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

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.