Mathematical modelling is being used in modern dentistry to solve a wide range of scientific problems. The models allow one to predict and estimate the medical intervention impact during the calculations of stress-strain state of prostheses and medical devices. In the present research a mathematical model of the lower jaw, considering the individual characteristics of the geometry, properties of bone tissue and activity of the patient’s mastication muscles using the finite element method is proposed. The work provides an example of determining the operational characteristics of dentoalveolar structures. The analysis of displacements, tensions, and deformations for a particular tooth as well as the selection of the implant diameter were presented as results.

The purpose of this paper is simulation parameters of human walking in normal and pathological conditions. Modeling does possible to determine dynamic characteristics of motion and to optimize designs of walking mechanisms, prostheses, orthoses, implants and more. In developing the model of human walking, we used a special case of the Lagrange equation of the second kind. The experiment was conducted by video analysis of real gait of people of different ages and sex. As a result of the simulation the speeds and accelerations of all links of the model, moments in joints, and peak values of moments are determined. Simulation of human walking makes it possible to develop technical specifications for the design of walking mechanisms, prostheses, implants and more.

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