Alcoholic polyneuropathy can lead to such serious complications as one- and two-sided deformities of the feet. In this case, the feet get a characteristic equinovarus deformation, which seriously changes the biomechanics of the walk of patients, sometimes making it just impossible. The article describes the results of treatment of 16 patients with alcoholic polyneuropathy with foot deformity. This group of patients also included patients with severe disease, when both lower limbs were affected. The results of the operative treatment are shown from the point of view of change of parameters of the biomechanics of walking. It was revealed that complex surgical treatment in combination with external fixation devices is able to return such patients to everyday life and walking without additional support.

Key words: alcoholic polyneuropathy, orthopedic correction, paralytic deformity of feet, biomechanics of walk.

Bone tissue is a heterogeneous, anisotropic material and consists of compact and cancellous bone tissues. The structure of cancellous bone tissue in different parts of the skeleton is not the same. It conforms to Wolff’s law: it aims to become optimal for the loading which acts on the corresponding bone; the bone remodelling by means of osteosynthesis and resorption mechanisms. The modern problems of biomechanics demand research of the history of formation of bone structures in the course of time at both physiological and pathological loadings. The mandible is one of the most liable to external and internal bone changes. It is liable to physiological changes that occur during the ontogenesis of the organism. Very often, one has to deal with pathological changes caused by incorrect loading of different regions of bone tissue due to dysfunction of a dentition, a temporomandibular joint and so on. For example, the Popov–Godon’s syndrome which connects with tooth loss is accompanied by pathological remodelling of the surrounding bone tissue. Thus, the mathematical modelling of the cancellous bone tissue behavior in the human maxillodental system is one of the topical problems of biomechanics and medicine. Structural features of cancellous bone tissue can be described by means of the fabric tensor. This is possible to implement if there is both a constitutive relation which connects the stress tensor, the fabric tensor, and the strain tensor, and kinetic equations which describe the evolution of the fabric tensor and bone density. The phenomenological Cowin’s equations are chosen and analyzed in detail as such ones. An initial boundary value problem of the cancellous bone tissue remodelling is stated. The solution of this problem allows us to trace changes in the stress-strain state at the trabecular structure formation according to Wolff’s law. The effective numerical algorithm allows us to solve the problem is developed. This algorithm is implemented as a complex of problem-oriented programs. Verification of the model and identification of its parameters are carried out. All numerical calculations are performed using the ANSYS software. Trabecular bone tissue evolution is demonstrated on the set of model examples when the stress–strain state is changed. The results demonstrate different character of influence of changes of loading conditions on the process of structure formation, which follows from Wolff’s law.

Key words: cancellous (trabecular) bone tissue, Wolff’s law, maxillodental system, mandible, fabric tensor, constitutive relation, evolution equation, initial boundary value problem of cancellous bone tissue structure remodelling, ramus of mandible.

Dental anomalies (malocclusion, crooked teeth, etc.) are a common problem. Due to them, violations of the aesthetics of the face, blood supply to the brain, respiration, posture, facial expressions, pronunciation of words, digestion and etc. are possible. Correction of dental anomalies consists in moving the teeth to a new position corresponding to the physiological norm under the influence of the orthodontic load (bracket system, elastopositioner, etc.). The main question in orthodontic treatment is the determination of such load (value, direction, place of application). This work continues a series of publications by authors dedicated to solving this question. Earlier, the concept of “center of resistance of a tooth” was introduced and determined. Using this consept, it is possible to study the initial movement of the tooth within the framework of the bone hole. In accordance with the introduced conditions for the existence of this point, it turned out that the "center of resistance of a tooth" does not exist always. Therefore, the authors proposed a new concept of “region of resistance of a tooth” determined by sets of translational action lines and a pair of rotation axes. The purpose of this work is to study them, namely, the conditions for the existence of these lines, the relative position and, on the basis of this, to demonstrate the classification of the types of tooth resistance region.

Key words: dentoalveolar biomechanics, region of resistance of tooth, orthodontics.

A method is proposed for taking into account the nonlinearity of the elastic behavior of the cornea of the eye, which makes it possible to effectively evaluate the influence of this factor on the results of experiments and clinical measurements. The cornea is modeled by a homogeneous isotropic momentless elastic surface. Its elastic properties are determined by a nonquadratic dependence of the strain energy on the components of the strain tensor. Strains are assumed tobe small. For the simplest exponential form of this function, a single additional parameter appears in comparison with the linear case. The model is tested on the problem of inflating the cornea with pressure, which corresponds to experiments with an isolated cornea. Predictions of the linear model do not agree with experimental data, whereas the proposed exponential model describes them well. The model allows us to consider the nonlinear behavior of the cornea, taking into account its real mechanical properties and the minimum number of parameters. The use of the nonlinear model is advisable in those cases where in the process under consideration the intraocular pressure and the stressed state of the cornea vary significantly, as a result of which the linearization of the constitutive relation can lead to noticeable errors.

