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Multiscale Approach to Understand the Multiphysics Phenomena in Bone Adaptation

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Multiscale Computer Modeling in Biomechanics and Biomedical Engineering

Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 14))

Abstract

The ability of bone tissue to adapt itself to its physical environment is the research focus of several teams all over the world. If the physical stimuli playing a role in bone remodelling are often identified, how they act and are converted into a cellular response is still an open question. The aim of this paper is, in a first part, to propose an overview on the physical factors participating in the bone remodelling process. In a second part, we present some recent developments concerning the implications of hydro–electro-chemical couplings that could modify the bone adaptation process. Since the phenomena that are involved in this mechanism are related both to the mechanical solicitations of the tissue and the physical phenomena in the vicinity of bone cells, different scales, from the organ to the cell, should be considered to go deeper in its understanding. That is why a multiscale strategy based on periodic homogenization has been carried out to propagate the multiphysics description at the cellular scale toward the macroscopic scale of the tissue. This multi-level approach is so adapted to connect macroscopic physical information to microscopic phenomena, et vice versa. Thus, using convenient simulations, we have brought a new light on classical interrogations dealing with bone adaptation. These five questions are: i. Can the sole hydro-mechanical coupling describe the poro-mechanical behaviour of bone or should we consider a modified Biot model including electro-chemical effects?; ii. Similarly, is the classical Darcy law sufficient to describe the bone interstitial fluid flow?; iii. What is the nature of the stress-induced electric potentials that can be measured in vivo?; iv. What are the consequences of the electro-chemical couplings on the shear sensitivity of the osteocytes?; v. What are the consequences of the microscopic physico-chemical properties of the bone microstructure on the mass transport within the lacuno-canalicular system? Finally, from these simple model-driven observations, we propose a new perspective to alter the current bone adaptation paradigm.

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References

  1. Adachi, T., Kameo, Y., Hojo, M.: Trabecular bone remodelling simulation considering osteocytic response to fluid-induced shear stress. Philos. T. R. Soc. A 368, 2669–2682 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ager, J.W. III, Balooch, G., Ritchie, R.O: Fracture, aging, and disease in bone. J. Mater. Res. 21, 1878–1892 (2006)

    Google Scholar 

  3. Ahn, A.C., Grodzinsky, A.J: Relevance of collagen piezoelectricity to wolff’s law: a critical review. Med. Eng. Phys. 31, 733–741 (2009)

    Article  Google Scholar 

  4. Ajubi, N.E., Klein-Nulend, J., Nijweide, P.J., Vrijheid-Lammers, T., Alblas, M.J., Burger, E.H: Pulsating fluid flow increases prostaglandin production by cultured chicken osteocytes-a cytoskeleton-dependent process. Biochem. Biophys. Res. Commun. 225, 62–68 (1996)

    Article  Google Scholar 

  5. Anderson, E., Kreuzer, S., Small, O., Knothe Tate, M.: Pairing computational and scaled physical models to determine permeability as a measure of cellular communication in micro- and nano-scale pericellular spaces. Microfluid. Nanofluidics 4, 193–204 (2008)

    Article  Google Scholar 

  6. Anderson, E.J., Knothe Tate, M.L: Idealization of pericellular fluid space geometry and dimension results in a profound underprediction of nano-microscale stresses imparted by fluid drag on osteocytes. J. Biomech. 41, 1736–1746 (2008)

    Article  Google Scholar 

  7. Auriault, J.-L., Adler, P.M.: Taylor dispersion in porous media: analysis by multiple scale expansions. Adv. Water Res. 18, 217–226 (1995)

    Article  Google Scholar 

  8. Auriault, J.-L., Sanchez-Palencia, E.: Etude du comportment macroscopique d’un milieu poreux saturé déformable. J. Mécanique 16, 575–603 (1977)

    MathSciNet  MATH  Google Scholar 

  9. Baron, R., Tross, R., Vignery, A.: Evidence of sequential remodeling in rat trabecular bone—morphology, dynamic histomorphometry, and changes during skeletal maturation. Anat. Rec. 208, 137–145 (1984)

    Article  Google Scholar 

  10. Bassett, C.A.L., Pawluk, R.J., Becker, R.O: Effects of electric currents on bone in vivo. Nature 204, 652–654 (1964)

    Article  Google Scholar 

  11. Baxter, F., Bowen, C., Turner, I., Dent, A.: Electrically active bioceramics: a review of interfacial responses. Ann. Biomed. Eng. 38, 2079–2092 (2010)

    Article  Google Scholar 

  12. Beno, T., Yoon, Y.-J., Cowin, S.C., Fritton, S.P: Estimation of bone permeability using accurate microsctructural measurements. J. Biomech. 39, 2378–2387 (2006)

    Article  Google Scholar 

  13. Biewener, A.A., Taylor, C.R: Bone strain: a determinant of gait and speed. J. Exp. Biol. 123, 383–400 (1986)

    Google Scholar 

  14. Binderman, I., Shimshoni, Z., Somjen, D.: Biochemical pathways involved in the translation of physical stimulus into biological message. Calcif. Tissue Int. 36, S82–S85 (1984)

