Digital models and 3D biomechanics analysis in orthodontics. Part 1: Vector calculations

Abstract

Biomechanics is essential for optimizing orthodontic appliances and controlling dental movement. Charles J. Burstone pioneered a three-dimensional (3D) approach in orthodontics, advocating for a shift beyond appliance-focused methods. Initially, biomechanics studies were constrained to two-dimensional (2D) analysis due to the complexities of 3D evaluation. Despite progress in computational tools and digital modeling, orthodontic biomechanics has largely maintained a 2D orientation. This paper advances orthodontic biomechanics into 3D, re-evaluating concepts previously limited to 2D frameworks. A dedicated software, DDP-Ortho (Ortolab, Poland), is introduced to enable orthodontists to analyze and resolve biomechanical challenges in 3D, facilitating appliance designs with precise 3D force systems. The representation and calculation of force vectors and moments in 3D are detailed, emphasizing the inherent complexity absent computational support. Key processes such as vector subtraction and addition, fundamental for assessing and refining orthodontic force systems, are explained. Additionally, the vector split (couple replacement) method, previously described in 2D, is extended to 3D, addressing the unique constraints and challenges of this approach. These tools promise to refine the accuracy and effectiveness of orthodontic treatments, setting the stage to examine the interactions between 3D force systems and dental movement, which will be addressed in a subsequent paper, to broaden the potential of contemporary orthodontic therapy.