Biomechanics and Modeling in Mechanobiology

, Volume 12, Issue 2, pp 249–265 | Cite as

A mechanobiological model of orthodontic tooth movement

Original Paper


Orthodontic tooth movement is achieved by the process of repeated alveolar bone resorption on the pressure side and new bone formation on the tension side. In order to optimize orthodontic treatment, it is important to identify and study the biological processes involved. This article presents a mechanobiological model using partial differential equations to describe cell densities, growth factor concentrations, and matrix densities occurring during orthodontic tooth movement. We hypothesize that such a model can predict tooth movement based on the mechanobiological activity of cells in the PDL. The developed model consists of nine coupled non-linear partial differential equations, and two distinct signaling pathways were modeled: the RANKL–RANK–OPG pathway regulating the communication between osteoblasts and osteoclasts and the TGF-β pathway mediating the differentiation of mesenchymal stem cells into osteoblasts. The predicted concentrations and densities were qualitatively validated by comparing the results to experiments reported in the literature. In the current form, the model supports our hypothesis, as it is capable of conceptually simulating important features of the biological interactions in the alveolar bone—PDL complex during orthodontic tooth movement.


Mechanobiology Mathematical model Tooth movement RANK–RANKL–OPG pathway TGF-β pathway 


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Supplementary material

10237_2012_396_MOESM1_ESM.eps (193 kb)
ESM 1 (EPS 193 kb)
10237_2012_396_MOESM2_ESM.eps (213 kb)
ESM 2 (EPS 214 kb)


  1. Alcañiz M, Montserrat C, Grau V, Chinesta F, Ramón A, Albalat S (1998) An advanced system for the simulation and planning of orthodontic treatment. Med Image Anal 2: 61–77CrossRefGoogle Scholar
  2. Bailón-Plaza A, van der Meulen MC (2001) A mathematical framework to study the effects of growth factor influences on fracture healing. J Theor Biol 212: 191–209CrossRefGoogle Scholar
  3. Baumrind S (1969) A reconsideration of the property of the “pressure-tension” hypothesis. Am J Orthod 55: 12–22CrossRefGoogle Scholar
  4. Beertsen W, McCulloch CA, Sodek J (1997) The periodontal ligament: a unique, multifunctional connective tissue. Periodontol 2000 13: 20–40CrossRefGoogle Scholar
  5. Bonewald LF (2006) Mechanosensation and transduction in Osteocytes. Bonekey Osteovision 3: 7–15CrossRefGoogle Scholar
  6. Bourauel C, Freudenreich D, Vollmer D, Kobe D, Drescher D, Jäger A (1999) Simulation of orthodontic tooth movements. A comparison of numerical models. J Orofac Orthop 60: 136–151CrossRefGoogle Scholar
  7. Bourauel C, Vollmer D, Jäger A (2000) Application of bone remodeling theories in the simulation of orthodontic tooth movements. J Orofac Orthop 61: 266–279CrossRefGoogle Scholar
  8. Bucay N, Sarosi I, Dunstan CR, Morony S, Tarpley J, Capparelli C, Scully S, Tan HL, Xu W, Lacey DL, Boyle WJ, Simonet WS (1998) osteoprotegerin-deficient mice develop early onset osteoporosis and arterial calcification. Genes Dev 12: 1260–1268CrossRefGoogle Scholar
  9. Carano A, Siciliano G (1996) Effects of continuous and intermittent forces on human fibroblasts in vitro. Eur J Orthod 18: 19–26CrossRefGoogle Scholar
