Skip to main content

Analysis of avian bone response to mechanical loading, Part Two: Development of a computational connected cellular network to study bone intercellular communication

Abstract

Mechanical loading-induced signals are hypothesized to be transmitted and integrated by connected bone cells before reaching the bone surfaces where adaptation occurs. A computational connected cellular network (CCCN) model is developed to explore how bone cells perceive and transmit the signals through intercellular communication. This is part two of a two-part study in which a CCCN is developed to study the intercellular communication within a grid of bone cells. The excitation signal was computed as the loading-induced bone fluid shear stress in part one. Experimentally determined bone adaptation responses (Gross et al. in J Bone Miner Res 12:982-988, 1997 and Judex et al. in J Bone Miner Res 12:1737-1745, 1997) are correlated with the fluid shear stress by the CCCN, which adjusts cell sensitivities (loading and signal thresholds) and connection weights. Intercellular communication patterns extracted by the CCCN indicate the cell population responsible for perceiving the loading-induced signal, and loading threshold is shown to play an important role in regulating the bone response.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Notes

  1. The back-propagation (BP) network is the most commonly used neural network (Haykin 1999). It is composed of a hierarchy of computational elements, organized in a series of two or more mutually exclusive layers. The first, or input layer, serves as a holding site for the values applied to the network. The last, or output layer is the point at which the final output of the network is read. Between these two extremes lie zero or more layers of hidden computational elements. Weights connect each element in one layer to only those in the next higher layer. The BP learning algorithm consists of two distinct passes, namely the forward pass and the backward pass. In the forward pass, the output of the network for a particular input is computed on an element-by-element and layer-by-layer basis as connection weights remain fixed. The error (difference between actual and desired output) is computed and this is proportionately propagated backward layer-by-layer to adjust the connection weights during the backward pass. This cycle is repeated until the error signal is within some acceptable range. At this point, the relationship between the network input and output is believed to have been encoded in the connection weights among computational elements/cells.

References

  • Aarden EM, Burger EH, Nijweide PJ (1994) Function of osteocytes in bone. J Cell Biochem 55(3):287–299

    Article  PubMed  Google Scholar 

  • Allen RE, Boxhorn LK (1989) Regulation of skeletal muscle satellite cell proliferation and differentiation by transforming growth factor-beta, insulin-like growth factor I, and fibroblast growth factor. J Cell Physiol 138(2):311–315

    Article  PubMed  Google Scholar 

  • Anderson JA, Rosenfeld E (eds) (1988) Neurocomputing: Foundations of Research. MIT Press, Cambridge

    Google Scholar 

  • Bloomfield SA (2001) Cellular and molecular mechanisms for the bone response to mechanical loading. Int J Sport Nutr Exerc Metab 11(Suppl):S128–S136

    PubMed  Google Scholar 

  • Burger EH, Klein-Nulend J (1999) Mechanotransduction in bone–role of the lacuno-canalicular network. FASEB J 13(Suppl):S101–S112

    PubMed  Google Scholar 

  • Chiba H, Sawada N, Oyamada M, Kojima T, Iba K, Ishii S, Mori M (1994) Hormonal regulation of connexin 43 expression and gap junctional communication in human osteoblastic cells. Cell Struct Funct 19(3):173–177

    PubMed  Google Scholar 

  • Chow JW, Fox S, Jagger CJ, Chambers TJ (1998) Role for parathyroid hormone in mechanical responsiveness of rat bone. Am J Physiol 274(1 Pt 1):E146–E154

    PubMed  Google Scholar 

  • Churchland PS, Sejnowski TJ (1992) The computational brain. MIT Press, Cambridge

    Google Scholar 

  • Cowin SC, Hegedus DH (1976) Bone remodeling I: theory of adaptive elasticity. J Elast 6(3):313–326

    Google Scholar 

  • Cowin SC, Hart RT, Balser JR, Kohn DH (1985) Functional adaptation in long bones: establishing in vivo values for surface remodeling rate coefficients. J Biomech 18(9):665–684

    Article  PubMed  Google Scholar 

  • Cowin SC, Moss-Salentijn L, Moss ML (1991) Candidates for the mechanosensory system in bone. J Biomech Eng 113: 191–197

