0
TECHNICAL PAPERS

On the Electric Potentials Inside a Charged Soft Hydrated Biological Tissue: Streaming Potential Versus Diffusion Potential

[+] Author and Article Information
W. Michael Lai, Van C. Mow, Daniel D. Sun, Gerard A. Ateshian

Departments of Mechanical Engineering, Biomedical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10027

J Biomech Eng 122(4), 336-346 (Feb 28, 2000) (11 pages) doi:10.1115/1.1286316 History: Received June 22, 1999; Revised February 28, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bachrach,  N. M., Valhmu,  W. B., Stazzone,  E. J., Ratcliffe,  A., Lai,  W. M., and Mow,  V. C., 1995, “Changes in Proteoglycan Synthesis of Chondrocytes in Articular Cartilage Are Associated With the Time-Dependent Changes in Their Mechanical Environment,” J. Biomech., 28, pp. 1561–1569.
Brighton,  C. T., Jenson,  L., Pollack,  S. R., Tolin,  B. S., and Clark,  C. C., 1989, “Proliferative and Synthetic Response of Bovine Growth Plate Chondrocytes to Various Capacitatively Coupled Electric Fields,” J. Orthop. Res., 7, pp. 759–765.
Freeman,  P. M., Natarajan,  R. N., Kimura,  J. H., and Andriachi,  T. P., 1994, “Chondrocyte Cells Respond Mechanically to Compressive Loads,” J. Orthop. Res., 12, pp. 311–320.
Gray,  M. L., Pizzanelli,  A. M., Grodzinsky,  A. J., and Lee,  R. C., 1988, “Mechanical and Physicochemical Determinants of the Chondrocyte Biosynthetic Response,” J. Orthop. Res., 6, pp. 777–792.
Guilak,  F. A., Meyers,  B. C., Ratcliffe,  A., and Mow,  V. C., 1994, “The Effect of Matrix Compression on Proteoglycan Metabolism in Articular Cartilage Explants,” Osteoarthritis Cartilage, 2, pp. 91–101.
Guilak, F. A., Sah, R. L., and Setton, L. A., 1997, “Physical Regulation of Cartilage Metabolism,” in: Basic Orthopaedic Biomechanics, Mow V. C., and Hayes, W. C., eds., Lippincott-Raven Pubs., Philadelphia, pp. 179–207.
Hall,  A. C., Urban,  J. P. G., and Gehl,  K. A., 1991, “The Effects of Hydrostatic Pressure on Matrix Synthesis in Articular Cartilage,” J. Orthop. Res., 9, pp. 1–10.
Kim,  Y. J., Bonassar,  L. J., and Grodzinsky,  A. J., 1995, “The Role of Cartilage Streaming Potential, Fluid Flow and Pressure in the Stimulation of Chondrocyte Biosynthesis During Dynamic Compression,” J. Biomech., 28, pp. 1055–1066.
Lafeber,  F., Veldhuijzen,  J. P., Vanroy,  A. M., Huber-Bruning,  O., and Bijlsma,  J. W. J., 1992, “Intermittent Hydrostatic Compressive Force Stimulates Exclusively the Proteoglycan Synthesis of Osteoarthritic Human Cartilage,” Br. J. Rheumatol., 31, pp. 437–442.
MacGinitie,  L. A., Gluzband,  Y. A., and Grodzinsky,  A. J., 1994, “Electric Field Stimulation Can Increase Protein Synthesis in Articular Cartilage Explants,” J. Orthop. Res., 12, pp. 151–160.
Sah,  R. L., Kim,  Y. J., Doong,  L.-Y. H., Grodzinsky,  A. J., Plaas,  A. H. K., and Sandy,  J. D., 1989, “Biosynthetic Response of Cartilage Explants to Dynamic Compression,” J. Orthop. Res., 7, pp. 619–636.
Sah, R. L., Grodzinsky, A. J., Plaas, A. H. K., and Sandy, J. D., 1992, “Effects of Static and Dynamic Compression on Matrix Metabolism in Cartilage Explants,” in: Articular Cartilage and Osteoarthritis, Kuettner, K. E., Schleyerback, R., Peyron, J. G., and Hascall, V. C., eds., Raven Press, New York, pp. 373–392.
Schneiderman,  R. D., Kevet,  A., and Maroudas,  A., 1986, “Effects of Mechanical and Osmotic Pressure on the Rate of Glycosaminoglycan Synthesis in the Human Adult Femoral Head Cartilage: An in Vitro Study,” J. Orthop. Res., 4, pp. 393–408.
