The contact problem of axial compression of an elastic, slender prismatic specimen by loading plates is considered, taking into account friction in the contact zone. The relevance of the work stems from the need for accurate evaluation of the elastic properties of materials with complex structures – such as functionally graded materials, composites, and biomaterials, where classical rod models produce systematic errors of up to 20–30 % due to neglected friction and contact effects. To solve the problem a variational approach combined with the Kantorovich method is used; this reduces the three-dimensional linear elasticity problem to a system of second-order ordinary differential equations with variable coefficients for generalized displacements. Analytical solutions are obtained for specimens with arbitrary and square cross-sections under constant elastic properties. An effective integral friction parameter is introduced – the ratio of tangential to normal generalized forces on the end faces. The inverse problem of reconstructing the elastic properties and the friction parameter from displacement data at several points on the lateral surface is solved. An iterative algorithm based on the contraction-mapping principle is developed, providing sufficiently accurate recovery of the unknown parameters in 3–5 iterations for the considered set of initial guesses. In addition, approximate asymptotic formulas based on solutions of the direct problem are proposed for rapid parameter recovery from measurements at a single point, together with recommendations for selecting measurement locations on the lateral surface. Numerical experiments on synthetic data generated by the direct problem confirm the effectiveness of the proposed methods and their robustness to noise (in the case of the iterative algorithm), demonstrating superiority over rod models. The approach enables improved processing of experimental compression test data, which is especially important for samples made of biomaterials and composites where friction significantly influences result interpretation.
The influence of a strong Allee effect in a prey population on the dynamics of a predator–prey model with ideal free distribution (IFD) is considered. A comparison of stationary solutions is given for two systems: with and without the Allee effect. It is shown that the prey always maintains its IFD, while the predator has complex IFD-like distribu-tions depending on the resource function and the Allee parameter. The presence of a strong Allee effect in the prey leads to a change in the stability of the trivial zero equilibrium and the emergence of a new unstable solution. In this case, the range of stability of the stationary state corresponding to the coexistence of two species decreases by an amount proportional to the Allee parameter and inversely proportional to the resource. It was found that changing the Allee parameter directly affects the popu-lation size of the predator (the larger the parameter, the smaller the population), while the population of the prey remains unchanged. It was found that with increasing Allee's parameter, for some points in the range (due to the dependence of the resource function on the spatial coordinate), the stationary solution with two species becomes unstable for small perturbations of the system. As a result, the population distribution contains regions where their abundance is zero. Computational experiments demonstrating the presence of an oscillatory regime for two species are presented. A system without the Allee effect maintains oscillations and the general form of its spatial distribution under small perturbations of the initial condi-tions. With a strong Allee effect, local oscillations are possible, caused by the fact that the condition for their occurrence depends on a spatially varying resource function.
The forming limit curve is a feature of the material that represents the limiting strains that lead to failure of the necking with respect to the direction of deformation strain. It displays the ductile damage & onsite necking failure limits, thickening of metal sheets that are very thin. Few-er than 100 microns, is challenging and demands greater accura-cy. Micro-forming is the term used to describe this kind of miniaturisation in the forming process, which produces components with dimensions as small as a few millimetres. When a macro process is transformed into a mi-cro process, there are significant varia-tions in the physics of the process and the characteristics of the materials. In order to identify the forming limit curves, an experimental test on a thin Nickel 200 sheet with a 50 m thickness was conducted with varied orientations to rolling directions (0°, 45°, and 90°). According to the test standard ASTM-2218-14, the hemispherical microform punch test is performed using uniaxial, intermediate-uniaxial, biaxial and plane strain specimens to determine the strains. Experimental values have been used to validate numerical find-ings. Nu-merical analysis is used to model the micro-forming process, and forming limit curves are shown. Numerical results have been validated using experimental observations.
