0
TECHNICAL PAPERS: Soft Tissue

A Comparison Between Mechano-Electrochemical and Biphasic Swelling Theories for Soft Hydrated Tissues

[+] Author and Article Information
W. Wilson, C. C. van Donkelaar, J. M. Huyghe

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

J Biomech Eng 127(1), 158-165 (Mar 08, 2005) (8 pages) doi:10.1115/1.1835361 History: Received December 02, 2003; Revised August 04, 2004; Online March 08, 2005
Copyright © 2005 by ASME
Your Session has timed out. Please sign back in to continue.

References

Urban,  J. P. G., Maroudas,  A., Bayliss,  M. T., and Dillon,  J., 1979, “Swelling Pressures of Proteoglycans at the Concentrations Found in Cartilagenous Tissues,” Biorheology, 16, pp. 447–464.
Mow,  V. C., Kuei,  S. C., Lai,  W. M., and Armstrong,  C. G., 1980, “Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments,” J. Biomech. Eng., 102, pp. 73–84.
Lai,  W. M., Hou,  J. S., and Mow,  V. C., 1991, “A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage,” J. Biomech. Eng., 113, pp. 245–258.
Huyghe,  J. M., and Janssen,  J. D., 1997, “Quadriphasic Theory of Swelling Incompressible Porous Media,” Int. J. Eng. Sci., 35, pp. 793–802.
Gu,  W. Y., Lai,  W. M., and Mow,  V. C., 1998, “A Mixture Theory for Charged-Hydrated Soft Tissues Containing Multi-Electrolytes: Passive Transport and Swelling Behaviors,” J. Biomech. Eng., 120, pp. 169–180.
Simon,  B. R., Liable,  J. P., Pflaster,  D., Yuan,  Y., and Krag,  M. H., 1996, “A Poroelastic Finite Element Formulation Including Transport and Swelling in Soft Tissue Structures,” J. Biomech. Eng., 118, pp. 1–9.
Frijns,  A. J. H., Huyghe,  J. M., and Janssen,  J. D., 1997, “A Validation of the Quadriphasic Mixture Theory for Intervertebral Disc Tissue,” Int. J. Eng. Sci., 35, pp. 1419–1429.
Levenston,  M. E., Frank,  E. H., and Grodzinksy,  A. J., 1999, “Electrokinetic and Poroelastic Coupling During Finite Deformations of Charged Porous Media,” J. Appl. Mech., 66, pp. 323–333.
Sun,  D. N., Gu,  W. Y., Guo,  X. E., Lai,  W. M., and Mow,  V. C., 1999, “A Mixed Finite Element Formulation of Triphasic Mechano-Electrochemical Theory for Charged, Hydrated Biological Soft Tissues,” Int. J. Numer. Methods Eng., 45, pp. 1375–1402.
van Meerveld,  J., Molenaar,  M. M., Huyghe,  J. M., and Baaijens,  F. P. T., 2003, “Analytical Solution of Compression, Free Swelling and Electrical Loading of Saturated Charged Porous Media,” Transp. Porous Media, 50, pp. 111–126.
van Loon,  R., Huyghe,  J. M. R. J., Wijlaars,  M. W., and Baaijens,  F. P. T., 2003, “3D FE Implementation of an Incompressible Quadriphasic Mixture Model,” Int. J. Numer. Methods Eng., 57, pp. 1243–1258.
Lanir,  Y., 1987, “Biorheology and Fluid Flux in Swelling Tissues. I. Bicomponent Theory for Small Deformations, Including Concentration Effects,” Biorheology, 24, pp. 173–187.
Maroudas,  A., 1975, “Biophysical Chemistry of Cartilaginous Tissues With Special Reference to Solute and Fluid Transport,” Biorheology, 12, pp. 233–248.
Maroudas, A., 1979, “Physiochemical Properties of Articular Cartilage,” in Adult Articular Cartilage, 2nd ed., Freemam, M. A. R., ed., Pitman Medical, pp. 233–248.
Simo,  J. C., and Ortiz,  M., 1985, “A Unified Approach to Finite Deformation Plasticity Based on the Use of Hyperelastic Constitutive Equations,” Comput. Methods Appl. Mech. Eng., 49, pp. 221–245.
Mow,  V. C., Atheshian,  G. A., Lai,  W. M., and Gu,  W. Y., 1998, “Effects of Fixed Charges on the Stress–Relaxation Behavior of Hydrated Soft Tissues in a Confined Compression Problem,” Int. J. Solids Struct., 35, pp. 4945–4962.
Wilson,  W., van Donkelaar,  C. C., van Rietbergen,  C., Ito,  K., and Huiskes,  R., 2004, “Stresses in the Local Collagen Network of Articular Cartilage: A Poroviscoelastic Fibril-Reinforced Finite Element Study,” J. Biomech., 37, pp. 357–366.
Huyghe,  J. M., Janssen,  C. F., van Donkelaar,  C. C., and Lanir,  Y., 2002, “Measuring Principles of Frictional Coefficients in Cartilaginous Tissues and Its Substitutes,” Biorheology, 39, pp. 47–53.

Figures

Grahic Jump Location
Schematic representation of a confined compression/free swelling test: (a) a cylindrical disc of tissue (thickness h), is placed inside a confined compression chamber with an impermeable piston on top and a permeable filter at the bottom. (b) At t=0 either a pressure P is applied to the piston (confined compression) or the external salt concentration is changed to c* (free swelling). At t=t* the external force is removed or the external salt concentration is returned to cext.
Grahic Jump Location
Finite element mesh and boundary conditions of the 2D simulation
Grahic Jump Location
Computed strain curves for the confined compression simulations of the reference case (the R2 values between the biphasic swelling and the mechano-electrochemical curves were 0.9571 and 0.9949 for the loading and unloading part, respectively)
Grahic Jump Location
Computed strain curves for the 1D swelling experiments of the reference case (the R2 values between the biphasic swelling and the mechano-electrochemical curves were 0.9560 and 0.9487 for the swelling and shrinking part, respectively)
Grahic Jump Location
Computed strain curves for the confined compression simulations of the reference case as a function of height at t=144 s
Grahic Jump Location
Computed strain curves for the 1D swelling simulations of the reference case as a function of height at t=149 s
Grahic Jump Location
The correlation between the biphasic swelling model and the mechano-electrochemical model during confined compression (R2=0.8828 for loading and 0.7702 for unloading curves)
Grahic Jump Location
The correlation between the biphasic swelling model and the mechano-electrochemical model during 1D swelling (R2=0.98254)
Grahic Jump Location
Computed displacement curves for the 2D simulation. ux and uy are the horizontal and vertical displacement of the top-right node of the model, respectively.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In