    Google Scholar 

  15. Biot, M.A: General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941)

    Article  MATH  Google Scholar 

  16. Buckwalter, J.A., Glimcher, M.J., Cooper, R.R., Recker, R.: Bone biology. Part I: Structure, blood supply, cells, matrix, and mineralization. J. Bone Joint Surg. Am. 77, 1256–1275 (1995)

    Google Scholar 

  17. Buckwalter, J.A., Glimcher, M.J., Cooper, R.R., Recker, R.: Bone biology. Part II: Formation, form, modeling, remodeling, and regulation of cell function. J. Bone Joint Surg. Am. 77, 1276–1289 (1995)

    Google Scholar 

  18. Burger, E.H., Klein-Nulend, J.: Mechanotransduction in bone: role of the lacuno-canalicular network. Faseb. J. 13(Suppl), S101–S112 (1999)

    Google Scholar 

  19. Burger, E.H., Klein-Nulend, J., Smit, T.H: Strain-derived canalicular fluid flow regulates osteoclast activity in a remodelling osteon—a proposal. J. Biomech. 36((10), 1453–1459 (2003)

    Article  Google Scholar 

  20. Burr, D.B., Martin, R.B: Calculating the probability that micro-cracks initiate resorption spaces. J. Biomech. 26, 613–616 (1993)

    Article  Google Scholar 

  21. Burr, D.B., Milgrom, C., Fyhrie, D., Forwood, M., Nyska, M., Finestone, A., Hoshaw, S., Saiag, E., Simkin, A.: In vivo measurement of human tibial strains during vigorous activity. Bone 18, 405–410 (1996)

    Article  Google Scholar 

  22. Cann, C.E., Adachi, R.R: Bone resorption and mineral excretion in rats during spaceflight. Am. J. Physiol. 224, R327–331 (1983)

    Google Scholar 

  23. Cochran, G.V.B., Dell, D.G., Palmieri, V.R., Johnson, M.W., Otter, M.W., Kadaba, M.P: An improved design of electrodes for measurement of streaming potentials on wet bone in vitro and in vivo. J. Biomech. 22, 745–750 (1989)

    Article  Google Scholar 

  24. Cowin, S.C: Bone poroelasticity. J. Biomech. 32, 217–238 (1999)

    Article  Google Scholar 

  25. Cowin, S.C: Bone mechanics handbook, 2nd edn. CRC Press, Boca Raton, FL (2001)

    Google Scholar 

  26. Cowin, S.C: Mechanosensation and fluid transport in living bone. J. Musculoskel. Neuron. Interact. 2, 256–260 (2002)

    Google Scholar 

  27. Cowin, S.C., Gailani, G., Benalla, M.: Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones. Philos. T. R. Soc. A 367, 3401–3444 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Crockett, J.C., Rogers, M.J., Coxon, F.P., Hocking, L.J., Helfrich, M.H: Bone remodelling at a glance. J. Cell Sci. 124, 991–998 (2011)

    Article  Google Scholar 

  29. Derjaguin, B.V., Churaev, N., Muller, V.: Surface Forces. Plenum Press, New York (1987)

    Google Scholar 

  30. Duncan, R.L., Turner, C.H: Mechanotransduction and the functional response of bone to mechanical strain. Calcif Tissue Int. 57((5), 344–358 (1995)

    Article  Google Scholar 

  31. Ehrlich, P.J., Lanyon, L.E: Mechanical strain and bone cell function: a review. Osteoporosis Int. 13((9), 688–700 (2002)

    Article  Google Scholar 

  32. Ferretti, M., Muglia, M.A., Remaggi, F., Cane, V., Palumbo, C.: Histomorphometric study on the osteocyte lacuno-canalicular network in animals of different species. II. Parallel-fibered and lamellar bones. Ital. J. Anat. Embryol. 104, 121–131 (1999)

    Google Scholar 

  33. Freemont, A.J: The tissues we deal with (i) bone. Curr. Orthopaed. 12, 181–192 (1998)

    Article  Google Scholar 

  34. Fritton, S.P., Mcleod, K.J., Rubin, C.T: Quantifying the strain history of bone: spatial uniformity and self-similarity of low-magnitude strains. J. Biomech. 33, 317–325 (2000)

    Article  Google Scholar 

  35. Fritton, S.P, Weinbaum, S.: Fluid and solute transport in bone: flow-induced mechanotransduction. Annu. Rev. Fluid Mech. 41, 347–374 (2009)

    Article  Google Scholar 

  36. Frost, H.M: From wolff’s law to the utah paradigm: insights about bone physiology and its clinical applications. Anat. Rec. 262, 398–419 (2001)

    Article  Google Scholar 

  37. Fukada, E., Yasuda, I.: On the piezoelectric effect of bone. J. Phys. Soc. Jpn 12, 1158–1162 (1957)

    Article  Google Scholar 

  38. Gailani, G., Benalla, M., Mahamud, R., Cowin, S.C., Cardoso, L.: Experimental determination of the permeability in the lacunar-canalicular porosity of bone. J. Biomech. Eng. 131((10), 101007 (2009)

    Article  Google Scholar 

  39. Gailani, G., Cowin, S.: Ramp loading in Russian doll poroelasticity. J. Mech. Phys. Sol. 59, 103–120 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Galley, S.A., Michalek, D.J., Donahue, S.W: A fatigue microcrack alters fluid velocities in a computational model of interstitial flow in cortical bone. J. Biomech. 39, 2026–2033 (2006)

