0
TECHNICAL PAPERS: Bone/Orthopedic

Micromechanically Based Poroelastic Modeling of Fluid Flow in Haversian Bone

[+] Author and Article Information
C. C. Swan

Civil and Environmental Engineering, University of Iowa, Iowa City, IA 52242

R. S. Lakes

Engineering Physics, University of Wisconsin-Madison

R. A. Brand

Orthopaedic Surgery, University of Iowa, Iowa City, IA 52242

K. J. Stewart

Civil & Environmental Engineering, University of Iowa, Iowa City, IA 52242

J Biomech Eng 125(1), 25-37 (Feb 14, 2003) (13 pages) doi:10.1115/1.1535191 History: Received February 01, 2002; Revised September 01, 2002; Online February 14, 2003
Copyright © 2003 by American Institute of Physics
Your Session has timed out. Please sign back in to continue.

References

Burger,  E. H., Klein-Nulend,  J., van der Plas,  A., and Nijweide,  P. J., 1995, “Function of Osteocytes in Bone–Their Role in Mechanotransduction,” J. Nutr., 125, pp. 2020S–2023S.
Cowin,  S. C., Moss-Salentijn,  L., and Moss,  M. L., 1991, “Candidates for the Mechanosensory System in Bone,” J. Biomech. Eng., 113, pp. 191–197.
Rubin,  C. T., and McLeod,  K. J., 1994, “Promotion of Bony Ingrowth by Frequency-Specific, Low-Amplitude Mechanical Strain,” Clin. Orthop., 298, pp. 165–174.
Qin,  Y. X., McLeod,  K. J., Guilak,  F., Chiang,  F. P., and Rubin,  C. T., 1996, “Correlation of Bony Ingrowth to the Distribution of Stress and Strain Parameters Surrounding a Porous-coated Implant,” J. Orthop. Res., 14, pp. 862–870.
Wolff, J., 1892, “Das Gezetz der Transformation der Knochen,” Verlag von August Hirschwald, Berlin.
Glücksman,  A., 1939, “Studies on Bone Mechanics In Vitro: II. The Role of Tension and Pressure in Chondrogenesis,” J. Anat., 73, pp. 39–55.
Frost,  H. M., 1966, “Bone as a Physiological Tool,” Henry Ford Hosp. Med. J., 14, pp. 63–70.
Lanyon,  L. E., and Smith,  R. N., 1970, “Bone Strain in the Tibia During Normal Quadrupedal Locomotion,” Acta Orthop. Scand. 41, pp. 238–248.
Chamay,  A., and Tschantz,  P., 1972, “Mechanical Influences in Bone Remodeling. Experimental Research on Wolff’s law,” J. Biomech., 5, pp. 173–180.
Hassler,  C. R., Rybicki,  E. F., Cummings,  K. D., and Clark,  L. C., 1977, “Quantitation of Compressive Stress and its Effects Upon Bone Remodeling [proceedings],” Bull Hosp. Jt. Dis. 38, pp. 90–93.
Lanyon,  L. E., and Bourn,  S., 1979, “The Influence of Mechanical Function on the Development and Remodeling of the Tibia. An Experimental Study in Sheep,” J. Bone Jt. Surg., Am. Vol., 61, pp. 263–273.
Frost,  H. M., 1982, “Mechanical Determinants of Bone Modeling,” Metab. Bone Dis. Relat. Res., 4, pp. 217–229.
Lanyon,  L. E., Goodship,  A. E., Pye,  C. J., and MacFie,  J. H., 1982, “Mechanically Adaptive Bone Remodelling,” J. Biomech., 15, pp. 141–154.
Rubin,  C. T., and Lanyon,  L. E., 1984, “Regulation of Bone Formation by Applied Dynamic Loads,” J. Bone Jt. Surg., Am. Vol., 66, pp. 397–402.
Carter,  D. R., Fyhrie,  D. P., and Whalen,  R. T., 1987, “Trabecular Bone Density and Loading History: Regulation of Connective Tissue Biology by Mechanical Energy,” J. Biomech., 20, pp. 785–794.
Yasuda,  L., 1954, “On the Piezoelectric Activity of Bone,” J Jpn Orthop Surg Soc, 28 , pp. 267.
Fukada,  E., and Yasuda,  L., 1957, “On the Piezoelectric Effect of Bone,” J. Phyiol. Soc. Jpn., 12 , p. 1158.
