Numerical Simulation of Streaming Potentials Due to Deformation-Induced Hierarchical Flows in Cortical Bone

[+] Author and Article Information
A. F. T. Mak

Jockey Club Rehabilitation Engineering Centre, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong

J. D. Zhang

Jockey Club Rehabilitation Engineering Centre, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong KongSchool of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing, China

J Biomech Eng 123(1), 66-70 (Aug 29, 2000) (5 pages) doi:10.1115/1.1336796 History: Received May 19, 1998; Revised August 29, 2000
Copyright © 2001 by ASME
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Yasuda,  I., 1954, “On the Piezoelectric Activity of Bone,” J. Jap. Orthop. Surg. Soc., 28, pp. 267–269.
Fukada,  E., and Yasuda,  I., 1957, “On the Piezoelectric Effect of Bone,” J. Phys. Soc. Jpn., 10, pp. 1158–1169.
Bassett,  C. A. L., and Becker,  R. O., 1962, “Generation of Electric Potentials by Bone in Response to Mechanical Stress,” Science, 137, pp. 1063–1064.
Gross,  D., and Williams,  W. S., 1982, “Streaming Potential and the Electromechanical Response of Physiologically Moist Bone,” J. Biomech., 15, pp. 277–295.
Peinkowski,  D., and Pollack,  S. R., 1983, “The Origin of Stress-Generated Potentials in Fluid-Saturated Bone,” J. Orthop. Res., 1, pp. 30–41.
Johnson,  M. W., Chakalakal,  D. A., Harper,  R., Katz,  J. L., and Rouhana,  S. W., 1982, “Fluid Flow in Bone in Vitro,” J. Biomech., 15, No. 11, pp. 881–885.
Pollack, S. R., Korostoff, E., Starkebaum, W., and Iannicone, W., 1979, “Microelectrode Studies of Stress Generated Potentials in Bone, ” in: Electrical Properties of Bone and Cartilage, C. T. Brighton, J. Black, and S. R. Pollack, eds., Grune and Stratton, New York, pp. 69–81.
Seliger,  W. G., 1970, “Tissue Fluid Movement in Compact Bone,” Anat. Rec., 166, pp. 247–256.
Dillaman,  R. M., 1984, “Movement of Ferritin in 2-Day-Old Chick Femur,” Anat. Rec., 209, pp. 445–453.
Montgomery,  R. J., Sutker,  B. D., Bronk,  J. T., Smith,  S. R., and Kelly,  P. J., 1988, “Interstitial Fluid Flow in Cortical Bone,” Microvasc. Res., 33, pp. 295–307.
Otter,  M. W., Palmieri,  V. R., and Cochran,  G. V. B., 1990, “Transcortical Streaming Potentials Are Generated by Circulatory Pressure Gradients in Living Canine Tibia,” J. Orthop. Res., 8, pp. 119–126.
Knothe Tate,  M. L., Niederer,  P., and Knothe,  U., 1998, “In Vivo Tracer Transport Though the Lacunocanalicular System of Rat Bone in an Environment Devoid of Mechanical Loading,” Bone, 22, No. 2, pp. 107–117.
Knothe Tate,  M. L., Niederer,  P., and Forwood,  M., 1997, “In Vivo Observation of Load-Induced Fluid Displacements Using Procion Red and Microperoxidase Tracers in the Rat Tibia,” J. Bone Miner. Res., 12, Suppl. 1, p. F641.
Salzstein,  R. A., Pollack,  S. R., Mak,  A. F. T., and Petrov,  N., 1987, “Electromechanical Potentials in Cortical Bone—I. A Continuum Approach,” J. Biomech., 20, No. 3, pp. 261–270.
Petrov,  N., Pollack,  S., and Blagoeva,  R., 1989, “A Discrete Model for Streaming Potentials in a Single Osteon,” J. Biomech., 22, pp. 517–521.
Pollack,  S. R., Petrov,  N., Salzstein,  R. S., Brnakov,  G., and Blagoeva,  R., 1984, “An Anatomical Model for Streaming Potentials in Osteons,” J. Biomech., 17, pp. 627–636.
Kufahl,  R. H., and Saha,  S., 1990, “A Theoretical Model for Stress-Generated Fluid Flow in the Canaliculi–Lacunae Network in Bone Tissue,” J. Biomech., 23, pp. 171–180.
Cowin,  S. C., Weinbaum,  S., and Zeng,  Y., 1995, “A Case for Bone Canaliculi as the Anatomical Site for Strain Generated Potentials,” J. Biomech., 28, No. 11, pp. 1281–1297.
Weinbaum,  S., Cowin,  S. C., and Zeng,  Y., 1994, “A Model for the Excitation of Osteocytes by Mechanical Loading-Induced Bone Fluid Shear Stresses, ” J. Biomech., 27, No. 3, pp. 339–360.
MacGinitie,  L. A., Seiz,  K. G., Otter,  M. W., and Cochran,  G. V., 1994, “Streaming Potential Measurements at Low Ionic Concentrations Reflect Bone Microstructure,” J. Biomech., 27, No. 7, pp. 969–978.
Dillaman,  R. M., Boer,  R. D., and Gay,  D. M., 1991, “Fluid Movement in Bone: Theoretical and Experimental,” J. Biomech., 24, Suppl. 1, pp. 163–177.
Keanini,  R. G., Roer,  R. D., and Dillamen,  R. M., 1995, “A Theoretical Model of Circulatory Interstitial Fluid Flow and Species Transport Within Porous Cortical Bone,” J. Biomech., 28, pp. 901–914.
Mak,  A. F. T., Huang,  D. T., Zhang,  J. D., and Tong,  P., 1997, “Deformation-Induced Hierarchical Flows and Drag Forces in Bone Canaliculi and Matrix Microporosity,” J. Biomech., 30, No. 1, p. 11.
Mow,  V. C., Kuei,  S. C., Lai,  W. H., and Armstrong,  C. G., 1980, “Biphasic Creep and Stress Relaxation of Articular Cartilage,” ASME J. Biomech. Eng., 102, pp. 73–84.
Bowen, R. M., 1976, “Theory of Mixtures,” in: Continuum Physics, Vol. III, A. C. Eringen, ed., Academic Press, New York.
Green,  A. E., and Naghdi,  P. M., 1969, “On Basic Equations for Mixtures,” Q. J. Mech. Appl. Math., 22, pp. 427–438.
Biot,  M. A., 1962, “Mechanics of Deformation and Acoustic Propagation in Porous Media,” J. Appl. Phys., 33, pp. 1482–1498.
Suh,  J. K., Spilker,  R. L., and Holmes,  M. H., 1991, “A Penalty Finite Element Analysis for Nonlinear Mechanics of Biphasic Hydrated Soft Tissues Under Large Deformation,” Int. J. Numer. Methods Eng., 32, pp. 1411–1439.
Xue, W. M., Mak, A. F. T., Huang, D. T., Hon, Y. C., and Lu, M. W., 1995, “On the Penalty Method of Stokes Equations and Biphasic Mixture Model of Soft Hydrated Tissues,” in: Contemporary Research in Engineering Science, R. C. Batra, ed., Springer-Verlag, New York, pp. 613 –623.
Shaw, D., 1969, Electrophoresis, Academic Press, New York.
Spilker,  R. L., Suh,  J. K., and Mow,  V. C., 1990, “A Finite Element Formulation of the Linear Biphasic Model for Cartilage and Hydrated Soft Tissue: I. Formulation and Validation,” ASME J. Biomech. Eng., 112, pp. 138–146.
Salzstein,  R. A., and Pollack,  S. R., 1987, “Electromechanical Potentials in Cortical Bone — II. Experimental Analysis,” J. Biomech., 20, No. 3, pp. 271–280.


