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

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## Abstract

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.

## Keywords

Orthodontic treatment Tooth movement Superimposition Digital dental study models Registration## Notes

### Acknowledgments

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

### Conflict of interest

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

## References

- 1.Alexander, R. M. Optimum strengths for bones liable to fatigue and accidental fracture.
*J. Theor. Biol.*109(4):621–636, 1984. https://doi.org/10.1016/S0022-5193(84)80162-9.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1007/s00056-015-0310-8.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1093/ejo/cjw033.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1067/mod.2002.120687.CrossRefGoogle Scholar - 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. https://doi.org/10.2319/120914-890.1.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1002/jor.1100080506.CrossRefPubMedGoogle Scholar - 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.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.Bourauel, C., D. Vollmer, and A. Jäger. Anwendung von Bone-Remodeling-Theorien zur Simulation orthodontischer Zahnbewegungen.
*J. Orofac. Orthop.*61(4):266, 2000. https://doi.org/10.1007/s000560050012.CrossRefPubMedGoogle Scholar - 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.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.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. https://doi.org/10.1088/0031-9155/61/13/4826.CrossRefPubMedPubMedCentralGoogle Scholar - 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. https://doi.org/10.1093/ejo/cjm019.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1111/j.1601-6343.2011.01510.x.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.4041/kjod.2012.42.5.235.CrossRefPubMedPubMedCentralGoogle Scholar - 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. https://doi.org/10.2319/101309-569.1.PubMedCrossRefGoogle Scholar - 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. https://doi.org/10.1016/j.ajodo.2007.07.009.CrossRefGoogle Scholar - 18.Cristofolini, L. In vitro evidence of the structural optimization of the human skeletal bones.
*J. Biomech.*48(5):787–796, 2015. https://doi.org/10.1016/j.jbiomech.2014.12.010.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1016/j.media.2003.06.001.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1093/ejo/cjx029.CrossRefGoogle Scholar - 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. https://doi.org/10.1093/ejo/cjv077.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1016/j.ajodo.2011.01.020.CrossRefGoogle Scholar - 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. https://doi.org/10.1016/j.media.2017.04.003.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1109/TMI.2013.2294539.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1093/ejo/26.6.585.CrossRefPubMedGoogle Scholar - 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.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. https://doi.org/10.2319/042308-225.1.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1080/10255840310001634403.CrossRefGoogle Scholar - 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. https://doi.org/10.2319/011314-45.1.CrossRefPubMedPubMedCentralGoogle Scholar - 30.Maintz, J. B. A., and M. A. Viergever. A survey of medical image registration.
*Med. Image Anal.*2(1):1–36, 1998. https://doi.org/10.1016/S1361-8415(01)80026-8.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1093/ejo/cjl001.CrossRefPubMedGoogle Scholar - 32.Mortazavi, H., and M. Baharvand. Review of common conditions associated with periodontal ligament widening.
*Imaging Sci. Dent.*46(4):229–237, 2016. https://doi.org/10.5624/isd.2016.46.4.229.CrossRefPubMedPubMedCentralGoogle Scholar - 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.Murray, C. D. The physiological principle of minimum work II: Oxygen exchange in capillaries.
*Proc. Natl. Acad. Sci.*12(5):299–304, 1926. https://doi.org/10.1073/pnas.12.5.299.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.4041/kjod.2015.45.2.82.CrossRefPubMedPubMedCentralGoogle Scholar - 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. https://doi.org/10.1016/j.ajodo.2013.06.022.CrossRefGoogle Scholar - 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.Pauls, A. H. Therapeutic accuracy of individualized brackets in lingual orthodontics.
*J. Orofac. Orthop.*71(5):348–361, 2010. https://doi.org/10.1007/s00056-010-1027-3.CrossRefPubMedGoogle Scholar - 39.Quinn, R. S., and D. Ken Yoshikawa. A reassessment of force magnitude in orthodontics.
*Am. J. Orthod.*88(3):252–260, 1985. https://doi.org/10.1016/S0002-9416(85)90220-9.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1016/j.ajodo.2003.02.005.CrossRefGoogle Scholar - 41.Ricketts, R. M. Bioprogressive Therapy (2nd ed.). Denver: Rocky Mountain Orthodontics, p. 457, 1984.Google Scholar
- 42.Schroeder, H. E. The Periodontium. Handbook of Microscopic Anatomy, Vol. 5/5. Berlin: Springer, 1986.Google Scholar
- 43.Schumacher, G.-H. (ed.). Anatomie und Biochemie der Zähne (3rd ed.). Berlin: Verl. Volk und Gesundheit, 1983.Google Scholar
- 44.Stein, M. Large sample properties of simulations using latin hypercube sampling.
*Technometrics*29(2):143–151, 1987. https://doi.org/10.2307/1269769.CrossRefGoogle Scholar - 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.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. https://doi.org/10.1093/ejo/cjn124.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1016/j.ajodo.2007.03.040.CrossRefGoogle Scholar - 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. https://doi.org/10.1016/j.ajodo.2011.12.018.CrossRefGoogle Scholar - 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. https://doi.org/10.1111/j.1601-6343.2010.01500.x.CrossRefPubMedGoogle Scholar - 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. https://doi.org/10.1038/s41598-017-06013-5.CrossRefPubMedPubMedCentralGoogle Scholar - 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. https://doi.org/10.1016/j.media.2016.06.030.CrossRefPubMedGoogle Scholar - 52.Weinans, H., R. Huiskes, and H. J. Grootenboer. The behavior of adaptive bone-remodeling simulation models.
*J. Biomech.*25(12):1425–1441, 1992. https://doi.org/10.1016/0021-9290(92)90056-7.CrossRefPubMedGoogle Scholar