Methodology of development and research of mathematical models in systems of diagnostics and functional analysis of orthopedic structures on dental implants

The article presents the results of analysis and research of modern projects of biomechanical systems and orthopedic structures in terms of their planning, as well as reliability. The method of mathematical modeling based on CAD - CAM technologies of digital models of these systems and their research under the conditions of setting and solving problems of prosthetics of patients is shown. The peculiarity of modeling and research of complex three - dimensional biomechanical object is the possibility of ensuring the unity of geometrical, physico-mechanical and biological parameters with individual characteristics of the patient. It is shown that in the development of the model of biomechanical system it is necessary to consider the surrounding biological tissues discretely in structure and physical and mechanical properties - epithelium, cortical and spongy bone zones. The method of analysis of biomechanical orthopedic models of structures, allowing one to establish the relationship of value and direction of functional loads in them and the internal stresses and strains. It is shown that a significant difference in the magnitude of the forces acting on the implants, and, accordingly, on the bone and adjacent tissues in the contact zone with them, as well as on the entire temporal - mandibular system from the workloads due to the individual characteristics of the chewing apparatus. The study of the three - dimensional mathematical model of this system and the nature of the relationship between the change in the direction of the initial loads and the redistribution of the values of tensile, compressive and transverse shear forces acting on implants. This allows the creation of a biomechanical system project to substantiate the most favorable scheme of transfer of forces to the cortical and spongy bones under the conditions when the tissue adjacent to the implant is most resistant in the forecast period to compressive forces, is 32% less resistant to stretching and 68% to the forces of transverse displacement, and the change in the angle of inclination of the implant in relation to the vector of the forces acting on it leads to a significant increase in stresses in the bone - implant contact zone.