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Locating the center of resistance in individual teeth via two- and three-dimensional radiographic data

Bestimmung des Widerstandszentrums einzelner Zähne auf Basis von 2-D und 3-D röntgenologischen Daten

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Journal of Orofacial Orthopedics / Fortschritte der Kieferorthopädie Aims and scope Submit manuscript



The preferred reference point to describe the force–moment system exerted upon a tooth is its center of resistance (CR). Morphological data on the dentoalveolar complex can be used to locate this point either three-dimensionally (3D) with the finite element (FE) method, or two-dimensionally (2D) with a mathematical method calculating the centroid of the projected dental root. This study aimed to compare and appraise these two methods with regard to their accuracy and time requirements.


Three radiological datasets with permanent teeth were included. Each single 3D dataset was used in each of these patients to derive both a 3D and 2D morphological model of the upper right central incisor. CR levels were evaluated in percent, indicating the relative height as measured from the (averaged levels of the mesial and distal) bony ridge margin to the tooth’s apex.


Mean CR levels of 42.8% for distalization and 56.5% for lingual movement were obtained from the 3D FE simulations of initial tooth movement. The 2D mathematical model yielded a mean CR level of 44.5%. Compared to this mathematical approach, the 3D FE simulations were around 15 times more time-consuming, with an interactive requirement of around 15 h.


Because they contain so much more morphological information, 3D FE simulations should offer superior predictability. In addition, they are the only method offering detailed CR identification for specific directions of tooth movement. Before this method can be used in clinical practice, however, there is still a major need to reduce time requirements via further automation of process steps and to investigate how it should be applied to different tooth types.



Der bevorzugte Referenzpunkt eines Zahnes zur Beschreibung eines auf ihn ausgeübten Kraft-Drehmoment-Systems ist das Widerstandszentrum (WZ). Eine Bestimmung des WZ auf Basis von morphologischen Daten des dentoalveolären Komplexes ist auf folgende Weise realisierbar: mit der 3-D-FE(Finite-Elemente)-Methode sowie einer 2-D mathematischen Methode mit Berechnung des Flächenschwerpunkts der projizierten Zahnwurzel. Ziel der Studie war es, diese beiden Methoden hinsichtlich der Aspekte Ergebnisgenauigkeit und Zeitaufwand zu vergleichen und zu bewerten.


Für drei rechte obere Inzisivi im bleibenden Gebiss wurden auf Basis eines 3-D-Datensatzes jeweils ein 3-D sowie ein 2-D morphologisches Modell erstellt.


Die 3-D-FE-Simulationen zur initialen Zahnbewegung ergaben für die distale Bewegungsrichtung eine relative Lage des WZ von durchschnittlich 42,8% der Distanz vom gemittelten mesialen und distalen Niveau des Limbus alveolaris zum Apex und für die linguale Bewegung eine entsprechende Höhe von 56,5%. Die mit der 2-D mathematischen Methode ermittelten WZ-Positionen lagen durchschnittlich auf einer relativen Höhe von 44,5%. Der notwendige interaktive Zeitaufwand pro Zahn zur Bestimmung des WZ mittels 3-D-FE-Simulationen lag bei etwa 15 h und war etwa 15-mal so groß wie derjenige der 2-D mathematischen Methode.


Insbesondere aufgrund des höheren morphologischen Informationsgehalts sollten die Ergebnisse der 3-D-FE-Simulationen die höchste Aussagekraft besitzen. Zudem ist nur mit der 3-D-Methode eine differenzierte Bestimmung des WZ für verschiedene Bewegungsrichtungen möglich. Vor einer klinischen Anwendung der Methode sind noch eine weitere Automatisierung der Prozessschritte zur Reduzierung des Zeitaufwandes sowie Untersuchungen bei verschiedenen Zahntypen im größeren Maßstab notwendig.

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The authors wish to thank Mr. Juergen Salk from the Communication and Information Center at University of Ulm for comprehensive support in using the segmentation and FE software. They are also indebted to Prof. Philippe Young of Simpleware (Exeter, UK).


Die Autoren möchten sich bei Herrn Jürgen Salk vom Kommunikations- und Informationszentrum der Universität Ulm für die umfassende Unterstützung bei der Anwendung der Segmentierungs- und FE-Programme bedanken. Ein weiterer Dank gilt Prof. Philippe Young von der Fa. Simpleware (Exeter, UK).

Compliance with ethical guidelines

Conflict of interest. M.E. Geiger and B.G. Lapatki state that there are no conflicts of interest.

The accompanying manuscript does not include studies on humans or animals.

Einhaltung ethischer Richtlinien

Interessenkonflikt. M.E. Geiger und B.G. Lapatki geben an, dass kein Interessenkonflikt besteht.

Dieser Beitrag beinhaltet keine Studien an Menschen oder Tieren.

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Geiger, M., Lapatki, B. Locating the center of resistance in individual teeth via two- and three-dimensional radiographic data. J Orofac Orthop 75, 96–106 (2014).

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