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Technical Briefs

# Theory of the Short Time Mechanical Relaxation in Articular Cartilage

[+] Author and Article Information
J. W. Ruberti

Department of Mechanical and Industrial Engineering,  Northeastern University, Boston, MA 02115

J. B. Sokoloff

Department of Physics and Center for Interdisciplinary, Research on Complex Systems,  Northeastern University, Boston, MA 02115 e-mail: j.sokoloff@neu.edu

This phenomenon is illustrated on the web site $math.unice.fr/~musacchi/tesi/node38.html$.

J Biomech Eng 133(10), 104504 (Nov 07, 2011) (3 pages) doi:10.1115/1.4005174 History: Received May 24, 2011; Accepted September 21, 2011; Published November 07, 2011; Online November 07, 2011

## Abstract

Articular cartilage is comprised of macromolecules, proteoglycans, with (charged) chondroitin sulfate side-chains attached to them. The proteoglycans are attached to longer hyaluronic acid chains, trapped within a network of type II collagen fibrils. As a consequence of their relatively long persistence lengths, the number of persistence lengths along the chondroitin sulfate and proteoglycan chains is relatively small, and consequently, the retraction times for these side chains are also quite short. We argue that, as a consequence of this, they will not significantly inhibit the reptation of the hyaluronic acid chains. Scaling arguments applied to this model allow us to show that the shortest of the mechanical relaxation times of cartilage, that have been determined by Fyhrie and Barone to be due to reptation of the hyaluronic acid polymers, should have a dependence on the load, i.e., force per unit interface area $P$, carried by the cartilage, proportional to $P3/2$.

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## Figures

Figure 1

The attachment of chondroitin sulfate to proteoglycan chains, which are in turn attached to longer hyaluronic acid chains is illustrated schematically. The mean contour length of a chondroitin sulfate chain is denoted by L, and the mean lengths of the proteoglycan and hyaluronic acid chains are given in terms of L. The dots represent counterions.

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