Mathematical Modelling of Destabilization Stress Factors of Stable-Elastic Fixation of Distal Trans- and Suprasyndesmotic Fibular Fractures

Introduction. Specification of possible stress factors destabilizing the fibula stable osteosynthesis by the intramedullary nail with distal blocking and elastic fixation of distal syndesmosis by the thread with endobuttons by mathematical modelling of distal unstable ankle injuries. Material and Methods. We studied the thread tension during the combined stable-elastic fixation of unstable injuries of the ankle joint in cross-syndesmosis fractures of the fibula (B, C Danis–Weber classification), which includes a one-time stable minimally invasive fixation with the intramedullary nail and elastic fixation by the thread with endobuttons. We used a titanium alloy for the intramedullary nail and polyester for the thread. The deformed state was studied using the methods of mechanics. Results. A model of a fractured fibula blocked with the intramedullary nail and fixed with the elastic thread was developed. A formulation to specify the rational tension forces of the elastic thread depending on the parameters of the fibula and intramedullary blocking nail and on the location of the bone injury was obtained. The effect of foot rotation on the thread tension was investigated. The results of theoretical research should be implemented in medical practice. Conclusions. A mathematical model of the damaged fibula blocked by the intramedullary nail and fixed with the elastic thread was developed. Dependences for calculation of tension of the fixing thread were obtained. A slight increase in thread tension during foot rotation was found.

Clinical outcomes of Tightrope system in the treatment of purely ligamentous Lisfranc injuries

Background Purely ligamentous Lisfranc injuries are mainly caused by low energy damage and often require surgical treatment. There are several operative techniques for rigid fixation to solve this problem clinically. This study evaluated the effect of using the Tightrope system to reconstruct the Lisfranc ligament for elastic fixation. Methods We retrospectively analyzed 11 cases with purely ligamentous Lisfranc injuries treated with the Tightrope system from 2016 to 2019, including 8 male and 3 female. X-ray was performed regularly after operation to measure the distance between the first and second metatarsal joint and the visual analogue scale (VAS) score was used to evaluate pain relief. American orthopedic foot & ankle society (AOFAS) and Maryland foot score were recorded at the last follow-up. Results The average follow-up time was 20.5 months (range, 17–24). There was statistically significant difference in the distance between the first and second metatarsal joint and VAS score at 3 months, 6 months, and the last follow-up when compared with preoperative values (P < 0.05).Mean of postoperative AOFAS mid-foot scale and Maryland foot score were 92.4 ± 4.3, 94.1 ± 3.5, respectively. The Tightrope system was not removed and the foot obtained better biomechanical stability. No complications occurred during the operation. Conclusion Tightrope system in the treatment of purely ligamentous Lisfranc injuries can stabilize the tarsometatarsal joint and achieve satisfactory effect.

The use of the combined stable-elastic fixation for unstable injuries of the ankle joint in trans-syndesmotic fractures of the tibia

The problem of complications and the frequency of poor outcomes in the surgical treatment of ankle fractures with ti-biofibular syndesmosis (TFS) rupture (4.8–36.8 % of cases) remains significant. It was interesting from a scientific and practical point of view to conduct a clinical study to determine the effectiveness of the newly developed method of metal osteosynthesis for tibial fractures with TFS rupture, which would combine stability of tibial fixation and not limit the elastic qualities of TFS. The aim of the study: to determine the effectiveness of combined stable-elastic fixation for unstable injuries of the ankle joint in trans-syndesmotic fractures of the tibia. Materials and methods. On the basis of own clinical researches and data of literature sources, the method of the combined stable-elastic fixation for unstable injuries of the ankle joint in trans-syndesmotic fractures of the tibia is developed. The effectiveness of the proposed technique was evaluated 6 months after surgery on the Kitaoka scale. We have examined 12 patients with tibial fractures type 44 B1, B2 and B3 according to the AO classification, who underwent surgery using our methods. Results. The high efficiency of using the technique of combined stable-elastic fixation for unstable injuries of the ankle joint due to trans-syndesmotic fractures of the tibia has been determined. Good and excellent treatment results 6 months after surgery were observed in all 12 people (100 %), with excellent outcomes observed in 75 % of cases. There were no satisfactory and unsatisfactory treatment results. Conclusions. The study proves the high efficiency of the proposed method for combined stable-elastic fixation of ankle injuries in unstable trans-syndesmotic fractures of the tibia with TFS damage. There were 75 % excellent and 25 % good results within 6 months after surgery. A wider introduction of this technique into the practice of traumatologists of Ukraine is proposed.

ON SMOOTHNESS OF SOLUTION OF ONE NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION

In this paper we consider a nonlocal problem with integral boundary condition for hyperbolic equation. The conditions of the problem contain derivatives of the first order with respect to both x and t,, which can be interpreted as an elastic fixation of the right end rod in the presence of a certain damper, and since the conditions also contain integral of the desired solution, this condition is nonlocal. It is known that problems with nonlocal integral conditions are non-self-adjoint and, therefore, the study of solvability encounters difficulties that are not characteristic of self-adjoint problems. Additional difficulties arise also due to the fact that one of the conditions is dynamic. The attention of the article is focused on studying thesmoothness of the solution of the nonlocal problem. The concept of a generalized solution is introduced, and the existence of second-order derivatives and their belonging to the space L2 are proved. The proof is basedon apriori estimates obtained in this work.

