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Computer-aided finite element model for biomechanical analysis of orthodontic aligners

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Abstract

Objectives

To design a finite element (FE) model that might facilitate understanding of the complex mechanical behavior of orthodontic aligners. The designed model was validated by comparing the generated forces — during 0.2-mm facio-lingual translation of upper left central incisor (Tooth 21) — with the values reported by experimental studies in literature.

Materials and methods

A 3D digital model, obtained from scanning of a typodont of upper jaw, was imported into 3-matic software for designing of aligners with different thicknesses: 0.4, 0.5, 0.6, 0.7 mm. The model was exported to Marc/Mentat FE software. Suitable parameters for FE simulation were selected after a series of sensitivity analyses. Different element classes of the model and different rigidity values of the aligner were also investigated.

Results

The resultant maximum forces generated on facio-lingual translation of Tooth 21 were within the range of 1.3–18.3 N. The force was direction-dependent, where lingual translation transmitted higher forces than facial translation. The force increases with increasing the thickness of the aligner, but not linearly. We found that the generated forces were almost directly proportional to the rigidity of the aligner. The contact normal stress map showed an uneven but almost repeatable distribution of stresses all over the facial surface and concentration of stresses at specific points.

Conclusions

A validated FE model could reveal a lot about mechanical behavior of orthodontic aligners.

Clinical relevance

Understanding the force systems of clear aligner by means of FE will facilitate better treatment planning and getting optimal outcomes.

Graphical abstract

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References

  1. Elshazly TM, Keilig L, Alkabani Y, Ghoneima A, Abuzayda M, Talaat S, Bourauel CP (2021) Primary evaluation of shape recovery of orthodontic aligners fabricated from shape memory polymer (a typodont study). Dent J 9(3):31. https://doi.org/10.3390/dj9030031

    Article  Google Scholar 

  2. Thukral R, Gupta A (2015) Invisalign: invisible orthodontic treatment-a review. J Adv Med Dent Sci Res 3(5):42

    Google Scholar 

  3. Elshazly TM, Keilig L, Alkabani Y, Ghoneima A, Abuzayda M, Talaat W, Talaat S, Bourauel CP (2022) Potential application of 4D technology in fabrication of orthodontic aligners. Front Mater. https://doi.org/10.3389/fmats.2021.794536

  4. Tamer İ, Öztaş E, Marşan G (2019) Orthodontic treatment with clear aligners and the scientific reality behind their marketing: a literature review. Turk J Orthod 32(4):241–246. https://doi.org/10.5152/TurkJOrthod.2019.18083

    Article  Google Scholar 

  5. Mehta F, Mehta S (2014) Aligners: the rapidly growing trend in orthodontics around the world. Indian J Basic Appl Med Res 3:402–409

    Google Scholar 

  6. Pinho T, Santos M (2021) Skeletal open bite treated with clear aligners and miniscrews. Am J Orthod Dentofac Orthop 159(2):224–233. https://doi.org/10.1016/j.ajodo.2019.07.020

    Article  Google Scholar 

  7. Schupp W, Haubrich J, Neumann I (2010) Invisalign® treatment of patients with craniomandibular disorders. Int Orthod 8(3):253–267. https://doi.org/10.1016/j.ortho.2010.07.010

    Article  Google Scholar 

  8. Morton J, Derakhshan M, Kaza S, Li C (2017) Design of the Invisalign system performance. Semin Orthod 23(1):3–11. https://doi.org/10.1053/j.sodo.2016.10.001

    Article  Google Scholar 

  9. Barone S, Paoli A, Razionale AV, Savignano R (2016) Design of customised orthodontic devices by digital imaging and CAD/FEM modelling. Int Conf Bioimaging 3:44–52. https://doi.org/10.5220/0005821000440052

    Article  Google Scholar 

  10. Savignano R (2014) Biomechanical analysis of orthodontic appliances through 3D computer aided engineering. In Doctoral Consortium on Biomedical Engineering Systems and Technologies 2:28–35

