title: An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.
abstract: BACKGROUND
  Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals.
  
  
  METHODS
  Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model.
  
  
  RESULTS
  The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry.
  
  
  CONCLUSIONS
  With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes.
authors.affiliation: Institute of Lightweight Engineering and Polymer Technology (ILK), Faculty of Mechanical Engineering, Technische Universität Dresden, Dresden, Germany. Electronic address: martin.dannemann@tu-dresden.de.
authors.forename: Martin
authors.initials: M
authors.lastname: Dannemann
authors.affiliation: Institute of Lightweight Engineering and Polymer Technology (ILK), Faculty of Mechanical Engineering, Technische Universität Dresden, Dresden, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Kucher
authors.affiliation: Clinic of Restorative Dentistry, Faculty of Medicine, Technische Universität Dresden, Dresden, Germany.
authors.forename: Jasmin
authors.initials: J
authors.lastname: Kirsch
authors.affiliation: Institute of Lightweight Engineering and Polymer Technology (ILK), Faculty of Mechanical Engineering, Technische Universität Dresden, Dresden, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Binkowski
authors.affiliation: Institute of Lightweight Engineering and Polymer Technology (ILK), Faculty of Mechanical Engineering, Technische Universität Dresden, Dresden, Germany.
authors.forename: Niels
authors.initials: N
authors.lastname: Modler
authors.affiliation: Clinic of Restorative Dentistry, Faculty of Medicine, Technische Universität Dresden, Dresden, Germany.
authors.forename: Christian
authors.initials: C
authors.lastname: Hannig
authors.affiliation: Clinic of Restorative Dentistry, Faculty of Medicine, Technische Universität Dresden, Dresden, Germany.
authors.forename: Marie-Theres
authors.initials: MT
authors.lastname: Weber
mesh_terms: D000465:Algorithms; D003786:Dental Pulp Cavity / Q000033:anatomy & histology* / Q000000981:diagnostic imaging; D006801:Humans; D008433:Mathematics / Q000379:methods; D015233:Models, Statistical; D008963:Molar / Q000033:anatomy & histology / Q000000981:diagnostic imaging; D055114:X-Ray Microtomography
keywords: Curvature; micro–computed tomographic imaging; parametric model; root canal