    Article  Google Scholar 

  41. Galli, M., Oyen, M.L: Fast identification of poroelastic parameters from indentation tests. Comput. Model. Eng. Sci. 48, 241–269 (2009)

    MathSciNet  MATH  Google Scholar 

  42. Gardinier, J.D., Townend, C.W., Jen, K.-P., Wu, Q., Duncan, R.L., Wang, L.: In situ permeability measurement of the mammalian lacunar-canalicular system. Bone 46, 1075–1081 (2010)

    Article  Google Scholar 

  43. Goulet, G., Coombe, D., Martinuzzi, R., Zernicke, R.: Poroelastic evaluation of fluid movement through the lacunocanalicular system. Ann. biomedical Engineering 37, 1390–1402 (2009)

    Article  Google Scholar 

  44. Gururaja, S., Kim, H., Swan, C., Brand, R., Lakes, R.: Modeling deformation-induced fluid flow in cortical bone’s canalicular-lacunar system. Ann. Biomed. Eng. 33, 7–25 (2005)

    Article  Google Scholar 

  45. Han, J., Fu, J., Schoch, R.B: Molecular sieving using nanofilters: past, present and future. Lab Chip 8, 23–33 (2008)

    Article  Google Scholar 

  46. Han, Y., Cowin, S.C., Schaffler, M.B., Weinbaum, S.: Mechanotransduction and strain amplification in osteocyte cell processes. Proc. Natl. Acad. Sci. U.S.A. 101, 16689–16694 (2004)

    Article  Google Scholar 

  47. Harding, I.S., Rashid, N., Hing, K.A: Surface charge and the effect of excess calcium ions on the hydroxyapatite surface. Biomaterials 26, 6818–6826 (2005)

    Article  Google Scholar 

  48. Hazenberg, J.G., Freeley, M., Foran, E., Lee, T.C., Taylor, D.: Microdamage: a cell transducing mechanism based on ruptured osteocyte processes. J. Biomech. 39, 2096–2103 (2006)

    Article  Google Scholar 

  49. Hert, J., Liskova, M., Landa, J.: Reaction of bone to mechanical stimuli. 1. Continuous and intermittent loading of tibia in rabbit. Folia Morphol. 19, 290–300 (1971)

    Google Scholar 

  50. Hilfiker, A., Kasper, C., Hass, R., Haverich, A.: Mesenchymal stem cells and progenitor cells in connective tissue engineering and regenerative medicine: is there a future for transplantation?. Langenbecks Arch. Surg. 396, 489–497 (2011)

    Article  Google Scholar 

  51. Hill, P.A: Bone remodelling. Brit. J. Orthodont 25, 101–107 (1998)

    Article  Google Scholar 

  52. Hunter, R.J: Zeta Potential in Colloid Science: Principles and Applications. Academic Press, London (1981)

    Google Scholar 

  53. Israelachvili, J.N: Intermolecular and Surface Forces, 3rd edn. Academic Press, New York (2011)

    Google Scholar 

  54. Johnson, D.L., McAllister, T.N., Frangos, J.A: Fluid flow stimulates rapid and continuous release of nitric oxide in osteoblasts. Am. J. Physiol. Endoc. Metob. 271, E205–E208 (1996)

    Google Scholar 

  55. Johnson, M.W., Chakkalakal, D.A., Harper, R.A., Katz, J.L., Rouhana, S.W: Fluid flow in bone in vitro. J. Biomech. 15, 881–885 (1982)

    Article  Google Scholar 

  56. Kaiser, J., Lemaire, T., Naili, S., Komarova, S.V., Sansalone, V.: Calcium fluxes within cortical bone fluid may affect osteocyte mechanosensitivity. Comput. Meth. Biomech. Biomed. Eng. 14, S141–S142 (2011)

    Article  Google Scholar 

  57. Kaiser, J., Lemaire, T., Naili, S., Sansalone, V.: Multiscale modelling of fluid flow in charged porous media including cationic exchanges: application to bone tissues. C.R. Mecanique 337, 768–775 (2009)

    Article  MATH  Google Scholar 

  58. Kaiser, J., Lemaire, T., Naili, S., Sansalone, V., Komarova, S.V.: Do calcium fluxes within cortical bone affect osteocyte mechanosensitivity? J. Theoret. Biol. 303, 75–86 (2012a)

    Google Scholar 

  59. Kaiser, J., Lemaire, T., Naili, S., Sansalone, Lemaire, T.: Effective chemical transport within cortical bone: a comparison between textural and electrochemical effects (submitted, 2012b)

    Google Scholar 

  60. Kameo, Y., Adachi, T., Hojo, M.: Transient response of fluid pressure in a poroelastic material under uniaxial cyclic loading. J. Mech. Phys. Sol. 5, 1794–1805 (2008)

    Article  Google Scholar 

  61. Kameo, Y., Adachi, T., Sato, N., Hojo, M.: Estimation of bone permeability considering the morphology of lacuno-canalicular porosity. J. Mech. Behav. Biomed. Mat. 3, 240–248 (2010)