Bassett,  C. A. L., and Becker,  R. O., 1962, “Generation of Electric Potentials in Bone in Response to Mechanical Stress,” Science, 137, pp. 1063–1064.
Piekarski,  K., and Munro,  M., 1977, “Transport Mechanism Operating Between Blood Supply and Osteocytes in Long Bones,” Nature (London), 269, pp. 80–82.
Iannacone,  W., Korostoff,  E., and Pollack,  S. R., 1979, “Microelectrode Study of Stress-Generated Potentials Obtained from Uniform and Nonuniform Compression of Human Bone,” J. Biomed. Mater. Res., 13, pp. 753–763.
Starkebaum,  W., Pollack,  S. R., and Korostoff,  E., 1979, “Microelectrode Studies of Stress-Generated Potentials in Four-point Bending of Bone,” J. Biomed. Mater. Res., 13, pp. 729–751.
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., 20-3, pp. 261–270.
Salzstein,  R. A., and Pollack,  S. R., 1987 “Electromechanical Potentials in Cortical Bone—II. Experimental Analysis,” J. Biomech., 20-3, pp. 271–280.
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, pp. 339–360.
Jacobs,  C. R., Yellowley,  C. E., Davis,  B. R., Zhou,  Z., Cimbala,  J. M., and Donahue,  H. J., 1998, “Differential Effect of Steady Versus Oscillating Flow on Bone Cells,” J. Biomech., 31, pp. 969–976.
Zhang,  D., Weinbaum,  S., and Cowin,  S. C., 1998, “Estimates of the Peak Pressures in Bone Pore Water,” J. Biomech. Eng., 120, pp. 697–703.
Zhang,  D., Weinbaum,  S., and Cowin,  S. C., 1998, “On the Calculation of Bone Pore Water Pressure Due to Mechanical Loading,” Int. J. Solids Struct., 35, pp. 4981–4997.
Cooper,  R. R., Milgram,  J. W., and Robinson,  R. A., 1966, “Morphology of the Osteon. An Electron Microscopic Study,” J. Bone Jt. Surg., Am. Vol., 48, pp. 1239–1271.
Biot,  M. A., 1941, “General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., 12, pp. 155–164.
Biot,  M. A., 1956, “Theory of Propagation of Elastic Waves in a Fluid-saturated Porous Solid. II. Higher Frequency Range,” J. Acoust. Soc. Am., 28-2, pp. 179–191.
Biot,  M. A., and Willis,  D. G., 1957, “The Elastic Coefficients of the Theory of Consolidation,” J. Appl. Mech., 24, pp. 594–601.
Guedes,  J., and Kikuchi,  N., 1991, “Preprocessing and Postprocessing for Materials Based on Homogenization Method and Adaptive Finite Element Methods,” Comput. Methods Appl. Mech. Eng., 83, pp. 143–198.
Suquet, P., 1987, “Elements of Homogenization for Inelastic Solid Mechanics,” in Homogenization Techniques for Composite Media, Sanchez-Palencia, E., and Zaoui, A. (Eds.), Springer-Verlag, pp. 193–278.
Swan,  C. C., 1994, “Techniques for Stress- and Strain-Controlled Homogenization of Inelastic Periodic Composites,” Comput. Methods Appl. Mech. Eng., 117, pp. 249–267.
Abramowitz, M., and Stegun, I. E., 1964, Handbook of Mathematical Functions, National Bureau of Standards, U.S. Department of Commerce.
Scheidegger, A. E., 1957, The Physics of Flow Through Porous Media, MacMillan, New York.
Stewart, K. J., 2000, Deformation Induced Fluid Flow as a Mechanism of Bone Adaptation, M.S. Thesis, The University of Iowa, Iowa City.
Ferry, J. D., 1980, Viscoelastic Properties of Polymers, Wiley, New York.
Cowin,  S. C., Weinbaum,  S., and Zeng,  Y., 1995, “A Case for Bone Canaliculi as the Atomical Site of Strain Generated Potentials,” J. Biomech., 28, pp. 1281–1297.
Garner,  E., Lakes,  R., Lee,  T., Swan,  C., and Brand,  R., 2000, “Viscoelastic Dissipation in Compact Bone: Implications for Stress-Induced Fluid Flow in Bone,” J. Biomech. Eng., 122, pp. 166–172.
