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Background <p>This study aims to quantify the space required to level the mandibular curve of Spee (COS) using three-dimensional (3D) digitizing techniques and to develop a corresponding mathematical model.</p> Methods <p>Dental models exhibiting various depths of COS were digitally scanned, segmented, and aligned. Crown-root-inclusive digital models replaced the initial scans to calculate the space needed for COS leveling. Coordinates of the contact points (CPs) were measured, and the relationships among CP depth, required space, and the two-dimensional (2D) arch circumference were analyzed. Several regression models were tested to fit these relationships, resulting in a mathematical model to predict the space necessary for COS leveling.</p> Results <p>Results revealed a linear relationship between the mesial CP depth of the second molar and the space required. No additional space was necessary when the mesial CP depth of the second molar was less than 3.5&#xa0;mm. Moreover, a linear association was observed between the 2D circumference of the dental arch and the mesial CP depth of the first molar.</p> Conclusions <p>This study proposes a predictive mathematical model for&#xa0;the space required to level the COS using 3D digitizing techniques, with variables based on CP changes.</p>

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3D digital space analysis for leveling the curve of Spee

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月5日

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  • Fang Yang,
  • Hongyu Hou,
  • Runge Yu,
  • Fang Hua,
  • Hong He,
  • Hui Xiong

摘要

Background

This study aims to quantify the space required to level the mandibular curve of Spee (COS) using three-dimensional (3D) digitizing techniques and to develop a corresponding mathematical model.

Methods

Dental models exhibiting various depths of COS were digitally scanned, segmented, and aligned. Crown-root-inclusive digital models replaced the initial scans to calculate the space needed for COS leveling. Coordinates of the contact points (CPs) were measured, and the relationships among CP depth, required space, and the two-dimensional (2D) arch circumference were analyzed. Several regression models were tested to fit these relationships, resulting in a mathematical model to predict the space necessary for COS leveling.

Results

Results revealed a linear relationship between the mesial CP depth of the second molar and the space required. No additional space was necessary when the mesial CP depth of the second molar was less than 3.5 mm. Moreover, a linear association was observed between the 2D circumference of the dental arch and the mesial CP depth of the first molar.

Conclusions

This study proposes a predictive mathematical model for the space required to level the COS using 3D digitizing techniques, with variables based on CP changes.