Technical Briefs

On the Thermodynamical Admissibility of the Triphasic Theory of Charged Hydrated Tissues

[+] Author and Article Information
J. M. Huyghe1

Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlandsj.m.r.huyghe@tue.nl

W. Wilson

Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands

K. Malakpoor

Department of Mathematics, University of Amsterdam,1081TV Amsterdam, The Netherlands


Corresponding author.

J Biomech Eng 131(4), 044504 (Feb 03, 2009) (5 pages) doi:10.1115/1.3049531 History: Received October 17, 2007; Revised September 08, 2008; Published February 03, 2009

The triphasic theory on soft charged hydrated tissues (Lai, W. M., Hou, J. S., and Mow, V. C., 1991, “A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage  ,” ASME J. Biomech. Eng., 113, pp. 245–258) attributes the swelling propensity of articular cartilage to three different mechanisms: Donnan osmosis, excluded volume effect, and chemical expansion stress. The aim of this study is to evaluate the thermodynamic plausibility of the triphasic theory. The free energy of a sample of articular cartilage subjected to a closed cycle of mechanical and chemical loading is calculated using the triphasic theory. It is shown that the chemical expansion stress term induces an unphysiological generation of free energy during each closed cycle of loading and unloading. As the cycle of loading and unloading can be repeated an indefinite number of times, any amount of free energy can be drawn from a sample of articular cartilage, if the triphasic theory were true. The formulation for the chemical expansion stress as used in the triphasic theory conflicts with the second law of thermodynamics.

Copyright © 2009 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The cartilage sample is subjected to four subsequent changes in boundary conditions: (1) increase in salt concentration, (2) increase in strain, (3) decrease in salt concentration, and (4) decrease in strain. The tissue returns after the four changes to its initial state in the lower left corner of the square, E=0, ϕw=ϕ0w, and cF=c0F.

Grahic Jump Location
Figure 2

Prediction of the triphasic theory of charged hydrated tissues. The ratio ΔW/ΔWmech of the net free energy ΔW produced in the closed loop shown in Fig. 1 over the mechanical work associated with phase 1 of the loop ΔWmech is plotted as a function of the external salt concentration step Δce. All positive values of ΔW/ΔWmech are unphysical.




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