Репозиторий Университета

The aim of the study was to provide a mathematical justification of the possibility of using 6.5 mm IRIS implants and to evaluate the results of orthopedic treatment in patients with partial loss of teeth. For the calculations was constructed of a composite three-dimensional computer models: the abutment screw-implant-bone. A total of 3 models were prepared: M1-implant in the spongy bone tissue, this model corresponds to the implantation on the HF when replacing one molar; M2-2 implants in the spongy bone tissue located at a distance of 4 mm connected via abutments, this model corresponds to the implantation of RF when replacing two molars; M3-implant in the cortical bone tissue, this model corresponds to the implantation of LF when replacing one molar. Loading of implants was carried out by occlusive force applied to its end surface. The results of the calculations showed that the equivalent stresses and limiting stresses of compression-tension are within the permissible values, which were obtained by us earlier in respect of the irregular implants and are consistent with the results of calculations for other systems of short implants. The clinical part of the work consisted in the treatment of 27 patients with partial loss of teeth, who had 41 iris evolution implants with a diameter of 5 mm, length of 6.5 mm after 3 years, there was a slow bone resorption in the cervical region not exceeding 0.35 mm, which corresponds to generally accepted international standards. During the first three years of operation there were no cases of loss of established implants. Thus, the data of mathematical modeling by finite element method and retrospective three-year analysis of prosthetics on IRIS evolution implants with length of 6.5 mm showed that the use of short implants in the recovery of upper and lower jaw molars is an effective method with a high success rate at long - term and resorption level of 0.34 mm.

© 2018 Society for Industrial and Applied Mathematics. We consider a vector-Laplace problem posed on a two-dimensional surface embedded in a three-dimensional domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and analysis of a finite element method for the discretization of this surface partial differential equation. We apply the trace finite element technique, in which finite element spaces on a background shape-regular tetrahedral mesh that is surface independent are used for discretization. In order to satisfy the constraint that the solution vector field is tangential to the surface we introduce a Lagrange multiplier. We show well-posedness of the resulting saddle point formulation. A discrete variant of this formulation is introduced which contains suitable stabilization terms and is based on trace finite element spaces. For this method we derive optimal discretization error bounds. Furthermore algebraic properties of the resulting discrete saddle point problem are studied. In particular an optimal Schur complement preconditioner is proposed. Results of a numerical experiment are included.