  10. Chiquet M, Renedo AS, Huber F, Flück M (2003) How do fibroblasts translate mechanical signals into changes in extracellular matrix production. Matrix Biol 22: 73–80CrossRefGoogle Scholar
  11. Dahl J, Li J, Bring DKI, Renström P, Ackermann P (2007) Intermittent pneumatic compression enhances neurovascular ingrowth and tissue proliferation during connective tissue healing: a study in the rat. J Orthop Res 25: 1185–1192CrossRefGoogle Scholar
  12. Dunn MD, Park CH, Kostenuik PJ, Kapila S, Giannobile W (2007) Local delivery of osteoprotegerin inhibits mechanically mediated bone modeling in orthodontic tooth movement. Bone 41: 446–455CrossRefGoogle Scholar
  13. Everts V, Korper W, Niehof A, Jansen I, Beertsen W (1995) Type VI collagen is phagocytosed by fibroblasts and digested in the lysosomal apparatus: involvement of collagenase, serine proteinases and lysosomal enzymes. Matrix Biol 14: 665–676CrossRefGoogle Scholar
  14. Frost HM (1988) Vital biomechanics: proposed general concepts for skeletal adaptations to mechanical usage. Calcif Tissue Int 42: 145–156CrossRefGoogle Scholar
  15. Fujihara S, Yokozeki M, Oba Y, Higashibata Y, Nomura S, Moriyama K (2006) Function and regulation of osteopontin in response to mechanical stress. J Bone Miner Res 21: 956–964CrossRefGoogle Scholar
  16. Gao J, Symons AL, Bartold PM (1998) Expression of transforming growth factor-beta1 (TGF-beta1) in the developing periodontium of rats. J Dent Res 77: 1708–1716CrossRefGoogle Scholar
  17. Garant PR (1976) Collagen resorption by fibroblasts. A theory of fibroblastic maintenance of the periodontal ligament. J Periodontol 47: 380–390CrossRefGoogle Scholar
  18. Garant PR (2003) Oral cells and tissues. Quintessence Publishing Co. Ltd., New Malden, Surrey, UKGoogle Scholar
  19. Garlet TP, Coelho U, Silva JS, Garlet PG (2007) Cytokine expression pattern in compression and tension sides of the periodontal ligament during orthodontic tooth movement in humans. Eur J Oral Sci 115: 355–362CrossRefGoogle Scholar
  20. Garlet TP, Coelho U, Repeke CE, Silva JS, de Queiroz Cunha F, Garlet PG (2008) Differential expression of osteoblast and osteoclast chemmoatractants in compression and tension sides during orthodontic movement. Cytokine 42: 330–335CrossRefGoogle Scholar
  21. Geris L, Gerisch A, Sloten J, Weiner R, Oosterwyck H (2008) Angiogenesis in bone fracture healing: a bioregulatory model. J Theor Biol 251: 137–158MathSciNetCrossRefGoogle Scholar
  22. Gerisch A, Chaplain MAJ (2006) Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Math Comput Model 43: 49–75MathSciNetMATHCrossRefGoogle Scholar
  23. Gerisch A, Chaplain MAJ (2008) Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion. J Theor Biol 250: 684–704MathSciNetCrossRefGoogle Scholar
  24. Grimm FM (1972) Bone bending, a feature of orthodontic tooth movement. Am J Orthod 62: 384–393CrossRefGoogle Scholar
  25. Henneman S, den Hoff JWV, Maltha JC (2008) Mechanobiology of tooth movement. Eur J Orthod 30: 299–306CrossRefGoogle Scholar
  26. Houde N, Chamoux E, Bisson M, Roux S (2009) Transforming growth factor-beta1 induces human osteoclast apoptosis by up-regulating Bim. J Biol Chem 284: 23397–23404CrossRefGoogle Scholar
  27. Isaacson KG, Muir JD, Reed RT (2003) Removable orthodontic appliances. Wright, Bristol, UKGoogle Scholar
  28. Ivanovski S, Gronthos S, Shi S, Bartold PM (2006) Stem cells in the periodontal ligament. Oral Dis 12: 358–363CrossRefGoogle Scholar
