Skip to main content
SpringerLink
Log in

Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu

A multi-parametric sensitivity analysis

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells’ metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte’s dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abdulagatov IM, Zeinalova AB, Azizov ND (2006) Viscosity of aqueous electrolyte solutions at high temperatures and high pressures. Viscosity B-coefficient. Sodium iodide. J Chem Eng Data 51: 1645–1659

    Article  Google Scholar 

  • Adachi T, Aonuma Y, Ito S-I, Tanaka M, Hojo M, Takano-Yamamoto T, Kamioka H (2009a) Osteocyte calcium signaling response to bone matrix deformation. J Biomech 42(1): 2507–2512

    Article  Google Scholar 

  • Adachi T, Aonuma Y, Tanaka M, Hojo M, Takano-Yamamoto T, Kamioka H (2009b) Calcium response in single osteocytes to locally applied mechanical stimulus: Differences in cell process and cell body. J Biomech 42(12): 1989–1995

    Article  Google Scholar 

  • Allen FD, Hung CT, Pollack SR, Brighton CT (2000) Serum modulates the intracellular calcium response of primary cultured bone cells to shear flow. J Biomech 33: 1585–1591

    Article  Google Scholar 

  • Beno T, Yoon YJ, Cowin SC, Fritton SP (2006) Estimation of bone permeability using accurate microstructural measurements. J Biomech 39: 2378–2387

    Article  Google Scholar 

  • Berretta DA, Pollack SR (1986) Ion concentration effects on the zeta potential of bone. J Orthop Res 4: 337–345

    Article  Google Scholar 

  • Bianchetti MG, Simonetti GD, Bettinelli A (2009) Body fluids and salt metabolism—part I. Italian J Pediatr 35(1): 1–6

    Article  Google Scholar 

  • Bluhm J, deBoer R (1997) The volume fraction concept in the porous media theory. Z Angew Math Mech 77(8): 563–577

    Article  MathSciNet  MATH  Google Scholar 

  • Bonfield W, Li CH (1968) The temperature dependence of the deformation of bone. J Biomech 1: 323–329

    Article  Google Scholar 

  • Buckwalter JA, Glimcher MJ, Cooper RR, Recker R (1995a) Bone biology part I: structure, blood supply, cells, matrix, and mineralization. J Bone Joint Surg 77(A8): 1256–1275

    Google Scholar 

  • Buckwalter JA, Glimcher MJ, Cooper RR, Recker R (1995b) Bone biology part II: formation, form, modeling, remodeling, and regulation of cell function. J Bone Joint Surg 77(A8): 1276–1289

    Google Scholar 

  • Carbone KD, Barrow LD, Bush AJ, Boatright MD, Michelson JA, Pitts KA, Pintea VN, Kang AH, Watsky MA (2005) Effects of a low sodium diet on bone metabolism. J Bone Miner Metab 23: 506–513

    Article  Google Scholar 

  • Catenaccio A, Daruich Y, Magallanes C (2003) Biomimetic modeling and three-dimension reconstruction of the artificial bone. Chem Phys Lett 367: 669–671

    Article  Google Scholar 

  • Chien SC, Ou CY, Wang MK (2009) Injection of saline solutions to improve the electro-osmotic pressure and consolidation of foundation soil. Appl Clay Sci 44(3–4): 218–224

    Article  Google Scholar 

  • Choi J, Hulseapple SM, Conklin MH, Harvey JW (1988) Modeling CO2 degassing and pH in a stream-aquifer system. J Hydrol 209(1–4): 297–310

    Google Scholar 

  • Cowin SC (2001) In: Bone mechanics, second edition. CRC Press LLC, Boca Raton

  • Fernández DP, Mulev Y, Goodwin ARH, Levelt Sengers JMH (1995) A database for the static dielectric constant of water and steam. J Phys Chem Ref Data 24(1): 33–69

    Article  Google Scholar 

  • Friedman A (2010) Fluid and electrolyte therapy: a primer. Pediatr Nephrol 25: 843–846

    Article  Google Scholar 

  • Friend JP, Hunter RJ (1970) Vermiculite as a model system in the testing of double layer theory. Clays Clay Miner 18: 275–283

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Gardinier JD, Townend CW, Jen KP, Wu Q, Duncan RL, Wang L (2010) In situ measurement of the mammalian lacunar-canalicular system. Bone 46: 1075–1081