    Article  Google Scholar 

  62. Kasiri, S., Taylor, D.: A critical distance study of stress concentrations in bone. J. Biomech. 41, 603–609 (2008)

    Article  Google Scholar 

  63. Klein-Nulend, J., Bacabac, R.G., Mullender, M.G: Mechanobiology of bone tissue. Path. Bio. 53, 576–580 (2005)

    Article  Google Scholar 

  64. Klein-Nulend, J., Bakker, A.: Osteocytes: mechanosensors of bone and orchestrators of mechanical adaptation. Clin. Rev. Bone Miner. Metabol. 5, 195–209 (2007)

    Article  Google Scholar 

  65. Klein-Nulend, J., van der Plas, A., Semeins, C.M., Ajubi, N.E., Frangos, J.A., Nijweide, P.J., Burger, E.H: Sensitivity of osteocytes to biomechanical stress in vitro. Faseb J. 9, 441–445 (1995)

    Google Scholar 

  66. Knothe Tate, M.L: Whither flows the fluid in bone? An osteocyte’s perspective. J. Biomech. 36(10), 1409–1424 (2003)

    Article  Google Scholar 

  67. Knothe Tate, M.L., Knothe, U., Niederer, P.: Experimental elucidation of mechanical load-induced fluid flow and its potential role in bone metabolism and functional adaptation. Am. J. Med. Sci. 316, 189–195 (1998a)

    Google Scholar 

  68. Knothe Tate, M.L., Niederer, P., Knothe, U.: In vivo tracer transport through the lacunocanalicular system of rat bone in an environment devoid of mechanical loading. Bone 22, 107–117 (1998b)

    Google Scholar 

  69. Knothe Tate, M.L., Steck, R., Forwood, M.R., Niederer, P.: In vivo demonstration of load-induced fluid flow in the rat tibia and its potential implications for processes associated with functional adaptation. J. Exp. Biol. 203, 2737–2745 (1998c)

    Google Scholar 

  70. Kubo, T.: Piezoelectricity of bone and electrical callus. J. Orthop. Sci. 17, 105–106 (2012)

    Article  Google Scholar 

  71. Lanyon, L.E., Hampson, W.G., Goodship, A.E., Shah, J.S: Bone deformation recorded in vivo from strain gauges attached to the human tibial shaft. Acta Orthop. Scand. 46, 256–268 (1975)

    Article  Google Scholar 

  72. Lanyon, L.E., Rubin, C.T: Static vs dynamic loads as an influence on bone remodelling. J. Biomech. 17(12), 897–905 (1984)

    Article  Google Scholar 

  73. Lemaire, T., Borocin, F., Naili, S.: Mechanotransduction of bone remodelling: role of micro-cracks at the periphery of osteons. C.R. Mecanique 336, 354–362 (2008)

    Article  MATH  Google Scholar 

  74. Lemaire, T., Capiez-Lernout, E., Kaiser, J., Naili, S., Rohan, E., Sansalone, V.: A multiscale theoretical investigation of electric measurements in living bone. Piezo-electricity and electrokinetics. Bull. Math. Biol. 73, 2649–2677 (2011)

    Article  MathSciNet  Google Scholar 

  75. Lemaire, T., Capiez-Lernout, E., Kaiser, J., Naili, S., Sansalone, V.: What is the importance of multiphysical phenomena in bone remodelling signals expression? A multiscale perspective. J. Mech. Behav. Biomed. Mat. 4, 909–920 (2011b)

    Google Scholar 

  76. Lemaire, T., Kaiser, J., Naili, S., Sansalone, V.: Modelling of the transport in charged porous media including ionic exchanges. Mech. Res. Commun. 37, 495–499 (2010a)

    Google Scholar 

  77. Lemaire, T., Kaiser, J., Sansalone, V., Rohan, E., Naili, S.: What is the nature of bone in vivo electricity? Comput. Meth. Biomech. Biomed. Eng. 14, S143–S144 (2011c)

    Google Scholar 

  78. Lemaire, T., Lemonnier, S., Naili, S.: On the paradoxical determinations of the lacuno-canalicular permeability of bone. Biomech. Model. Mechanobiol. 11, 933–946 (2012)

    Google Scholar 

  79. Lemaire, T., Moyne, C., Stemmelen, D.: Imbibition test in a clay powder (mx-80 bentonite). Appl. Clay Sci. 26, 235–248 (2004)

    Article  Google Scholar 

  80. Lemaire, T., Moyne, C., Stemmelen, D.: Modelling of electro-osmosis in clayey materials including ph effects. Phys. Chem. Earth 32, 441–452 (2007)

    Article  Google Scholar 

  81. Lemaire, T., Moyne, C., Stemmelen, D., Murad, M.A.: Electro-chemo-mechanical couplings in swelling clays derived by homogenization: electroviscous effects and onsager’s relations. In: Poromechanics II, proceedings of the second Biot conference on poromechanics, Grenoble, France, pp. 489–500. Balkema Publishers, Lisse (2002)

    Google Scholar 

  82. Lemaire, T., Naili, S.: Stimuli physiques du remodelage osseux. In: Reconstruction osseuse et cutanée: Biomécanique et Techniques de l’Ingénieur, pp. 57–71. Sauramps Medical, Montpellier (2008)