    PubMed  Google Scholar 

  • Cowin SC, Weinbaum S, Zeng Y (1995) A case for bone canaliculi as the anatomical site of strain generated potentials. J Biomech 28(11):1281–1297

    Article  PubMed  Google Scholar 

  • Currey JD (1960) Differences in the blood-supply of bone of different histological types. J Microsc Sci 101:351–370

    Google Scholar 

  • Curtis TA, Ashrafi SH, Weber DF (1985) Canalicular communication in the cortices of human long bones. Anat Rec 212:336–344

    Article  PubMed  Google Scholar 

  • D’Andrea P, Vittur F (1997) Propagation of intercellular Ca2+ waves in mechanically stimulated articular chondrocytes. FEBS Lett 400(1):58–64

    Article  PubMed  Google Scholar 

  • Demer LL, Wortham CM, Dirksen ER, Sanderson MJ (1993) Mechanical stimulation induces intercellular calcium signaling in bovine aortic endothelial cells. Am J Physiol 264(6 Pt 2):H2094–H2102

    PubMed  Google Scholar 

  • Donahue HJ, McLeod KJ, Rubin CT, Andersen J, Grine EA, Hertzberg EL, Brink PR (1995) Cell-to-cell communication in osteoblastic networks: cell line-dependent hormonal regulation of gap junction function. J Bone Miner Res 10(6):881–889

    PubMed  Google Scholar 

  • Doty SB (1981) Morphological evidence of gap junctions between bone cells. Calcif Tissue Int 33:509–512

    PubMed  Google Scholar 

  • Duncan RL, Turner CH (1995) Mechanotransduction and the functional response of bone to mechanical strain. Calcif Tissue Int 57(5):344–358

    Article  PubMed  Google Scholar 

  • Enomoto K, Furuya K, Yamagishi S, Maeno T (1992) Mechanically induced electrical and intracellular calcium responses in normal and cancerous mammary cells. Cell Calcium 13(8):501–511

    Article  PubMed  Google Scholar 

  • Frost HM (1964) Dynamics of bone remodeling. In: Frost HM (ed) Bone biodynamics. Little and Brown, Boston

  • Frost HM (1986) Intermediary organization of the skeleton, vols I and II. CRC Press, Boca Raton

    Google Scholar 

  • Garven HSD (1965) A Student’s histology. Williams and Wilkins, Baltimore

    Google Scholar 

  • Greene EA, Allen RE (1991) Growth factor regulation of bovine satellite cell growth in vitro. J Anim Sci 69(1): 146–152

    PubMed  Google Scholar 

  • Gross TS, Edwards JL, McLeod KJ, Rubin CT (1997) Strain gradients correlate with sites of periosteal bone formation. Bone Miner 12:982–988

    Google Scholar 

  • Gu Y, Publicover SJ (2000) Expression of functional metabotropic glutamate receptors in primary cultured rat osteoblasts. Cross-talk with N-methyl-D-aspartate receptors. J Biol Chem 275(44):34252–34259

    Article  PubMed  Google Scholar 

  • Hart RT, Davy DT, Heiple KG (1984) A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. J Biomech Eng 106(4):342–350

    PubMed  Google Scholar 

  • Haykin S (1999) Neural networks: a comprehensive foundation 2nd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Hegedus DM, Cowin SC (1976) Bone remodeling, II: small strain adaptive elasticity. J Elast 6:337–352

    Google Scholar 

  • Hinoi E, Fujimori S, Nakamura Y, Yoneda Y (2001) Group III metabotropic glutamate receptors in rat cultured calvarial osteoblasts. Biochem Biophys Res Commun 281(2):341–346

    Article  PubMed  Google Scholar 

  • Hsieh YF, Robling AG, Ambrosius WT, Burr DB, Turner CH (2001) Mechanical loading of diaphyseal bone in vivo: the strain threshold for an osteogenic response varies with location. J Bone Miner Res 16:2291–2297

    PubMed  Google Scholar 

  • Huggett JF, Mustafa A, O’neal L, Mason DJ (2002) The glutamate transporter GLAST-1 (EAAT-1) is expressed in the plasma membrane of osteocytes and is responsive to extracellular glutamate concentration. Biochem Soc Trans 30(Pt 6):890–893

