Russian Journal of Biomechanics

The structure of the cancellous bone tissue in different parts of the skeleton is not the same and tends to become optimal for bone-affecting load, remodelling itself through the mechanisms of bone formation and resorption. Jaw is the one of the most liable bone to change its structure. In addition to the normal changes associated with the replacement of primary teeth by permanent ones, we often have to deal with pathological changes in the internal architecture of the bone caused by underloading of certain areas of bone tissue due to tooth loss, jaw injuries, and malocclusion. Among the pathologies of the dentoalveolar system, for example, Popov - Godon phenomenon takes place, expressed in abnormal dental shifts, provoked by the antagonists loss or adjacent tooth and accompanied by adaptation of surrounding bone tissues. Assuming that the mechanical load is the factor that leads to the adaptation process in the bone, the paper considers a numerical algorithm that simulates the reconstruction of the cancellous bone at the mesolevel through rate equations including the deviator of the fabric tensor. The results are given for the geometry of the lower jaw, for simplicity consisting entirely of cancellous bone tissue and loaded with efforts from the chewing muscles and the reaction of the temporomandibular joint. As a critical load, single force is applied to the molar of the lower jaw. The purpose of the numerical analysis is to obtain a pattern of stress intensity distribution and porosity in ramus of the mandible at each discrete stage of evolution under load and compare the results with previously published data of other authors.

The goal of research is application of dynamic analysis methods in dentofacial biomechanics using polymethylmethacrylate dental bridge as a pilot example. Plane strain formulation is used. Experimental verification is carried out based on results of ceramic dental bridge with identical design. Natural frequencies and Rayleigh damping ratios are determined. Influence of force duration on stresses occurring in dental bridge is investigated. Local areas of maximal equivalent stresses are determined using von Mises criterion. Moreover, the study shows high increase in deformation and stresses (excessing the yield stress) in the case when force duration equal or close to natural period. The results of dynamic analysis tend to results of static analysis in the case of force duration increase. The influence of pulp can be neglected during solving static analysis problems. But, the research approved pulp’s role as a natural shock absorber in the dentofacial system. As a result, consideration of pulp leads to decrease of deformation, stresses, intense energy absorption and oscillation damping.

This paper is devoted to theblood flow symmetryloss study in the branching vessels with the aneurysm. Aneurysm appearance is possible in the damaged blood vessels localized in different parts of the circulatory system with different types of flow (convergent and divergent). Aneurysms of aorta, peripheral vessels, heart, and brain can be distinguished. Regardless of the localization, the disease leads to serious consequences and requires surgical intervention. This paper presents mathematical modelling of blood flow in vessels with small diameter, which is characterized by small values of Reynolds number and rigidity. This representation corresponds to the cerebral vessels. The blood flow simulation is performed using rheological viscoelastic fluid model (FENE-P). This model predicts the blood flow properties corresponding to the real biological fluid, namely, the viscosity anomaly, variable longitudinal viscosity, and the finite time of stress relaxation. The governing parameters of the flows of such fluids is the Weissenberg number (We) characterizing the ratio of elastic properties of biological liquid to viscous ones, the Reynolds number (Re) describing the ratio of inertial to viscous properties, the ability of macromolecules of proteins included in blood change their orientation in the flow, the degree of disentanglement of macromolecules of protein L2 and retardation coefficient β characterizing the concentration of macromolecules in the blood. In this paper, the possibility of blood flow symmetry loss in bifurcation areas of the circulatory system at certain values of the parameters of the mathematical model for converging flow is discussed. The effect of the shape of aneurysm occurrence on the blood flow pattern is performed. Results comparison for blood flow in the channel with two types of cavities is performed.

A model is constructed for changing the intracellular conductivity of the myocardium with its deformation on the basis of an analysis of the microstructural model of P.E. Hand, B.E. Griffith, C.S. Peski (Bull Math. Boil (2009)) model. The cardiac tissue was considered as a periodic lattice, where the cells are rectangular prisms filled with isotropic electrolyte, and the conductivity of the gap junctions is taken into account through the boundary conditions on the sides of these prisms and is assumed to be constant. Using the homogenization method in the form proposed in the paper G. Richardson and S.J. Chapman (SIAM Journal Appl. Math (2011)), the conductivity values are analytically expressed in terms of cell sizes, lattice periodicity parameters, electrical properties of myoplasm and gap junctions. On the basis of these relationships, the dependence of the tissue conductivity on its deformation is determined. A comparison is made with the model proposed in the book F.B. Sachse. Computational Cardiology (Springer (2004)). It is shown that both models can be well matched for elongations in the range from 0.8 to 1.2. A numerical algorithm based on the splitting method and its software implementation based on the finite element library FEniCS are developed. Conductivities calculated for different deformation dependences are compared. Corresponding profiles of the excitation waves in a rectangular two-dimensional region are considered. The effect of deformation is strongly "diluted" by extracellular conductivity. The appearance of depolarization and hyperpolarization regions (virtual electrodes) is also considered when an electric current is applied to the myocardium in a small domain. In this case, the effect of deformation is more significant.

The purpose of this study is to identify the degree of the lumbar spine curvature of pregnant women in the different trimesters of pregnancy. In addition, we can identify the levels of low back pain in various stages of pregnancy and manifestations of imbalance on some kinematic variables in the walking cycle. In order to achieve the goals of this study, the descriptive approach has been applied to 24 healthy patients. The researchers used two rulers to measure the degree of the lumbar spine curvature, and a questionnaire to quantify the level of low back pain and imbalance disruption. Also, the researchers used two cameras to filmed patients while walking on the treadmill: one camera was put laterally (60 f/sec) and the other was put on the front (50 f/sec). Furthermore, the results of the study showed that the degree of the lumbar backbone curvature, the low back pain and imbalance increase in the transition to the next trimester of pregnancy. The results also showed decrease of length and speed of the walking step, increasing the time of dual and individual reinforcement.