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Objectives <p>This study aims to clarify the growth curves of the long axis and apical foramen diameter of permanent maxillary canines (PMCs), and to create and evaluate a new nonlinear age estimation (NAGE) model by integrating their inverse functions within a machine learning framework.</p> Methods <p>CT measurements of length (L), apical shortest width (SW) and longest width (LW) were obtained from 726 PMCs (aged 1 to 23 years). Growth curves were modeled using Gompertz function for L and Gamma-type function for SW and LW. Inverse functions were integrated into the NAGE model: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:\text{P}\text{A}=a*L^b+c*log(1+(SW+LW)/2)+\text{d}\)</EquationSource> </InlineEquation>. Parameters were optimized using Soft-L1 robust least squares (SciPy, NumFOCUS, USA). Validation applied to 14 independent longitudinal cases (75 PMCs, 3–15 years). Agreement between predicted age (PA) and chronological age (CA) was evaluated using root mean squared error (RMSE), coefficient of determination (R<sup>2</sup>), and Wilcoxon signed-rank test.</p> Results <p>The Gompertz and Gamma-type functions effectively captured PMC growth, with RMSE of 2.5&#xa0;mm (L), 1.07&#xa0;mm (SW), and 1.45&#xa0;mm (LW). The NAGE achieved RMSE of 1.89 years (R<sup>2</sup> = 0.85) in the 1–23 years group, improving to 1.29 years (R<sup>2</sup> = 0.89) in the 1–16 years group. In longitudinal cases, the overall mean difference between PA and CA was 0.12 years (1.4 months) with an RMSE of 0.99 years (R<sup>2</sup> = 0.86) and individual errors ranging from 0.25 to 2.09 years.</p> Conclusions <p>The proposed NAGE model showed promising performance for dental age estimation based on PMC length and apical foramen widths. Further studies in other teeth are needed.</p>

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Application of a novel age estimation model based on permanent maxillary canine morphometric features in a Japanese population

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Beshlina Fitri Widayanti Roosyanto Prakoeswa,
  • Hideyoshi Nishiyama,
  • Taichi Kobayashi,
  • Makiko Ike,
  • Masaki Takamura,
  • Yutaka Nikkuni,
  • Kouji Katsura,
  • Diem T. Vo,
  • Takafumi Hayashi

摘要

Objectives

This study aims to clarify the growth curves of the long axis and apical foramen diameter of permanent maxillary canines (PMCs), and to create and evaluate a new nonlinear age estimation (NAGE) model by integrating their inverse functions within a machine learning framework.

Methods

CT measurements of length (L), apical shortest width (SW) and longest width (LW) were obtained from 726 PMCs (aged 1 to 23 years). Growth curves were modeled using Gompertz function for L and Gamma-type function for SW and LW. Inverse functions were integrated into the NAGE model: \(\:\text{P}\text{A}=a*L^b+c*log(1+(SW+LW)/2)+\text{d}\) . Parameters were optimized using Soft-L1 robust least squares (SciPy, NumFOCUS, USA). Validation applied to 14 independent longitudinal cases (75 PMCs, 3–15 years). Agreement between predicted age (PA) and chronological age (CA) was evaluated using root mean squared error (RMSE), coefficient of determination (R2), and Wilcoxon signed-rank test.

Results

The Gompertz and Gamma-type functions effectively captured PMC growth, with RMSE of 2.5 mm (L), 1.07 mm (SW), and 1.45 mm (LW). The NAGE achieved RMSE of 1.89 years (R2 = 0.85) in the 1–23 years group, improving to 1.29 years (R2 = 0.89) in the 1–16 years group. In longitudinal cases, the overall mean difference between PA and CA was 0.12 years (1.4 months) with an RMSE of 0.99 years (R2 = 0.86) and individual errors ranging from 0.25 to 2.09 years.

Conclusions

The proposed NAGE model showed promising performance for dental age estimation based on PMC length and apical foramen widths. Further studies in other teeth are needed.