    Article  Google Scholar 

  • Goldsack DE, Franchetto RC (1977a) The viscosity of concentrated electrolyte solutions. I.Concentration dependence at fixed temperature. Can J Chem 55: 1062–1072

    Article  Google Scholar 

  • Goldsack DE, Franchetto RC (1977b) The viscosity of concentrated electrolyte solutions. III. A mixture law. Electrochimica Acta 22(11): 1287–1294

    Article  Google Scholar 

  • Goldsack DE, Franchetto RC (1978) The viscosity of concentrated electrolyte solutions. II. Temperature dependence. Can J Chem 56: 1442–1450

    Article  Google Scholar 

  • Han Y, Cowin SC, Schaffler MB, Weinbaum S (2004) Mechanotransduction and strain amplification in osteocyte cell processes. P Natl Acad Sci USA 101(47): 16689–16694

    Article  Google Scholar 

  • Haut Donahue TL, Haut TR, Yellowley CE, Donahue HJ, Jacobs CR (2003) Mechanosensitivity of bone cells to oscillating fluid flow induced shear stress may be modulated by chemotransport. J Biomech 36: 1363–1371

    Article  Google Scholar 

  • Heaney RP (2006) Role of dietary sodium in osteoporosis. J Am Coll Nutr 3(3): 271S–276S

    Google Scholar 

  • Herr AE, Molho JI, Santiago JG, Mungal MG, Kenny TW, Garguilo MG (2000) Electroosmotic capillary flow with nonuniform zeta potential. Anal Chem 72: 1053–1057

    Article  Google Scholar 

  • Hunter RJ (2001) Foundations of colloid science, 2nd edn. Oxford universtiy press, Oxford

    Google Scholar 

  • Jacobasch HJ, Bauböck G, Schurz J (1985) Problems and results of zeta-potential measurements on fibers. Colloid Polym Sci 263: 3–24

    Article  Google Scholar 

  • Kaatze U, Pottel R (1992) Dielectric properties of organic solute/water mixtures. Hydrophobic hydration and relaxation. J Mol Liq 52: 181–210

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Kaltreider NL, Meneely GR, Allen JR, Bale WF (1941) Determination of the volume of the extracellular fluid of the body with radioactive sodium. J Exp Med 74(6): 569–590

    Article  Google Scholar 

  • Kestin J, Khalifa HE, Correia RJ (1981a) Tables of the dynamic and kinematic viscosity of aqueous kcl solutions in the temperature range 25–150 °C and the pressure range 0.1–35 MPa. J Phys Chem Ref Data 10(1): 57–70

    Article  Google Scholar 

  • Kestin J, Khalifa HE, Correia RJ (1981b) Tables of the dynamic and kinematic viscosity of aqueous nacl solutions in the temperature range 25−150°C and the pressure range 0.1–35 MPa. J Phys Chem Ref Data 10(1): 71–87

    Article  Google Scholar 

  • Kim YW, Kim JJ, Kim YH, Rho JY (2002) Effects of organic matrix proteins on the interfacial structure at the bone-biocompatible nacre interface in vitro. Biomaterials 23: 2089–2096

    Article  Google Scholar 

  • Klein-Nulend J, Nijweide PJ, Burger EH (2003) Osteocyte and bone structure. Curr Osteoporos Rep 1(1): 5–10

    Article  Google Scholar 

  • Knothe Tate ML (2003) Whither flows the fluid in bone? An osteocyte’s perspective. J Biomech 36: 1409–1424

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lemaire T, Naïli S, Rémond A (2008) Study of the influence of fibrous pericellular matrix in the cortical interstitial fluid movement with hydroelectrochemical effects. J Biomech Eng 130: 111–011001

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lemaire T, Sansalone V, Naili S (2010b) Multiphysical modelling of fluid transport through osteo-articular media. Ann Brazilian Acad Sci 82(1): 127–144

    Article  MATH  Google Scholar 

  • Lemaire T, Capiez-Lernout E, Kaiser J, Naïli S, Rohan E, Sansalone V (2011a) A multiscale theoretical investigation of electric measurements in living bone piezoelectricity and electrokinetics. Bull Math Biol 73(11): 2649–2677