Buechner,  P. M., Lakes,  R. S., Swan,  C., and Brand,  R. A., 2001, “A Broadband Viscoelastic Spectroscopic Study of Bovine Bone: Implications for Fluid Flow,” Ann. Biomed. Eng., 29, pp. 719–728.
Rouhana, S. W., Johnson, M. W., Chakkalakal, D. A., Harper, R. A., and Katz, J. L., 1981, “Permeability of Compact Bone.” Joint ASME-ASCE Conference. AMD, 169–172.
Cohen,  J., and Harris,  W. H., 1958, “The Three-Dimensional Anatomy of Haversian Systems,” J. Bone Jt. Surg., Am. Vol., 40, pp. 419–434.
Baltadzhiev,  G., 1994, “Morphology of the Haversian Canal. An Electron Microscopic Study,” Folia Med. (Plovdiv), 36, pp. 21–28.
Hert,  J., Fiala,  P., and Petrtyl,  M., 1994, “Osteon Orientation of the Diaphysis of the Long Bones in Man,” Bone (N.Y.), 15, pp. 269–277.
Petrtyl,  M., Hert,  J., and Fiala,  P., 1996, “Spatial Organization of the Haversian Bone in Man,” J. Biomech., 29, pp. 161–169.
Martin, R. B., and Burr, D. B., 1989, Structure, Function, and Adaptation of Compact Bone, Raven Press, New York.
Tappen,  N. C., 1982, “The Orientation and Spatial Interrelationships of Osteons in Long Bones,” Anat. Rec., 202, p. 187A.
Koltze,  H., 1951, “Studie sur ausseren Form der Osteone,” Z. Anat. Entwicklungsgesch, 115, pp. 584–596.
Gaillard,  P. J., Herrmann-Erlee,  M. P., Hekkelman,  J. W., Burger,  E. H., and Nijweide,  P. J., 1979, “Skeletal Tissue in Culture. Hormonal Regulation of Metabolism and Development,” Clin. Orthop., 142, pp. 196–214.
Nijweide,  P. J., Burger,  E. H., and Feyen,  J. H., 1986, “Cells of Bone: Proliferation, Differentiation, and Hormonal Regulation,” Physiol. Rev., 66, pp. 855–886.
Turner,  C. H., 1999, “Toward a Mathematical Description of Bone Biology: The Principle of Cellular Accommodation,” Calcif. Tissue Int., 65, pp. 466–471.
Lanyon,  L. E., 1992, “The Success and Failure of the Adaptive Response to Functional Load-bearing in Averting Bone Fracture,” Bone (N.Y.), 13, pp. S17–21.
Dieudonne,  S. C., Semeins,  C. M., Goei,  S. W., Vukicevic,  S., Nulend,  J. K., Sampath,  T. K., Helder,  M., and Burger,  E. H., 1994, “Opposite Effects of Osteogenic Protein and Transforming Growth Factor Beta on Chondrogenesis in Cultured Long Bone Rudiments,” J. Bone Miner. Res., 9, pp. 771–780.
Klein-Nulend,  J., Semeins,  C. M., Veldhuijzen,  J. P., and Burger,  E. H., 1993, “Effect of Mechanical Stimulation on the Production of Soluble Bone Factors in Cultured Fetal Mouse Calvariae,” Cell Tissue Res., 271, pp. 513–517.
Salter,  D. M., Wallace,  W. H., Robb,  J. E., Caldwell,  H., and Wright,  M. O., 2000, “Human Bone Cell Hyperpolarization Response to Cyclical Mechanical Strain is Mediated by an Interleukin-1 Beta Autocrine/Paracrine Loop [In Process Citation],” J. Bone Miner. Res., 15, pp. 1746–1755 [MEDLINE record in process].
Skerry,  T. M., 1999, “Identification of Novel Signaling Pathways During Functional Adaptation of the Skeleton to Mechanical Loading: The Role of Glutamate as a Paracrine Signaling Agent in the Skeleton,” J Bone Miner Metab, 17, pp. 66–70.
Sterck,  J. G., Klein-Nulend,  J., Burger,  E. H., and Lips,  P., 1996, “1,25-dihydroxyvitamin D3-mediated Transforming Growth Factor-beta Release is Impaired in Cultured Osteoblasts from Patients with Multiple Pituitary Hormone Deficiencies,” J. Bone Miner. Res., 11, pp. 367–376.