Key words: eye, cornea, nonlinear elastic properties, intraocular pressure, static tonometry, mathematical models.

Dental implantology practice shows that oblique load on the implant is more dangerous than the vertical one. Of particular importance is the study of the implant-jaw system under oblique load studying the primary stability of dental implants, when osseointegration has not yet occurred and there is no adhesion at the bone-implant interface. The damaging effect of excessive loads in this case is associated with the danger of superfluous micromotions on the bone-implant interface (mutual displacements of corresponding points) arising under their action, which leads to disruption of the osseointegration process. On the simplest model of a dental implant with a square thread profile, the influence of the load tilt angle on the primary stability of the implant in the jaw is examined. Calculations are carried out by the finite element method in the ANSYS package. Graphs of changes in micromotion along the bone-implant interface are presented, tables of magnitudes and localizations of micromotion maximums and graphs of their dependence on the loading angle are given. It is shown that for non-integrated implants, transition from vertical to horizontal loading leads to a sharp decrease in implant stability, which at sufficiently high occlusal loads impairs osseointegration.

Key words: dental implants, biomechanics, primary stability, modeling, oblique loading, finite element method.

The main objective of the research was to study the stress-strain state in biotechnical systems formed in the performance of corrective osteotomies of the first metatarsal bone. The hallux valgus is a common pathology in humans. The incidence of this pathology in females is up to 64 % and 25 % – in males. Surgical reconstructive treatment remains an urgent problem in modern orthopedics. The situation is caused by unsatisfactory results of treatment. In addition, there is a question about the admissibility of the load in the early postoperative period in patients with quantitative individual assessment. This assessment can be performed using biomechanics. The paper presents methodology for assessing the bone – screw system when performing corrective osteotomies of the first metatarsal bone. The technique allows us to perform a comparative analysis of various methods of osteotomy for a particular patient. In this study, chevron and scarf osteotomy with displacement of bone fragments by 1/3 and 2/3 with different variants of their fixation were examined. To solve this problem, personalized geometric models of the first metatarsal bone were built on the basis of computed tomography data using 3D Slicer and SolidWorks systems. Also models of implants were built. The finite element analysis was carried out in the Ansys Workbench software. The focus was on analyzing the stresses that occur on the plantar surface of the first metatarsal bone head during walking. An assessment of the maximum allowable shear of bone fragments for the normalization of deformities of the forefoot was carried out. The developed technique allows us the choice of an osteotomy variant with the justification of the possibility of simultaneous surgery on both feet for a particular patient.

Key words: biomechanics, osteotomy, first metatarsal bone, finite element modelling, stress-strain state.

Pain in the lumbar region or other part of the spine is the important reason for the decline of the life quality and the population efficiency, which directly affects the economy as a whole. Every year, a money huge amount is allocated in health care to prevent this disease. The causes of this pain are very diverse: muscle spasms, kidney diseases, the vertebrae osteoporosis, herniated discs and etc. It is proved that the intervertebral disc L4–L5 is the most vulnerable part of the lumbar spine, so the biomechanical modelling problem of the intervertebral disc is considered important and relevant in the modern world. A comprehensive analysis of the literature for period 2006–2018 is performed. The work aim is to consider various approaches to modelling of the intervertebral symphysis, strong and weak parts of models and methods of obtaining the disc geometric shape. In article, the parameters are analyzed: the constitutive relations choice, the use of a set of images of computerized tomography or magnetic resonance imaging, the geometric shape of any component of the model, the finite element type, software packages (choice of stress-strain state calculation and obtaining a geometric shape from a set of computed tomography or magnetic resonance imaging), the age and gender impact on the overall model. Detailed analysis of each component of the intervertebral cartilage: nucleus pulposus, fibrous ring (matrix and elastic fibers), cartilage endplate and bone endplate is performed.

Key words: biomechanical modelling, intervertebral disc, finite element model, modelling theory, lumbar spine.

