Математическое моделирование формы и размеров зубных дуг для выбора тактики и объема ортодонтического лечения у пациентов с аномалиями зубочелюстной системы

Aim. Development of an algorithm for forecasting the shape and size of dental arches in view of the teeth size and the major maxillofacial parameters. Materials and methods. The materials of the research were the results of measurements of the cephalometric parameters and diagnostic gypsum models of the dentition series of 103 people of the first period of adulthood with a complete set of permanent teeth, physiological occlusion and various gnathic and dental types of the face and dental arches. To determine the dental type of face (normodontia, macrodontia, microdontia), the diagonal dimensions of the facial head were evaluated between the cephalometric points t (tragion) and sn (subnasale). When establishing the gnathic type of face (mesognathy, dolichognathy, brachygnathy), the gnathic index was calculated, calculated as the percentage of diagonal and transversal dimensions of the facial part of the head. Transversal dimensions represented the width of the face between the goat-bearing landmarks t-t. Gnathic variants (mesognathy, dolichognathy, brachygnathy) of dental arches (Dmitrienko S.V., 2015) were determined taking into account the dental index calculated as the ratio of the half-sum of the width of the crowns of 14 teeth to the width of the dental arch between the second molars. The types of the dental system (normodontia, macrodontia, microdontia) were determined from the results of summation of the width of the crowns of the upper teeth. Results. As a result, an algorithm was proposed for forecasting the shape and dimensions of the dental arches, which is based on measuring relatively stable parameters, namely, the dimensions of the anterior teeth and the basic features in the maxillofacial area. The algorithm is based on mathematical calculations of the circle geometry and the dependence of the length of the arch, chord and height. The circle diameter was calculated as the ratio of the dental arch width between the canines to the sine of the central angle shaped by the radii of the circle limiting the chord. The size of the front-canine diagonal is comparable to the size of the front teeth in a certain ratio. Conclusion. Optimization of diagnostic and treatment methods for adult patients with anomalies of the dentoalveolar system not only makes it advisable to revise the conventional traditional diagnostic regimens for determining the shape and size of dental arches in order to increase the effectiveness of orthodontic treatment, but also implies the expansion of existing modern ideas about the morphology of the craniophatic complex and its relationship to the shape, the size of the dental arches. in clinical orthodontics, the introduction of a forecast algorithm based on the measuring the relatively stable parameters will reveal the deviations in the teeth location as well as in the shape and size of the upper dental arch in the transversal and sagittal planes, reducing the time spent in the early diagnostics phase and increasing the effectiveness of monitoring the outcomes of orthodontic correction.