  29. Jimi E, Nakamura I, Amano H, Taguchi Y, Tsurukai T, Tamura M, Takahashi N, Suda T (1996) Osteoclast function is activated by osteoblastic cells through a mechanism involving cell-to-cell contact. Endocrinology 137: 90–2187CrossRefGoogle Scholar
  30. Kameda T, Mano H, Yuasa T, Mori Y, Miyazawa K, Shiokawa M, Nakamaru Y, Hiroi E, Hiura K, Kameda A, Yang NN, Hakeda Y, Kumegawa M (1997) Estrogen inhibits bone resorption by directly inducing apoptosis of the bone-resorbing osteoclasts. J Exp Med 186: 489–495CrossRefGoogle Scholar
  31. Kanzaki H, Chiba M, Shimizu Y, Mitani H (2002) Periodontal ligament cells under mechanical stress induce osteoclastogenesis by receptor activator of nuclear factor kappaB ligand up-regulation via prostaglandin E2 synthesis. J Bone Miner Res 17: 210–220CrossRefGoogle Scholar
  32. Kawakami M, Takano-Yamamoto T (2004) Local injection of 1,25-dihydroxyvitamin D3 enhanced bone formation for tooth stabilization after experimental tooth movement in rats. J Bone Miner Metab 22: 541–546CrossRefGoogle Scholar
  33. Kawarizadeh A, Bourauel C, Zhang D, Götz W, Jäger A (2004) Correlation of stress and strain profiles and the distribution of osteoclastic cells induced by orthodontic loading in rat. Eur J Oral Sci 112: 140–147CrossRefGoogle Scholar
  34. Kawarizadeh A, Bourauel C, Götz W, Jäger A (2005) Early responses of periodontal ligament cells to mechanical stimulus in vivo. J Dent Res 84: 902–906CrossRefGoogle Scholar
  35. Kimoto S, Matsuzawa M, Matsubara S, Komatsu T, Uchimura N, Kawase T, Saito S (1999) Cytokine secretion of periodontal ligament fibroblasts derived from human deciduous teeth: effect of mechanical stress on the secretion of transforming growth factor-beta 1 and macrophage colony stimulating factor. J Periodontal Res 34: 235–243CrossRefGoogle Scholar
  36. King GJ, Keeling SD, Wronski J (1991) Histomorphometric study of alveolar bone turnover in orthodontic tooth movement. Bone 12: 401–409CrossRefGoogle Scholar
  37. Klein-Nulend J, Bacabac RG, Mullender MG (2005) Mechanobiology of bone tissue. Pathol Biol (Paris) 53: 576–580CrossRefGoogle Scholar
  38. Kobayashi Y, Hashimoto F, Miyamoto H, Kanaoka K, Miyazaki- Kawashita Y, Nakashima T, Shibata M, Kobayashi K, Kato Y, Sakai H (2000) Force-induced osteoclast apoptosis in vivo is accompanied by elevation in transforming growth factor beta and osteoprotegerin expression. J Bone Miner Res 15: 1924–1934CrossRefGoogle Scholar
  39. Kojima Y, Fukui H (2005) Numerical simulation of canine retraction by sliding mechanics. Am J Orthod Dentofac Orthop 127: 542–551CrossRefGoogle Scholar
  40. Kojima Y, Fukui H (2006) A numerical simulation of tooth movement by wire bending. Am J Orthod Dentofac Orthop 130: 452–459CrossRefGoogle Scholar
  41. Kojima Y, Fukui H, Miyajima K (2006) The effects of friction and flexural rigidity of the archwire on canine movement in sliding mechanics: a numerical simulation with a 3-dimensional finite element method. Am J Orthod Dentofac Orthop 130: 275.e1–10Google Scholar
  42. Krishnan V, Davidovitch Z (2006) Cellular, molecular, and tissue-level reactions to orthodontic force. Am J Orthod Dentofac Orthop 129: 469.e1–32CrossRefGoogle Scholar
  43. Krishnan V, Davidovitch Z (2009) On a path to unfolding the biological mechanisms of orthodontic tooth movement. J Dent Res 88: 597–608CrossRefGoogle Scholar
  44. Lawrence DA (2001) Latent-TGF-beta: an overview. Mol Cell Biochem 219: 163–170CrossRefGoogle Scholar