Wang,  N., Butler,  J. P., and Ingber,  D. E., 1993, “Mechano-transduction Across the Cell Surface and Through the Cytoskeleton,” Science, 260, pp. 1124–1127.
Valhmu,  W. B., Stazzone,  E. J., Bachrach,  N. M., Saed-Nejad,  F., Fischer,  S. G., Mow,  V. C., and Ratcliffe,  A., 1998, “Constant Compressive Loading of Articular Cartilage Induces a Transient Stimulation of Aggrecan Gene Expression,” Arch. Biochem. Biophys., 353, pp. 29–36.
Comper, W. D., 1996, Extracellular Matrix, 2 , Harwood Academic Publishers, Australia.
Mow, V. C., and Ratcliffe, A., 1997, “Structure and Function of Articular Cartilage and Meniscus,” in: Basic Orthopaedic Biomechanics, Mow, V. C., and Hayes, W. C., eds., Lippincott-Raven Pubs., Philadelphia, pp. 113–177.
Muir,  H., 1983, “Proteoglycans as Organizers of the Extracellular Matrix,” Biochem. Soc. Trans., 11, pp. 613–622.
Bassett,  C. A. L., and Pawluk,  R. J., 1972, “Electrical Behavior of Cartilage During Loading,” Science, 178, pp. 982–983.
Buschmann,  M. D., and Grodzinsky,  A. J., 1995, “A Molecular Model of Proteoglycan-Associated Electrostatic Forces in Cartilage Mechanics,” ASME J. Biomech. Eng., 117, pp. 180–192.
Chen,  A. C., Nguyen,  T. T., and Sah,  R. L., 1997, “Streaming Potentials During the Confined Compression Creep Test of Normal and Proteoglycan-Depleted Cartilage,” Ann. Biomed. Eng., 25, pp. 269–277.
Frank,  E. H., and Grodzinsky,  A. J., 1987, “Cartilage Electromechanics. I. Electrokinetic Transduction and the Effects of Electrolyte pH and Ionic Strength,” J. Biomech., 20, pp. 615–627.
Frank,  E. H., and Grodzinsky,  A. J., 1987, “Cartilage Electromechanics. II. A Continuum model of Cartilage Electrokinetics and Correlation With Experiments,” J. Biomech., 20, pp. 629–639.
Frank,  E. H., Grodzinsky,  A. J., Koob,  T. J., and Eyre,  D. R., 1987, “Streaming Potentials: A Sensitive Index of Enzymatic Degradation in Articular Cartilage,” J. Orthop. Res., 5, pp. 497–508.
Eisenberg,  S. R., and Grodzinsky,  A. J., 1985, “Swelling of Articular Cartilage and Other Connective Tissues: Electromechanochemical Forces,” J. Orthop. Res., 3, pp. 148–159.
Grodzinsky,  A. J., Lipshitz,  H., and Glimcher,  M. J., 1978, “Electromechanical Properties of Articular Cartilage During Compression and Stress Relaxation,” Nature (London), 275, pp. 448–450.
Gu,  W. Y., Lai,  W. M., and Mow,  V. C., 1993, “Transport of Fluid and Ions Through a Porous-Permeable Charged-Hydrated Tissue, and Streaming Potential Data on Normal Bovine Articular Cartilage,” J. Biomech., 26, pp. 709–723.
Lee,  R. C., Frank,  E. H., Grodzinsky,  A. J., and Roylance,  D. K., 1981, “Oscillatory Compressional Behavior of Articular Cartilage and Its Associated Electromechanical Properties,” ASME J. Biomech. Eng., 103, pp. 280–292.
Lotke,  P. A., Black,  J., and Richardson,  S. J., 1974, “Electromechanical Properties in Human Articular Cartilage,” J. Bone Jt. Surg., 56A, pp. 1040–1046.
Maroudas,  A., 1968, “Physicochemical Properties of Cartilage in the Light of Ion Exchange Theory,” Biophys. J., 8, pp. 575–595.
Maroudas,  A., 1975, “Swelling Pressure Versus Collagen Tension in Normal and Degenerate Articular Cartilage,” Nature (London), 260, p. 808.
Maroudas, A., 1979, “Physicochemical Properties of Articular Cartilage,” in: Adult Articular Cartilage, 2nd ed., Freeman, M. A. R., ed., Pitman Medical Pub., Kent, U.K., pp. 215–290.
Maroudas,  A., Muir,  H., and Wingham,  J., 1969, “The Correlation of Fixed Negative Charge With Glycosaminoglycan Content of Human Articular Cartilage,” Biochim. Biophys. Acta, 177, pp. 492–500.
