## 3 Results and Discussion
### Numerical Assessment of Broken Fibula Deflections, Which Is Fixed with an Extracortical Plate
However, these studies do not take into account the elastic fixation of the tibofibrular syndesmosis with a tightrope. The problem set in this research is studied in terms of practical orthopedics, technology development, biomechanics and mechanics of deformable solids. One of the frequent complications of broken shin bones is damage to the tibofibrular syndesmosis. In such injuries, the restoration of the distal tibofibrular joint should be carried out taking into account the need to maintain a sufficient range of motion to prevent disturbances in the biomechanics of the supracalcaneal-shin joint. At present, it is considered necessary to perform tibofibrular syndesmosis fixation even if it is partially damaged. The device for restoring the tibofibrular syndesmosis should optimally combine fixation stability while maintaining mobility in the considered site of joining. In previous studies, the authors of this paper proposed a method for broken shin metal osteosynthesis with rupture of the tibofibrular syndesmosis, which combines the stability of fibula fixation and does not limit the elastic properties of the tibofibrular syndesmosis [74]. In this study, this method has further been developed. In general, it includes stable fixation of the fibula with an extracortical fixator metal plate and elastic fixation of the syndesmosis with a tightrope on the fixation devices of the Endobutiton class. The choice of the tightrope tightening force value for the effective fixation of tibofibrular syndesmosis during extracortical osteomeatial synthesis of the broken fibula has been substantiated. Efficient fixation means the following:  
* the tightening force is sufficient for reliable fixation of the distal fibula syndesmosis;
* the tightening force is such that the tightrope material works within the limits of elasticity and the fixation is actually elastic;
* the fibula displacements, caused by the tightrope tightening force, do not exceed the permissible values. The permissible displacement value has been chosen from the conditions for maintaining the geometrically correct shape of the bone after rupture healing. In the case of exceeding the permissible displacement values, excessive opening of the rupture edges, displacement of bone fragments, etc., may occur. At the first stage of research, the behavior of an intact fibula bone under the action of a local transverse loading has been assessed. The value of stresses that occur in the bone tissue in response to the tightrope tightening has been determined. The angular and linear displacements of the bone that occur under the action of the ultimate loading, which are safe in terms of fulfilling the bone strength condition, have been calculated. At the second stage of research, an analytical model of the broken fibula, which is blocked with an extracortical fixator metal plate and is elastically fixed with a tightrope, has been developed. At this stage, the research object is the stress-strain state of the \"broken fibula-extracortical titanium plate\" composition under the action of tightening the fixing elastic tightrope. The main research result is an analytical dependence that makes it possible to determine the permissible tightrope tightening force for elastic fixation of the tibofibrular syndesmosis. Having used the obtained expression, Equation (21), and taking into account (8) and (9), a program with a simple user interface for entering input data can be developed for practical application. When entering data, the user only needs to enter the article number of the plate selected for extracortical osteosynthesis. Then, using the results of X-ray examination in standard projections (or the results of computed tomography or MRI), it is possible to select from a drop-down list the geometrical parameters for a fibula, as well as the coordinates of the rupture site and the coordinates of the tightrope insertion. At the output, the user can obtain a permissible tightrope tightening force.