Annals of Biomedical Engineering

, Volume 46, Issue 8, pp 1160–1172 | Cite as

Novel Method for Superposing 3D Digital Models for Monitoring Orthodontic Tooth Movement

  • Falko SchmidtEmail author
  • Fatih Kilic
  • Neltje Emma Piro
  • Martin Eberhard Geiger
  • Bernd Georg Lapatki


Quantitative three-dimensional analysis of orthodontic tooth movement (OTM) is possible by superposition of digital jaw models made at different times during treatment. Conventional methods rely on surface alignment at palatal soft-tissue areas, which is applicable to the maxilla only. We introduce two novel numerical methods applicable to both maxilla and mandible. The OTM from the initial phase of multi-bracket appliance treatment of ten pairs of maxillary models were evaluated and compared with four conventional methods. The median range of deviation of OTM for three users was 13–72% smaller for the novel methods than for the conventional methods, indicating greater inter-observer agreement. Total tooth translation and rotation were significantly different (ANOVA, p < 0.01) for OTM determined by use of the two numerical and four conventional methods. Directional decomposition of OTM from the novel methods showed clinically acceptable agreement with reference results except for vertical translations (deviations of medians greater than 0.6 mm). The difference in vertical translational OTM can be explained by maxillary vertical growth during the observation period, which is additionally recorded by conventional methods. The novel approaches are, thus, particularly suitable for evaluation of pure treatment effects, because growth-related changes are ignored.


Orthodontic treatment Tooth movement Superimposition Digital dental study models Registration 



We thank Ian Davies, copy-editor, for English language revision.

Conflict of interest

We declare that this article is free from conflicts of interest.