    Article  MathSciNet  Google Scholar 

  • Lemaire T, Capiez-Lernout E, Kaiser J, Naili S, Sansalone V (2011b) What is the importance of multiphysical phenomena in bone remodelling signals expression? A multiscale perspective. J Mech Behav Biomed Mater 4(6): 909–920

    Article  Google Scholar 

  • Lemaire T, Lemonnier S, Naili S et al (2012) On the paradoxical determinations of the lacuno-canalicular permeability of bone. Biomech Model Mechanobiol. doi:10.1007/s10237-011-0363-6

  • Lemonnier S, Naili S, Oddou C, Lemaire T (2011) Numerical determination of the lacuno-canalicular permeability of bone. Comput Methods Biomech Biomed Eng 14: 133–135

    Article  Google Scholar 

  • Martin RB. Sharkey NA (2001) Muchanical effects of post mortem changes, preservation, and allograft bone treatment. In: Cowin SC (ed) Bone mechanics handbook, Chapter 20. CRC Press, Boca Ralon, FL

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

    Article  Google Scholar 

  • Matsumoto M, Miyake T, Noshi H, Kambara M, Konishi K (1989) Zeta potential studies on the adsorption of proteins on a synthetic hydroxyapatite. Coll Surf 40: 77–84

    Article  Google Scholar 

  • Mbuyi-Muamba JM, Dequeker J, Gevers G (1988) Biochemistry of bone. Baillière’s Clin Rheum 2: 63–101

    Article  Google Scholar 

  • McDonald F (2004) Ion channels in osteoblasts: a story of two intracellular organelles. Surg J R Coll Surg E 2(2): 63–69

    Google Scholar 

  • McElhaney JH (1967) The charge distribution of the human femur due to load. J Bone Joint Surg 49(A(8)): 1561–1571

    Google Scholar 

  • Messer HH (1982) Bone cell membranes. Clin Orthop Relat Res 166: 256–276

    Google Scholar 

  • Mohajeri A, Narsilio GA, Pivonka P, Smith DW (2010) Numerical estimation of effective diffusion coefficients for charged porous materials based on micro-scale analyses. Comput Geotech 37(3): 280–287

    Article  Google Scholar 

  • Monkos K (1996) Viscosity of bovine serum albumin aqueous solutions as a function of temperature and concentration. Int J Biol Macromol 18(1–2): 61–68

    Article  Google Scholar 

  • Mullender MG, Huiskes R, Versleyen H, Buma P (1996) Osteocyte density and histomorphometric parameters in cancellous bone of the proximal femur in five mammalian species. J Orthop Res 14(6): 972–979

    Article  Google Scholar 

  • Munro DS (1959) The effects of sodium depletion on bone sodium metabolism. Proc R Soc Med 52(4): 258–259

    Google Scholar 

  • Munro DS, Satoskar RS, Wilson GM (1957) The exchange of bone sodium with isotopes in rats. J Physiol 139(3): 474–488

    Google Scholar 

  • Nörtemann K, Hilland J, Kaatze U (1997) Dielectric properties of aqueous nacl solutions at microwave frequencies. J Phys Chem A 101: 6864–6869

    Article  Google Scholar 

  • Owen M, Triffitt JT (1976) Extravascular albumin in bone tissue. J Physiol 257(2): 293–6869

    Google Scholar 

  • Pashley DH, Thompson SM, Stewart FP (1983) Dentin permeability: effects of temperature on hydraulic conductance. J Dent Res 62(9): 956–959

    Article  Google Scholar 

  • Reilly GC, Knapp HF, Stemmer A, Niederer P, Knothe Tate ML (2001) Investigation of the morphology of the lacunocanalicular system of cortical bone using atomic force microscopy. Ann Biomed Eng 29: 1074–1081

    Article  Google Scholar 

  • Saeed R, Uddin F, Masood S, Asif N (2009) Viscosities of ammonium salts in water and ethanol+water systems at different temperatures. J Mol Liq 146(3): 112–115

    Article  Google Scholar 

  • Sauren YMHF, Mieremet RHP, Groot CG, Scherft JP (1992) An electron microscopic study on the presence of proteoglycans in the mineralized matrix of rat and human compact lamellar bone. Anat Rec 232(1): 36–44

    Article  Google Scholar 

  • Senapati S, Chandra A (2001) Dielectric constant of water confined in a nanocavity. J Phys Chem B 105: 5106–5109