    Google Scholar 

  83. Lemaire, T., Naili, S.: Possible role of calcium permselectivity in bone adaptation. Med. Hyp. 78, 367–369 (2012)

    Article  Google Scholar 

  84. Lemaire, T., Naili, S., Rémond, A.: Multiscale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone. Biomech. Model. Mechanobiol. 5(1), 39–52 (2006)

    Article  Google Scholar 

  85. Lemaire, T., Naili, S., Rémond, A.: Study of the influence of fibrous pericellular matrix in the cortical interstitial fluid movement with hydroelectrochemical effects. J. Biomech. Eng. 130(1), 011001 (2008)

    Article  Google Scholar 

  86. Lemaire, T., Sansalone, V., Naili, S.: Multiphysical modelling of fluid transport through osteo-articular media. An. Acad. Bras. Cienc. 82, 127–144 (2010)

    Article  MATH  Google Scholar 

  87. Lemaire, V., Tobin, F.L., Greller, L.D., Cho, C.R., Suva, L.J.: Modeling the interactions between osteoblast and osteoclast activities in bone remodeling. J. Theoret. Biol. 229, 293–309 (2004b)

    Google Scholar 

  88. Low, P.F: The clay/water interface and its role in the environment. Prog. Colloid Polym. Sci. 95, 98–107 (1994)

    Article  Google Scholar 

  89. Mak, A.F.T., Qin, L., Hung, L.K., Cheng, C.W., Tin, C.F: A histomorphometric observation of flows in cortical bone under dynamic loading. Microvasc. Res. 59, 290–300 (2000)

    Article  Google Scholar 

  90. Malone, A.M.D., Anderson, C.T., Tummala, P., Kwon, R.Y., Johnston, T.R., Stearns, T., Jacobs, C.R.: Primary cilia mediate mechanosensing in bone cells by a calcium-independent mechanism. Proc. Natl. Acad. Sci. U.S.A. 104, 13325–13330 (2007)

    Article  Google Scholar 

  91. Marenzana, M., Shipley, A.M., Squitiero, P., Kunkel, J.G., Rubinacci, A.: Bone as an ion exchange organ: evidence for instantaneous cell-dependent calcium efflux from bone not due to resorption. Bone 37, 545–554 (2005)

    Article  Google Scholar 

  92. Martin, R.B., Burr, D.B., Sharkey, N.A: Skeletal Tissue Mechanics, 1st edn. Springer, New York (1998)

    Google Scholar 

  93. Mattern, K.J., Nakornchai, C., Deen, W.M: Darcy permeability of agarose-glycosaminoglycan gels analyzed using fiber-mixture and donnan models. Biophys. J. 95, 648–656 (2008)

    Article  Google Scholar 

  94. Mbuyi-Muamba, J.-M., Dequeker, J., Gevers, G.: Biochemistry of bone. Baillière Clin. Rheum. 2, 63–101 (1988)

    Article  Google Scholar 

  95. Mc Elhaney, J.H: The charge distribution on the human femur due to load. J. Bone Joint Surg. 49, 1561–1571 (1967)

    Google Scholar 

  96. McAllister, T.N., Frangos, J.A: Steady and transient fluid shear stress stimulate no release in osteoblasts through distinct biochemical pathways. J. Bone Miner. Res. 14, 930–936 (1999)

    Article  Google Scholar 

  97. McNamara, L.M., Majeska, R.J., Weinbaum, S., Friedrich, V., Schaffler, M.B: Attachment of osteocyte cell processes to the bone matrix. Anat. Rec. 292, 355–363 (2009)

    Article  Google Scholar 

  98. Messer, H.H: Bone cell membranes. Clin. Orthop. Relat. Res. 166, 256–276 (1982)

    Google Scholar 

  99. Miara, B., Rohan, E., Zidi, M., Labat, B.: Piezomaterials for bone regeneration design—homogenization approach. J. Mech. Phys. Sol. 53, 2529–2556 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  100. Mishra, S., Knothe Tate, M.L: Effect of lacunocanalicular architecture on hydraulic conductance in bone tissue: implications for bone health and evolution. Anat. Rec. A 273, 752–762 (2003)

    Article  Google Scholar 

  101. Morey, E.R., Baylink, D.J: Inhibition of bone formation during space flight. Science 201, 1138–1141 (1978)

    Article  Google Scholar 

  102. Moyne, C., Murad, M.A: Electro-chemo-mechanical couplings in swelling clays derived from a micro/macro-homogenization procedure. Int. J. Sol. Struct. 39, 6159–6190 (2002)

    Article  MATH  Google Scholar 

  103. Muir, P., Sample, S.J, Barrett, J.G., McCarthy, J., Vanderby, R. Jr., Markel, M.D., Prokuski, L.J., Kalscheur, V.L: Effect of fatigue loading and associated matrix microdamage on bone blood flow and interstitial fluid flow. Bone 40, 948–956 (2007)

    Google Scholar 

  104. Nagatomi, J., Arulanandam, B.P., Metzger, D.W., Meunier, A., Bizios, R.: Frequency- and duration-dependent effects of cyclic pressure on select bone cell functions. Tissue Eng. 7, 717–728 (2001)

    Article  Google Scholar 

  105. Nagatomi, J., Arulanandam, B.P., Metzger, D.W., Meunier, A., Bizios, R.: Effects of cyclic pressure on bone marrow cell cultures. J. Biomech. Eng. 124, 308–314 (2002)

    Article  Google Scholar 

  106. M. Nakamura, R. Hiratai, and K. Yamashita. Bone mineral as an electrical energy reservoir. J. Biomed. Mater. Res. A, 100A: 1368–1374, 2012.