Grahic Jump Location
The finite element mesh for three neighboring osteons, where a=0.93×10−4 m, u0=0.46×10−5 m for the time varying displacement boundary condition. Discrete one-dimensional flow channels superimposed on the mesh are in bold.
Grahic Jump Location
Changes in the normalized drag force and channel fluid velocity in the canaliculi versus canalicular solidity, i.e., the amount of solid filling in the canaliculi. These results were normalized with the corresponding values for the case of no canalicular filling.
Grahic Jump Location
Fluid velocity profile in the three osteons (canalicular filling=0.5) (a) through microporosity matrix with a scaling factor of 1000; (b) in canaliculi with a scaling factor of 5. One could note that microporosity flow patterns were somewhat affected by the presence of the one-dimensional channels and became less radially directed.
Grahic Jump Location
(a) Normalized streaming potential distribution along the line of symmetry predicted by the current model. The magnitude of the potential at the Haversian canal was normalized to be one. The bold segment along the horizontal axis indicated the positions of the Haversian canals. (b) Experimental data reported in Pollack et al. 7 were schematically reproduced. The potential measured for the same osteon during the tensile and compressive phases of dynamic bending. Under tension, the cusp-shaped electrical field was upward. Under compression, the cusp turned downward. The location of the Haversian canal was indicated in bold along the horizontal axis.
Grahic Jump Location
The normalized isopotential contour lines around the three osteons. The magnitude of the potential at the Haversian canal boundary was normalized to be one.




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