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The Frankfurt proportion: The ratio between anterior tooth size and occlusal vertical dimension
Kathrin Seidel1, Sabrina Schäfer2, Basel El-Sabbagh3
1Postdoctoral Researcher, Goethe University Frankfurt, Department of Prosthetic Dentistry, Center for Dentistry and Oral Medicine (Carolinum), Frankfurt, Germany.
Statement Of Problem:
Extensive tooth wear compromises both incisal length and occlusal vertical dimension (OVD). Evidence-based reference values correlating anterior tooth morphology with OVD are needed to guide reconstruction in patients with severely worn dentitions.
Purpose:
The purpose of this clinical study was to analyze correlations between anterior tooth dimensions and OVD in young adults, assess the validity of commonly used reference ratios, and develop updated morphometric guidelines for clinical application.
Material And Methods:
Eighty-one participants underwent digital intraoral scanning (Primescan 3D; Dentsply Sirona) with subsequent analysis using a metrology software program (GOM inspect pro 2022 Service Pack 2 V2.0.1; Carl Zeiss GOM Metrology GmbH). Measured parameters included gingival-incisal height (GI), papillary mesiodistal width (PMD), gingival-gingival distance (GG), horizontal overlap (HO), and vertical overlap (VO) for maxillary (Mx) and mandibular (Md) central incisors. Analysis focused on participants with physiological vertical overlap (1.0 to 4.5 mm, n=66). Statistical analysis comprised paired t tests for bilateral symmetry, Pearson correlations for dimensional relationships, and 1-sample t tests comparing calculated ratios (length-to-width, vertical-to-width, vertical-to-length) against established references. Novel reference values (Frankfurt proportions) were derived and compared with classic indices (α=.05).
Results:
Mean ±standard deviation values for the normocclusive group were: GG 16.4 ±1.74 mm, GI-Mx 10.3 ±1.00 mm, PMD-Mx 8.42 ±0.54 mm, GI-Md 8.60 ±0.82 mm, PMD-Md 5.12 ±0.37 mm, HO 2.73 ±1.34 mm, and VO 2.75 ±0.94 mm. Statistically significant correlations were found between PMD-Mx and GG (P=.049) and between GI-Mx and GG (P<.001). Both length-to-width (1.23 ±0.12) and vertical-to-width (1.95 ±0.22) ratios were significantly lower than reference values (P<.001), while vertical-to-length ratio (1.59 ±0.13) showed no significant difference (P=.076). Reference predictions overestimated GI-Mx by 0.55 ±0.10 mm and GG by 1.25 ±0.26 mm. No clinically relevant bilateral differences were observed despite statistical significance for PMD-Mx (P=.040; difference 0.05 mm).
Conclusions:
Width-based measurements show statistically significant correlation with OVD, validating their clinical utility. The Frankfurt proportion provided evidence-based reference values that differed significantly from classic references, suggesting conventional indices may not accurately represent morphometric relationships in contemporary populations.
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