    Google Scholar 

  107. Nakamura, S., Kobayashi, T., Nakamura, M., Yamashita, K.: Enhanced in vivo responses of osteoblasts in electrostatically activated zones by hydroxyapatite electrets. J. Mater. Sci. Mater. M. 20, 99–103 (2009)

    Article  Google Scholar 

  108. Nguyen, V.-H., Lemaire, T., Naili, S.: Anisotropic poroelastic hollow cylinders with damaged periphery under harminically axial loading: relevance to bone remodelling. Multidisc. Model. Mater. Struct. 5, 205–222 (2009)

    Google Scholar 

  109. Nguyen, V.-H., Lemaire, T., Naili, S.: Poroelastic behaviour of cortical bone under harmonic axial loading: theoretical study at the osteonal tissue scale. Med. Eng. Phys. 32, 384–390 (2010)

    Article  Google Scholar 

  110. Nguyen, V.-H., Lemaire, T., Naili, S.: Influence of interstitial bone micro-cracks on strain-induced fluid flow. Biomech. Model. Mechanobiol. 10, 963–972 (2011)

    Article  Google Scholar 

  111. Noble, B.: Bone microdamage and cell apoptotsis. Europ. Cells Mater. 6, 46–56 (2003)

    Google Scholar 

  112. Noris-Suárez, K., Lira-Olivares, J., Ferreira, A.M., Feijoo, J.L., Suárez, N., Hernández, M.C., Barrios, E.: In vitro deposition of hydroxyapatite on cortical bone collagen stimulated by deformation-induced piezoelectricity. Biomacromolecules 8, 941–948 (2007)

    Article  Google Scholar 

  113. Norman, T.L., Wang, Z.: Microdamage of human cortical bone: incidence and morphology in long bones. Bone 20, 375–379 (1997)

    Article  Google Scholar 

  114. O’Brien, F.J., Taylor, D., Dickson, G.R., Lee, T.C.: Visualisation of three-dimensional micro-cracks in compact bone. J. Ana. 197, 413–420 (2000)

    Article  Google Scholar 

  115. C. Oddou, T. Lemaire, J. Pierre, and B. David. Hydrodynamics in porous media with applications to tissue engineering. In K. Vafai, editor, Porous media: applications in biological systems and biotechnology, pages 75–119. CRC Press, 2011.

    Google Scholar 

  116. Otter, M., Shoenung, J., Williams, W.S: Evidence for different sources of stress-generated potentials in wet and dry bone. J. orthop. Res. 3, 321–324 (1985)

    Article  Google Scholar 

  117. Otter, M.W., Palmieri, V.R., Wu, D.D., Seiz, K.G., MacGinitie, L.A., Cochran, G.V.B: A comparative analysis of streaming potentials in vivo and in vitro. J. Orthop. Res. 10, 710–719 (1992)

    Article  Google Scholar 

  118. Oyen, M.L: Poroelastic nanoindentation responses of hydrated bone. J. Mater. Res. 23, 1307–1314 (2008)

    Article  Google Scholar 

  119. Petrov, N., Pollack, S.R: Comparative analysis of diffusive and stress induced nutrient transport efficiency in the lacunar-canalicular system of osteons. Biorheology 40, 347–353 (2003)

    Google Scholar 

  120. Piccolino, M.: Animal electricity and the birth of electrophysiology: the legacy of luigi galvani. Brain Res. Bull. 46, 381–407 (1998)

    Article  Google Scholar 

  121. Piekarski, K., Munro, M.: Transport mechanism operating between blood supply and osteocytes in long bones. Nature 269, 80–82 (1977)

    Article  Google Scholar 

  122. Plecis, A., Schoch, R.B., Renaud, P.: Ionic transport phenomena in nanofluidics: experimental and theoretical study of the exclusion-enrichment effect on a chip. Nano Lett. 5, 1147–1155 (2005)

    Article  Google Scholar 

  123. Pollack, S.R., Petrov, N., Salzstein, R., Brankov, G., Blagoeva, R.: An anatomical model for streaming potentials in osteons. J. Biomech. 17, 627–636 (1984)

    Article  Google Scholar 

  124. Price, C., Zhou, X., Li, W., Wang, L.: Real-time measurement of solute transport within the lacunar-canalicular system of mechanically loaded bone: direct evidence for load-induced fluid flow. J. Bone Miner. Res. 26, 277–285 (2011)

    Article  Google Scholar 

  125. Qing, H., Ardeshirpour, L., Divieti Pajevic, P., Dusevich, V., Jähn, K., Kato, S., Wysolmerski, J., Bonewald, L.F: Demonstration of osteocytic perilacunar/canalicular remodeling in mice during lactation. J. Bone Miner. Res. 27, 1018–1029 (2012)

    Article  Google Scholar 

  126. Qing, H., Bonewald, L.F: Osteocyte remodeling of the perilacunar/canalicular matrix. Int. J. Oral Sci. 1, 59–65 (2009)

    Article  Google Scholar 

  127. K.M. Reich and J.A. Frangos. Effect of flow on prostaglandin e2 and inositol triphosphate levels in osteoblasts. Am. J. Physiol., 261: C428–432, 1991.