    Article  Google Scholar 

  • Smit TH, Huyghe JM, Cowin SC (2002) Estimation of the poroelastic parameters of cortical bone. J Biomech 35: 829–835

    Article  Google Scholar 

  • Stein A, Whitlock JP Jr, Bina M (1979) Acidic polypeptides can assemble both histones and chromatin in vitro at physiological ionic strength. Proc Natl Acad Sci USA 76(10): 5000–5004

    Article  Google Scholar 

  • Sze A, Erickson D, Ren L, Li D (2003) Zeta-potential measurement using the Smoluchowski equation and the slope of the current–time relationship in electroosmotic flow. J Colloid Interf Sci 261(2): 402–410

    Article  Google Scholar 

  • Teutenberg T, Wiese S, Wagner P, Gmehling J (2009a) High-temperature liquid chromatography. Part II: determination of the viscosities of binary solvent mixtures—implications for liquid chromatographic separations. J Chromatogr A 1216: 8470–8479

    Article  Google Scholar 

  • Teutenberg T, Wiese S, Wagner P, Gmehling J (2009b) High-temperature liquid chromatography. Part III: determination of the static permittivities of pure solvents and binary solvent mixtures—implications for liquid chromatographic separations. J Chromatogr A 1216: 8480–8487

    Article  Google Scholar 

  • Vayá A, Simó M, Santaloria M, Carrasco P, Corella D (2007) Plasma viscosity and related cardiovascular risk factors in a Spanish Mediterranean population. Thromb Res 120: 489–495

    Article  Google Scholar 

  • Venditti R, Xuan X, Li D (2006) Experimental characterization of the temperature dependence of zeta potential and its effect on electroosmotic flow velocity in microchannels. Microfluid Nanofluid 2: 493–499

    Article  Google Scholar 

  • Walsh WR, Guzelsu N (1993) Ion concentration effects on bone streaming potentials and zeta potentials. Biomaterials 14(5): 331–336

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wang L, Wang Y, Han H, Henderson SC, Majeska RJ, Weinbaum S, Schaffler MB (2005) In situ measurement of solute transport in the bone lacunar-canalicular system. P Natl Acad Sci USA 102(33): 11911–11916

    Article  Google Scholar 

  • Warkentin RK, Schofield BP (1958) Swelling pressures of dilute na-montmorillonite pastes. Clays Clay Miner 7: 343–349

    Article  Google Scholar 

  • Warkentin BP, Schofield RK (1962) Swelling pressure of na-montmorillonite in nacl solutions. Eur J Soil Sci 13(1): 98–105

    Article  Google Scholar 

  • Watts DC, El Mowafy OM, Grant AA (1987) Temperature-dependence of compressive properties of human dentin. J Dent Res 66(1): 29–32

    Article  Google Scholar 

  • Weast, RC, Astle, MJ, Beyer, WH (eds) (1989) Handbook of chemistry and physics, 69th edn. CRC Press, Boca Raton

    Google Scholar 

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

    Article  Google Scholar 

  • You L, Cowin SC, Schaffler MB, Weinbaum S (2001) A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J Biomech 34(11): 1375–1386

    Article  Google Scholar 

  • You LD, Weinbaum S, Cowin SC, Schaffler MB (2004) Ultrastructure of the osteocyte process and its pericellular matrix. Anat Rec 278: 505–513

    Article  Google Scholar 

  • Zhang D, Weinbaum S, Cowin SC (1998) On the calculation of bone pore water pressure due to mechanical loading. Int J Solids Struct 35(34–35): 4981–4997

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Author notes

  1. Joanna Kaiser

    Present address: Engineering Computational Biology Group, University of Western Australia, Crawley, WA, 6009, Australia

Authors and Affiliations

  1. Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Vittorio Sansalone, Joanna Kaiser, Salah Naili & Thibault Lemaire

Authors
  1. Vittorio Sansalone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joanna Kaiser
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Salah Naili
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thibault Lemaire
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vittorio Sansalone.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sansalone, V., Kaiser, J., Naili, S. et al. Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu. Biomech Model Mechanobiol 12, 533–553 (2013). https://doi.org/10.1007/s10237-012-0422-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-012-0422-7

Keywords

Mathematics Subject Classification (2000)

Search

Navigation