Spatio-temporal structure of cell distribution in cortical Bone Multicellular Units: A mathematical model

Bone

Volumn 48, Issue 4, 2011, Pages 918-926

  Buenzli, P R ^a   Pivonka, P ^a   Smith, D W ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Bone cell interactions; Cortical BMU; Mathematical modeling; RANK RANKL OPG; Spatio temporal bone remodeling

Indexed keywords

APOPTOSIS; ARTICLE; BONE CELL; BONE REMODELING; CELL DENSITY; CELL DIFFERENTIATION; CELLULAR DISTRIBUTION; CORTICAL BONE; MATHEMATICAL MODEL; OSTEOBLAST; OSTEOCLAST;

BONE AND BONES; HUMANS; MODELS, THEORETICAL;

EID: 79952709863     PISSN: 87563282     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bone.2010.12.009     Document Type: Article

References (34)

1. Martin R.B., Burr D.B., Sharkey N.A. Skeletal tissue mechanics 1998, Springer, New York.
2. Bone mechanics handbook 2001, CRC Press, Boca Raton. 2nd Ed. S.C. Cowin (Ed.).
3. Frost H.M. The skeletal intermediary organization. Metab Bone Dis Rel Res 1983, 4:281-290.
4. Frost H.M. Dynamics of bone remodeling. Bone Biodynamics 1964, Little, Brown & Co, Boston. H.M. Frost (Ed.).
5. Parfitt A.M. Quantum concept of bone remodeling and turnover: implications for the pathogenesis of osteoporosis. Calcif Tissue Int 1979, 28:1-5.
6. Parfitt A.M. The cellular basis of bone remodeling: the quantum concept reexamined in light of recent advances in the cell biology of bone. Calcif Tissue Int 1984, 36:S37-S45.
7. Parfitt A.M. Osteonal and hemi-osteonal remodeling: the spatial and temporal framework for signal traffic in adult human bone. J Cell Biochem 1994, 55:273-286.
8. Jaworski Z.F.G., Hooper C. Study of cell kinetics within evolving secondary haversian systems. J Anat London 1980, 131:91-102.
9. Jaworski Z.F.G., Duck B., Sekaly G. Kinetics of osteoclasts and their nuclei in evolving secondary Haversian systems. J Anat 1981, 133:397-405.
10. Väänänen H.K., Liu Y.-K., Lehenkari P., Uemara T. How do osteoclasts resorb bone?. Mater Sci Eng C 1998, 6:205-209.
11. Roodman G.D. Cell biology of the osteoclast. Exp Hematol 1999, 27:1229-1241.
12. Martin T.J. Paracrine regulation of osteoclast formation and activity: milestones in discovery. J Musculoskel Neuron Interact 2004, 4:243-253.
13. 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 Theor Biol 2004, 29:293-309.
14. Pivonka P., Zimak J., Smith D.W., Gardiner B.S., Dunstan C.R., Sims N.A., Martin T.J., Mundy G.R. Model structure and control of bone remodeling: a theoretical study. Bone 2008, 43:249-263.
15. Komarova S.V., Smith R.J., Dixon S.J., Sims S.M., Wahl L.M. Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling J. Theor Biol 2003, 229:293-309.
16. Ryser M.D., Nigam N., Komarova S.V. Mathematical modeling of spatio-temporal dynamics of a single bone multicellular unit. J Bone Miner Res 2009, 24:860-870.
17. Ryser M.D., Komarova S.V., Nigam N. The cellular dynamics of bone remodelling: a mathematical model. SIAM J Appl Math 2010, 70:1899-1921.
18. 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 2008, 42:250-259.
19. Bird R.B., Stewart W.E., Lightfoot E.N. Transport phenomena 2002, Wiley, New York. 2nd Ed.
20. Evans D.J., Morriss G. Statistical mechanics of nonequilibrium liquids 2008, Cambridge University Press. 2nd Ed.
21. Scheurer P.B., Stueckelberg de Breidenbach E.C.G. Thermocinétique Phénoménologique Galiléenne 1974, Birkhäuser, Basel.
22. Bronckers A.L.J.J., Goel W., Luo G., Karsenty G., D'Souza R.N., Lyaruu D.M., Burger E.H. DNA fragmentation during bone formation in neonatal rodents assessed by transferase-mediated end labeling. J Bone Miner Res 1996, 11:1281-1291.
23. Lauffenburger D.A., Linderman J.J. Receptors: models for binding, trafficking, and signaling 1993, Oxford Univ. Press, New York.
24. 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 2003, 36:1453-1459.
25. Ishii M., Egen J.G., Klauschen F., Meier-Schellersheim M., Saeki Y., Vacher J., Proia R.L., Germain R.N. Sphingosine-1-phosphate mobilizes osteoclast precursors and regulates bone homeostasis. Nature 2009, 458:524-529.
26. Ishii T., Kikuta J., Kubo A., Ishii M. Control of osteoclast precursor migration: a novel point of control for osteoclastogenesis and bone homeostasis. IBMS BoneKEy 2010, 7:279-286.
27. Harada S.-I., Rodan G.A. Control of osteoblast function and regulation of bone mass. Nature 2003, 423:349-355.
28. Iqbal J., Sun L., Zaidi M. Coupling bone degradation to formation. Nat Med 2009, 15:729-731.
29. Tang Y., et al. TGF-β1-induced migration of bone mesenchymal stem cells couples bone resorption with formation. Nat Med 2009, 15:757-766.
30. Gori F., Hofbauer L.C., Dunstan C.R., Spelsberg T.C., Kholsa S., Riggs B.L. The expression of osteoprotegerin and RANK ligand and the support of osteoclast formation by stromal-osteoblast linearge cells is developmentally regulated. Endocrinology 2000, 141:4768-4776.
31. Thomas G.P., Baker S.U., Eisman J.A., Gardiner E.M. Changing RANKL/OPG mRNA expression in differentiating murine primary osteoblasts. J Endocrinol 2001, 170:451-460.
32. Wolfram Research Inc Mathematica edition: version 7.0 2008, Wolfram Research, Inc, Champaign, Illinois.
33. Buenzli P.R., Pivonka P., Gardiner B.S., Smith D.W., Dunstan C.R., Mundy G.R. Theoretical analysis of the spatio-temporal structure of bone multicellular units. IOP Conf Ser Mater Sci Eng 2010, 10:012132.
34. Halmos P.R. Measure theory 1974, Springer, New York.