Study of the Stress-Strain State of the "Bone–Fixation Plate" System in Conjunction With Cortical Tissue Mechanical Properties

Abstract

Background. Bone osteosynthesis is considered one of the most efficient methods of treating fractures of long tubular bones. Deve­lopment of modern computer technology and specialized software makes it possible for a traumatologist to perform preliminary efficiency estimation of osteosynthesis using fixation plates of various designs. Results of such studies can significantly depend on calculation model parameters. In most papers related to the study of a stress-strain state of “bone–fixator” systems, bone tissue is considered as a homogeneous, isotropic, elastic medium. However, in fact it is heterogeneous and has an anisotropy of mechanical characteristics. Accordingly in a case of using a simplified isotropic model of bone tissue, when performing calculations, there is a possibility of obtaining inaccurate results. Objective. Estimation of influence of orthotropy of the bone tissue physical and mechanical properties on a stress-strain state of the “bone–fixator” system. Methods. The study is performed in the software environment based on the finite element method. Osteosynthesis of a low transverse fracture of a fibula using a smooth plate is selected as a computational case. Two computational models simplified in terms of geometry are constructed to solve the problem. These models are different only in properties of cortical bone tissue. Results. Analysis of a stress state in elements of models indicated that normal stresses reached the highest values, and tangential stresses are relatively small. In addition, the character of stress distribution turned out to be significantly inhomogeneous. However, stress state patterns are qualitatively similar for both computational models. A common feature of the maximum stresses both in the bone and in the plate turned out to be that all the maximum stresses are the result of their concentration. Conclusions. Consideration of orthotropy of elastic parameters of a bone led to significant quantitative changes in the indicators of a stress state. It is established that the minimum safety margins for both models turned out to be considered by the maximum tensile stresses acting in the vertical direction. A similar result in estimating bone strength also occurs in a case when only elastic orthotropy is considered, but the orthotropy of strength indicators is not considered. If the strength orthotropy is considered for the isotropic model of cortical bone, the pattern changes qualitatively. The normal tensile stress directed along the tangent to a circumference of bone cross-section is considered unsafe. Calculations results indicate a possibility of using an isotropic model of cortical tissue when performing comparative estimations in order to identify the most efficient, in terms of strength, fixation plate designs.