The purpose of the study was a numerical analysis of the stress-strain state of novel designs of fixed adhesive dental bridges made of polymethylmethacrylate (PMMA) to replace the missing second premolar of the mandible with first premolar and molar as abutments. Three-dimensional models of dental bridges (with the traditional (vertical) (T) insertion direction, as well as those developed with the vestibulo-oral (VO) insertion direction and the oral-vestibular (OV) insertion direction) were obtained by scanning with 3D scanner S600 ARI (ZirkonZahn GmbH) and subsequent processing in the Modellier program (ZirkonZahn GmbH). To evaluate the stress-strain state of the adhesive dental bridges, the ANSYS FEM software was used. 100 N force acting in the oral-vestibular direction was applied at various angles to the nodes localized in the areas of enamel ridges to simulate the occlusal contacts of antagonistic teeth. It was established that the direction of the occlusal force vector has a significant effect on the values of equivalent (von Mises) stresses and displacements in the dental bridge. It was shown that the lowest displacements and stresses occurred in the type (T) adhesive bridge, while the highest displacements and stresses occurred in the type (OV) over the entire range of the load angle variation. An increase in the elastic modulus of the bridge material leads to a decrease in maximum displacements, while the stresses in the prosthesis change very slightly. The numerical calculation showed that the PMMA-manufactured dental bridges’ durability equals to 233 days for (OV), 780 days  for (VO) and 1458 days for (T) with an average chewing load of 100 N, which indicates the possibility of using these novel designs as temporary dental bridges.

Key words: dentofacial biomechanics, dental bridge, finite element method, dental resins.

In order to determine the degree of stability of osteosynthesis, four basic fixation systems have been identified. These principles are based on the interaction of the fixator and bone fragments. 1. Fixator–bone, this part of the element is directly connected to a bone. 2. Intermediate fragment, this is the space between the bone and the supporting part of the retainer. 3. Fixator–fixator, this level concerns the assembly in general. 4. The bone–bone through the fixator. In this paper, the main methods and approaches of structural mechanics that can be applied to the analysis of the first fixation level, i.e. fixator–bone are used. These methods can be used to select the components of the external fixation device providing the required stiffness and strength of the apparatus. The calculation schemes and constitutive equations to calculate stress–strain state of the apparatus elements providing its attachment to the bone are given. Based on the calculations results, graphs and tables for selecting external fixator elements are presented, and the deformation of the components is shown.

Key words: external fixation of fractures, Illysarov's apparatus, strength, rigidity, deformations, transosseous osteosynthesis.

The article deals with the models of dental implants of cylindrical, conical, cylindrical reverse-conical and conical reverse-conical shape, installed in the central part of the maxilla. The maxilla model is made in accordance with the sizes of the three-dimensional tomographic image of the patient's maxilla. The stress-strain state of the cortical and cancellous bones, depending on the shape of the implant, as well as the degree of bone mineralization is investigated. The isotropic model of bone material at normal and critical degree of bone mineralization, which depends on the patient's age, is considered. According to the results of the study, the use of the reverse-conical shape of implants significantly reduces stress not only in the cancellous bone, but also in the cortical bone, as well as in the implant during critical bone mineralization.

Key words: implants, dentistry, stress-strain state, modelling, finite element method, bioceramic.

The actual task of modern biomechanics of bone tissue is to determine the elastic properties. Nowadays computed tomography coupled with computer technology allows the use of numerical experiments to determine the mechanical properties of biological objects. This paper presents such a technique. The technique is based on the hypothesis that the anisotropy of bone tissue is determined by the uneven distribution of pore volume. In the proposed approach, the organ under study is proposed to be divided into a set of representative volumes. A set of numerical experiments is carried out for each volume, which makes it possible to determine the components of the elastic tensor. Then, the axes of orthotropy and elastic constants are determined. The described technique is applied for diaphysis of the femoral bone rat. It is shown that the resulting elastic constants remain constant in the organ, and the body is transversally isotropic.

Key words: bone tissue, orthotropy, numerical experiments, representative volume.

Mitral regurgitation is the second most frequent indication for valve surgery [17]. The problem of a therapeutic decision during mitral valve insufficiency is quite timely. The unfavorable prognosis for disease depends largely on left ventricular dysfunction and levels of ventricular dysfunction are thoroughly studied. High level of ventricular dilation during mitral valve insufficiency is one surgical indication. Due to the fact that it is impossible to separate the contribution of coronary insufficiency and volume overload components to the process of left ventricular remodeling such parameters as ventricular size and left ventricular ejection fraction can't be used as parameters of hemodynamically relevant regurgitation [1, 7]. The role of the left atrium in global dilation of the heart against the backdrop of the mitral insufficiency is poorly studied. Left atrial dilation is powerful mortality prediction. It is well known that the atria contribution is essential to a ventricular ejection in the course of the left ventricular dysfunction. The strain and the strain rate of the left atrium are the prior markers of volume overload versus the dimensional changes [7]. The computer tomography experiment of the left atrium property investigation was set up in the Federal Center of Cardiovascular Surgery Named after S.G. Sukhanov in Perm. The experiment data technique was developed. Quantitative characteristics of displacement and strain of the left atrium wall were obtained as a result of data conditioning. The properties of the left atrium wall were analyzed and stress–strain curves were plotted along and across muscle fibers for different parts of the wall. The shear strain was found in the tangent plane of the left atrium.

Key words: the wall of the left atrium, deformation properties, experimental data, strain.