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Mathematical beta function formulation for maxillary arch form prediction in normal occlusion population.

Morteza Mina1, Ali Borzabadi-Farahani2,3, Azita Tehranchi4,5

  • 1Department of Orthodontics, School of Dentistry, North Khorasan University of Medical Sciences, Bojnourd, Iran.

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Summary

This study developed a beta function formula to predict maxillary dental arch form in Iranian adolescents with normal occlusion. The formula accurately predicts arch form using mandibular measurements, aiding in customized orthodontic treatments.

Keywords:
Beta functionDental arch formNormal occlusionOrthodontics

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Area of Science:

  • Orthodontics
  • Dental Anthropology
  • Biometrics

Background:

  • Assessing dental arch curvature is crucial for orthodontic diagnosis and treatment planning.
  • Predictive models for dental arch form can aid in fabricating customized appliances and surgical planning.
  • Limited research exists on predicting maxillary arch form using mandibular dimensions in specific populations.

Purpose of the Study:

  • To assess dental arch curvature in Iranian adolescents with normal occlusion.
  • To propose a beta function formula for predicting maxillary arch form.
  • To utilize mandibular intermolar width (IMW) and intermolar depth (IMD) for prediction.

Main Methods:

  • Utilized 3D laser scanning of dental casts from 54 adolescents (mean age 14.1 years) with normal occlusion.
  • Performed curve-fitting analyses on the dental arch curves.
  • Developed and validated a beta function formula using measured IMW and IMD.

Main Results:

  • No significant gender dimorphism was observed for IMW and IMD (P > 0.05).
  • The proposed beta function formula demonstrated high accuracy in predicting maxillary arch length (adjusted r-squared = 0.97 for the whole arch, 0.90 for the anterior arch).
  • The formula showed a strong positive association between measured and predicted arch lengths (r = 0.98).

Conclusions:

  • The developed beta function formula accurately predicts maxillary arch form in the Iranian population.
  • This predictive tool can guide the fabrication of customized arch wires.
  • The formula may serve as an aid in maxillary reconstructive surgery.