# Association between frankfurt horizontal–referenced vertical position of the maxillary first molar and mandibular asymmetry: a cross-sectional study

## TL;DR

This study explores the link between the vertical position of a maxillary molar and jaw asymmetry, finding a small but notable association.

## Contribution

The study introduces a novel analysis of localized dental vertical discrepancies in relation to mandibular asymmetry using 3D cephalometric methods.

## Key findings

- Weak positive correlations were found between maxillary molar vertical discrepancy and mandibular asymmetry indices.
- Patients with greater mandibular asymmetry showed slightly larger vertical discrepancies compared to controls.
- Correlations were not statistically significant after false discovery rate adjustment.

## Abstract

Facial symmetry is a key determinant of aesthetic balance and functional harmony. Unilateral vertical discrepancies in the maxillary dentition, particularly side-to-side discrepancy in the FH-referenced vertical position of the maxillary first molar (U6), has been hypothesized to be associated with functional mandibular deviation and skeletal asymmetry. However, the relationship between localized dentoalveolar vertical discrepancy and mandibular morphology remains poorly understood.

Eighty-seven patients aged 16–35 years with mandibular asymmetry ≥ 2 mm on MSCT, operationally defined as a side-to-side difference in total mandibular length (ΔCo-Go-Gn) ≥ 2 mm, were included. Three-dimensional cephalometric analysis was performed using ProPlan CMF (Materialise, Belgium). Four variants of the Frankfort horizontal (FH) plane (FH1-FH4) were constructed to evaluate the influence of reference-plane definition on the measurements. Mandibular asymmetry was quantified by differences in ramus length (Co-Go), body length (Go-Gn), and total side length (Co-Go-Gn). The primary independent variable was the vertical discrepancy between FH and U6 (ΔFH-U6). In addition, a control group of patients (n = 63) with mandibular asymmetry (ΔCo-Go-Gn) < 2 mm was included for between-group comparison of ΔFH-U6.

Weak positive correlations were observed between ΔFH-U6 and mandibular asymmetry indices, particularly ΔCo-Go and ΔCo-Go-Gn (Spearman’s ρ = 0.21–0.28). ΔFH-U6 differed across FH-plane definitions (Friedman test, p = 0.012), but correlation estimates were comparable across FH constructions. However, the observed correlations were small, and none of the primary correlations remained statistically significant after Benjamini–Hochberg false discovery rate (FDR) adjustment. Patients with mandibular asymmetry ≥ 2 mm showed a slightly greater ΔFH-U6 than controls with asymmetry < 2 mm (median [IQR]: 0.9 [0.45–1.75] mm vs 0.8 [0.2–1.3] mm; Mann–Whitney U test, p = 0.049).

FH-referenced vertical discrepancy of the maxillary first molar may show a small exploratory association with mandibular asymmetry and was slightly greater in patients with clinically relevant mandibular asymmetry than in controls.