Combined effects and weight analysis of factors affecting initial maxillary central incisor retraction: a three-dimensional finite element study

Introduction Investigating the stress distribution generated by orthodontic forces within the periodontal ligament (PDL) is critical for quantifying mechanical stimuli, correlating them with subsequent histological responses, and ultimately identifying evidence-based optimal force levels. This study aimed to evaluate the combined biomechanical effects of alveolar bone height loss, tooth movement type, and alveolar bone density on the initial retraction of the maxillary central incisor, and to quantify the weighting of each factor on PDL stress. Methods A three-dimensional (3D) finite element model of the maxilla, dentition, PDL, and orthodontic appliances was constructed based on cone-beam computed tomography (CBCT) data. Eighty experimental conditions were established by combining five levels of alveolar bone height loss (0–4 mm), four tooth movement types, and four alveolar bone density levels (simulated via cortical bone Young’s modulus: 12,500–27,500 MPa). A 1 N bilateral retraction force was applied. The initial displacements of the crown and root and the maximum PDL von Mises stress were calculated. Multiple linear regression was used to quantify the factor contributions. Results Alveolar bone height loss significantly increased both tooth displacement and PDL stress. Uncontrolled and controlled tipping resulted in greater sagittal retraction and root intrusion, whereas bodily and controlled root movements were associated with more distolingual rotation. However, bone density affected displacement but had no significant effect on PDL stress. The regression model (R 2 = 0.80) revealed that tooth movement types exerted the strongest influence on PDL stress, followed by alveolar bone height loss (β = 0.535, p Conclusion These findings provided novel quantitative biomechanical evidence regarding the combined effects of these variables and could guide individualized force control strategies and the development of AI-assisted orthodontic decision-making systems.