title: Quantitative Comparison of Mathematical Models to Measure Surface Area of Canine Teeth Prepared to Receive Full Veneer Crowns in Dogs.
abstract: OBJECTIVE
  This study was performed in order to determine if mathematical modeling of the canine teeth in dogs could be utilized to provide an accurate and reliable estimation of crown surface area that could be used in both a research and a clinical setting.
  
  
  METHODS
  Actual surface area (aSA) calculations for 32 stone dies of clinical crown preparations were acquired utilizing a tridimensional (3D) laser scanner and 3D computer-aided design and manufacturing (CAD/CAM) software applications. These calculations were used as a control. Seventeen unique mathematical models from eight geometric shapes were used to calculate estimated surface area (eSA) of each stone die. Linear association and agreement between eSA and aSA calculations were assessed with multiple statistical methods.
  
  
  RESULTS
  All methods of eSA showed a significant linear association with aSA. Five of the mathematical models [right elliptical frustum (H3), right elliptical cone (G3), right pyramidal cone (A3), right circular frustum (F2), and right circular cone (E1)] were superior to the other 12 models.
  
  
  CONCLUSIONS
  The H3 mathematical model based on the right elliptical frustum provided the most accurate estimate of crown surface area of dog teeth. However, H3 requires the use of laser scans and a 3D CAD software program. As a result, this model would be recommended for research applications. The E1 mathematical model was similar in accuracy to H3 and, given it requires only two measurements and a comparatively simple equation for calculation, this method would be recommended for clinical chair-side use.
authors.affiliation: Bone and Joint Biomechanics Laboratory, Department of Mechanical Engineering, University of Wisconsin-Madison , Madison, WI , USA.
authors.forename: Caitlyn J
authors.initials: CJ
authors.lastname: Collins
authors.affiliation: Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison , Madison, WI , USA.
authors.forename: Scott Joseph
authors.initials: SJ
authors.lastname: Hetzel
authors.affiliation: Bone and Joint Biomechanics Laboratory, Department of Mechanical Engineering, University of Wisconsin-Madison , Madison, WI , USA.
authors.forename: Sarah
authors.initials: S
authors.lastname: Siverling
authors.affiliation: Bone and Joint Biomechanics Laboratory, Department of Mechanical Engineering, University of Wisconsin-Madison , Madison, WI , USA.
authors.forename: Heidi-Lynn
authors.initials: HL
authors.lastname: Ploeg
authors.affiliation: Dentistry and Oral Surgery, School of Veterinary Medicine, University of Wisconsin-Madison , Madison, WI , USA.
authors.forename: Jason W
authors.initials: JW
authors.lastname: Soukup
keywords: crown preparation; crown preparation design; crown surface area; dogs; full veneer crown; mathematical models; prosthodontics; tooth preparation