Turner,  C. H., 1992, “Functional Determinants of Bone Structure: Beyond Wolff’s Law of Bone Transformation [editorial],” Bone (N.Y.), 13, pp. 403–409.
Dillaman,  R. M., Roer,  R. D., and Gay,  D. M., 1991, “Fluid Movement in Bone: Theoretical and Empirical,” J. Biomech., 24Suppl 1, pp. 163–177.
Zeng,  Y., Cowin,  S. C., and Weinbaum,  S., 1994, “A Fiber Matrix Model for Fluid Flow and Streaming Potentials in the Canaliculi of an Osteon,” Ann. Biomed. Eng., 22, pp. 280–292.
Turner,  C. H., Anne,  V., and Pidaparti,  R. M., 1997, “A Uniform Strain Criterion for Trabecular Bone Adaptation: Do Continuum-Level Strain Gradients Drive Adaptation?,” J. Biomech., 30, pp. 555–563.
Srinivasan,  S., and Gross,  T. S., 2000, “Canalicular Fluid Flow Induced by Bending of a Long Bone,” Med. Eng. Phys., 22, pp. 127–133.
Cowin,  S. C., and Weinbaum,  S., 1998, “Strain Amplification in the Bone Mechanosensory System,” Am. J. Med. Sci., 316, pp. 184–188.
Reich,  K. M., Gay,  C. V., and Frangos,  J. A., 1990, “Fluid Shear Stress as a Mediator of Osteoblast Cyclic Adenosine Monophosphate Production,” J. Cell Physiol., 143, pp. 100–104.
Klein-Nulend,  J., Semeins,  C. M., Ajubi,  N. E., Nijweide,  P. J., and Burger,  E. H., 1995, “Pulsating Fluid Flow Increases Nitric Oxide (NO) Synthesis by Osteocytes but Not Periosteal Fibroblasts—Correlation with Prostaglandin Upregulation,” Biochem. Biophys. Res. Commun., 217, pp. 640–648.
Hung,  C. T., Pollack,  S. R., Reilly,  T. M., and Brighton,  C. T., 1995, “Real-time Calcium Response of Cultured Bone Cells to Fluid Flow,” Clin. Orthop., 313, pp. 256–69.
Ajubi,  N. E., Klein-Nulend,  J., Nijweide,  P. J., Vrijheid-Lammers,  T., Alblas,  M. J., and Burger,  E. H., 1996, “Pulsating Fluid Flow Increases Prostaglandin Production by Cultured Chicken Osteocytes—a Cytoskeleton-Dependent Process,” Biochem. Biophys. Res. Commun., 225, pp. 62–68.
Hung,  C. T., Allen,  F. D., Pollack,  S. R., and Brighton,  C. T., 1996, “Intracellular Ca2+ Stores and Extracellular Ca2+ are Required in the Real-Time Ca2+ Response of Bone Cells Experiencing Fluid Flow,” J. Biomech., 29, pp. 1411–1417.
Klein-Nulend,  J., Burger,  E. H., Semeins,  C. M., Raisz,  L. G., and Pilbeam,  C. C., 1997, “Pulsating Fluid Flow Stimulates Prostaglandin Release and Inducible Prostaglandin G/H Synthase mRNA Expression in Primary Mouse Bone Cells,” J. Bone Miner. Res., 12, pp. 45–51.
Owan,  I., Burr,  D. B., Turner,  C. H., Qiu,  J., Tu,  Y., Onyia,  J. E., and Duncan,  R. L., 1997, “Mechanotransduction in Bone: Osteoblasts are More Responsive to Fluid Forces than Mechanical Strain,” Am. J. Physiol., 273, pp. C810–815.
Ajubi,  N. E., Klein-Nulend,  J., Alblas,  M. J., Burger,  E. H., and Nijweide,  P. J., 1999, “Signal Transduction Pathways Involved in Fluid Flow-Induced PGE2 Production by Cultured Osteocytes,” Am. J. Physiol., 276, pp. E171–178.
Westbroek,  I., Ajubi,  N. E., Alblas,  M. J., Semeins,  C. M., Klein-Nulend,  J., Burger,  E. H., and Nijweide,  P. J., 2000, “Differential Stimulation of Prostaglandin G/H Synthase-2 in Osteocytes and Other Osteogenic Cells by Pulsating Fluid Flow,” Biochem. Biophys. Res. Commun., 268, pp. 414–9.
Kurokouchi,  K., Jacobs,  C. R., and Donahue,  H. J., 2001, “Oscillating Fluid Flow Inhibits TNF-Alpha-Induced NF-Kappa B Activation via an Ikappa B Kinase Pathway in Osteoblast-Like UMR106 Cells,” J. Biol. Chem., 276, pp. 13499–13504.