  45. Maeda S, Dean DD, Gomez R, Schwartz Z, Boyan BD (2002) The first stage of transforming growth factor beta1 activation is release of the large latent complex from the extracellular matrix of growth plate chondrocytes by matrix vesicle stromelysin-1 (MMP-3). Calcif Tissue Int 70: 54–65CrossRefGoogle Scholar
  46. Marotti G (2000) The osteocyte as a wiring transmission system. J Musculoskelet Neuronal Interact 1: 133–136Google Scholar
  47. Masella RS, Meister M (2006) Current concepts in the biology of orthodontic tooth movement. Am J Orthod Dentofacial Orthop 129: 458–468CrossRefGoogle Scholar
  48. McKee MD, Nanci A (1995) Osteopontin and the bone remodeling sequence. Colloidal-gold immunocytochemistry of an interfacial extracellular matrix protein. Ann N Y Acad Sci 760: 177–189CrossRefGoogle Scholar
  49. McKee MD, Glimcher MJ, Nanci A (1992) High-resolution immunolocalization of osteopontin and osteocalcin in bone and cartilage during endochondral ossification in the chicken tibia. Anat Rec 234: 479–492CrossRefGoogle Scholar
  50. Meikle MC (2006) The tissue, cellular, and molecular regulation of orthodontic tooth movement: 100 years after Carl Sandstedt. Eur J Orthod 28: 221–240CrossRefGoogle Scholar
  51. Melsen B (2001) Tissue reaction to orthodontic tooth movement—a new paradigm. Eur J Orthod 23: 671–681CrossRefGoogle Scholar
  52. Mengoni M, Ponthot J-P (2010) Isotropic continuum damage/repair model for alveolar bone remodeling. J Comput Appl Math 234: 2036–2045MathSciNetMATHCrossRefGoogle Scholar
  53. Middleton J, Jones M, Wilson A (1996) The role of the periodontal ligament in bone modeling: the initial development of a time-dependent finite element model. Am J Orthod Dentofac Orthop 109: 155–162CrossRefGoogle Scholar
  54. Miyoshi K, Igarashi K, Saeki S, Shinoda H, Mitani H (2001) Tooth movement and changes in periodontal tissue in response to orthodontic force in rats vary depending on the time of day the force is applied. Eur J Orthod 23: 329–338CrossRefGoogle Scholar
  55. Natali AN, Pavan PG, Scarpa C (2004) Numerical analysis of tooth mobility: formulation of a non-linear constitutive law for the periodontal ligament. Dent Mater 20: 623–629CrossRefGoogle Scholar
  56. Nishijima Y, Yamaguchi M, Kojima T, Aihara N, Nakajima R, Kasai K (2006) Levels of RANKL and OPG in gingival crevicular fluid during orthodontic tooth movement and effect of compression force on releases from periodontal ligament cells in vitro. Orthod Craniofac Res 9: 63–70CrossRefGoogle Scholar
  57. Ogasawara T, Yoshimine Y, Kiyoshima T, Kobayashi I, Matsuo K, Akamine A, Sakai H (2004) In situ expression of RANKL, RANK, osteoprotegerin and cytokines in osteoclasts of rat periodontal tissue. J Periodontal Res 39: 42–49CrossRefGoogle Scholar
  58. Palsson BO, Bhatia S (2003) Tissue engineering. Pearson Prentice Hall BioengineeringGoogle Scholar
  59. Pfeilschifter J, Diel I, Scheppach B, Bretz A, Krempien R, Erdmann J, Schmid G, Reske N, Bismar H, Seck T, Krempien B, Ziegler R (1998) Concentration of transforming growth factor beta in human bone tissue: relationship to age, menopause, bone turnover, and bone volume. J Bone Miner Res 13: 716–730CrossRefGoogle Scholar
  60. Pinkerton MN, Wescott DC, Gaffey BJ, Beggs KT, Milne TJ, Meikle MC (2008) Cultured human periodontal ligament cells constitutively express multiple osteotropic cytokines and growth factors, several of which are responsive to mechanical deformation. J Periodontal Res 43: 343–351CrossRefGoogle Scholar