    Article  PubMed  Google Scholar 

  • Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ (1987) Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech 20:1135–1150

    Article  PubMed  Google Scholar 

  • Inaoka T, Lean JM, Bessho T, Chow JW, Mackay A, Kokubo T, Chambers TJ (1995) Sequential analysis of gene expression after an osteogenic stimulus: c-fos expression is induced in osteocytes. Biochem Biophys Res Commun 217(1):264–270

    Article  PubMed  Google Scholar 

  • Jagger CJ, Chow JW, Chambers TJ (1996) Estrogen suppresses activation but enhances formation phase of osteogenic response to mechanical stimulation in rat bone. J Clin Invest 98(10):2351–2357

    PubMed  Google Scholar 

  • Jeansonne BG, Feagin FF, McMinn RW, Shoemaker RL, Rehm WS (1979) Cell-to-cell communication of osteoblasts. J Dent Res 58(4):1415–1423

    PubMed  Google Scholar 

  • Jones SJ, Gray C, Sakamaki H, Arora M, Boyde A, Gourdie R, Green C (1993) The incidence and size of gap junctions between bone cells in rat calvaria. Anat Embryol (Berl) 187:343–352

    Google Scholar 

  • Judex S, Gross TS, Zernicke RG (1997) Strain gradients correlate with sites of exercise-induced bone-forming surfaces in the adult skeleton. Bone Miner Res 12:1737–1745

    Google Scholar 

  • Kamioka H, Honjo T, Takano-Yamamoto T (2001) A three-dimensional distribution of osteocyte processes revealed by the combination of confocal laser scanning microscopy and differential interference contrast microscopy. Bone 28(2):145–149

    Article  PubMed  Google Scholar 

  • Kasperk C, Fitzsimmons R, Strong D, Mohan S, Jennings J, Wergedal J, Baylink D (1990) Studies of the mechanism by which androgens enhance mitogenesis and differentiation in bone cells. J Clin Endocrinol Metab 71(5):1322–1329

    PubMed  Google Scholar 

  • Koch JC (1917) The laws of bone architecture. Am J Anat 21:177–298

    Article  Google Scholar 

  • Konieczynski DD, Truty MJ, Biewener AA (1998) Evaluation of a bone’s in vivo 24-hour loading history for physical exercise compared with background loading. J Orthop Res 16(1):29–37

    Article  PubMed  Google Scholar 

  • Lean JM, Mackay AG, Chow JW, Chambers TJ (1996) Osteocytic expression of mRNA for c-fos and IGF-I: an immediate early gene response to an osteogenic stimulus. Am J Physiol 270(6 Pt 1):E937–E945

    PubMed  Google Scholar 

  • Lecanda F, Towler DA, Ziambaras K, Cheng SL, Koval M, Steinberg TH, Civitelli R (1998) Gap junctional communication modulates gene expression in osteoblastic cells. Mol Biol Cell 9(8):2249–2258

    PubMed  Google Scholar 

  • Mason DJ, Suva LJ, Genever PG, Patton AJ, Steuckle S, Hillam RA, Skerry TM (1997) Mechanically regulated expression of a neural glutamate transporter in bone: a role for excitatory amino acids as osteotropic agents? Bone 20(3):199–205

    Article  PubMed  Google Scholar 

  • Mattheck C, Huber-Betzer H (1991) CAO: computer simulation of adaptive growth in bones and trees. In: Held KD, Brebbia CA, Ciskowski RD (eds) Computers in biomedicine. Computational Mechanics Publicatins, Southampton

    Google Scholar 

  • Mikuni-Takagaki Y (1999) Mechanical responses and signal transduction pathways in stretched osteocytes. J Bone Miner Metab 17(1):57–60

    Article  PubMed  Google Scholar 

  • Moss ML (1991) Bone as a connected cellular network: modeling and testing. In: Ross G (ed) Topics in biomedical engineering. Pergamon, New York

    Google Scholar 

  • Palumbo C, Palazzini S, Marotti G (1993) Morphological study of intercellular junctions during osteocyte differentiation. Bone 11(6):401–406

