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Orthodontic path planning for virtual teeth via the multi-strategy improved particle swarm optimization algorithm

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Abstract

Orthodontic path planning is a critical dental problem that directly affects the orthodontic outcome and patient experience. To improve the accuracy and efficiency of orthodontics, this paper proposes an orthodontic path planning method that combines an improved particle swarm optimization algorithm with a collision avoidance movement prioritization strategy. First, the efficiency of orthodontic path planning is improved by designing a local coordinate system based on the direction of tooth growth and the direction of neighboring teeth to reduce manual intervention. Second, a multi-strategy improved particle swarm optimization algorithm is proposed for orthodontic path planning, where the population is initialized by cosine sequence mapping interference linear interpolation, and the particles are adaptively updated using linear inertia weights and trigonometric function factors. An annealing-PSO strategy and particle stochastic learning strategy are also introduced to enhance the ability of the algorithm to jump out of the local optimum. In addition, a collision avoidance movement prioritization strategy based on low orthodontic costs and OBBTree is proposed to detect and avoid collisions between teeth effectively. Finally, through experimental validation on nine benchmark functions and a set of orthodontic cases involving both maxillary and mandibular regions, the MSIPSO algorithm demonstrated a reduction of 31.43% in maxillary orthodontic translation and 10.03% in rotation compared to the traditional PSO algorithm. Furthermore, comparisons with other optimization algorithms, including NSMPSO, CSPSO, and PSO-SA, further highlight the superior performance of the MSIPSO algorithm in terms of convergence speed and optimization accuracy. The results show that the method can effectively plan high-quality orthodontic paths, which can be used as a reference for medical aid diagnosis.

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Funding

This work was partly supported by the Natural Science Basis Research Plan in Shaanxi Province of China under Grant 2023-JC-YB-517, the Open Project Program of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University under Grant VRLAB2023B08, the Research on Key Technologies of Sushui River Digital Twin Watershed under Grant 2024GM13, and the Key Laboratory of Optical Information Processing and Visualization Technology of Tibet Autonomous Region under Grant KLFPXZMU2301.

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Authors and Affiliations

  1. College of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an, 710054, China

    Hong-an Li & Xue Hu

  2. State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, 100191, China

    Hong-an Li

  3. Department of Information and Engineer, Shanxi Conservancy Technical Institute, Yuncheng, 044000, China

    Zhihua Zhao

  4. Shaanxi Technical College of Finance and Economics, Xianyang, 712099, China

    Jun Liu

Authors
  1. Hong-an Li
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Contributions

All authors contributed to the study conception and design. Hong-an Li was responsible for proposing the research topic, designing the research protocol, designing the algorithmic innovation, directing the experiments, revising the paper, final reviewing the paper and providing technical and supervisory support. Xue Hu was responsible for researching and organizing the literature, conducting the research, conducting the experiments, performing the statistical analyses, and writing and revising the paper. Zhihua Zhao collected experimental data, algorithm design, result validation, paper revision, final review, and technical and supervisory support. Jun Liu was responsible for designing the paper’s framework, designing and supervising the comparative experiments, technical and supervisory support, and proofreading the paper.

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Correspondence to Hong-an Li.

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Li, Ha., Hu, X., Zhao, Z. et al. Orthodontic path planning for virtual teeth via the multi-strategy improved particle swarm optimization algorithm. J Supercomput 81, 550 (2025). https://doi.org/10.1007/s11227-025-07039-7

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  • DOI: https://doi.org/10.1007/s11227-025-07039-7

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