  61. Pivonka P, Zimak J, Smith DW, Gardiner BS, Dunstan CR, Sims NA, Martin TJ, Mundy GR (2008) Model structure and control of bone remodeling: a theoretical study. Bone 43: 249–263CrossRefGoogle Scholar
  62. Provatidis CG (2001) An analytical model for stress analysis of a tooth in translation. Int J Eng Sci 39: 1361–1381CrossRefGoogle Scholar
  63. Roberts WE, Huja S, Roberts JA (2004) Bone modeling: biomechanics, molecular mechanisms, and clinical perspectives. Semin Orthod 10: 123–161CrossRefGoogle Scholar
  64. Roberts-Harry D, Sandy J (2004) Orthodontics. Part 11: orthodontic tooth movement. Br Dent J 196: 391–394CrossRefGoogle Scholar
  65. Robling AG, Castillo AB, Turner CH (2006) Biomechanical and molecular regulation of bone remodeling. Annu Rev Biomed Eng 8: 455–498CrossRefGoogle Scholar
  66. Rody WJ, King GJ, Gu G (2001) Osteoclast recruitment to sites of compression in orthodontic tooth movement. Am J Orthod Dentofac Orthop 120: 477–489CrossRefGoogle Scholar
  67. Roodman GD (1998) Osteoclast differentiation and activity. Biochem Soc Trans 26: 7–13Google Scholar
  68. Roodman GD (1999) Cell biology of the osteoclast. Exp Hematol 27: 1229–1241CrossRefGoogle Scholar
  69. Ryser MD, Nigam N, Komarova S (2009) Mathematical modeling of spatio-temporal dynamics of a single bone multicellular unit. J Bone Miner Res 24: 860–870CrossRefGoogle Scholar
  70. Sandberg M, Vuorio T, Hirvonen H, Alitalo K, Vuorio E (1988) Enhanced expression of TGF-beta and c-fos mRNAs in the growth plates of developing human long bones. Development 102: 461–470Google Scholar
  71. Schneider J, Geiger M, Sander F-G (2002) Numerical experiments on long-time orthodontic tooth movement. Am J Orthod Dentofac Orthop 121: 257–265CrossRefGoogle Scholar
  72. Shiotani A, Shibasaki Y, Sasaki T (2001) Localization of receptor activator of NFkappaB ligand, RANKL, in periodontal tissues during experimental movement of rat molars. J Electron Microsc (Tokyo) 50: 365–369CrossRefGoogle Scholar
  73. Simonet WS, Lacey DL, Dunstan CR, Kelley M, Chang MS, Lüthy R, Nguyen HQ, Wooden S, Boone T, Shimamoto G, DeRose M, Elliot R, Colombero A, Tan HL, Trail G, Sullivan J, Davy E, Bucay N, Renshaw-Gegg K, Hughes TM, Hill D, Pattison W, Campbell P, Sander S, Van G, Tarpley J, Derby P, Lee R, Boyle WJ (1997) Osteoprotegerin: a novel secreted protein involved in the regulation of bone density. Cell 89: 309–319CrossRefGoogle Scholar
  74. Sodek J, McKee MD (2000) Molecular and cellular biology of alveolar bone. Periodontol 2000 24: 99–126CrossRefGoogle Scholar
  75. Soncini M, Pietrabissa R (2002) Quantitative approach for the prediction of tooth movement during orthodontic treatment. Comput Methods Biomech Biomed Eng 5: 361–368CrossRefGoogle Scholar
  76. Tan SD, Kuijpers-Jagtman AM, Semeins CM, Bronckers ALJJ, Maltha JC, Vonden Hoff JW, Everts V, Klein-Nulend J (2006) Fluid shear stress inhibits TNFalpha-induced osteocyte apoptosis. J Dent Res 85: 905–909CrossRefGoogle Scholar
  77. Tang L, Lin Z, Ming Li Y (2006) Effects of different magnitudes of mechanical strain on Osteoblasts in vitro. Biochem Biophys Res Commun 344: 122–128CrossRefGoogle Scholar
  78. Teng YT, Nguyen H, Gao X, Kong YY, Gorczynski RM, Singh B, Ellen RP, Penninger JM (2000) Functional human T-cell immunity and osteoprotegerin ligand control alveolar bone destruction in periodontal infection. J Clin Invest 106: R59–R67CrossRefGoogle Scholar
