Three-Dimensional Quantitative Analysis of Maxillary Arch Morphology Across Sagittal and Vertical Skeletal Patterns

Background: Contemporary three-dimensional morphometric analysis emphasizes quantitative modeling of anatomical interactions. However, the interplay between sagittal and vertical dimensions in determining maxillary transverse morphology remains inadequately characterized. This study introduces the Sagittal Modulation Effect (SME) framework—a model characterizing how sagittal relationships modify the association between vertical pattern and maxillary arch morphology. Methods: A retrospective cross-sectional analysis was conducted on 165 skeletally mature adults (mean age: 25.4 ± 4.8 years), stratified into skeletal Class I, II, and III groups (n = 55 each). Lateral cephalometric analysis and 3D maxillary digital models were obtained. A validated automated algorithm performed arch morphometric analyses. The primary hypothesis was tested using multiple linear regression with interaction terms, validated via bootstrap analysis and cross-validation. Results: A significant SME was identified (p < 0.001). The inverse correlation between SN-MP and maxillary width intensified progressively: minimal in Class I (r = −0.047, p_adj = 0.891), moderate in Class II (r = −0.387, p_adj_ = 0.024), and strong in Class III (r = −0.645, p_adj_ < 0.001). Regression confirmed significant interaction effects (SN-MP × Class III: β = −0.45, p < 0.001; SN-MP × Class II: β = −0.31, p = 0.003). Exploratory analysis identified cohort-specific statistical descriptors associated with narrower arches: SN-MP > 34.2° in Class III (AUC = 0.84) and SN-MP > 36.5° in Class II (AUC = 0.78). These require external validation. Conclusions: This study provides evidence that sagittal classification modulates the vertical–transverse relationship. The SME framework offers class-specific coefficients and exploratory stratification tools for future research pending multi-center validation.