Russian Journal of Biomechanics

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.

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.

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.

The purpose of the study was a numerical analysis of the stress-strain state of new designs of fixed adhesive bridges made of polymethylmethacrylate to replace the missing second premolar of the lower jaw based on the first premolar and first molar. Three-dimensional models of prostheses (with the traditional (T) route of administration, as well as those developed with the vestibulo-oral (VO) route of administration and the oral-vestibular (OV) route of administration) were obtained by scanning in a 3D scanner S 600 ARI ( ZirkonZahn GmbH ) and subsequent processing in the Modellier program ( ZirkonZahn GmbH ). To determine the stress-strain state of the adhesive bridge, the ANSYS finite element modelling package was used. The load acting in the oral-vestibular direction and equal to 100 N was applied at different 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 significantly affects the values of equivalent (according to Mises) stresses and displacements in the adhesive bridge. It was shown that the smallest displacements and stresses occurred in the type (T) adhesive bridge, while the displacements and stresses in the adhesive bridge type (OV) took the greatest values over the entire range of the load angle. An increase in the elastic modulus of the first kind (Young’s) modulus of the structural material of the prosthesis leads to a decrease in maximum displacements, while the stresses in the prosthesis change very slightly. The calculation showed that the durability of the structures of the adhesive bridge of polymethyl methacrylate is 233 days (OV), 780 days (VO) and 1458 days (T) with an average chewing load of 100 N, which indicates the possibility of using these prostheses as preliminary (temporary).

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.

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.