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

Abstract

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.

Simulating the sensitivity of cell nutritive environment to composition changes within the intervertebral disc

“…The osmo-poroviscoelastic formdulation used in this study was duly verified against thermodynamical consistency (Huyghe et al 2009). At the tissue level, the model was also validated, with parameter values that represented healthy tissues (Schroeder et al 2007).…”

A Review of the Combination of Experimental Measurements and Fibril-Reinforced Modeling for Investigation of Articular Cartilage and Chondrocyte Response to Loading

“…Lai et al [143] introduced a triphasic mixture model, which includes three phases: an incompressible solid, an incompressible fluid, and a monovalent ionic phase. In the triphasic model, swelling behavior is explained by three mechanisms: Donnan osmosis, excluded volume effect, and chemical expansion [144]. Simon et al [145] introduced an alternative model by including the swelling effects in fluid equilibrium.…”

“…However, the inclusion of the chemical expansion term as proposed by Lai et al [143] may not be appropriate, as it conflicts with the second law of thermodynamics. Huyghe et al demonstrated that the chemical expansion stress part could produce free energy during closed loading cycles if the theory were true [144]. Nevertheless, osmotic swelling alone may not fully simulate the swelling behavior in cartilage [144].…”

“…Huyghe et al demonstrated that the chemical expansion stress part could produce free energy during closed loading cycles if the theory were true [144]. Nevertheless, osmotic swelling alone may not fully simulate the swelling behavior in cartilage [144]. However, when splitting the fluid phase into intra- and extrafibrillar portions [8, 150], implementation of chemical potential may not be needed.…”

Multiscale Mechanics of Articular Cartilage: Potentials and Challenges of Coupling Musculoskeletal, Joint, and Microscale Computational Models

“…The combination of the swelling and the restriction against swelling determines the mechanical properties of the cartilage tissue 144,154 . Cartilage mechanical models have attempted to capture these effects of swelling with triphasic representations (solid, fluid, and ionic) 79,100,147 , fitting parameters to tissue-level consolidation experiments, or into computationally less expensive biphasic swelling models that assume ion flux is significantly faster than water flow 149 . To better capture the nature of the tissue, models with fiber-reinforcement were developed in the last decade 101,150,151 .…”