Restricted accessResearch articleFirst published online 2017-1
Mechanical equilibrium of forces and moments applied on orthodontic brackets of a dental arch: Correlation with literature data on two and three adjacent teeth
Although orthodontics have greatly improved over the years, understanding of its associated biomechanics remains incomplete and is mainly based on two dimensional (2D) mechanical equilibrium and long-time clinical experience. Little experimental information exists in three dimensions (3D) about the forces and moments developed on orthodontic brackets over more than two or three adjacent teeth. We define here a simplified methodology to quantify 3D forces and moments applied on orthodontic brackets fixed on a dental arch and validate our methodology using existing results from the literature by means of simplified hypotheses.
AngleE.H., The latest and best in orthodontic mechanism, Dental Cosmos70 (1928), 1143–1158.
2.
BurstoneC.J., Physics and clinical orthodontics: 100 years ago and today, American Journal of Orthodontics and Dentofacial Orthopedics147 (2015), 293–294. doi:10.1016/j.ajodo.2014.12.011.
3.
AndrewsL.F., The straight-wire appliance. Origin, controversy, commentary, Journal of Clinical Orthodontics10 (1976), 99–114.
4.
AndrewsL.F., The straight-wire appliance. Explained and compared, Journal of Clinical Orthodontics10 (1976), 174–195.
5.
KusyR.P. and TullochC., Analysis of moment-force ratios in the mechanics of tooth movement, American Journal of Orthodontics and Dentofacial Orthopedics90 (1986), 127–131. doi:10.1016/0889-5406(86)90044-2.
6.
SandstedtC., EinigeBeiträgezurTheorie der Zahn-regulierung, Nordisk TandlakareTidsskrift5 (1904), 236–256.
7.
OppenheimA., Human tissue response to orthodontic intervention of short and long duration, American Journal of Orthodontics and Oral Surgery28 (1942), 263–301. doi:10.1016/S0096-6347(42)90492-7.
8.
StoreyE. and SmithR., Force in orthodontics and its relation to tooth movement, Australian Journal of Dentistry56 (1952), 11–18.
9.
ReitanK., Tissue behavior during orthodontic tooth movement, American Journal of Orthodontics46 (1960), 881–890. doi:10.1016/0002-9416(60)90091-9.
10.
MelsenB., Tissue reaction to orthodontic tooth movement – a new paradigm, European Journal of Orthodontics23 (2001), 671–681. doi:10.1093/ejo/23.6.671.
11.
DavidovitchZ., Tooth movement, Critical Reviews in Oral Biology and Medicine2 (1991), 411–450. doi:10.1177/10454411910020040101.
12.
PavlinD. and Gluhak-HeinrichJ., Effect of mechanical loading on periodontal cells, Critical Reviews in Oral Biology and Medicine12 (2001), 414–424. doi:10.1177/10454411010120050401.
13.
BourauelD. and DrescherM., An experimental apparatus for the simulation of three-dimensional movements in orthodontics, Journal of Biomedical Engineering14(5) (1992), 371–378. doi:10.1016/0141-5425(92)90081-U.
14.
JonesM.HickmanJ.MiddletonJ.KnoxJ. and VolpC., A validated finite element method study of orthodontic tooth movement in the human subject, Journal of Orthodontics28(1) (2001), 29–38. doi:10.1093/ortho/28.1.29.
15.
LekszyckiT., Modeling of bone adaptation based on an optimal response hypothesis, Meccanica37 (2002), 343–354. doi:10.1023/A:1020831519496.
16.
CattaneoP.M.DalstraM. and MelsenB., The finite element method: A tool to study orthodontic tooth movement, Journal of Dental Research84 (2005), 428–433. doi:10.1177/154405910508400506.
17.
BourauelC.KeiligL.RahimiA.ReimannS.ZieglerA. and JagerA., Computer-aided analysis of the biomechanics of tooth movements, International Journal of Computerized Dentistry10 (2007), 25–40.
18.
FieldC.IchimI.SwainM.V.ChanE.DarendelilerM.A. and LiX., Mechanical responses to orthodontic loading: A 3-dimensional finite element multi-tooth model, American Journal of Orthodontics and Dentofacial Orthopedics135 (2009), 174–181. doi:10.1016/j.ajodo.2007.03.032.
19.
MadeoA.GeorgeD.LekszyckiT.NierenbergerM. and RémondY., A second gradient continuum model accounting for some effects of microstructure on reconstructed bone remodeling, Comptes Rendus Mécanique340 (2012), 575–589. doi:10.1016/j.crme.2012.05.003.
20.
CanalesC.LarsonM.GrauerD.SheatsR.StevensC. and KowC.C., A novel biomechanical model assessing continuous orthodontic archwire activation, American Journal of Orthodontics and Dentofacial Orthopedics143 (2013), 281–290. doi:10.1016/j.ajodo.2012.06.019.
