Skip to main content
SpringerLink
Log in

Effects of Hydration and Fixed Charge Density on Fluid Transport in Charged Hydrated Soft Tissues

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

The effects of tissue hydration and fixed charge density on hydraulic permeability and creep behavior of cartilaginous tissues have been investigated using the triphasic theory and finite element methods. The empirical model for hydraulic permeability of uncharged gels and Mackie and Meares (1955) model for ion diffusivity were used in the numerical analysis. The hydraulic permeabilities of normal and trypsin-treated porcine annulus fibrosus tissues were measured indirectly. Analysis of the experimental data from this study and in literature indicates that the water content plays a more important role in regulating tissue permeability than fixed charge density for normal tissues. A change in glycosaminoglycan content will change both triphasic closed-circuit (or intrinsic) and biphasic open-circuit permeabilities of cartilaginous tissues. Analysis also shows that both fixed charge density and water content play an important role in tissue creep response. This study adds new knowledge to the permeability and creep behavior of cartilaginous tissues and is important for understanding the nutrition in intervertebral disk. © 2003 Biomedical Engineering Society.

PAC2003: 8719Tt, 8710+e, 8719Uv

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Argoubi, M., and A. Shirazi-Adl. Poroelastic creep response analysis of a lumbar motion segment in compression. J. Biomech. 29:1331–1339, 1996.

    Google Scholar 

  2. Best, B. A., F. Guilak, L. A. Setton, W. Zhu, F. Saed-Nejad, A. Ratcliffe, M. Weidenbaum, and V. C. Mow. Compressive mechanical properties of the human anulus fibrosus and their relationship to biochemical composition. Spine19:212–221, 1994.

    Google Scholar 

  3. Bibby, S. R., J. C. Fairbank, M. R. Urban, and J. P. Urban. Cell viability in scoliotic discs in relation to disc deformity and nutrient levels. Spine27:2220–2228, 2002.

    Google Scholar 

  4. Chammas, P., W. J. Federspiel, and S. R. Eisenberg. A microcontinuum model of electrokinetic coupling in the extracellular matrix: Perturbation formulation and solution. J. Colloid Interface Sci. 168:526–538, 1994.

    Google Scholar 

  5. Crock, H. V., and M. Goldwasser. Anatomic studies of the circulation in the region of the vertebral end-plate in adult Greyhound dogs. Spine9:702–706, 1984.

    Google Scholar 

  6. Drost, M. R., P. Willems, H. Snijders, J. M. Huyghe, J. D. Janssen, and A. Huson. Confined compression of canine annulus fibrosus under chemical and mechanical loading. J. Biomech. Eng. 117:390–396, 1995.

    Google Scholar 

  7. Ehlers, W., and B. Markert. A linear viscoelastic biphasic model for soft tissues based on the theory of porous media. J. Biomech. Eng. 123:418–424, 2001.

    Google Scholar 

  8. Eisenberg, S. R., and A. J. Grodzinsky. Electrokinetic micromodel of extracellular-matrix and other polyelectrolyte networks. PhysicoChemical Hydrodynamics10:517–539, 1988.

    Google Scholar 

  9. Frank, E. H., and A. J. Grodzinsky. Cartilage electromechanics—I. Electrokinetic transduction and the effects of electrolyte pH and ionic strength. J. Biomech. 20:615–627, 1987.

    Google Scholar 

  10. Frank, E. H., and A. J. Grodzinsky. Cartilage electromechanics—II. A continuum model of cartilage electrokinetics and correlation with experiments. J. Biomech. 20:629–639, 1987.

    Google Scholar 

  11. Frank, E. H., A. J. Grodzinsky, S. L. Phillips, and P. E. Grimshaw. Physiochemical and bioelectrical determinants of cartilage material properties. In: Biomechanics of Diarthrodial Joints, edited by V. C. Mow, D. O. Wood, and S. L. Woo. New York: Springer, 1990, pp. 261–282.

    Google Scholar 

  12. Grodzinsky, A. J. Electromechanical and physicochemical properties of connective tissue. Crit. Rev. Biomed. Eng. 9:133–199, 1983.

    Google Scholar 

  13. Gu, W. Y., M. A. Justiz, and H. Yao. Electrical conductivity of lumbar annulus fibrosis: Effects of porosity and fixed charge density. Spine27:2390–2395, 2002.

    Google Scholar 

  14. Gu, W. Y., and M. A. Justiz. Apparatus for measuring the swelling dependent electrical conductivity of charged hydrated soft tissues. J. Biomech. Eng. 124:790–793, 2002.

    Google Scholar 

  15. Gu, W. Y., W. M. Lai, and V. C. Mow. Theoretical basis for measurements of cartilage fixed-charge density using streaming current and electro-osmosis effects. Adv. Bioeng. 26:55–58, 1993.

    Google Scholar 

  16. Gu, W. Y., W. M. Lai, and V. C. Mow. Transport of fluid and ions through a porous-permeable charged-hydrated tissue, and streaming potential data on normal bovine articular cartilage. J. Biomech. 26:709–723, 1993.

