Osseointegrated implants often fail because of excessive masticatory forces that cause extremely large stresses in bone tissue. We hypothesized that a proper dental implant could be selected by comparing the ultimate masticatory forces of a wide range of commercially available implants. We determined ultimate oblique masticatory forces for different cylindrical implants, taking into consideration the biomechanical correlation between implant dimensions and stresses in supporting bone. For this purpose, we used the finite element (FE) method and studied von Mises stresses in implant-bone interface areas to evaluate the influence of implant dimensions on stress concentration and on the value of an implant's ultimate masticatory load. Geometric models of a mandibular segment were generated from computed tomography (CT) images and were analyzed with osseointegrated cylindrical implants. Masticatory forces were applied in their natural direction. All materials were assumed to be linearly elastic and isotropic. Critical point in the peri-implant area of bone was determined. The ultimate value of the masticatory load, which generates ultimate stresses at the critical point, was calculated for each implant. These findings provide correct selection of implant dimensions in clinical cases, because corresponding ultimate values of masticatory force were used as a criterion for assessment of their load-carrying capacity and applicability.

Implant dimensions greatly influence load transfer characteristics and the lifetime of a dental system. Excessive stresses at peri-implant area may result in bone failure. Finding the critical point at the implant-bone interface and evaluating the influence of implant diameter-to-length ratio on adjacent bone stresses makes it possible to select implant dimensions. For this, different cylindrical implants were numerically analysed using geometrical models generated from computed tomography images of mandible with osseointegrated implants. All materials were assumed to be linearly elastic and isotropic. Masticatory load was applied in its natural direction, oblique to occlusal plane. Maximum von Mises stresses were located around the implant neck at the critical point of its intersection with the plane of loading and were functions of implant diameter-to-length ratio. It was demonstrated that there exists a certain spectrum of diameter-to-length ratios, which will keep maximum bone stresses at a preset level chosen in accordance with patient's bone strength.

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In this paper a discrete mathematical model of the diffraction of a plane electromagnetic wave by pre-Cantor impedance strips on a shielded dielectric layer is developed. The TM wave case is considered. The mathematical model is based on the boundary singular integral equation (SIE) of the first kind with supplementary conditions and the Volterra integral equation (IE) of the second kind. Numerical experiments may be carried out based on this discrete mathematical model using the discrete singularities method (DSM).