Abstract:Dental crowding is the most prevalent type of malocclusion. To alleviate the condition of tooth crowding in orthodontic treatment, the typical approach involves the extraction of the first premolars and subsequent comprehensive retraction of the anterior teeth. During the retraction process, a combination of vertical closing loops and micro-implant anchorage is often used to close the gaps between the teeth. However, in the course of treatment, physicians often rely on qualitative non-quantitative methods to describe forces and movements, which makes it challenging to accurately predict the treatment outcomes. To address this problem, the superposition theorem was used to obtain a model for predicting the orthodontic force and torque of vertical closing loop combined with micro-implant anchorage, which was parameterized by the cross-section size and shape of the archwire and the height of micro-implant traction. The theoretical and simulated values for each operational condition were compared, and the error was determined through finite element analysis. The error between the simulated and theoretical values for corrective force was within 0.09 N, while for corrective torque, it was within 0.75 N·mm. Further measurements of orthodontic force and moment on mandibular wax models revealed that, with low traction, the error between theoretical and experimental values for orthodontic force ranged from 0.03~0.18 N, and for orthodontic moment from 0.51~1.1 N·mm. With high traction, the force error ranged from 0.03~0.17 N, and the moment error from 0.23~1.30 N·mm. This serves to validate the accuracy of the theoretical model and the reliability of the simulation conditions. The model can parametrically represent the force in the correction process, thus providing a foundation for personalized treatment planning and enhancing treatment efficacy and safety.