    Google Scholar 

  17. Gu, W. Y., W. M. Lai, and V. C. Mow. A mixture theory for charged-hydrated soft tissues containing multielectrolytes: passive transport and swelling behaviors. J. Biomech. Eng. 120:169–180, 1998.

    Google Scholar 

  18. Gu, W. Y., W. M. Lai, and V. C. Mow. Transport of multi-electrolytes in charged hydrated biological soft tissues. Transp. Porous Media34:143–157, 1999.

    Google Scholar 

  19. Gu, W. Y., X. G. Mao, R. J. Foster, M. Weidenbaum, V. C. Mow, and B. A. Rawlins. The anisotropic hydraulic permeability of human lumbar anulus fibrosus. Influence of age, degeneration, direction, and water content. Spine24:2449–2455, 1999.

    Google Scholar 

  20. Gu, W. Y., H. Yao, C.-Y. Huang, and H. S. Cheung. New insight into deformation-dependent hydraulic permeability of gels and cartilage, and dynamic behavior of agarose gels in confined compression. J. Biomech. 36:593–598, 2003.

    Google Scholar 

  21. Happel, J. Viscous flow relative to arrays of cylinders. AIChE J. 5:174–177, 1959.

    Google Scholar 

  22. Helfferich, F. Ion Exchange. New York: McGraw-Hill, 1962.

    Google Scholar 

  23. Holm, S., A. Maroudas, J. P. Urban, G. Selstam, and A. Nachemson. Nutrition of the intervertebral disc: Solute transport and metabolism. Connect. Tissue Res. 8:101–119, 1981.

    Google Scholar 

  24. Holm, S., and A. Nachemson. Nutritional changes in the canine intervertebral disc after spinal fusion. Clin. Orthop. 169:243–258, 1982.

    Google Scholar 

  25. Holmes, M. H., and V. C. Mow. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. J. Biomech. 23:1145–1156, 1990.

    Google Scholar 

  26. Horner, H. A., and J. P. Urban. 2001 Volvo Award Winner in Basic Science Studies: Effect of nutrient supply on the viability of cells from the nucleus pulposus of the intervertebral disc. Spine26:2543–2549, 2001.

    Google Scholar 

  27. Houben, G. B., M. R. Drost, J. M. Huyghe, J. D. Janssen, and A. H. Husson. Nonhomogeneous permeability of canine anulus fibrosus. Spine1:7–16, 1997.

    Google Scholar 

  28. Huyghe, J. M., and J. D. Janssen. Quadriphasic mechanics of swelling incompressible porous media. Int. J. Eng. Sci. 35:793–802, 1997.

    Google Scholar 

  29. Iatridis, J. C., L. A. Setton, R. J. Foster, B. A. Rawlins, M. Weidenbaum, and V. C. Mow. Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression. J. Biomech. 31:535–544, 1998.

    Google Scholar 

  30. Jackson, G. W., and D. F. James. The permeability of fibrous porous media. Can. J. Chem. Eng. 64:364–374, 1986.

    Google Scholar 

  31. Johnson, E. M., and W. M. Deen. Hydraulic permeability of agarose gels. AIChE J. 42:1220–1224, 1996.

    Google Scholar 

  32. Katchalsky, A., and P. F. Curran. Nonequilibrium Thermodynamics in Biophysics. Cambridge: Harvard University Press, 1975.

    Google Scholar 

  33. Klisch, S. M., and J. C. Lotz. A special theory of biphasic mixtures and experimental results for human annulus fibrosus tested in confined compression. J. Biomech. Eng. 122:180–188, 2000.

    Google Scholar 

  34. Koneshan, S., J. C. Rasaiah, R. M. Lynden-Bell, and S. H. Lee. Solvent structure, dynamics, and ion mobility in aqueous solution at 25°C. J. Phys. Chem. 102:4193–4204, 1998.

    Google Scholar 

  35. Koponen, A., M. Kataja, and J. Timonen. Permeability and effective porosity of porous media. Phys. Rev. E56:3319–3325, 1997.

    Google Scholar 

  36. Lai, W. M., J. S. Hou, and V. C. Mow. A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113:245–258, 1991.

    Google Scholar 

  37. Lai, W. M., and V. C. Mow. Drag-induced compression of articular cartilage during a permeation experiment. Biorheology17:111–123, 1980.

    Google Scholar 

  38. Lai, W. M., V. C. Mow, D. D. Sun, and G. A. Ateshian. On the electric potentials inside a charged soft hydrated biological tissue: Streaming potential versus diffusion potential. J. Biomech. Eng. 122:336–346, 2000.

    Google Scholar 

  39. Lee, R. C., E. H. Frank, A. J. Grodzinsky, and D. K. Roylance. Oscillatory compressional behavior of articular cartilage and its associated electro-mechanical properties. J. Biomech. Eng. 103:280–292, 1981.

    Google Scholar 

  40. Mackie, J. S., and P. Meares. The diffusion of electrolytes in a cation-exchange resin—I. theoretical. Proc. R. Soc. London, Ser. A232:498–509, 1955.