    Article  Google Scholar 

  • Patton AJ, Genever PG, Birch MA, Suva LJ, Skerry TM (1998) Expression of an N-methyl-D-aspartate-type receptor by human and rat osteoblasts and osteoclasts suggests a novel glutamate signaling pathway in bone. Bone 22(6):645–649

    Article  PubMed  Google Scholar 

  • Prendergast PJ, Taylor D (1994) Prediction of bone adaptation using damage accumulation. J Biomech 27(8):1067–1076

    Article  PubMed  Google Scholar 

  • Rasmussen H, Bordier P (1975) The physiological and cellular basis of metabolic bone disease. Williams and Wilkins, Baltimore

    Google Scholar 

  • Rawlinson SC, Pitsillides AA, Lanyon LE (1996) Involvement of different ion channels in osteoblasts’ and osteocytes’ early responses to mechanical strain. Bone 19(6):609–614

    Article  PubMed  Google Scholar 

  • Riedmiller M, Braun H (1993) A direct adaptive method for faster backpropagation learning: the RPROP algorithm. In: Proceedings of the IEEE International Conference on Neural Networks, pp 586–591

  • Romanello M, Veronesi V, D’Andrea P (2003) Mechanosensitivity and intercellular communication in HOBIT osteoblastic cells: a possible role for gap junction hemichannels. Biorheology 40(1–3):119–121

    PubMed  Google Scholar 

  • Rubin CT, Lanyon LE (1987) Osteoregulatory nature of mechanical stimuli: function as a determinant for adaptive remodeling in bone. J Orthop Res 5(2):300–310

    Article  PubMed  Google Scholar 

  • Saunders MM, You J, Trosko JE, Yamasaki H, Li Z, Donahue HJ, Jacobs CR (2001) Gap junctions and fluid flow response in MC3T3-E1 cells. Am J Physiol Cell Physiol 281(6):C1917–C1925

    PubMed  Google Scholar 

  • Seino Y (1994) Cytokines and growth factors which regulate bone cell function. Acta Astronaut 33:131–136

    Article  PubMed  Google Scholar 

  • Spencer GJ, Genever PG (2003) Long-term potentiation in bone– role for glutamate in strain-induced cellular memory?. BMC Cell Biol 4(1):9

    Article  PubMed  Google Scholar 

  • Turner CH (1991) Toward a mathematical description of bone biology: the principle of cellular accommodation. Calcif Tissue Int 65:466–481

    Article  Google Scholar 

  • Turner CH, Robling AG, Duncan RL, Burr DB (2002) Do bone cells behave like a neuronal network? Calcif Tissue Int 70(6):435–442

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Google Scholar 

  • Wolff J (1986) The law of bone remodelling. Springer, Berlin Heidelberg NewYork

    Google Scholar 

  • Yellowley CE, Li Z, Zhou Z, Jacobs CR, Donahue HJ (2001) Functional gap junctions between osteocytic and osteoblastic cells. J Bone Miner Res 15(2):209–217

    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  PubMed  Google Scholar 

  • Ypey DL, Weidema AF, Hold KM, Van der Laarse A, Ravesloot JH, Van Der Plas A, Nijweide PJ (1992) Voltage, calcium, and stretch activated ionic channels and intracellular calcium in bone cells. J Bone Miner Res 7(Suppl 2):S377–S387

    PubMed  Google Scholar 

Download references

Acknowledgements

The authors thank Dr. Ted Gross and Dr. Stefan Judex for providing the experimental data reported in Gross et al. (1997) and Judex et al. (1997), Dr. John Currey for providing turkey bone sections and Dr. Stephen Doty for histological examination of turkey bone sections. This study has been supported by NIH grant AR48699 and by PSC-CUNY 64429 and 65734.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stephen C. Cowin.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mi, L.Y., Basu, M., Fritton, S.P. et al. Analysis of avian bone response to mechanical loading, Part Two: Development of a computational connected cellular network to study bone intercellular communication. Biomech Model Mechanobiol 4, 132–146 (2005). https://doi.org/10.1007/s10237-004-0066-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-004-0066-3

Keywords

  • Connection Weight
  • Network Parameter
  • Neutral Axis
  • Fluid Shear Stress
  • Shear Stress Distribution