Independent and Combined Effects of Björk Polygon on Skeletal Class II Division 1 Malocclusion in Libyan Patients: A Retrospective Cephalometric Analysis

Abstract

The Björk polygon, comprising the saddle, articular, and gonial angles, plays a fundamental role in craniofacial growth, rotation, and sagittal jaw relationships. However, its independent and combined influence on skeletal Class II Division 1 malocclusion remains insufficiently disclosed in Libyan populations. To evaluate the independent and combined effects of Björk polygon components on sagittal skeletal discrepancy (ANB angle) in Libyan patients, and how they implement their effect on the relevant craniofacial covariates of class II (SNA, SNB, SN-MP). A retrospective cephalometric study was conducted on 116 Libyan patients diagnosed with skeletal Class II Division 1 malocclusion. The ANB angle was used as the dependent variable. Independent variables included saddle angle (N-S-Ar), articular angle (S-Ar-Go), and gonial angle (Ar-Go-Me). Covariates included SNA, SNB, and SN-MP. Statistical analyses included Pearson correlation, multiple linear regression, logistic regression, principal component analysis (PCA), and structural equation modeling (SEM). The usefulness of the last three analyses was emphasized. Significant correlations were found between ANB and saddle angle (r = 0.42, p < 0.001), articular angle (r = 0.32, p = 0.001), and the gonial angle (r = 0.28, p =0.002). Multiple regression demonstrated that saddle angle and articular angle were the strongest predictors of ANB (p < 0.001 and 0.02, respectively). Logistic regression confirmed that increased saddle angle significantly increased the odds of severe Class II discrepancy. PCA identified two principal components explaining 72% of the variance. SEM revealed both direct and indirect pathways linking Björk polygon angles to sagittal discrepancy via mandibular posterior positioning and clockwise rotation. The saddle and articular angles position B point more posteriorly, and the gonial angle contributes indirectly by promoting clockwise mandibular rotation, which reduces SNB. The Björk polygon exerts both independent and synergistic effects on skeletal Class II Division 1 malocclusion in Libyan patients. The saddle angle is the most influential component, primarily through its association with posterior positioning of the glenoid fossa and SNB reduction. In Libyan patients, the combined effect of the saddle, articular, and or gonial angles is additive.