Mandiblemath: External validation of a predictive tool for mandibular reconstruction

Mandiblemath is an artificial intelligence-driven software for predictive mandibular reconstruction that infers three-dimensional mandibular morphology from two-dimensional craniofacial data. We developed and externally validated Mandiblemath using a modular Python implementation integrating scientific computing, 3D visualization, and supervised learning. Ninety-one computed tomography scans (46 female, 45 male) yielded 12 craniomaxillary angles per subject; partial least squares regression generated 12 patient-specific mandibular configurations (Y₁-Y₁₂). Sex-specific classifiers - random forest, XGBoost, linear SVM, RBF-SVM, and gradient boosting - were trained with 10-fold cross-validation. External validation used 18 independent scans (nine female, nine male). Geometric correspondence between predicted and real mandibles was quantified using standard surface-based metrics. The best internal classifiers were linear SVM for females (68% accuracy) and random forest for males (82.8%). External validation achieved 88.8% accuracy for group identification in both sexes and ranking accuracy (top-three suggestions) of 66.6% in females and 70.4% in males. Predicted models exhibited broad global congruence with reference mandibles, maintaining clinically acceptable discrepancies (RMSD 1.2-3.3 mm) and strong overlap (F1@2.5 mm ≥ 0.85; Surface Dice@2.5 mm ≥ 0.80). Mandiblemath demonstrated technical feasibility and clinical potential as a decision-support tool, providing low-cost, reproducible predictions and printable meshes for reconstructive planning. The findings support future multicenter validation and integration into digital surgical workflows.