title: Reference points suitable for evaluation of the additional arch length required for leveling the curve of Spee.
abstract: OBJECTIVE
  The additional arch length required for leveling (AALL) the curve of Spee (COS) can be estimated by subtracting the two-dimensional (2D) arch circumference, which is the projection of the three-dimensional (3D) arch circumference onto the occlusal plane, from the 3D arch circumference, which represents the arch length after leveling the COS. The purpose of this study was to determine whether the cusp tips or proximal maximum convexities are more appropriate reference points for estimating the AALL.
  
  
  METHODS
  Sixteen model setups of the mandibular arch with COS depths ranging from 0 mm to 4.7 mm were constructed using digital simulation. Arch circumferences in 2D and 3D were measured from the cusp tips and proximal maximum convexities and used to calculate the AALL. The values obtained using the two reference points were compared with the pairedt-test.
  
  
  RESULTS
  Although the 3D arch circumference should be constant regardless of the COS depth, it decreased by 3.8 mm in cusp tip measurements and by 0.4 mm in proximal maximum convexity measurements as the COS deepened to 4.7 mm. AALL values calculated using the cusp tips as reference points were significantly smaller than those calculated using the proximal maximum convexities (p= 0.002).
  
  
  CONCLUSIONS
  The AALL is underestimated when the cusp tips are used as measurement reference points; the AALL can be measured more accurately using the proximal maximum convexities.
authors.affiliation: Department of Orthodontics, School of Dentistry, Chosun University, Gwangju, Korea.
authors.forename: Yong-Hwa
authors.initials: YH
authors.lastname: Cho
authors.affiliation: Department of Orthodontics, School of Dentistry, Chosun University, Gwangju, Korea.
authors.forename: Sung-Hoon
authors.initials: SH
authors.lastname: Lim
authors.affiliation: Department of Orthodontics, School of Dentistry, Chosun University, Gwangju, Korea.
authors.forename: Sung-Nam
authors.initials: SN
authors.lastname: Gang
keywords: 3-Dimensional diagnosis and treatment planning; Curve of Spee; Dental cast analysis; Digital models