Hascall, V. C., and Hascall, G. K., 1983, “Proteglycans,” in: Cell Biology of Extracellular Matrix, Hay, E. D., ed., Plenum Press, pp. 39–63.
Lai,  W. M., Hou,  J. S., and Mow,  V. C., 1991, “A Triphasic Theory for Swelling and Deformation Behavior of Articular Cartilage,” ASME J. Biomech. Eng., 113, pp. 245–258.
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,” ASME J. Biomech. Eng., 120, pp. 169–180.
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,” ASME J. Biomech. Eng., 102, pp. 73–84.
Donnan,  F. G., 1924, “The Theory of Membrane Equilibria,” Chem. Rev., 1, pp. 73–90.
Helfferich, F., 1962, Ion Exchange, McGraw-Hill, New York.
Lai, W. M., Ateshian, G. A., Sun, D. N., and Mow, V. C., 1999, “The Electrical Environment of Chondrocytes in Normal and OA Cartilage: Streaming Potential vs. Nernst Potential,” Proc. ASME Bioengng. Conf., Y. C. Fung 80th Anniversary Biomechanics Symposium, ASME BED-Vol. 42, pp. 135–136.
Katchalsky, A., and Curran, P. F., 1975, Non Equilibrium Thermodynamics in Biophysics, Harvard University Press, Boston, MA.
Mow,  V. C., Wang,  C. B., and Hung,  C. T., 1999, “The Extracellular Matrix, Interstitial Fluid and Ions as a Mechanical Signal Transducer in Articular Cartilage,” Osteoarthritis Cartilage, 7, pp. 41–58.
Huyghe,  J. M., and Janssen,  J. D., 1997, “Quadriphasic Mechanics of Swelling Incompressible Porous Media,” Int. J. Eng. Sci., 35, pp. 793–802.
Hasse, R., 1969, Thermodynamics of Irreversible Processes, Addison-Wesley, Reading, MA (also, Dover reprinted ed., 1990).
Holmes,  M. H., and Mow,  V. C., 1990, “The Nonlinear Characteristics of Soft Gels and Hydrated Connective Tissues in Ultrafiltration,” J. Biomech., 23, pp. 1145–1156.
Lai,  W. M., and Mow,  V. C., 1980, “Drag-Induced Compression of Articular Cartilage During Permeation Experiment,” Biorheology, 17, pp. 111–123.
Ateshian,  G. A., Warden,  W. H., Kim,  J. J., Grelsamer,  R. P., and Mow,  V. C., 1997, “Finite Deformation Biphasic Material Properties of Bovine Articular Cartilage From Confined Compression Experiments,” J. Biomech., 30, pp. 1157–1164.
Holmes,  M. H., Lai,  W. M., and Mow,  V. C., 1985, “Singular Perturbation Analysis of the Nonlinear, Flow-Dependent, Compressive Stress Relaxation Behavior of Articular Cartilage,” ASME J. Biomech. Eng., 107, pp. 206–218.
Lai,  W. M., Mow,  V. C., and Roth,  V., 1981, “Effects of Nonlinear Strain-Dependent Permeability and Rate of Compression on the Stress Behavior of Articular Cartilage,” ASME J. Biomech. Eng., 103, pp. 61–66.
Mow,  V. C., Ateshian,  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.
Sun,  D. N., Gu,  W. Y., Guo,  X. E., Lai,  W. M., and Mow,  V. C., 1999, “A Mixed Finite Element Formation of Triphasic Mechano-Electrochemical Theory for Charged, Hydrated Biological Soft Tissues,” Int. J. Numer. Methods Eng., 45, pp. 1375–1402.
Ateshian,  G. A.Lai,  W. M.Gu,  W. Y.Mow,  V. C., 1998, “Ionic Polarization in Charged Hydrated Soft Tissues,” Advances in Bioengineering, ASME BED-Vol. 39, pp. 253–254.
Armstrong,  C. G., and Mow,  V. C., 1982, “Variations in the Intrinsic Mechanical Properties of Human Cartilage With Age, Degeneration and Water Content,” J. Bone Jt. Surg., 64A, pp. 88–94.
Overbeek,  J. T. G., 1961, “The Donnan Equilibrium,” Prog. Biophys. Mol. Biol., 6, pp. 57–126.
Setton,  L. A., Elliot,  D. M., and Mow,  V. C., 1999, “Altered Mechanics of Cartilage with Osteoarthritis: Human OA and Animal Model of Joint Degeneration,” Osteoarthritis Cartilage, 7, pp. 2–14.

