A New Method for 3D Dental Records Related to Orthopedic Treatments: The Hemimaxillary Plane Reference System and Its Clinical Implications

The purpose of this explementary method study was to demonstrate, within the hemimaxillary, the three-dimensional skeletal and dental displacements of upper permanent first molars in patients undergoing rapid maxillary expansion (RME) with anchorage on deciduous teeth or paramedian miniscrews. Five post-treatment cases were analyzed on frontal and axial views before (T0) and after expansion (T1), adopting a new hemimaxillary reference system. Three-dimensional landmarks were selected to evaluate molar changes; buccal tipping and rotation were calculated, in addition to intermolar angle, molar angle of rotation, and orthopedic expansion angles. The origins (dental and/or orthopedic) of molar displacements were investigated by alternate interior angle demonstration according to the parallel lines theorem. Through inverse geometric functions of right triangles, it was possible to determine theoretical-experimental forms to calculate angles from periapical radiographs taken at T1. These findings have significant clinical implications, enabling the assessment of treatment outcomes while adhering to radioprotection principles. Reproducible formulas enable the calculation of expansion angles without CBCT. For RME to allow clinical improvement, molar rotation and intermolar angles at T1 should be less than the difference between the respective angles at T0 and the orthopedic expansion angle. This method provides a reproducible, radiation-efficient method to assess maxillary changes, enhancing treatment precision in orthodontics.