MATHEMATICAL JUSTIFICATION OF THE CHOICE OF RODS FOR EXTERNAL FIXATION DEVICES FOR POLYSTRUCTURAL PELVIC INJURIES

Aim - In order to fulfill the purpose of biomechanical substantiation for extrafocal pelvic osteosynthesis in osteoporosis we studied the stress-strain state (SSS) of LEG under conditions of external fixation by apparatuses with cylindrical and conical rods. Studies of the stress-strain state of the lower extremity belt by the finite element method were carried out under conditions of external fixation by devices with cylindrical and conical rods. In the finite element method, the approximate solution is constructed as a superposition of approximating functions. At the first stage of solving the problem, the object is divided into areas of a simpler form - finite elements whose geometric dimensions are significantly smaller than the dimensions of the entire biomechanical system. Modern software systems generate finite elements of the grid automatically using elements with triangular faces in most cases. At the junctions of the elements (nodal points), the real stress field is replaced by the action of forces and movements. The type of finite elements is characterized by the number of nodes and the degree of approximation of unknowns within the domain and largely determines the accuracy of the resulting solution in the finite element method. Various types of biological tissues were taken into account in the conducted studies: compact and spongy bone, cartilage tissue, intervertebral disc, ligaments. In this study, the material was considered homogeneous and isotropic. The main load is body weight. In the calculation, the body weight was taken to be equal to 700 N. The geometric model was built on the basis of tomographic sections of the pelvis carried out through 0.5 - 1 cm for irregular zones. A pelvis with rotationally unstable (type B1 according to AO classification) damage after osteosynthesis by an external fixation device was modeled in the variants of using cylindrical and conical rods. Mises stresses were used to assess the stress state. The resulting model consists of 75,845 finite elements and has 132253 nodes. The construction of the geometric model was carried out in the SolidWorks program. VAT calculations and analysis were carried out in the ANSYS program. In the first variant of the study of the pelvic model with normal bone tissue and cylindrical rods, the calculation results showed that with a single support standing (support on the left limb), the supporting side with pronounced stress concentration zones in the sacroiliac joint, the place of entry of the rod into the bone and in the area of reducing the thickness of the iliac wing is more tense. Two stress concentration zones are observed along the passage of the rod. The most intense is the area of the screw entry into the bone (18.5 MPa). There is also an area of increased stress at the site of a decrease in the thickness of the iliac wing (8.1 MPa), where the rod passes closest to the cortical layers. The calculation of the model using conical shaped rods showed that the nature of the VAT distribution for the model as a whole has not changed, and the stress state level has decreased. So, at the point of entry of the screw into the bone, the value of the Mises stresses is 16.4 MPa, and at the point of reduction of the thickness of the iliac bone - 6.3 MPa. It is worth noting that the area with an increased stress state along the passage of a conical rod is smaller than for a cylindrical one. In the second variant of the study for a pelvic model with osteoporotic bone tissue, a comparative analysis of VAT when using cylindrical rods of an external fixation device showed that the general nature of the distribution of stresses and deformations for the model as a whole did not change, but the VAT level increased. At the point where the screws enter the bone, it is 28.4 MPa, at the point where the thickness of the iliac wing decreases - 9.1 MPa. The level of tension has also increased throughout the "rod-bone" contact. A comparative analysis of VAT for the variant of conical rods of the external fixation apparatus and osteoporotic bone tissue showed that the general nature of the VAT distribution for the model as a whole has not changed, and the level of stress state has increased as well as in the model with cylindrical screws. At the point where the screws enter the bone, it is 26.5 MPa. At the site of the reduction in the thickness of the iliac wing, the stress level is 7 MPa. The use of conical shaped rods in the external fixation device of the pelvis makes it possible to reduce the level of stress-strain state both in the area of the entry of screws into the bone and in the area of the thinnest part of the iliac wing. For external osteosynthesis of the pelvis in polystructural injuries, lowering the stress state when using conical rods plays an important role, since the strength characteristics of osteoporotic bone tissue are significantly lower than those of normal. Thus, the use of conical rods in external pelvic fixation devices improves the strength characteristics of the "pelvis - rod" system, which makes it possible to recommend their testing in clinical practice.