  1. 1.
    Alexander, R. M. Optimum strengths for bones liable to fatigue and accidental fracture. J. Theor. Biol. 109(4):621–636, 1984. Scholar
  2. 2.
    An, K., I. Jang, D.-S. Choi, P.-G. Jost-Brinkmann, and B.-K. Cha. Identification of a stable reference area for superimposing mandibular digital models. J. Orofac. Orthop. 76(6):508–519, 2015. Scholar
  3. 3.
    Aragón, M. L. C., L. F. Pontes, L. M. Bichara, C. Flores-Mir, and D. Normando. Validity and reliability of intraoral scanners compared to conventional gypsum models measurements: a systematic review. Eur. J. Orthod. 38(4):429–434, 2016. Scholar
  4. 4.
    Ashmore, J. L., B. F. Kurland, G. J. King, T. T. Wheeler, J. Ghafari, and D. S. Ramsay. A 3-dimensional analysis of molar movement during headgear treatment. Am. J. Orthod. Dentofac. Orthop. 121(1):18–29, 2002. Scholar
  5. 5.
    Barreto, M. S., J. Faber, C. J. Vogel, and T. M. Araujo. Reliability of digital orthodontic setups. Angle Orthod. 86(2):255–259, 2016. Scholar
  6. 6.
    Beaupre, G. S., T. E. Orr, and D. R. Carter. An approach for time-dependent bone modeling and remodeling—theoretical development. J. Orthop. Res. 8(5):651–661, 1990. Scholar
  7. 7.
    Bell, G. H. Bone as a mechanical Engineering problem. In: The Biochemistry and Physiology of Bone, edited by G. H. Bourne. New York: Elsevier, 1956, pp. 27–52.CrossRefGoogle Scholar
  8. 8.
    Bourauel, C., L. Keilig, A. Rahimi, S. Reimann, A. Ziegler, and A. Jäger. Computer-aided analysis of the biomechanics of tooth movements. Int. J. Comput. Dent. 10(1):25–40, 2007.PubMedGoogle Scholar
  9. 9.
    Bourauel, C., D. Vollmer, and A. Jäger. Anwendung von Bone-Remodeling-Theorien zur Simulation orthodontischer Zahnbewegungen. J. Orofac. Orthop. 61(4):266, 2000. Scholar
  10. 10.
    Bro-Nielsen, M., C. Gramkow, and S. Kreiborg. Non-rigid image registration using bone growth model. In: CVRMed-MRCAS’97, edited by J. Troccaz, E. Grimson, and R. Mösges. Berlin: Springer, 1997, pp. 1–12.Google Scholar
  11. 11.
    Burstone, C. J. The biomechanics of tooth movement. In: Vistas in Orthodontics: Presented to Alton W. Moore, edited by B. S. Kraus, and R. A. Riedel. Philadelphia: Lea & Febiger, 1962, pp. 197–213.Google Scholar
  12. 12.
    Cazoulat, G., D. Owen, M. M. Matuszak, J. M. Balter, and K. K. Brock. Biomechanical deformable image registration of longitudinal lung CT images using vessel information. Phys. Med. Biol. 61(13):4826–4839, 2016. Scholar
  13. 13.
    Cha, B. K., J. Y. Lee, P.-G. Jost-Brinkmann, and N. Yoshida. Analysis of tooth movement in extraction cases using three-dimensional reverse engineering technology. Eur. J. Orthod. 29(4):325–331, 2007. Scholar
  14. 14.
    Chen, G., S. Chen, X. Y. Zhang, R. P. Jiang, Y. Liu, F. H. Shi, and T. M. Xu. Stable region for maxillary dental cast superimposition in adults, studied with the aid of stable miniscrews. Orthod. Craniofac. Res. 14(2):70–79, 2011. Scholar
  15. 15.
    Choi, J.-I., B.-K. Cha, P.-G. Jost-Brinkmann, D.-S. Choi, and I.-S. Jang. Validity of palatal superimposition of 3-dimensional digital models in cases treated with rapid maxillary expansion and maxillary protraction headgear. Korean J. Orthod. 42(5):235–241, 2012. Scholar
  16. 16.
    Choi, D.-S., Y.-M. Jeong, I. Jang, P. G. Jost-Brinkmann, and B.-K. Cha. Accuracy and reliability of palatal superimposition of three-dimensional digital models. Angle Orthod. 80(4):497–503, 2010. Scholar
  17. 17.
    Christou, P., and S. Kiliaridis. Vertical growth-related changes in the positions of palatal rugae and maxillary incisors. Am. J. Orthod. Dentofac. Orthop. 133(1):81–86, 2008. Scholar
  18. 18.
    Cristofolini, L. In vitro evidence of the structural optimization of the human skeletal bones. J. Biomech. 48(5):787–796, 2015. Scholar
  19. 19.
    Ganser, K. A., H. Dickhaus, R. Metzner, and C. R. Wirtz. A deformable digital brain atlas system according to Talairach and Tournoux. Med. Image Anal. 8(1):3–22, 2004. Scholar
  20. 20.
    Ganzer, N., I. Feldmann, P. Liv, and L. Bondemark. A novel method for superimposition and measurements on maxillary digital 3D models-studies on validity and reliability. Eur. J. Orthod. 2017. Scholar
  21. 21.
    Goracci, C., L. Franchi, A. Vichi, and M. Ferrari. Accuracy, reliability, and efficiency of intraoral scanners for full-arch impressions: a systematic review of the clinical evidence. Eur. J. Orthod. 38(4):422–428, 2016. Scholar
  22. 22.
    Grauer, D., and W. R. Proffit. Accuracy in tooth positioning with a fully customized lingual orthodontic appliance. Am. J. Orthod. Dentofac. Orthop. 140(3):433–443, 2011. Scholar
  23. 23.
    Han, L., H. Dong, J. R. McClelland, L. Han, D. J. Hawkes, and D. C. Barratt. A hybrid patient-specific biomechanical model based image registration method for the motion estimation of lungs. Med. Image Anal. 39:87–100, 2017. Scholar
  24. 24.
    Han, L., J. H. Hipwell, B. Eiben, D. Barratt, M. Modat, S. Ourselin, and D. J. Hawkes. A nonlinear biomechanical model based registration method for aligning prone and supine MR breast images. IEEE Trans. Med. Imaging 33(3):682–694, 2014. Scholar
  25. 25.
    Hayashi, K., J. Uechi, M. Murata, and I. Mizoguchi. Comparison of maxillary canine retraction with sliding mechanics and a retraction spring: a three-dimensional analysis based on a midpalatal orthodontic implant. Eur. J. Orthod. 26(6):585–589, 2004. Scholar
