ПИТАННЯ ПОБУДОВИ СУЧАСНИХ МАТЕМАТИЧНИХ МОДЕЛЕЙ БІОМЕХАНІКИ ПРИ ВИРІШЕННІ ПРОБЛЕМ ЕНДОПРОТЕЗУВАННЯ КУЛЬШОВОГО СУГЛОБА

Endoprosthetics is now a widespread way of treating diseases of the musculoskeletal system. Implantation of an artificial joint allows to eliminate or significantly reduce the pain syndrome, to ensure endurance of the limb, to restore movement in the joint. Although total endoprosthetics is one of the most successful of all surgical procedures, a number of issues related to design, materials, implant placement remain open. Nowadays, there is no complete understanding of the real processes that determine the biomechanical behavior of artificial joints in real physiological conditions under various anatomical variants of the structure of articular structures. Therefore, the study of the behavior of the implant-bone system by experimental methods, as well as methods based on mathematical analysis, becomes more and more important. A large number of studies aimed at studying the mechanical aspects of the interaction of endoprosthesis and bone tissue, special attention is paid to determining the impact of the design of the endoprosthesis on the stress-strain state of the bone. Experimental studies reveal the peculiarities of the influence of the design of the endoprosthesis on the redistribution of external load in the bone tissue. But, nevertheless, the disadvantage are technical limitations that do not allow to simulate complicated loading conditions of the bone-implant system due to human physiological activity. In addition, to describe the processes occurring in the bone tissue, it is necessary to record tension within the bone, which is extremely difficult in the experimental approach. Therefore, methods of mathematical modeling of mechanical behavior of the bone-endoprosthesis system are becoming increasingly popular. The paper analyzes the current state of the problem of studying the mechanical aspects of hip arthroplasty. Particular attention is paid to the choice of physical and mechanical characteristics of materials, strength criteria, load models and boundary conditions. The results of a several design schemes consideration that allowed to determine the further steps in the search for the most effective ways of development of these biomechanical models are presented.