title: Locating the center of resistance in individual teeth via two- and three-dimensional radiographic data.
abstract: OBJECTIVE
  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.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Orthodontics, Clinic of Orthodontics, University of Ulm Dental School, Albert-Einstein-Allee 11, 89081, Ulm, Germany, martin.geiger@uni-ulm.de.
authors.forename: M E
authors.initials: ME
authors.lastname: Geiger
authors.forename: B G
authors.initials: BG
authors.lastname: Lapatki
mesh_terms: D000465:Algorithms; D001732:Bite Force; D003198:Computer Simulation; D003799:Dental Stress Analysis / Q000379:methods*; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D007180:Incisor / Q000000981:diagnostic imaging* / Q000502:physiology*; D008954:Models, Biological; D011856:Radiographic Image Enhancement / Q000379:methods; D011861:Radiography, Dental / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014087:Tooth Movement Techniques / Q000379:methods*; D014092:Tooth Root / Q000000981:diagnostic imaging / Q000502:physiology*