Skip to main content

Advertisement

Log in

Orthodontic Tooth Movement Studied by Finite Element Analysis: an Update. What Can We Learn from These Simulations?

  • Craniofacial Skeleton (TG Chu and S Akintoye, Section Editors)
  • Published:
Current Osteoporosis Reports Aims and scope Submit manuscript

Abstract

Purpose of Review

To produce an updated overview of the use of finite element (FE) analysis for analyzing orthodontic tooth movement (OTM). Different levels of simulation complexity, including material properties and level of morphological representation of the alveolar complex, will be presented and evaluated, and the limitations will be discussed.

Recent Findings

Complex formulations of the PDL have been proposed, which might be able to correctly predict the behavior of the PDL both when chewing forces and orthodontic forces are simulated in FE models. The recent findings do not corroborate the simplified view of the classical OTM theories.

Summary

The use of complex and biologically coherent FE models can help understanding the mechanisms leading to OTM as well as predicting the risk of root resorption related to specific force systems and magnitudes.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

  1. Asiri SN, Tadlock LP, Buschang PH. The prevalence of clinically meaningful malocclusion among US adults. Orthod Craniofacial Res. 2019;22(4):321–8. https://doi.org/10.1111/ocr.12328.

    Article  Google Scholar 

  2. Thilander B, Pena L, Infante C, Parada SS, de Mayorga C. Prevalence of malocclusion and orthodontic treatment need in children and adolescents in Bogota, Colombia. An epidemiological study related to different stages of dental development. Eur J Orthod. 2001;23(2):153–67. https://doi.org/10.1093/ejo/23.2.153.

    Article  CAS  PubMed  Google Scholar 

  3. Lombardo G, Vena F, Negri P, Pagano S, Barilotti C, Paglia L, et al. Worldwide prevalence of malocclusion in the different stages of dentition: a systematic review and meta-analysis. Eur J Paediatr Dent. 2020;21(2):115–22. https://doi.org/10.23804/ejpd.2020.21.02.05.

    Article  CAS  PubMed  Google Scholar 

  4. Burgersdijk R, Truin GJ, Frankenmolen F, Kalsbeek H, van't Hof M, Mulder J. Malocclusion and orthodontic treatment need of 15-74-year-old Dutch adults. Community Dent Oral Epidemiol. 1991;19(2):64–7. https://doi.org/10.1111/j.1600-0528.1991.tb00111.x.

    Article  CAS  PubMed  Google Scholar 

  5. Jang AT, Chen L, Shimotake AR, Landis W, Altoe V, Aloni S, et al. A force on the crown and tug of war in the periodontal complex. J Dent Res. 2018;97(3):241–50. https://doi.org/10.1177/0022034517744556. A rather comprehensive description of the role of the PDL as a fibrous joint is presented, taking into account the role of the PDL in relation to OTM, as well as during mastication.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Turner CH, Pavalko FM. Mechanotransduction and functional response of the skeleton to physical stress: the mechanisms and mechanics of bone adaptation. J Orthop Sci. 1998;3(6):346–55. https://doi.org/10.1007/s007760050064.

    Article  CAS  PubMed  Google Scholar 

  7. Schwarz AM. Tissue changes incidental to orthodontic tooth movement. Int J Orthod Oral Surg Radiogr. 1932;18(4):331–52. https://doi.org/10.1016/S0099-6963(32)80074-8.

    Article  Google Scholar 

  8. Reitan K. The initial tissue reaction incident to orthodontic tooth movement as related to the influence of function; an experimental histologic study on animal and human material. Acta Odontol Scand Suppl. 1951;6:1–240.

    CAS  PubMed  Google Scholar 

  9. Baumrind S. A reconsideration of the propriety of the "pressure-tension" hypothesis. Am J Orthod. 1969;55(1):12–22. https://doi.org/10.1016/s0002-9416(69)90170-5.

    Article  CAS  PubMed  Google Scholar 

  10. Heller IJ, Nanda R. Effect of metabolic alteration of periodontal fibers on orthodontic tooth movement. An experimental study. Am J Orthod. 1979;75(3):239–58. https://doi.org/10.1016/0002-9416(79)90272-0.

    Article  CAS  PubMed  Google Scholar 

  11. Melsen B. Biological reaction of alveolar bone to orthodontic tooth movement. Angle Orthod. 1999;69(2):151–8. https://doi.org/10.1043/0003-3219(1999)069<0151:Broabt>2.3.Co;2.