  11. Boyd RL, Waskalic V (2001) Three-dimensional diagnosis andorthodontic treatment of complex malocclusions with the invisalign appliance. Semin Orthod 7(4):274–293. https://doi.org/10.1053/sodo.2001.25414

    Article  Google Scholar 

  12. Ryu JH, Kwon JS, Jiang HB, Cha JY, Kim KM (2018) Effects of thermoforming on the physical and mechanical properties of thermoplastic materials for transparent orthodontic aligners. Korean J Orthod 48(5):316–325

    Article  Google Scholar 

  13. Elkholy F, Schmidt F, Jäger R, Lapatki BG (2016) Forces and moments delivered by novel, thinner PET-G aligners during labiopalatal bodily movement of a maxillary central incisor: an in vitro study. Angle Orthod 86(6):883–890. https://doi.org/10.2319/011316-37R.1

    Article  Google Scholar 

  14. Vardimon AD, Robbins D, Brosh T (2010) In-vivo von Mises strains during Invisalign treatment. Am J Orthod Dentofac Orthop 138(4):399–409. https://doi.org/10.1016/j.ajodo.2008.11.027

    Article  Google Scholar 

  15. Shi Y, Ren C, Hao W, Zhang M, Bai Y, Wang Z (2011) An ultra-thin piezoresistive stress sensor for measurement of tooth orthodontic force in invisible aligners. IEEE Sens J 12(5):1090–1097. https://doi.org/10.1109/JSEN.2011.2166065

    Article  Google Scholar 

  16. Son HJ, Lee KH, Sim JY, Kim HY, Kim JH, Kim WC (2020) Pressure differences from clear aligner movements assessed by pressure sensors. Biomed Res Int. https://doi.org/10.1155/2020/8376395

    Article  Google Scholar 

  17. Xiang B, Wang X, Wu G, Xu Y, Wang M, Yang Y, Wang Q (2021) The force effects of two types of polyethylene terephthalate glyc-olmodified clear aligners immersed in artificial saliva. Sci Rep 11(1):1–10. https://doi.org/10.1038/s41598-021-89425-8

    Article  Google Scholar 

  18. Li X, Ren C, Wang Z, Zhao P, Wang H, Bai Y (2016) Changes in force associated with the amount of aligner activation and lingual bodily movement of the maxillary central incisor. Korean J Orthod 46(2):65–72. https://doi.org/10.4041/kjod.2016.46.2.65

    Article  Google Scholar 

  19. Cervinara F, Cianci C, De Cillis F, Pappalettera G, Pappalettere C, Siciliani G, Lombardo L (2019) Experimental study of the pressures and points of application of the forces exerted between aligner and tooth. Nanomaterials 9(7):1010. https://doi.org/10.3390/nano9071010

    Article  Google Scholar 

  20. Barbagallo LJ, Shen G, Jones AS, Swain MV, Petocz P, Darendeliler MA (2008) A novel pressure film approach for determining the force imparted by clear removable thermoplastic appliances. Ann Biomed Eng 36(2):335–341. https://doi.org/10.1007/s10439-007-9424-5

    Article  Google Scholar 

  21. Simon M, Keilig L, Schwarze J, Jung BA, Bourauel C (2014) Forces and moments generated by removable thermoplastic aligners: incisor torque, premolar derotation, and molar distalization. Am J Orthod Dentofac Orthop 145(6):728–736. https://doi.org/10.1016/j.ajodo.2014.03.015

    Article  Google Scholar 

  22. Hahn W, Fialka-Fricke J, Dathe H et al (2009) Initial forces generated by three types of thermoplastic appliances on an upper central incisor during tipping. Eur J Orthod 31(6):625–631. https://doi.org/10.1093/ejo/cjp047

    Article  Google Scholar 

  23. Elkholy F, Panchaphongsaphak T, Kilic F, Schmidt F, Lapatki BG (2015) Forces and moments delivered by PET-G aligners to an upper central incisor for labial and palatal translation. J Orofac Orthop 76:460–475. https://doi.org/10.1007/s00056-015-0307-3