    Google Scholar 

  128. Reich, K.M., Frangos, J.A.: Protein kinase c mediates flow-induced prostaglandin e2 production in osteoblasts. Calcif. Tissue Int. 52, 62–66 (1993)

    Article  Google Scholar 

  129. Reilly, G.C., Knapp, H.F., Stemmer, A., Niederer, P., Knothe Tate, M.L: Investigation of the morphology of the lacunocanalicular system of cortical bone using atomic force microscopy. Ann. Biomed. Eng. 29, 1074–1081 (2001)

    Article  Google Scholar 

  130. Remaggi, F., Cane, V., Palumbo, C., Ferretti, M.: Histomorphometric study on the osteocyte lacuno-canalicular network in animals of different species. I. Woven-fibered and parallel-fibered bones. Ital. J. Anat. Embryol. 103, 145–155 (1998)

    Google Scholar 

  131. Rémond, A., Naili, S., Lemaire, T.: Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study. Biomech. Model. Mechanobiol. 7, 487–495 (2008)

    Article  Google Scholar 

  132. Rohan, E., Naili, S., Cimrman, R., Lemaire, T.: Multiscale modelling of a uid saturated medium with double porosity: relevance to the compact bone. J. Mech. Phys. Sol. 60, 857–881 (2012)

    Article  MathSciNet  Google Scholar 

  133. Rubin, C.T: Skeletal strain and the functional significance of bone architecture. Calcif. Tissue Int. 36, S11–S18 (1984)

    Article  Google Scholar 

  134. Rubin, C.T., Lanyon, L.E: Limb mechanics as a function of speed and gait: a study of functional strains in the radius and tibia of horse and dog. J. Exp. Biol. 101, 187–211 (1982)

    Google Scholar 

  135. Rubin, C.T., Lanyon, L.E: Regulation of bone formation by applied dynamic loads. J. Bone Joint Surg. Am. 66, 397–402 (1984)

    Google Scholar 

  136. Rubin, C.T., Lanyon, L.E: Regulation of bone mass by mechanical strain magnitude. Calcif. Tissue Int. 37, 411–417 (1985)

    Article  Google Scholar 

  137. Ruff, C., Holt, B., Trinkaus, E.: Who’s afraid of the big bad wolff?: ”wolff’s law” and bone functional adaptation. Am. J. Phys. Anthropol. 129, 484–498 (2006)

    Article  Google Scholar 

  138. Salzstein, R.A., Pollack, S.R: Electromechanical potentials in cortical bone-ii: experimental analysis. J. Biomech. 20, 271–280 (1987)

    Article  Google Scholar 

  139. Salzstein, R.A., Pollack, S.R., Mak, A.F.T., Petrov, N.: Electromechanical potentials in cortical bone. I: a continuum approach. J. Biomech. 20, 261–270 (1987)

    Article  Google Scholar 

  140. Schaffer, M.B., Choi, K., Milgrom, C.: Aging and matrix microdamage accumulation in human compact bone. Bone 17, 521–525 (1995)

    Article  Google Scholar 

  141. Schimdt, S.M., McCready, M.J., Ostafin, A.E: Effect of oscillationg fluid shear on solute transport in cortical bone. J. Biomech. 28, 2337–2343 (2005)

    Article  Google Scholar 

  142. Sikavitsas, V.I., Temenoff, J.S., Mikos, A.G: Biomaterials and bone mechanotransduction. Biomaterials 22, 2581–2593 (2001)

    Article  Google Scholar 

  143. Skerry, T.M., Bitenski, L., Chayen, J., Lanyon, L.E: Early strain-related changes in enzyme activity in osteocytes following bone loading in vivo. J. Bone Miner. Res. 4, 783–788 (1989)

    Article  Google Scholar 

  144. Smit, T.H., Huyghe, J.M., Cowin, S.C: Estimation of the poroelastic parameters of cortical bone. J. Biomech. 35, 829–835 (2002)

    Article  Google Scholar 

  145. Spencer, H.: First Principles. Williams and Norgate, 2nd edn, London (1867)

    Google Scholar 

  146. Sposito, G.: The Surface Chemistry of Soils. Oxford University Press, Oxford (1981)

    Google Scholar 

  147. Tami, A.E., Schaffler, M.B., Knothe Tate, M.L: Probing the tissue to subcellular level structure underlying bone’s molecular sieving function. Biorheology 40, 577–590 (2003)

    Google Scholar 

  148. Tatsumi, S., Ishii, K., Amizuka, N., Li, M., Kobayashi, T., Kohno, K., Ito, M., Takeshita, S., Ikeda, K.: Targeted ablation of osteocytes induces osteoporosis with defective mechanotransduction. Cell Metab. 5, 464–475 (2007)

    Article  Google Scholar 

  149. Turner, C.H., Yoshikawa, T., Forwood, M.R., Sun, T.C., Burr, D.B: High frequency components of bone strain in dogs measured during various activities. J. Biomech. 28(1), 39–44 (1995)

    Article  Google Scholar 

  150. van Oers, R.F.M., Ruimerman, R., Tanck, E., Hilbers, P.A.J., Huiskes, R.: A unified theory for osteonal and hemi-osteonal remodeling. Bone 42, 250–259 (2008)