Figures

Grahic Jump Location
(a) Schematic diagram to show the flow convection effect on a uniform distribution of cation ⊕ corresponding to a uniform distribution of fixed negative charges (not shown). The convection effect causes a convection current, which is countered by the conduction current driven by the streaming potential. (b) Schematic diagram to show the diffusion effect on a nonuniform distribution of cation ⊕ corresponding to a nonuniform distribution of fixed negative charges (not shown). The diffusion effect causes a diffusion current, which is countered by the conduction current driven by the diffusion potential.
Grahic Jump Location
Schematic of open circuit one-dimensional permeation experiment with the upstream pressure greater than the downstream pressure (pu*>pd*); flow is from left to right
Grahic Jump Location
Steady permeation: electric potential across the tissue from the inside (Δψ), and electric potential across the tissue from the outside(Δψ*), as a function of initial fixed charge density. For Ha=0.3 MPa, the diffusion potential dominates over streaming potential. (D+=0.5×10−9m2/s,D=0.8×10−9m2/s,K=7×1014Ns/m4ow=0.80,c+=0.15M,Δp=30 KPa).
Grahic Jump Location
Steady permeation: electric potential across the tissue from the inside (Δψ), and electric potential across the tissue from the outside(Δψ*), as a function of the initial fixed charge density. For Ha=0.60 MPa, the streaming potential effect dominates over the diffusion potential effect, except for a region of low FCD. Other parameters same as in Fig. 3.
Grahic Jump Location
Steady permeation: compressive strain distribution inside the tissue for three values of Ha. The strain is caused by frictional force of permeation between water and solid matrix. The strain increases monotonically in the downstream direction. (coF=0.2 mEq/ml, other parameters same as in Fig. 3).
Grahic Jump Location
Steady permeation: fixed charge density increases in the downstream direction due to drag-induced compaction (see Fig. 5)
Grahic Jump Location
Steady permeation: electric potential distribution inside the tissue for four values of aggregate modulus. Again, the diffusion potential dominates over the streaming potential for tissues with small aggregate modulus, the reverse is true for tissues with larger aggregate modulus (same parameter values as in Fig. 5).
Grahic Jump Location
(a) Schematic of an open-circuit, one dimensional ramped-displacement, stress-relaxation experiment. The bathing solution NaCl concentration c* is kept fixed during the experiment, and the motion of the loading piston is prescribed in (b). The surface to surface strain is −0.1, to=200 s and h=2 mm.
Grahic Jump Location
Stress relaxation: electric potential distribution inside the tissue at various times for Ha=0.3 MPa. The potential increases in the direction toward the bottom indicating that it is dominated by the diffusion potential effect. Fluid flow is in the upward direction into the porous-permeable, loading-platen during the entire compression phase. (coF=0.2 mEq/ml, other parameters same as in Fig. 3).
Grahic Jump Location
Stress relaxation: compressive strain distribution inside the tissue at various times. The nonuniformity of the strain is caused by frictional drag force of permeation between water and solid matrix. The strain increases monotonically in the upward (flow) direction.
Grahic Jump Location
Stress relaxation: FCD distribution caused by the drag-induced compaction (see Fig. 10)
Grahic Jump Location
Stress relaxation: electric potential distribution inside the tissue at time t=200 s (i.e., at the end of the compression-ramp phase) for four values of aggregate modulus. For more rigid tissue (Ha>0.61 MPa), the streaming potential effect dominates whereas for softer tissues (Ha<0.61 MPa), the diffusion potential effect dominates. (coF=0.2 mEq/ml, other parameters same as in Fig. 3).
Grahic Jump Location
Stress relaxation: electric potential across the tissue from the inside (Δψ) and the electrochemical potential for anion across the tissue (Δμ̃). Note: Ag/AgCl electrodes measure the electrochemical potentials (−M/Fc)Δμ̃.

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