    Article  Google Scholar 

  24. Ren Y, Maltha JC, Kuijpers-Jagtman AM (2003) Optimum force magnitude for orthodontic tooth movement: a systematic literature review. Angle Orthod 73(1):86–92

    Google Scholar 

  25. Farah JW, Craig RG, Sikarskie DL (1973) Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J Biomech 6(5):511–520. https://doi.org/10.1016/0021-9290(73)90009-2

    Article  Google Scholar 

  26. Lee JS, Lim YJ (2013) Three-dimensional numerical simulation of stress induced by different lengths of osseointegrated implants in the anterior maxilla. Comput Methods Biomech Biomed Engin 16(11):1143–1149. https://doi.org/10.1080/10255842.2012.654780

    Article  Google Scholar 

  27. Kettenbeil A, Reimann S, Reichert C, Keilig L, Jäger A, Bourauel C (2013) Numerical simulation and biomechanical analysis of an orthodontically treated periodontally damaged dentition. J Orofac Orthop/Fortschr Kieferorthop 74(6):480–493. https://doi.org/10.1007/s00056-013-0182-2

    Article  Google Scholar 

  28. Huang Y, Keilig L, Rahimi A, Reimann S, Bourauel C (2012) Torque capabilities of self-ligating and conventional brackets under the effect of bracket width and free wire length. Orthod Craniofac Res 15(4):255–262. https://doi.org/10.1111/j.1601-6343.2012.01553.x

    Article  Google Scholar 

  29. Mascarenhas R, Shenoy S, Parveen S, Chatra L, Husain A (2017) Evaluation of lingual orthodontic appliances. J Comput Methods Sci Eng 17(2):253–260. https://doi.org/10.3233/JCM-170714

    Article  Google Scholar 

  30. Hamanaka R, Yamaoka S, Anh TN, Tominaga JY, Koga Y, Yoshida N (2017) Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method. Am J Orthod Dentofac Orthop 152(5):601–612. https://doi.org/10.1016/j.ajodo.2017.03.021

    Article  Google Scholar 

  31. Barone S, Paoli A, Razionale AV, Savignano R (2016) Computer aided modelling to simulate the biomechanical behaviour of customised orthodontic removable appliances. Int J Interact Des Manuf (IJIDeM) 10(4):387–400. https://doi.org/10.1007/s12008-014-0246-z

    Article  Google Scholar 

  32. Cai Y, Yang X, He B, Yao J (2015) Finite element method analysis of the periodontal ligament in mandibular canine movement with transparent tooth correction treatment. BMC Oral Health 15(1):1–11. https://doi.org/10.1186/s12903-015-0091-x

    Article  Google Scholar 

  33. Gomez JP, Peña FM, Martínez V, Giraldo DC, Cardona CI (2015) Initial force systems during bodily tooth movement with plastic aligners and composite attachments: a three-dimensional finite element analysis. Angle Orthod 85(3):454–460. https://doi.org/10.2319/050714-330.1

    Article  Google Scholar 

  34. Hahn W, Zapf A, Dathe H, Fialka-Fricke J et al (2010) Torquing an upper central incisor with aligners—acting forces and biomechanical principles. Eur J Orthod 32(6):607–613. https://doi.org/10.1093/ejo/cjq007

    Article  Google Scholar 

  35. Elkholy F, Schmidt F, Jäger R, Lapatki BG (2017) Forces and moments applied during derotation of a maxillary central incisor with thinner aligners: an in-vitro study. Am J Orthod Dentofac Orthop 151(2):407–415. https://doi.org/10.1016/j.ajodo.2016.08.020

    Article  Google Scholar 

  36. Ryokawa H, Miyazaki Y, Fujishima A, Miyazaki T, Maki K (2006) The mechanical properties of dental thermoplastic materials in a simulated intraoral environment. Orthod Waves 65(2):64–72. https://doi.org/10.1016/j.odw.2006.03.003

    Article  Google Scholar 

  37. Hahn W, Dathe H, Fialka-Fricke J et al (2009) Influence of thermoplastic appliance thickness on the magnitude of force delivered to a maxillary central incisor during tipping. Am J Orthod Dentofac Orthop 136(1):12.e1-12.e7. https://doi.org/10.1016/j.ajodo.2008.12.015