    Article  CAS  PubMed  Google Scholar 

  12. Cattaneo PM, Dalstra M, Melsen B. The finite element method: a tool to study orthodontic tooth movement. J Dent Res. 2005;84(5):428–33. https://doi.org/10.1177/154405910508400506.

    Article  CAS  PubMed  Google Scholar 

  13. Epker BN, Frost HM. Correlation of bone resorption and formation with the physical behavior of loaded bone. J Dent Res. 1965;44:33–41. https://doi.org/10.1177/00220345650440012801.

    Article  CAS  PubMed  Google Scholar 

  14. Frost HM. Bone "mass" and the "mechanostat": a proposal. Anat Rec. 1987;219(1):1–9. https://doi.org/10.1002/ar.1092190104.

    Article  CAS  PubMed  Google Scholar 

  15. Henneman S, Von den Hoff JW, Maltha JC. Mechanobiology of tooth movement. Eur J Orthod. 2008;30(3):299–306. https://doi.org/10.1093/ejo/cjn020.

    Article  CAS  PubMed  Google Scholar 

  16. Alikhani M, Sangsuwon C, Alansari S, Nervina JM, Teixeira CC. Biphasic theory: breakthrough understanding of tooth movement. J World Fed Orthod. 2018;7(3):82–8. https://doi.org/10.1016/j.ejwf.2018.08.001.

    Article  Google Scholar 

  17. McCormack SW, Witzel U, Watson PJ, Fagan MJ, Gröning F. The biomechanical function of periodontal ligament fibres in orthodontic tooth movement. PLoS One. 2014;9(7):e102387. https://doi.org/10.1371/journal.pone.0102387.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Fill TS, Toogood RW, Major PW, Carey JP. Analytically determined mechanical properties of, and models for the periodontal ligament: critical review of literature. J Biomech. 2012;45(1):9–16. https://doi.org/10.1016/j.jbiomech.2011.09.020. In this article, a critical and updated review of the material properties of the PDL available in the literature is presented. The inaccuracies, inconsistencies, and shortcomings of the presented formulations of the behavior of the PDL are critically discussed.

    Article  PubMed  Google Scholar 

  19. Berkovitz BKB. The structure of the periodontal ligament: an update. Eur J Orthod. 1990;12(1):51–76. https://doi.org/10.1093/ejo/12.1.51.

    Article  CAS  PubMed  Google Scholar 

  20. Lin JD, Özcoban H, Greene JP, Jang AT, Djomehri SI, Fahey KP, et al. Biomechanics of a bone-periodontal ligament-tooth fibrous joint. J Biomech. 2013;46(3):443–9. https://doi.org/10.1016/j.jbiomech.2012.11.010.

    Article  PubMed  Google Scholar 

  21. Embery G. An update on the biochemistry of the periodontal ligament. Eur J Orthod. 1990;12(1):77–80. https://doi.org/10.1093/ejo/12.1.77.

    Article  CAS  PubMed  Google Scholar 

  22. Lin JD, Jang AT, Kurylo MP, Hurng J, Yang F, Yang L, et al. Periodontal ligament entheses and their adaptive role in the context of dentoalveolar joint function. Dent Mater. 2017;33(6):650–66. https://doi.org/10.1016/j.dental.2017.03.007. The PDL is presented using a “multiscale biomechanics and mechanobiology approach,” where its physiological and non-physiological (including therapeutic loads) function as a dentoalveolar joint is described. The level of strain felt by the bone-PDL-cementum complex is considered as the key factor in the joint adaptation to various loading conditions.

  23. Wills DJ, Picton DC, Davies WI. A study of the fluid systems of the periodontium in macaque monkeys. Arch Oral Biol. 1976;21(3):175–85. https://doi.org/10.1016/0003-9969(76)90127-8.

    Article  CAS  PubMed  Google Scholar 

  24. Cattaneo PM, Dalstra M, Melsen B. Analysis of stress and strain around orthodontically loaded implants: an animal study. Int J Oral Maxillofac Implants. 2007;22(2):213–25.

    PubMed  Google Scholar 

  25. Dalstra M, Cattaneo PM, Laursen MG, Beckmann F, Melsen B. Multi-level synchrotron radiation-based microtomography of the dental alveolus and its consequences for orthodontics. J Biomech. 2015;48(5):801–6. https://doi.org/10.1016/j.jbiomech.2014.12.014.

