. (b) An enlarged view for the essential components.

Figure 3

(a) A typical M-mode ultrasound image display showing the changes happened for the ultrasound echoes from cartilage tissues at different depths after the saline was changed from 2Mto0.15M. (b) A-mode display of ultrasound signals. Using the custom-designed software, tracking windows can be selected (indicated by the number from 1 to n) to track the time shifts of the echoes from the recorded A-mode ultrasound signal during the swelling process. (c) The shifts of the tissues at different depths were measured from the ultrasound signals.

Figure 4

Sketch of the compensation for the time shifts measured at different depths using the time shift of the uncalcified-calcified cartilage interface to correct the error caused by the change of the sound speed in the cartilage. At depth x, Tx is the original time shift value measured before compensation; tx denotes the flight time from the surface to depth x at time 0 (just after changing the solution); T is the flight time from the surface to the bottom at time 0; ΔT denotes the real time shift of the uncalcified-calcified cartilage interface at equilibrium.

Figure 5

(a) Schematic diagram of the inhomogeneous two-layer model with four parameters (Ha1, Ha2, Ha3, h1) for cartilage used in this study. The cartilage-bone sample is modeled as a two-layer triphasic material. The first layer (layer 1) is the deep region attached to the subchondral bone, where the modulus is taken to vary linearly from Ha1 at the uncalcified-calcified cartilage interface to the value Ha2. The second layer (layer 2) is the upper region, where the aggregate modulus is taken to vary linearly from Ha2 to the value Ha3 at the articular surface. The parameter h1 is defined as the normalized depth of layer 1. The distance of the different cartilage layer to the uncalcified-calcified cartilage interface is normalized. (b) A two-layer model used by Narmoneva (16).

Figure 6

Depth-dependent distribution of (a) fixed charge density c0F and (b) water volume fraction ϕ0W of bovine cartilage used in this study (65-66). (c)–(f) Two other types of distributions of c0F and ϕ0W assumed in this study. One is the constant distributions of c0F and ϕ0W in (c) and (d); and the other is varying distributions of c0F and ϕ0W in (e) and (f) reverse to those in (a) and (b), respectively.

Figure 7

A typical set of ultrasound echoes reflected by the articular cartilage tissue at different depths. (a) Echoes obtained after changing the concentration of the saline solution from 2Mto0.15M, (b) echoes obtained 10min after the change of the solution, (c) echoes obtained 60min after the change of the solution.

Figure 8

Nonuniform swelling-induced strains in cartilage grouped into three zones; the swelling-induced strains were compressive in the deep zone and tensile in the middle and surface zones.

Figure 9

The nonuniform distribution of the swelling-induced strains measured for a typical cartilage specimen (1.6mm in thickness) caused by changing the NaCl concentration from 2Mto0.15M. The solid line represents the theoretical prediction of the strain distribution obtained using the new model.

Figure 10

The estimated parameters Ha1, Ha2, Ha3, h1 (mean±SD; n=14) for the new layered triphasic model. The cartilage thickness was normalized from the articulating surface to the tidemark, i.e., the uncalcified-calcified cartilage interface.

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