    Article  Google Scholar 

  38. Cowley DP, Mah J, O’Toole B (2012) The effect of gingival-margin design on the retention of thermoformed aligners. J Clin Orthod JCO 46(11):697

    Google Scholar 

  39. Sadyrin E, Swain M, Mitrin B, Rzhepakovsky I et al (2020) Characterization of enamel and dentine about a white spot lesion: mechanical properties, mineral density, microstructure and molecular composition. Nanomaterials 10(9):1889. https://doi.org/10.3390/nano10091889

    Article  Google Scholar 

  40. Ausiello P, Dal Piva AMDO, Borges ALS, Lanzotti A, Zamparini F, Epifania E, Mendes Tribst JP (2021) Effect of shrinking and no shrinking dentine and enamel replacing materials in posterior restoration: a 3D-FEA study. Appl Sci 11(5):2215. https://doi.org/10.3390/app11052215

    Article  Google Scholar 

  41. Aboel-Fadl AK, El-Desoky MA (2017) Influence of endocrown pulpal extension on stress distribution in endodontically treated maxillary premolars a three-dimensional finite element analysis. Egypt Dent J 63(4):3895–3905. https://doi.org/10.21608/EDJ.2017.76455

    Article  Google Scholar 

  42. Tamburrino F, D’Antò V, Bucci R, Alessandri-Bonetti G, Barone S, Razionale AV (2020) Mechanical properties of thermoplastic polymers for aligner manufacturing: In vitro study. Dent J 8(2):47. https://doi.org/10.3390/dj8020047

    Article  Google Scholar 

  43. Al Noor HSS, Al-Joubori SK (2018) Comparison of the hardness and elastic modulus of different orthodontic aligner’s materials. Int J Med Res Pharm Sci 5(9):19–25. https://doi.org/10.5281/zenodo.1443358

    Article  Google Scholar 

  44. Ren Y, Maltha J, Van’t Hof MA, Kuijpers-Jagtman AM (2004) Optimum force magnitude for orthodontic tooth movement: a mathematic model. Am J Orthod Dentofac Orthop 125(1):71–77. https://doi.org/10.1016/j.ajodo.2003.02.005

    Article  Google Scholar 

  45. Dumont ER, Piccirillo J, Grosse IR (2005) Finite-element analysis of biting behavior and bone stress in the facial skeletons of bats. Anat Rec A: Discov Mol Cell Evol Biol: Off Publ Am Assoc Anatomists 283(2):319–330. https://doi.org/10.1002/ar.a.20165

    Article  Google Scholar 

  46. Kawarizadeh A, Bourauel C, Jäger A (2003) Experimental and numerical determination of initial tooth mobility and material properties of the periodontal ligament in rat molar specimens. Eur J Orthod 25(6):569–578. https://doi.org/10.1093/ejo/25.6.569

    Article  Google Scholar 

  47. Kwon JS, Lee YK, Lim BS, Lim YK (2008) Force delivery properties of thermoplastic orthodontic materials. Am J Orthod Dentofac Orthop 133(2):228–234

    Article  Google Scholar 

  48. Proffit WR, Fields HW, Sarver DM, Ackerman JL (2006) Contemporary orthodontics. Elsevier Health Sciences

  49. Tominaga JY, Ozaki H, Chiang PC, Sumi M, Tanaka M et al (2014) Effect of bracket slot and archwire dimensions on anterior tooth movement during space closure in sliding mechanics: a 3-dimensional finite element study. Am J Orthod Dentofac Orthop 146(2):166–174. https://doi.org/10.1016/j.ajodo.2014.04.016

    Article  Google Scholar 

  50. Poppe M, Bourauel C, Jäger A (2002) Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth a study of autopsy specimens and their conversion into finite element models. J Orofac Orthop 63(5):358–370. https://doi.org/10.1007/s00056-002-0067-8

    Article  Google Scholar 

  51. Vollmer D, Bourauel C, Maier K, Jäger A (1999) Determination of the centre of resistance in an upper human canine and idealized tooth model. Eur J Orthod 21(6):633–648. https://doi.org/10.1093/ejo/21.6.633

