Abstract
A multiscale approach (periodic homogenization) is carried out to model osteon’s behaviour, and especially the coupled phenomena that govern its interstitial fluid movement. Actions of electro-osmotic and osmotic motions in addition to the classical Poiseuille flow are studied at the mesoscale of the canaliculus and within the micropores of the collagen-apatite matrix. Use of this fully coupled modelling leads to a comparison of these different effects. Limitation of a classical Darcian description of the fluid flow at the two scales is so studied. For each of these studies a special attention is given to the pore’s geometry influence and to their electrical and hydraulic properties
Similar content being viewed by others
References
Arramon Y, Nauman E (2001) The intrinsic permeability of cancellous bone. In: Cowin S (eds). Bone mechanics handbook, chap 5, 2nd edn. CRC, Boca Raton, FL, pp 1–17
Auriault J-L (1991) Heterogeneous medium. Is an equivalent macroscopic description possible?. Int J Eng Sci 29:785–795
Basset C, Becker R (1962) Generation of electrical potentials by bone in response to mechanical stress. Science 137:1063–1064
Berreta D, Pollack S (1986) Ion concentration effects on the zeta potential of bone. J orthop Res 4:337–341
Biot M (1941) General theory of three-dimensional consolidation. J Appl Phys 12(2):155–164
Buckwalter J, Glimcher M, Cooper R, Recker R (1995) Bone biology. Part i: Structure, blood supply, cells, matrix, and mineralization. JBone Joint Surg Am 77:1256–1275
Cowin S (2001) Bone poroelasticity. In: Cowin S (eds). Bone mechanics handbook, chap23, 2nd edn. CRC, Boca Raton, FL, pp 1–31
Cowin S (2002) Mechanosensation and fluid transport in living bone. JMusculoskel Neuron Interaction 2(3):256–260
Cowin S, Weinbaum S, Zeng Y (1995) A case for bone canaliculi as the anatomical site of strain generated potentials. J Biomech 28(11):1281–1297
Donnan F (1924) The theory of membrane equilibrium. Chem Rev 1:73–90
Dormieux L, Barboux P, Coussy O, Dangla P (1995) A macroscopic model of the swelling phenomenon of a saturated clay. Eur J Mech A/Solids 14(6):981–1004
Gu W, Lai W, Mow V (1998) A mixture theory for charged-hydrated soft tissues containing multi-electrolytes : passive transport and swelling behaviors. J Biomech Eng 120:169–180
Gururaja S, Kim H, Swan C, Brand R, Lakes R (2005) Modeling deformation-induced fluid flow in cortical bone’s canalicular-lacunar system. Ann Biomed Eng 33:7–25
Holmes J, Davies D, Meath W, Beebe RA (1953) Gas adsorption and surface structure of bone mineral. Biochemistry 3:2019–2024
Hornung U (1997) Homogenization and porous media. Springer, Berlin Heidelberg New York
Hunter R (1981) Zeta potential in colloid science: principles and applications. Academic, New York
Hunter R (2001) Foundations of colloid science. Oxford University Press, New York
Israelachvili J (1991) Intermolecular and surface forces. Academic, New-York
Kang Y, Yang C, Huang X (2002) Electroosmotic flow in a capillary annulus with high zeta potentials. J Colloid Interf Sci 253:285–294
Kim Y, Kim J, Kim Y, Rho J (2002) Effects of organic matrix proteins on the interfacial structure at the bone-biocompatible nacre interface in vitro. Biomaterials 23:2089–2096
Landau L, Lifshitz E (1960) Electrodynamics of continuous media. Pergamon Press, Oxford
Lemaire T (2004) Couplages Tlectro-chimio-hydro-mTcaniques dans les milieux argileux. PhD thesis, Institut National Polytechnique de Lorraine, Nancy
Lemaire T, Moyne C, Stemmelen D, Murad M (2002) Electro-chemo-mechanical couplings in swelling clays derived by homogenization : electroviscous effects and onsager’s relations. In: Auriault J, Geindreau C, Royer P, Bloch J-F, Boutin C, Lewandowska J (eds) Poromechanics II, proceedings of the second Biot conference on poromechanics, Grenoble, France. Balkema Publishers, Lisse, pp 489–500
Lyklema J (1995) Foundamentals of interface and colloid science. Academic, London
Mak A, Zhang J (2001) Numerical simulation of streaming potentials due to deformation-induced hierarchical flows in cortical bone. J Biomech Eng 123(1):66–70
Moyne C, Murad M (2002a) Electro-chemo-mechanical couplings in swelling clays derived from a micro/macro-homogenization procedure. Int J Solids and Structures 39(25):6159–6190
Moyne C, Murad M (2002b) Macroscopic behavior of swelling porous media derived from micromechanical analysis. Transport Porous Med 50:127–151
Philip J, Wooding R (1970) Solution of the poisson-boltzmann equation about a cylindrical particle. J Chem Phys 52:953–959
Piekarski K, Munro M (1977) Transport mechanism operating between blood supply and osteocytes in long bones. Nature 269(5623):80–82
Pollack S (2001) Streaming potentials in bone. In: Cowin S (eds) Bone mechanics handbook, Chap 24, 2nd edition. CRC, Boca Raton, FL, pp 1–22
Pollack S, Petrov N, Salzstein R, Brankov G, Blagoeva R (1984) An anatomical model for streaming potentials in osteons. J Biomech 17:627–636
RTmond A, Naili S (2004) Cyclic loading of a transverse isotropic poroelastic cylinder: a model for the osteon. C R Mec 332(9):759–766
Samson E, Marchand J, Robert J-L, Bournazel J-P (1999) Modelling ion diffusion mechanisms in porous media. Int J Numer Meth Eng 46:2043–2060
Sanchez-Palencia E (1980) Non-homogenous media and vibration theory. In: Lectures notes in Physics, vol 127. Springer, Berlin Heidelberg New York
Sasidhar V, Ruckenstein E (1981) Electrolyte osmosis through capillaries. J Colloid Interf Sci 8:439–457
Starkenbaum W, Pollack S, Korostoff E (1979) Microelectrode studies of stress generated potentials in four point bending of bone. J Biomed Mater Res 13:729–751
Tsay R, Weinbaum S (1991) Viscous flow in a channel with periodic cross-bridging fibers: exact solutions and brinkman approximation. J Fluid Mech 226:125–148
Wang L, Fritton SP, Weinbaum S, Cowin S (2003) On bone adaptation due to venous stasis. J Biomech 36(10):1439–1451
Weinbaum S, Cowin S, Zeng Y (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J Biomech 27(3):339–360
Yasuda I (1964) Piezoelectricity of living bone. J Kyoto Pref Med 53:2019–2024
You L, Weinbaum S, Cowin S, Schaffler M (2004) Ultrastructure of the osteocyte process and its pericellular matrix. Anat Rec 278A(2):505–513
Zhang D, Weinbaum S, Cowin S (1998) On the calculation of bone pore water pressure due to mechanical loading. Int J Solids and Structures 35(34-35):4981–4997
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lemaire, T., Naïli, S. & Rémond, A. Multiscale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone. Biomech Model Mechanobiol 5, 39–52 (2006). https://doi.org/10.1007/s10237-005-0009-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-005-0009-7