    Article  CAS  PubMed  Google Scholar 

  26. Leder Horina J, van Rietbergen B, Jurčević LT. Finite element model of load adaptive remodelling induced by orthodontic forces. Med Eng Phys. 2018;62:63–8. https://doi.org/10.1016/j.medengphy.2018.10.005.

    Article  PubMed  Google Scholar 

  27. Field C, Ichim I, Swain MV, Chan E, Darendeliler MA, Li W, et al. Mechanical responses to orthodontic loading: a 3-dimensional finite element multi-tooth model. Am J Orthod Dentofac Orthop. 2009;135(2):174–81. https://doi.org/10.1016/j.ajodo.2007.03.032.

    Article  Google Scholar 

  28. Frost HM. Skeletal structural adaptations to mechanical usage (SATMU): 1. redefining Wolff's law: the bone modeling problem. Anat Rec. 1990;226(4):403–13. https://doi.org/10.1002/ar.1092260402.

    Article  CAS  PubMed  Google Scholar 

  29. Jones ML, Hickman J, Middleton J, Knox J, Volp C. A validated finite element method study of orthodontic tooth movement in the human subject. J Orthod. 2001;28(1):29–38. https://doi.org/10.1093/ortho/28.1.29.

    Article  CAS  PubMed  Google Scholar 

  30. Lanyon LE, Rubin CT. Static vs dynamic loads as an influence on bone remodelling. J Biomech. 1984;17(12):897–905. https://doi.org/10.1016/0021-9290(84)90003-4.

    Article  CAS  PubMed  Google Scholar 

  31. Rubin CT, Lanyon LE. Regulation of bone formation by applied dynamic loads. J Bone Joint Surg Am. 1984;66(3):397–402.

    Article  CAS  Google Scholar 

  32. Ingber DE. Tensegrity and mechanotransduction. J Bodyw Mov Ther. 2008;12(3):198–200. https://doi.org/10.1016/j.jbmt.2008.04.038.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Binderman I, Bahar H, Yaffe A. Strain relaxation of fibroblasts in the marginal periodontium is the common trigger for alveolar bone resorption: a novel hypothesis. J Periodontol. 2002;73(10):1210–5. https://doi.org/10.1902/jop.2002.73.10.1210.

    Article  PubMed  Google Scholar 

  34. Farah JW, Craig RG, Sikarskie DL. Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J Biomech. 1973;6(5):511–20. https://doi.org/10.1016/0021-9290(73)90009-2.

    Article  CAS  PubMed  Google Scholar 

  35. McCormack SW, Witzel U, Watson PJ, Fagan MJ, Groning F. Inclusion of periodontal ligament fibres in mandibular finite element models leads to an increase in alveolar bone strains. PLoS One. 2017;12(11):e0188707. https://doi.org/10.1371/journal.pone.0188707.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Fill TS, Carey JP, Toogood RW, Major PW. Experimentally determined mechanical properties of, and models for, the periodontal ligament: critical review of current literature. J Dent Biomech. 2011;2011:312980. https://doi.org/10.4061/2011/312980.

    Article  PubMed  PubMed Central  Google Scholar 

  37. Nyashin Y, Nyashin M, Osipenko M, Lokhov V, Dubinin A, Rammerstorfer F, et al. Centre of resistance and centre of rotation of a tooth: experimental determination, computer simulation and the effect of tissue nonlinearity. Comput Methods Biomech Biomed Engin. 2016;19(3):229–39. https://doi.org/10.1080/10255842.2015.1007961.

    Article  CAS  PubMed  Google Scholar 

  38. Müller R, Rüegsegger P. Micro-tomographic imaging for the nondestructive evaluation of trabecular bone architecture. Stud Health Technol Inform. 1997;40:61–79.

    PubMed  Google Scholar 

  39. Bonse U, Busch F, Günnewig O, Beckmann F, Pahl R, Delling G, et al. 3D computed X-ray tomography of human cancellous bone at 8 microns spatial and 10(-4) energy resolution. Bone Miner. 1994;25(1):25–38. https://doi.org/10.1016/s0169-6009(08)80205-x.

    Article  CAS  PubMed  Google Scholar 

  40. Dalstra M, Cattaneo PM, Beckmann F. Synchrotron radiation-based microtomography of alveolar support tissues. Orthod Craniofacial Res. 2006;9(4):199–205. https://doi.org/10.1111/j.1601-6343.2006.00376.x.