    Google Scholar 

  41. Maroudas, A. Physicochemical properties of cartilage in the light of ion exchange theory. Biophys. J. 8:575–595, 1968.

    Google Scholar 

  42. Maroudas, A. Biophysical chemistry of cartilaginous tissues with special reference to solute and fluid transport. Biorheology12:233–248, 1975.

    Google Scholar 

  43. Maroudas, A., R. A. Stockwell, A. Nachemson, and J. Urban. Factors involved in the nutrition of the human lumbar intervertebral disc: Cellularity and diffusion of glucose. J. Anat. 120:113–130, 1975.

    Google Scholar 

  44. Moore, R. J., O. L. Osti, B. Vernon-Roberts, and R. D. Fraser. Changes in endplate vascularity after an outer anulus tear in the sheep. Spine17:874–878, 1992.

    Google Scholar 

  45. Mow, V. C., G. A. Ateshian, W. M. Lai, and W. Y. Gu. Effects of fixed charge density on the stress-relaxation behavior of hydrated soft tissues in a confined compression problem. Int. J. Space Struct. 35:4945–4962, 1998.

    Google Scholar 

  46. Mow, V. C., S. C. Kuei, W. M. Lai, and C. G. Armstrong. Biphasic creep and stress relaxation of articular cartilage in compression: Theory and experiments. J. Biomech. Eng. 102:73–84, 1980.

    Google Scholar 

  47. Mow, V. C., and W. M. Lai. Selected unresolved problems in synovial joint biomechanics. In: Proceedings of Biomechanics Symposium, edited by W. Van Buskirk. New York: ASME, 1979, pp. 19–52.

    Google Scholar 

  48. Nachemson, A., T. Lewin, A. Maroudas, and M. A. Freeman. diffusion of dye through the end-plates and the annulus fibrosus of human lumbar inter-vertebral discs. Geotech. Eng. 41:589–607, 1970.

    Google Scholar 

  49. Ogata, K., and L. A. Whiteside. 1980 Volvo award winner in basic science. Nutritional pathways of the intervertebral disc. An experimental study using hydrogen washout technique. Int. J. Space Struct. 6:211–216, 1981.

    Google Scholar 

  50. Ohshima, H., H. Tsuji, N. Hiarano, H. Ishihara, Y. Katoh, and H. Yamada. Water diffusion pathway, swelling pressure, and biomechanical properties of the intervertebral disc during compression load. Int. J. Space Struct. 14:1234–1244, 1989.

    Google Scholar 

  51. Riches, P. E., N. Dhillon, J. Lotz, A. W. Woods, and D. S. McNally. The internal mechanics of the intervertebral disc under cyclic loading. J. Biomech. 35:1263–1271, 2002.

    Google Scholar 

  52. Roberts, S., J. P. Urban, H. Evans, and S. M. Eisenstein. Transport properties of the human cartilage endplate in relation to its composition and calcification. Int. J. Space Struct. 21:415–420, 1996.

    Google Scholar 

  53. Setton, L. A., W. Zhu, M. Weidenbaum, A. Ratcliffe, and V. C. Mow. Compressive properties of the cartilaginous end-plate of the baboon lumbar spine. J. Orthop. Res. 11:228–239, 1993.

    Google Scholar 

  54. Sun, D. N., W. Y. Gu, X. E. Guo, W. M. Lai, and V. C. Mow. A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues. Int. J. Numer. Methods Eng. 45:1375–1402, 1999.

    Google Scholar 

  55. Urban, J. P. The role of the physicochemical environment in determining disc cell behaviour. Biochem. Soc. Trans. 30:858–864, 2001.

    Google Scholar 

  56. Urban, J. P., S. Holm, and A. Maroudas. Diffusion of small solutes into the intervertebral disc: As study. Biorheology15:203–221, 1978.

    Google Scholar 

  57. Urban, J. P. G., S. Holms, A. Maroudas, and A. Nachemson. Nutrition of the intervertebral disc: An study of solute transport. Clin. Orthop. 129:101–114, 1977.

    Google Scholar 

  58. Yao, H., and W. Y. Gu. New insight into deformation-dependent hydraulic permeability of hydrogels and cartilage. Adv. Bioeng. 53:32520, 2002.

    Google Scholar 

  59. Yao, H., M. A. Justiz, D. Flagler, and W. Y. Gu. Effects of swelling pressure and hydraulic permeability on dynamic compressive behavior of lumbar annulus fibrosus. Ann. Biomed. Eng. 30:1234–1241, 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tissue Biomechanics Laboratory, Department of Biomedical Engineering, University of Miami, Coral Gables, FL

    Wei Yong Gu & Hai Yao

Authors
  1. Wei Yong Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hai Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gu, W.Y., Yao, H. Effects of Hydration and Fixed Charge Density on Fluid Transport in Charged Hydrated Soft Tissues. Annals of Biomedical Engineering 31, 1162–1170 (2003). https://doi.org/10.1114/1.1615576

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1114/1.1615576

Search

Navigation