Physical and Mathematical Modeling of the Distribution of Load Forces on the Feminal Component of an Endoprosthesis of the Hip Joint Under Real Conditions

Abstract

Determination of the factors causing the development of aseptic instability of endoprosthesis components is one of the main tasks of modern traumatology and orthopedics. It is important from a scientific and medical point of view to carry out physical and mathematical modeling of the distribution of load forces and their moments on the femoral component of a hip endoprosthesis. The purpose of the study: to conduct a physical and mathematical modeling of the distribution of load forces on the femoral component of a hip endoprosthesis under real conditions of incomplete axially symmetrical contact of the femoral component of the endoprosthesis and the femur, when the surface of the lower end of the endoprosthesis is not in contact with the surface of the bone. In the work, mathematical modeling of the distribution of point load forces and their moments on the contact surface between the femoral endoprosthesis stem and the bone marrow canal of the femur in real conditions is carried out. For qualitative estimates of point distributions of the load force, based on the analysis of previous results, an estimated empirical formula was obtained for these distributions: g(λ,λ1)=Р(λ,λ1) / 140λ7/2, in which the pressure Р(λ,λ1) is taken in kilograms per square centimeter (kg/cm2), and the point force g(λ,λ1) is in kilograms (kg). It was determined that the best, from the point of view of minimizing the harmful mechanical impact of the prosthesis on the femur, is the situation when the length of the prosthesis stem is not less than half the length of the femur (λ≥0.5). In this case, the values of the point load forces do not exceed 0.1 kg, at least for the length of the area of real contact, which is not less than half the length of the prosthesis stem (λ1≥0.5λ). It has been proven that the use of a prosthesis stem that is less than a third of the length of the femur is not advisable. Since already at the length of the prosthesis stem, which is 30 % of the length of the femur (λ=0.3), point loads increase rapidly and can reach from 0.55 to 1.5 kg depending on the length of the contact area. Such point loads are undesirable for the femur in the area of contact with the prosthesis in terms of the integrity of the femur.