  26. 26.
    Hocevar, R. A. Understanding, planning, and managing tooth movement: orthodontic force system theory. Am. J. Orthod. 80(5):457–477, 1981.CrossRefPubMedGoogle Scholar
  27. 27.
    Jang, I., M. Tanaka, Y. Koga, S. Iijima, J. H. Yozgatian, B. K. Cha, and N. Yoshida. A novel method for the assessment of three-dimensional tooth movement during orthodontic treatment. Angle Orthod. 79(3):447–453, 2009. Scholar
  28. 28.
    Keilig, L., K. Piesche, A. Jäger, and C. Bourauel. Applications of surface-surface matching algorithms for determination of orthodontic tooth movements. Comput. Methods Biomech. Biomed. Eng. 6(5–6):353–359, 2003. Scholar
  29. 29.
    Li, S., Z. Xia, S. S.-Y. Liu, G. Eckert, and J. Chen. Three-dimensional canine displacement patterns in response to translation and controlled tipping retraction strategies. Angle Orthod. 85(1):18–25, 2015. Scholar
  30. 30.
    Maintz, J. B. A., and M. A. Viergever. A survey of medical image registration. Med. Image Anal. 2(1):1–36, 1998. Scholar
  31. 31.
    Meikle, M. C. The tissue, cellular, and molecular regulation of orthodontic tooth movement: 100 years after Carl Sandstedt. Eur. J. Orthod. 28(3):221–240, 2006. Scholar
  32. 32.
    Mortazavi, H., and M. Baharvand. Review of common conditions associated with periodontal ligament widening. Imaging Sci. Dent. 46(4):229–237, 2016. Scholar
  33. 33.
    Murray, C. D. The physiological principle of minimum work I: The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. U.S.A. 12(3):207–214, 1926.CrossRefPubMedPubMedCentralGoogle Scholar
  34. 34.
    Murray, C. D. The physiological principle of minimum work II: Oxygen exchange in capillaries. Proc. Natl. Acad. Sci. 12(5):299–304, 1926. Scholar
  35. 35.
    Nalcaci, R., A. B. Kocoglu-Altan, A. A. Bicakci, F. Ozturk, and H. Babacan. A reliable method for evaluating upper molar distalization: superimposition of three-dimensional digital models. Korean J. Orthod. 45(2):82–88, 2015. Scholar
  36. 36.
    Nickel, J. C., H. Liu, D. B. Marx, and L. R. Iwasaki. Effects of mechanical stress and growth on the velocity of tooth movement. Am. J. Orthod. Dentofac. Orthop. 145(4 Suppl):S74–81, 2014. Scholar
  37. 37.
    Osipenko, M. A., M. Y. Nyashin, and Y. I. Nyashin. Center of resistance and center of rotation of a tooth: the definitions, conditions of existence, properties. Russ. J. Biomech. 1999(1):5–15, 1999.Google Scholar
  38. 38.
    Pauls, A. H. Therapeutic accuracy of individualized brackets in lingual orthodontics. J. Orofac. Orthop. 71(5):348–361, 2010. Scholar
  39. 39.
    Quinn, R. S., and D. Ken Yoshikawa. A reassessment of force magnitude in orthodontics. Am. J. Orthod. 88(3):252–260, 1985. Scholar
  40. 40.
    Ren, Y., J. C. Maltha, M. A. van’t Hof, and A. M. Kuijpers-Jagtman. Optimum force magnitude for orthodontic tooth movement: a mathematic model. Am. J. Orthod. Dentofac. Orthop. 125(1):71–77, 2004. Scholar
  41. 41.
    Ricketts, R. M. Bioprogressive Therapy (2nd ed.). Denver: Rocky Mountain Orthodontics, p. 457, 1984.Google Scholar
  42. 42.
    Schroeder, H. E. The Periodontium. Handbook of Microscopic Anatomy, Vol. 5/5. Berlin: Springer, 1986.Google Scholar
  43. 43.
    Schumacher, G.-H. (ed.). Anatomie und Biochemie der Zähne (3rd ed.). Berlin: Verl. Volk und Gesundheit, 1983.Google Scholar
  44. 44.
    Stein, M. Large sample properties of simulations using latin hypercube sampling. Technometrics 29(2):143–151, 1987. Scholar
  45. 45.
    Storey, E., and R. Smith. Force in orthodontics and its relation to tooth movement. Aust. J. Dent. 56(1):11–18, 1952.Google Scholar
  46. 46.
    Thilander, B. Dentoalveolar development in subjects with normal occlusion. A longitudinal study between the ages of 5 and 31 years. Eur. J. Orthod. 31(2):109–120, 2009. Scholar
  47. 47.
    Thiruvenkatachari, B., M. Al-Abdallah, N. C. Akram, J. Sandler, and K. O’Brien. Measuring 3-dimensional tooth movement with a 3-dimensional surface laser scanner. Am. J. Orthod. Dentofac. Orthop. 135(4):480–485, 2009. Scholar
  48. 48.
    Tong, H., D. Kwon, J. Shi, N. Sakai, R. Enciso, and G. T. Sameshima. Mesiodistal angulation and faciolingual inclination of each whole tooth in 3-dimensional space in patients with near-normal occlusion. Am. J. Orthod. Dentofac. Orthop. 141(5):604–617, 2012. Scholar
  49. 49.
    van Leeuwen, E. J., A. M. Kuijpers-Jagtman, J. W. von den Hoff, F. A. D. T. G. Wagener, and J. C. Maltha. Rate of orthodontic tooth movement after changing the force magnitude: an experimental study in beagle dogs. Orthod. Craniofac. Res. 13(4):238–245, 2010. Scholar
  50. 50.
    Vasilakos, G., R. Schilling, D. Halazonetis, and N. Gkantidis. Assessment of different techniques for 3D superimposition of serial digital maxillary dental casts on palatal structures. Sci. Rep. 7(1):5838, 2017. Scholar
  51. 51.
    Viergever, M. A., J. B. A. Maintz, S. Klein, K. Murphy, M. Staring, and J. P. W. Pluim. A survey of medical image registration—under review. Med. Image Anal. 33:140–144, 2016. Scholar
  52. 52.
    Weinans, H., R. Huiskes, and H. J. Grootenboer. The behavior of adaptive bone-remodeling simulation models. J. Biomech. 25(12):1425–1441, 1992. Scholar

Copyright information

© Biomedical Engineering Society 2018

Authors and Affiliations

  1. 1.Department of Orthodontics, Centre of DentistryUniversity of UlmUlmGermany

Personalised recommendations