A Triphasic Theory for the Swelling Properties of Hydrated Charged Soft Biological Tissues

  • W. M. Lai
  • J. S. Hou
  • V. C. Mow


Many hydrated soft tissues, such as articular cartilage, meniscus and intervertebral disc, change their dimensions, volume and weight when the ion concentration in the external bathing solution is changed (Parsons and Black 1979; Maroudas 1975, 1979; Maroudas and Bannon 1981; Myers et al 1984; Mow and Schoonbeck 1984; Eisenberg and Grodzinsky 1985, 1987). For example, for an unloaded specimen of cartilage soaked in NaCl solutions at constant temperature, the tissue dimensions decrease nonlinearly in an exponential manner with increasing NaCl concentration; this decrease approaches an asymptote at a high concentration, e.g., 2.5M NaCl (Mow and Schoonbeck 1984). Therefore, at the physiological state of 0.15M NaCl, cartilage is in a swollen state, with a swelling pressure resisted by the elastic stress developed in the collagen-proteoglycan solid matrix. This is often referred to as the collagen pre-stress or elastic stress in the solid matrix (Maroudas 1975, 1976, 1979; Maroudas and Bannon 1981; Grodzinsky et al 1981). For a normal cartilage bathed in 0.15M NaCl solution, the swelling pressure has been measured to be around 0.17 MPa (Maroudas 1975,1979; Maroudas and Bannon 1981).


Articular Cartilage Osmotic Pressure Biological Tissue Bathing Solution Solid Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akizuki S, Mow VC, Müller F, Pita JC, Howell DS, Manicourt DH: Tensile properties of human knee joint cartilage: I. Influence of ionic conditions, weight bearing, and fibrillation on the tensile modulus. J Orthop Res 1986;4:379–392.CrossRefGoogle Scholar
  2. Bowen RM: Incompressible porous media models by use of the theory of mixtures. Int J Eng Sei 1980;18:1129–1148.MATHCrossRefGoogle Scholar
  3. Donnan FG: The theory of membrane equilibria. Chemical Review 1924; 1: 73–90.CrossRefGoogle Scholar
  4. Eisenberg SR, Grodzinsky AJ: Swelling of articular cartilage and other connective tissues: electromechanochemical forces. J Orthop Research 1985;3:148–159.CrossRefGoogle Scholar
  5. Eisenberg SR, Grodzinsky, AJ: The kinetics of chemically induced nonequilibrium swelling of articular cartilage and corneal stroma. J Biomech Eng 1987; 109:79–89.CrossRefGoogle Scholar
  6. Gabler R: Electrical Interactions in Molecular Biophysics, An Introduction. Academic Press, 1978.Google Scholar
  7. Grodzinsky AJ, Roth V, Myers E, Grossman WK, Mow VC: The significance of electromechanical and osmotic forces in the nonequilibrium swelling behavior of articular cartilage in tension. J Biomech, Eng 1981;103:221–231.CrossRefGoogle Scholar
  8. Hascall VC, Hascall GK: Proteoglycans, in Hay ED (ed): Cell Biology of Extracellular Matrix. Plenum, 1983, pp 39–60.Google Scholar
  9. Hou JS, Holmes MH, Lai WM, Mow VC: Interface conditions between fluids, mixtures and solids: applications to biomechanics problems, in 1989 Adv in Bioeng, pp 175–176.Google Scholar
  10. Katchalsky A, Curran PF: (1965), Nonequilibrium Thermodynamics in Biophysics. Cambridge, Harvard University Press, 1965.Google Scholar
  11. Lai WM, Hou JS, Mow VC: A triphasic theory for swelling and deformation behavior of articular cartilage. Submitted to J Biomech Eng 1990.Google Scholar
  12. Lai WM, Mow VC: Drag-induced compression of articular cartilage during a permeation experiment. Biorheology 1980;17:111–123.Google Scholar
  13. Lanir Y: Biorheology and fluid flux in swelling tissues. I. Bicomponent theory for small deformations, including concentration effects. Biorheology 1987; 23:173–188.Google Scholar
  14. Maroudas A: Swelling pressure versus collagen tension in normal and degenerate articular cartilage. Nature 1975;260:808.CrossRefGoogle Scholar
  15. Maroudas A: Biophysical chemistry of cartilaginous tissues with special reference to solute and fluid transport. Biorheology 1975;12:233–248.Google Scholar
  16. Maroudas A : Physicochemical properties of articular cartilage, in Freeman MAR (ed): Adult Articular Cartilage, 2nd ed. Pitman Medical, 1979, pp 215–290.Google Scholar
  17. Maroudas A, Bannon C: Measurement of swelling pressure in cartilage and comparison with the osmotic pressure of constituent proteoglycans. Biorheology 1981;18:619–632.Google Scholar
  18. Mow VC, Kuei SC, Lai WM, Armstrong CG: Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiment. J Biomech Eng 1980;102:73–84.CrossRefGoogle Scholar
  19. Mow VC, Holmes MH, Lai WM: Fluid transport and mechanical properties of articular cartilage. J Biomech 1984;17:377–394.CrossRefGoogle Scholar
  20. Mow VC, Schoonbeck JM: Contribution of Donnan osmotic pressure towards the biphasic compressive modulus of articular cartilage. Trans Orthop Res Soc 1984;9:262.Google Scholar
  21. Mow VC, Kwan MK, Lai WM, Holmes MH: A finite deformation theory for nonlinearly permeable soft hydrated biological tissues, in S L-Y Woo, G Schmid-Schönbein, B Zweifach (eds): Frontiers in Biomechanics. New York, Springer- Verlag, 1986, pp 153–179.Google Scholar
  22. Muir H: Proteoglycans as organizers of the extracellular matrix. Biochem Soc Trans 1983;11:613–622.Google Scholar
  23. Myers ER, Lai WM, Mow V C: A continuum theory and an experiment for the ion- induced swelling behavior of articular cartilage. J Biomech Eng 1984;106:151–158.CrossRefGoogle Scholar
  24. Parsons JR, Black J: Mechanical behavior of articular cartilage, quantitative changes with alteration of ionic environment. J Biomech 1979;12:765–773.CrossRefGoogle Scholar
  25. Robinson RA, Stokes RH: Electrolyte Solutions. London, Butterworths, 1968.Google Scholar
  26. Tombs MP, Peacocke AR: The Osmotic Pressure of Biological Macromolecules. Oxford, Clarendon Press, 1974.Google Scholar
  27. Urban JPG, Maroudas A, Bayliss MT, Dillon J: Swelling pressures of proteoglycans at the concentrations found in cartilaginous tissues. Biorheology 1979;16:447–464.Google Scholar
  28. Urban JPG, Maroudas A: Swelling of the intervertebral disc in vivo. Connect Tissue Res 1979;9:1–10.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • W. M. Lai
  • J. S. Hou
  • V. C. Mow

There are no affiliations available

Personalised recommendations