21.
GeorgeD.SpingarnC.MadéoA. and RémondY., Effects of mechanical loading conditions on a 3D bone reconstruction: a theoretical numerical study for application to maxillo-facial surgery, in: 9th European Solid Mechanics Conference, Madrid, Spain, 2015.
22.
ScalaI.SpingarnC.RemondY.MadeoA. and GeorgeD., Mechanically-driven bone remodeling simulation: Application to LIPUS treated rat calvarial defects, Mathematics and Mechanics of Solids (2016), in press. doi:10.1177/1081286516651473.
23.
GiorgioI.AndreausU.ScerratoD. and Dell’IsolaF., A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials, Biomechanics and Modeling in Mechanobiology (2016), 1–19.
24.
LiaoZ.ChenaJ.LiaW.DarendelilerM.A. and SwainS., Biomechanical investigation into the role of the periodontal ligament in optimising orthodontic force: A finite element case study, Archives of Oral Biology66 (2016), 98–107. doi:10.1016/j.archoralbio.2016.02.012.
25.
BurstoneC.J. and KoenigH.A., Force systems from an ideal arch, American Journal of Orthodontics and Dentofacial Orthopedics65 (1974), 270–289. doi:10.1016/S0002-9416(74)90332-7.
26.
SmithR.J. and BurstoneC.J., Mechanics of tooth movement, American Journal of Orthodontics85 (1984), 294–307. doi:10.1016/0002-9416(84)90187-8.
27.
BarbatoG. and BrayA., Sensors for measuring force, in: Sensors Set: A Comprehensive SurveyGoepelW.HesseJ. and ZemelJ.N., eds, Vol. 7, Wiley-VCH Verlag GmbH, Weinheim, Germany, 1995, pp. 437–482. doi:10.1002/9783527620203.ch12.
28.
FriedrichD.RosariusN.RauG. and DiedrichP., Measuring system for in vivo recording of force systems in orthodontic treatment-concept and analysis of accuracy, Journal of Biomechanics32(1) (1999), 81–85. doi:10.1016/S0021-9290(98)00112-2.
29.
BadawiH.M.ToogoodR.W.CareyJ.P.R.HeoG. and MajorP.W., Three-dimensional orthodontic force measurements, American Journal of Orthodontics and Dentofacial Orthopedics136 (2009), 518–528. doi:10.1016/j.ajodo.2009.02.025.
30.
BecquartP.CruelM.HocT.SudreL.PemelleK.BiziosR.Logeart-AvramoglouD.PetiteH. and BensidhoumM., Human mesenchymal stem cell responses to hydrostatic pressure and shear stress, European Cells and Materials31 (2016), 160–173. doi:10.22203/eCM.v031a11.
31.
WagnerD.BolenderY.RemondY. and GeorgeD., Mathematical writing of forces and moments applied to three teeth in the three dimensions of space: The forgotten bucco lingual dimension, in: 92th Congress of the European Orthodontics Society, Stockholm, Sweden, 2016.
32.
KusyR.P. and WhitleyJ.Q., Friction between different wire-bracket configurations and materials, Seminars in Orthodontics3 (1997), 166–177. doi:10.1016/S1073-8746(97)80067-9.
33.
FrictionP.E.R., An overview, Seminars in Orthodontics9(4) (2003), 218–222. doi:10.1016/j.sodo.2003.08.002.
34.
BurrowS.J., Friction and resistance to sliding in orthodontics: A critical review, American Journal of Orthodontics and Dentofacial Orthopedics135 (2009), 442–447. doi:10.1016/j.ajodo.2008.09.023.
35.
ViecilliR.F.BudimanA. and BurstoneC.J., Axes of resistance for tooth movement: Does the center of resistance exist in 3-dimensional space?American Journal of Orthodontics and Dentofacial Orthopedics143 (2013), 163–172. doi:10.1016/j.ajodo.2012.09.010.
36.
SmithR.J. and BurstoneC.J., Mechanics of tooth movement, American Journal of Orthodontics85(4) (1984), 294–307. doi:10.1016/0002-9416(84)90187-8.
37.
BurstoneC.J., The biomechanics of tooth movement, in: Vistas in OrthodonticsKrausB.S. and RiedelR.A., eds, Lea & Febiger, Philadelphia, PA, 1962, pp. 197–213.
38.
AshM.M. and NelsonS., Wheeler’s Dental Anatomy, Physiology and Occlusion, 9ème édition, Elsevier, 2010.
39.
ChoyK.PaeE.K.ParkY.KimK.H. and BurstoneC.J., Effect of root and bone morphology on the stress distribution in the periodontal ligament, American Journal of Orthodontics and Dentofacial Orthopedics117(1) (2000), 98–105.