    Article  CAS  Google Scholar 

  41. Nicolella DP, Bonewald LF, Moravits DE, Lankford J. Measurement of microstructural strain in cortical bone. Eur J Morphol. 2005;42(1–2):23–9. https://doi.org/10.1080/09243860500095364.

    Article  PubMed  PubMed Central  Google Scholar 

  42. Sifakakis I, Eliades T. Laboratory evaluation of orthodontic biomechanics: the clinical applications revisited. Semin Orthod. 2017;23(4):382–9. https://doi.org/10.1053/j.sodo.2017.07.008.

    Article  Google Scholar 

  43. Hartmann M, Dirk C, Reimann S, Keilig L, Konermann A, Jäger A, et al. Influence of tooth dimension on the initial mobility based on plaster casts and X-ray images : a numerical study. J Orofac Orthop. 2017;78(4):285–92. https://doi.org/10.1007/s00056-016-0082-9.

    Article  PubMed  Google Scholar 

  44. Schmidt F, Geiger ME, Jäger R, Lapatki BG. Comparison of methods to determine the centre of resistance of teeth. Comput Methods Biomech Biomed Engin. 2016;19(15):1673–82. https://doi.org/10.1080/10255842.2016.1177822. This paper explores whether it is possible to predict OTM using a semi-analytical approach based on few clinical parameters (e.g., crown and root lengths) and to determine the relative errors produced following this procedure against morphologically correct and sample-specific FE models. This study has the potential to be used in a “real” and patient-specific clinical setting, so that individualized treatment planning can be achieved.

    Article  PubMed  Google Scholar 

  45. Gameiro GH, Bocchiardo JE, Dalstra M, Cattaneo PM. Individualization of the three-piece base arch mechanics according to various periodontal support levels: a finite element analysis. Orthod Craniofacial Res. 2020. https://doi.org/10.1111/ocr.12420.

  46. Boldt J, Knapp W, Proff P, Rottner K, Richter E-J. Measurement of tooth and implant mobility under physiological loading conditions. Ann Anat. 2012;194(2):185–9. https://doi.org/10.1016/j.aanat.2011.09.007.

  47. Christiansen RL, Burstone CJ. Centers of rotation within the periodontal space. Am J Orthod. 1969;55(4):353–69. https://doi.org/10.1016/0002-9416(69)90143-2.

    Article  CAS  PubMed  Google Scholar 

  48. Tuna M, Sunbuloglu E, Bozdag E. Finite element simulation of the behavior of the periodontal ligament: a validated nonlinear contact model. J Biomech. 2014;47(12):2883–90. https://doi.org/10.1016/j.jbiomech.2014.07.023.

    Article  PubMed  Google Scholar 

  49. Cattaneo PM, Dalstra M, Melsen B. Moment-to-force ratio, center of rotation, and force level: a finite element study predicting their interdependency for simulated orthodontic loading regimens. Am J Orthod Dentofac Orthop. 2008;133(5):681–9. https://doi.org/10.1016/j.ajodo.2006.05.038.

    Article  Google Scholar 

  50. Nikolaus A, Currey JD, Lindtner T, Fleck C, Zaslansky P. Importance of the variable periodontal ligament geometry for whole tooth mechanical function: a validated numerical study. J Mech Behav Biomed Mater. 2017;67:61–73. https://doi.org/10.1016/j.jmbbm.2016.11.020.

    Article  PubMed  Google Scholar 

  51. Mehari Abraha H, Iriarte-Diaz J, Ross CF, Taylor AB, Panagiotopoulou O. The mechanical effect of the periodontal ligament on bone strain regimes in a validated finite element model of a macaque mandible. Front Bioeng Biotechnol. 2019;7:269. https://doi.org/10.3389/fbioe.2019.00269.

    Article  PubMed  PubMed Central  Google Scholar 

  52. Kondo T, Hotokezaka H, Hamanaka R, Hashimoto M, Nakano-Tajima T, Arita K, et al. Types of tooth movement, bodily or tipping, do not affect the displacement of the tooth's center of resistance but do affect the alveolar bone resorption. Angle Orthod. 2017;87(4):563–9. https://doi.org/10.2319/110416-794.1.

    Article  PubMed  Google Scholar 

  53. Huang H, Tang W, Yan B, Wu B, Cao D. Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method. Comput Methods Biomech Biomed Engin. 2016;19(2):188–98. https://doi.org/10.1080/10255842.2015.1006207.

