APPLICATION OF MATHEMATICAL MODELING IN ORTHODONTICS (literature review)

Relevance. The introduction of digital technologies has significantly changed the capabilities of modern orthodontics, both at the diagnostic stage and in treatment planning. The use of CBCT, digital intraoral scanners, CAD/CAM technologies, and software packages has significantly increased the amount of diagnostic information available to the practitioner. However, the accumulation of large amounts of data alone does not improve the quality of treatment, necessitating the use of tools for their comprehensive analysis and clinical interpretation. One such tool is mathematical modeling, which allows for the study of processes occurring in the dental system under the influence of orthodontic forces. Mathematical modeling acquires additional value in the context of a personalized approach to treatment. The use of individual digital models allows for the consideration of the anatomical structure and functional state of the dental system of a particular patient, improving the accuracy of orthodontic intervention planning. Purpose of the study. To analyze current scientific data on the use of mathematical modeling methods in orthodontics and evaluate their role in diagnosis, orthodontic treatment planning, and outcome prediction. Materials and Methods. An analysis of domestic and international scientific publications on the use of mathematical modeling in orthodontics was conducted. The search included PubMed, Scopus, Web of Science, Google Scholar, and eLIBRARY. The final analysis included 34 publications that most fully reflect the current state of the art. Results. It was established that the development of mathematical modeling in orthodontics is associated with a transition from two-dimensional analytical calculations to three-dimensional digital models based on CBCT and digital scanning data. The most popular tool is finite element analysis, which allows for the assessment of stress and strain distribution in the dental system, the prediction of treatment outcomes, and the optimization of orthodontic appliance designs. A promising area is the creation of personalized digital models using artificial intelligence technologies, which can improve the accuracy, safety, and predictability of orthodontic treatment.