    Article  Google Scholar 

  52. Hahn W, Engelke B, Jung K, Dathe H et al (2010) Initial forces and moments delivered by removable thermoplastic appliances during rotation of an upper central incisor. Angle Orthod 80(2):239–246. https://doi.org/10.2319/033009-181.1

    Article  Google Scholar 

  53. Kohda N, Iijima M, Muguruma T, Brantley WA, Ahluwalia KS, Mizoguchi I (2013) Effects of mechanical properties of thermoplastic materials on the initial force of thermoplastic appliances. Angle Orthod 83(3):476–483. https://doi.org/10.2319/052512-432.1

    Article  Google Scholar 

  54. Ihssen BA, Willmann JH, Nimer A, Drescher D (2019) Effect of in vitro aging by water immersion and thermocycling on the mechanical properties of PETG aligner material. J Orofac Orthop/Fortschr Kieferorthop 80(6):292–303

    Article  Google Scholar 

  55. Liu DS, Chen YT (2015) Effect of thermoplastic appliance thickness on initial stress distribution in periodontal ligament. Adv Mech Eng. https://doi.org/10.1177/1687814015578362

    Article  Google Scholar 

  56. Min S, Hwang CJ, Yu HS, Lee SB, Cha JY (2010) The effect of thickness and deflection of orthodontic thermoplastic materials on its mechanical properties. Korean J Orthod 40(1):16–26. https://doi.org/10.4041/kjod.2010.40.1.16

    Article  Google Scholar 

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Funding

This work was supported by a grant (MBRU-AlMahmeed Collaborative Research Award 2019) from Mohammed Bin Rashid University of Medicine and Health Sciences (MBRU), project no: ALM1931.

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Authors and Affiliations

  1. Oral Technology Department, Dental School, University Hospital Bonn, Welschnonnenstr. 17, 53111, Bonn, Germany

    Tarek M. Elshazly, Christoph Bourauel, Mostafa Aldesoki, Sameh Talaat & Ludger Keilig

  2. Department of Orthodontics, College of Dental Medicine, MBRU, Dubai, United Arab Emirates

    Ahmed Ghoneima

  3. Department of Prosthodontics, College of Dental Medicine, MBRU, Dubai, United Arab Emirates

    Moosa Abuzayda

  4. Department of Oral and Craniofacial Health Sciences, College of Dental Medicine, University of Sharjah, Sharjah, United Arab Emirates

    Wael Talaat

  5. Department of Oral and Maxillofacial Surgery, Faculty of Dentistry, Suez Canal University, Ismailia, Egypt

    Wael Talaat

  6. Department of Orthodontics, Future University in Egypt, Cairo, Egypt

    Sameh Talaat

  7. Department of Dental Prosthetics, Propaedeutics and Materials Science, Dental School, University Hospital Bonn, Bonn, Germany

    Ludger Keilig

Authors
  1. Tarek M. Elshazly
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  2. Christoph Bourauel
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Contributions

Conceptualization: TE. Data curation and analysis, investigation, and methodology: TE and LK. Resources: TE, CB, MA, and AG. Software: TE, CB, MA, and LK. Supervision, validation, and visualization: TE, LK, MA, CB, AG, MA, WT, and ST. Writing—original draft: TE. Writing—review and editing: TE, MA, CB, AG, MA, WT, and ST. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Tarek M. Elshazly.

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Highlights

• Experimental biomechanical studies of aligners have many limitations.

• Finite element method might help for better understanding of force transmission by aligners.

• The deformation of the aligner is a combination of bending and stretching.

• The generated forces are almost directly proportional to the rigidity of the aligner.

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Elshazly, T.M., Bourauel, C., Aldesoki, M. et al. Computer-aided finite element model for biomechanical analysis of orthodontic aligners. Clin Oral Invest 27, 115–124 (2023). https://doi.org/10.1007/s00784-022-04692-7

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  • DOI: https://doi.org/10.1007/s00784-022-04692-7

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