    Article  PubMed  Google Scholar 

  54. Van Schepdael A, Geris L, Vander SJ. Analytical determination of stress patterns in the periodontal ligament during orthodontic tooth movement. Med Eng Phys. 2013;35(3):403–10. https://doi.org/10.1016/j.medengphy.2012.09.008.

    Article  PubMed  Google Scholar 

  55. Provatidis CG. An analytical model for stress analysis of a tooth in translation. Int J Eng Sci. 2001;39(12):1361–81. https://doi.org/10.1016/S0020-7225(00)00098-7.

    Article  Google Scholar 

  56. Maceri F, Marino M, Vairo G. A unified multiscale mechanical model for soft collagenous tissues with regular fiber arrangement. J Biomech. 2010;43(2):355–63. https://doi.org/10.1016/j.jbiomech.2009.07.040.

    Article  PubMed  Google Scholar 

  57. Schmidt F, Lapatki BG. Effect of variable periodontal ligament thickness and its non-linear material properties on the location of a tooth's centre of resistance. J Biomech. 2019;94:211–8. https://doi.org/10.1016/j.jbiomech.2019.07.043.

    Article  PubMed  Google Scholar 

  58. Bourauel C, Vollmer D, Jäger A. Application of bone remodeling theories in the simulation of orthodontic tooth movements. J Orofac Orthop. 2000;61(4):266–79. https://doi.org/10.1007/s000560050012.

    Article  CAS  PubMed  Google Scholar 

  59. Schneider J, Geiger M, Sander FG. Numerical experiments on long-time orthodontic tooth movement. Am J Orthod Dentofac Orthop. 2002;121(3):257–65. https://doi.org/10.1067/mod.2002.121007.

    Article  Google Scholar 

  60. Kojima Y, Fukui H. A finite element simulation of initial movement, orthodontic movement, and the centre of resistance of the maxillary teeth connected with an archwire. Eur J Orthod. 2014;36(3):255–61. https://doi.org/10.1093/ejo/cjr123.

    Article  PubMed  Google Scholar 

  61. Kojima Y, Kawamura J, Fukui H. Finite element analysis of the effect of force directions on tooth movement in extraction space closure with miniscrew sliding mechanics. Am J Orthod Dentofac Orthop. 2012;142(4):501–8. https://doi.org/10.1016/j.ajodo.2012.05.014.

    Article  Google Scholar 

  62. Wang C, Han J, Li Q, Wang L, Fan Y. Simulation of bone remodelling in orthodontic treatment. Comput Methods Biomech Biomed Engin. 2014;17(9):1042–50. https://doi.org/10.1080/10255842.2012.736969.

    Article  PubMed  Google Scholar 

  63. Roscoe MG, Meira JB, Cattaneo PM. Association of orthodontic force system and root resorption: a systematic review. Am J Orthod Dentofac Orthop. 2015;147(5):610–26. https://doi.org/10.1016/j.ajodo.2014.12.026.

    Article  Google Scholar 

  64. Hohmann A, Wolfram U, Geiger M, Boryor A, Kober C, Sander C, et al. Correspondences of hydrostatic pressure in periodontal ligament with regions of root resorption: a clinical and a finite element study of the same human teeth. Comput Methods Prog Biomed. 2009;93(2):155–61. https://doi.org/10.1016/j.cmpb.2008.09.004.

    Article  Google Scholar 

  65. Zhong J, Chen J, Weinkamer R, Darendeliler MA, Swain MV, Sue A, et al. In vivo effects of different orthodontic loading on root resorption and correlation with mechanobiological stimulus in periodontal ligament. J R Soc Interface. 2019;16(154). https://doi.org/10.1098/rsif.2019.0108.

  66. Frost HM. Skeletal structural adaptations to mechanical usage (SATMU): 3. the hyaline cartilage modeling problem. Anat Rec. 1990;226(4):423–32. https://doi.org/10.1002/ar.1092260404.

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paolo M. Cattaneo.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Human and Animal Rights and Informed Consent

This article does not contain any experiments with animal subjects. The reported studies with human subjects performed by the authors complied with all applicable ethical standards (including the Helsinki declaration and its amendments, institutional/national research committee standards, and international/national/institutional guidelines).

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the Topical Collection on Craniofacial Skeleton

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cattaneo, P.M., Cornelis, M.A. Orthodontic Tooth Movement Studied by Finite Element Analysis: an Update. What Can We Learn from These Simulations?. Curr Osteoporos Rep 19, 175–181 (2021). https://doi.org/10.1007/s11914-021-00664-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11914-021-00664-0

Keywords

Navigation