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

Peri-acetabular bone remodelling after uncemented total hip arthroplasty with monoblock press-fit cups: an observational study

Background: Bone stock preservation in total hip replacement is essential to allow for later revisions in an increasingly younger and fitter index patient population. While contemporary modular press-fit acetabular cups lead to rigid fixation with equatorial stress and central osteolysis, more elastic fixation may cause different peri-acetabular bone remodelling. The purpose of this study was to investigate changes in peri-acetabular bone mineral density (BMD) in uncemented elastic fixation with monoblock press-fit cups.Methods: This prospective observational study included 45 patients with monoblock cups. We evaluated peri-acetabular BMD using dual-energy X-ray absorptiometry and reported functional outcomes and complications.Results: At a mean follow-up of 24.2 ± 2.2 months, we found that BMD stabilised in DeLee and Charnley zones I and III and recovered to baseline value in zone II. The mean Harris Hip Scores improved significantly from 56.9 ± 20.0 to 97.2 ± 4.0 (p < 0001). Other than one peri-operative dislocation, we saw no post-operative complications.Conclusions: We found favourable adaptive bone changes with BMD stabilisation in the equatorial zones and recovery to pre-operative values in the central zone. Additionally, excellent clinical outcomes and few prosthesis-related complications strengthened the favourable results of monoblock acetabular cups.Trial registration: Registration number DRKS00017076.

Peri-acetabular bone remodelling after uncemented total hip arthroplasty with monoblock press-fit cups: an observational study

Background Bone stock preservation in total hip replacement is essential to allow for later revisions in an increasingly younger and fitter index patient population. While contemporary modular press-fit acetabular cups lead to rigid fixation with equatorial stress and central osteolysis, more elastic fixation may cause different peri-acetabular bone remodelling. The purpose of this study was to investigate changes in peri-acetabular bone mineral density (BMD) in uncemented elastic fixation with monoblock press-fit cups. Methods This prospective observational study included 45 patients with monoblock cups. We evaluated peri-acetabular BMD using dual-energy X-ray absorptiometry and reported functional outcomes and complications. Results At a mean follow-up of 24.2 ± 2.2 months, we found that BMD stabilised in DeLee and Charnley zones I and III and recovered to baseline value in zone II. The mean Harris Hip Scores improved significantly from 56.9 ± 20.0 to 97.2 ± 4.0 (p < 0001). Other than one peri-operative dislocation, we saw no post-operative complications. Conclusions We found favourable adaptive bone changes with BMD stabilisation in the equatorial zones and recovery to pre-operative values in the central zone. Additionally, excellent clinical outcomes and few prosthesis-related complications strengthened the favourable results of monoblock acetabular cups. Trial registration Registration number DRKS00017076.

Peri-acetabular bone remodelling after uncemented total hip arthroplasty with monoblock press-fit cups: an observational study

Background: Bone stock preservation in total hip replacement is essential to allow for later revisions in an increasingly younger and fitter index patient population. While contemporary modular press-fit acetabular cups lead to rigid fixation with equatorial stress and central osteolysis, more elastic fixation may cause different peri-acetabular bone remodelling. The purpose of this study was to investigate changes in peri-acetabular bone mineral density (BMD) in uncemented elastic fixation with monoblock press-fit cups.Methods: This prospective observational study included 45 patients with monoblock cups. We evaluated peri-acetabular BMD using dual-energy X-ray absorptiometry and reported functional outcomes and complications.Results: At a mean follow-up of 24.2 ± 2.2 months, we found that BMD stabilised in DeLee and Charnley zones I and III and recovered to baseline value in zone II. The mean Harris Hip Scores improved significantly from 56.9 ± 20.0 to 97.2 ± 4.0 (p < 0001). Other than one peri-operative dislocation, we saw no post-operative complications.Conclusions: We found favourable adaptive bone changes with BMD stabilisation in the equatorial zones and recovery to pre-operative values in the central zone. Additionally, excellent clinical outcomes and few prosthesis-related complications strengthened the favourable results of monoblock acetabular cups.Trial registration: Registration number DRKS00017076.

Reducing the vibration of bearing units of electric vehicle asynchronous traction motors

The impact of the accuracy class of bearings, rotational speed, load, clearances, and fits on the vibration levels of electric motor bearing units is investigated. The ways to reduce the vibrations of mechanical origin are offered. The boundary vibration levels of asynchronous motors limited by vibration levels of 40 dB at a frequency of 5 Hz and 80 dB at a frequency of 10,000 Hz are determined. The effect of increasing the rotational speed and load on the vibration levels of bearing units has been determined, and reserves for reducing vibration while ensuring the optimum bearing preload on the shaft journal have been identified. It is established that the clearance between the cap and the bearing when it is fixed in the housing (primer) does not ensure the unambiguity of the bearing unit assembly, which results in a large variation in vibration levels compared with rigid and elastic fixation. The results of this research can be applied to all types of traction electric motors.