    Article  Google Scholar 

  151. Verborgt, O., Tatton, N.A., Majeska, R.J., Schaffler, M.B: Spatial distribution of bax and bcl-2 in osteocytes after bone fatigue: complementary roles in bone remodeling regulation?. J. Bone Miner. Res. 17, 907–914 (2002)

    Article  Google Scholar 

  152. Wang, L., Cowin, S.C., Weinbaum, S., Fritton, S.P: Modeling tracer transport in an osteon under cyclic loading. Ann. Biomed. Eng. 28, 1200–1209 (2000)

    Article  Google Scholar 

  153. Wang, L., Fritton, S.P., Cowin, S.C., Weinbaum, S.: Fluid pressure relaxation depends upon osteonal microstructure: modeling an oscillatory bending experiment. J. Biomech. 32, 663–672 (1999)

    Article  Google Scholar 

  154. Wang, L., Fritton, S.P., Weinbaum, S., Cowin, S.C: On bone adaptation due to venous stasis. J. Biomech. 36, 1439–1451 (2003)

    Article  Google Scholar 

  155. Wang, L., Wang, Y., Han, H., Henderson, S.C., Majeska, R.J., Weinbaum, S., Scaffler, M.B: In situ measurement of solute transport in the bone lacunar-canalicular system. Proc. Natl Acad. Sci. U.S.A. 102, 11911–11916 (2005)

    Article  Google Scholar 

  156. Wang, Y., McNamara, L.M., Schaffler, M.B., Weinbaum, S.: A model for the role of integrins in flow induced mechanotransduction in osteocytes. Proc. Natl Acad. Sci. U.S.A. 104, 15941–15946 (2007)

    Article  Google Scholar 

  157. Webster, D., Müller, R.: In silico models of bone remodeling from macro to nano-from organ to cell. WIREs Syst. Biol. Med. 3, 241–251 (2011)

    Article  Google Scholar 

  158. Weinbaum, S., Cowin, S.C., Zeng, Y.: A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J. Biomech. 27, 339–360 (1994)

    Article  Google Scholar 

  159. Weinbaum, S., Duan, Y., Thi, M., You, L.: An integrative review of mechanotransduction in endothelial, epithelial (renal) and dendritic cells (osteocytes). Cell Molec. Bioeng. 4, 510–537 (2011)

    Article  Google Scholar 

  160. Westbroek, I., Ajubi, N.E., Ablas, M.J., Semeins, C.M., Klein-Nulend, J., Burger, E.H., Nijweide, P.J: Differential stimulation of prostaglandin g/h synthase-2 in osteocytes and other osteogenic cells by pulsating fluid flow. Biochem. Biophys. Res. Commun. 268, 414–419 (2000)

    Article  Google Scholar 

  161. Williams, J.L., Iannotti, J.P., Ham, A., Bleuit, J., Chen, J.H: Effects of fluid shear stress on bone cells. Biorheology 31, 163–170 (1994)

    Google Scholar 

  162. Wolff, J.: Das Gesetz der Transformation der Knochen. Hirschwald, Berlin (1892)

    Google Scholar 

  163. Yamashita, K., Oikawa, N., Umegaki, T.: Acceleration and deceleration of bone-like crystal growth on ceramic hydroxyapatite by electric poling. Chem. Mater. 8, 2697–2700 (1996)

    Article  Google Scholar 

  164. Yasuda, I.: Piezoelectricity of living bone. J. Kyoto Pref. Univ. Med. 53, 2019–2024 (1964)

    Google Scholar 

  165. You, L., Cowin, S.C., Schaffler, M.B., Weinbaum, S.: A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J. Biomech. 34, 1375–1386 (2001)

    Article  Google Scholar 

  166. You, L.D., Weinbaum, S., Cowin, S.C., Schaffler, M.B: Ultrastructure of the osteocyte process and its pericellular matrix. Anat. Rec. 278, 505–513 (2004)

    Article  Google Scholar 

  167. Zhang, D., Weinbaum, S., Cowin S., C.: On the calculation of bone pore water pressure due to mechanical loading. Int. J. Sol. Struct. 35, 4981–4997 (1998)

    Article  MATH  Google Scholar 

  168. Zhang, D., Weinbaum, S., Cowin S., C.: Estimates of the peak pressures in bone pore water. J. Biomech. Eng. 120, 697–703 (1998)

    Article  Google Scholar 

  169. Zhou, X., Novotny, J., Wang, L.: Modeling fluorescence recovery after photobleaching in loaded bone: potential applications in measuring fluid and solute transport in the osteocytic lacunar-canalicular system. Ann. Biomed. Eng. 36, 1961–1977 (2008)

    Article  Google Scholar 

  170. Zhou, X., Novotny, J.E., Wang, L.: Anatomic variations of the lacunar-canalicular system influence solute transport in bone. Bone 45, 704–710 (2009)

    Article  Google Scholar 

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Lemaire, T., Naili, S. (2013). Multiscale Approach to Understand the Multiphysics Phenomena in Bone Adaptation. In: Gefen, A. (eds) Multiscale Computer Modeling in Biomechanics and Biomedical Engineering. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/8415_2012_149

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