Figures

Grahic Jump Location
Three-dimensional idealizations of Haversian bone. a) transverse section with square-packed non-overlapping osteons; b) transverse section with hexagonally packed, overlapping osteons; c) unit cell for non-overlapping osteons; d) unit cell for overlapping osteons.
Grahic Jump Location
a) Idealized transverse section through Haversian bone with lamellar structure neglected and bone matrix treated as linear, isotropic, homogeneous elastic medium; b) finite element mesh of unit cell model with 4% Haversian porosity. To estimate poroelastic model coefficients, five strain-controlled tests were performed on this model: (1) undrained ε̄11≠0; (2) undrained ε̄33≠0; (3) undrained γ̄12≠0; (4) undrained γ̄13≠0; and (5) drained ε̄11≠0.
Grahic Jump Location
a) Finite element model of prismatic cortical bone specimen; b) Haversian canals oriented in alignment with longitudinal axis of specimen; c) Haversian canals oriented transverse to longitudinal axis of bone specimen.
Grahic Jump Location
Computed fluid pressure relaxation responses in the model of cortical bone specimens for both sets of poroelastic properties, and for both longitudinal and transverse orientation of the Haversian canals. A uniaxial stress of 1 MPa was applied to the bone model. When the Haversian canals are oriented longitudinally in the prismatic bone specimen, initial fluid pressures are smaller but pressure relaxation takes longer.
Grahic Jump Location
Computed peak Haversian fluid pressures versus frequency for material assumptions A and B, and both transverse and longitudinal orientation of the osteonal bone in the prismatic specimen model. At each frequency, the computed fluid pressures have been normalized by the peak bone pressure in the corresponding model at that same frequency.
Grahic Jump Location
Computed peak Haversian shear stresses versus frequency for material assumptions A and B, and both transverse and longitudinal orientation of the osteonal bone in the prismatic specimen model. At each frequency, the computed fluid shear stresses have been normalized by the peak bone pressure in the corresponding model at that same frequency.
Grahic Jump Location
Computed peak bone pressures versus frequency for material assumptions A and B, and both longitudinal and transverse orientation of osteonal bone within the prismatic specimen model. For each model, the computed dynamic peak bone pressures have been normalized by the static peak bone pressure for that same model.
Grahic Jump Location
Computed tan δ versus frequency for material assumptions A and B, and both longitudinal and transverse orientation of osteonal bone within the prismatic specimen model. The computed values are compared with experimentally measured tan δ by Garner et al. (2000).

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