Three-Dimensional Displacement Patterns in Maxillary Molar Distalization: A Comparative Finite Element Study

Objectives: This study aimed to analyze the three-dimensional displacement of maxillary first molars using a finite element model with two headgear configurations, namely cervical and horizontal pull headgears, as well as pendulum, infrazygomatic miniscrews, Bollard miniplates, Advanced Molar Distalization Appliance (AMDA), and Beneslider. The goal was to clarify how variations in anchorage design and force direction influence molar movement across the sagittal, vertical, and transverse planes. Methods: A three-dimensional finite element model of the maxillary dentition and supporting structures was constructed using reference anatomical data and standardized material properties. Each appliance was virtually simulated under its clinically recommended force magnitude and direction to ensure realistic biomechanical conditions. The orientation of each force vector relative to the molar's center of resistance (CR) was analyzed, and resulting tooth displacements were quantified along the sagittal (Z), vertical (Y), and transverse (X) axes using 49-node reference paths connecting key anatomical landmarks. Results: Appliances applying forces through or above the molar CR, such as the AMDA, infrazygomatic miniscrews, and Bollard miniplates, produced nearly bodily distalization with minimal tipping (<0.6° (range 0.3-0.6°)) and slight intrusion (-0.12 to -0.18 mm). Conversely, systems delivering forces below the CR, such as the cervical headgear and pendulum, resulted in greater crown tipping and extrusion. The Beneslider exhibited an intermediate displacement pattern with moderate vertical control. Conclusions: Force vector height and direction relative to the molar CR critically determine 3D displacement behavior. Skeletal anchorage and adjustable systems, particularly the AMDA, demonstrated the most controlled distalization pattern with minimal tipping, whereas conventional tooth-borne designs induced more tipping and extrusion.