Extensive Iterative Finite Element Analysis of Molar Uprighting with the Introduction of a Novel Method for Estimating Clinical Treatment Time

The aim of this study was to analyze the biomechanical effects of a conventional molar uprighting spring on a mesially tilted mandibular second molar through a novel iterative finite element (FE) approach in order to estimate clinical treatment duration. A new model was developed utilizing data from previous canine retraction experimental studies to aid in correlating each individual FE iteration with its real-time value. Another model consisting of a 30° mesially titled mandibular second molar and a conventional molar uprighting spring was developed to evaluate kinetic and kinematic responses. The iterative FE simulation of the treatment was then carried out. The molar uprighting simulation was completed in 180 iterations, which was equivalent to almost 12 weeks of clinical treatment time. The average stress-normalized bone remodeling velocity was found to be ~0.9 μm/(KPa·day). During the simulation, the spring initially produced a 15 N·mm (∼1530 g·mm) counterclockwise moment responsible for molar uprighting. The mandibular second molar showed 3.75 mm of distal movement, 2.15 mm of vertical extrusion, and a 22° counterclockwise rotation at the end of the treatment. This study provides a foundation for the future estimation of biomechanical responses as a function of treatment time in various orthodontic applications using iterative FE simulations.