  79. Terai K, Takano-Yamamoto T, Ohba Y, Hiura K, Sugimoto M, Sato M, Kawahata H, Inaguma N, Kitamura Y, Nomura S (1999) Role of osteopontin in bone remodeling caused by mechanical stress. J Bone Miner Res 14: 839–849CrossRefGoogle Scholar
  80. Vander A, Sherman J, Luciano D (1998) Human physiology: the mechanisms of body function. McGraw-Hill, BostonGoogle Scholar
  81. Vatsa A, Smit TH, Klein-Nulend J (2007) Extracellular NO signalling from a mechanically stimulated osteocyte. J Biomech 40(Suppl 1): S89–S95CrossRefGoogle Scholar
  82. Verna C, Dalstra M, Lee TC, Cattaneo PM, Melsen B (2004) Microcracks in the alveolar bone following orthodontic tooth movement: a morphological and morphometric study. Eur J Orthod 26: 459–467CrossRefGoogle Scholar
  83. Weiner R, Schmitt BA, Podhaisky H (1997) ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs. Appl Numer Math 25: 303–319MathSciNetMATHCrossRefGoogle Scholar
  84. Wescott DC, Pinkerton MN, Gaffey BJ, Beggs KT, Milne TJ, Meikle MC (2007) Osteogenic gene expression by human periodontal ligament cells under cyclic tension. J Dent Res 86: 1212–1216CrossRefGoogle Scholar
  85. Wise GE, King GJ (2008) Mechanisms of tooth eruption and orthodontic tooth movement. J Dent Res 87: 414–434CrossRefGoogle Scholar
  86. Xie R, Kuijpers-Jagtman AM, Maltha JC (2009) Osteoclast differentiation and recruitment during early stages of experimental tooth movement in rats. Eur J Oral Sci 117: 43–50CrossRefGoogle Scholar
  87. Yamaguchi M, Shimizu N, Goseki T, Shibata Y, Takiguchi H, Iwasawa T, Abiko Y (1994) Effect of different magnitudes of tension force on prostaglandin E2 production by human periodontal ligament cells. Arch Oral Biol 39: 877–884CrossRefGoogle Scholar
  88. Yamaguchi M, Aihara N, Kojima T, Kasai K (2006) RANKL increase in compressed periodontal ligament cells from root resorption. J Dent Res 85: 751–756CrossRefGoogle Scholar
  89. Yamashiro T, Takano-Yamamoto T (2001) Influences of ovariectomy on experimental tooth movement in the rat. J Dent Res 80: 1858–1861CrossRefGoogle Scholar
  90. Yokoya K, Sasaki T, Shibasaki Y (1997) Distributional changes of osteoclasts and pre-osteoclastic cells in periodontal tissues during experimental tooth movement as revealed by quantitative immunohistochemistry of H(+)-ATPase. J Dent Res 76: 580–587CrossRefGoogle Scholar
  91. Yoshimatsu M, Shibata Y, Kitaura H, Chang X, Moriishi T, Hashimoto F, Yoshida N, Yamaguchi A (2006) Experimental model of tooth movement by orthodontic force in mice and its application to tumor necrosis factor receptor-deficient mice. J Bone Miner Metab 24: 20–27CrossRefGoogle Scholar
  92. Zauli G, Melloni E, Capitani S, Secchiero P (2009) Role of full-length osteoprotegerin in tumor cell biology. Cell Mol Life Sci 66: 841–851CrossRefGoogle Scholar
  93. Zohar R, Cheifetz S, McCulloch CA, Sodek J (1998) Analysis of intracellular osteopontin as a marker of osteoblastic cell differentiation and mesenchymal cell migration. Eur J Oral Sci 106(Suppl 1): 401–407Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Biomechanics SectionKU LeuvenHeverleeBelgium
  2. 2.Biomechanics Research UnitU. LiègeLiègeBelgium
  3. 3.Prometheus Division of Skeletal Tissue EngineeringKU LeuvenLeuvenBelgium

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