Transcatheter aortic valve implantation (TAVI) is a minimally invasive approach for the treatment of aortic stenosis in patients with a high risk of postoperative complica-tions who are not candidates for open surgery operation. Despite the rapidly growing number of such operations, they have a number of complications with limited choice of parameters and types of implants that do not take into account the individual characteris-tics of the patient. This leads to the question of customization of TAVI implants. The de-velopment of personalized prosthetic designs can reduce the incidence of postoperative complications, such as paravavular regurgitation or damage to the annulus fibrosus, thereby improving patients’ quality of life by optimizing hemodynamic indicators. Thus, the purpose of this study is to numerically simulate the hemodynamic characteristics in the aorta after TAVI to assess the impact of the prosthesis design on its effectiveness. This paper presents eight parametrized prosthesis geometries: two represent models of commercial valves (Evolut R PRO and SAPIEN 3), and the remaining six were developed by the authors. A coupled problem involving fluid-structure interaction was solved. A velocity profile based on echocardiography data was prescribed as the inlet boundary condition at the aorta, while a pressure determined by a two-element Windkessel model was prescribed at the outlet. Based on a comprehensive analysis of the integral parame-ters, three geometries were selected. These geometries demonstrate optimal hemody-namic performance: effective orifice areas exceeding 1.5 cm², moderate pressure gradi-ents (7–12 mmHg), and peak systolic velocities below 2 m/s. Additionally, they exhibit low OSI values (OSI < 0.25), which is indicative of a reduced risk of thrombosis and prema-ture leaflet fatigue. The obtained results provide a basis for the design, engineering, and manufacture of personalized TAVI prostheses that take into account the specific anatomi-cal and physiological features of each patient.
Aim of the study was to experimentally characterize the microstructure and mechanical properties of the bovine xenopericardial patch “Neokor” modified with ethylene glycol diglycidyl ether, and to develop a hyperelastic constitutive model for finite-element simulations of the patch mechanical response. Bovine pericardium specimens (n = 7) were analyzed using small-angle light scattering (SALS) to quantify the distribution of collagen fiber orientations. Mechanical behavior was assessed under planar biaxial tension using a custom-built biaxial testing device. A series of loading protocols with different principal stretch ratios along the specimen axes was performed, and stress – stretch responses were recorded in two orthogonal directions. Combining SALS and biaxial data, parameters of an anisotropic hyperelastic Gasser – Ogden – Holzapfel model were identified, with particular emphasis on inter-specimen variability and the feasibility of using a single parameter set across the batch. Planar biaxial testing confirmed a nonlinear and anisotropic deformation response. A single fiber family model with fixed fiber dispersion provided an adequate description of the experimental data for all loading protocols: the root mean square error did not exceed 5–10 % of the maximum stress level, and the averaged parameter set reproduced the behavior of all specimens in the batch. The resulting microstructural and mechanical characteristics, together with the identified constitutive relation, can be used in computational modeling of interactions between “Neokor” xenopericardial patches and native tissues in vascular and intracardiac reconstruction, and may serve as a basis for rational selection of patch material and orientation.
It is known that the main element of hard tooth tissues is calcium, which is part of hydroxyapatite. Usually, fluoride ions help to retain calcium ions in the surface layers of enamel and with a sharp decrease in the pH of saliva, which makes the enamel acid-resistant. Glass ionomer cements (SIC) are a long-recognized material in dentistry due to their unique properties, including high adhesion to tooth enamel and dentin. SICs have low toxicity and biological inertness, which makes them safe for use. The main compo-nents of cement are silicon dioxide, aluminum oxide and calcium fluoride, where the latter provides a karyesstatic effect due to the release of fluorine ions. Modern SIC formulas are being investigated using various copolymers and the addition of tartaric acid to increase the curing time. The main goal of the work is to improve the healing properties of materials by changing their composition, which will increase the regeneration of hard tooth tissues, while maintaining the necessary physical and mechanical characteristics. In the course of experiments, it was found that fluorapatite is the optimal substance for upgrading the SIC, since during the preparation of the powder, this element did not foam during sinter-ing, and the finished powder was satisfactorily dispersed in the solvent. It was found that the optimal properties for practical use are the ratio of the mixture Glassin Rest + Ca10(PO4)6F2 1: 0.5 by weight. When analyzing the mechanical properties of cubes made from a mixture of Glassin Rest + Ca10(PO4)6F2 1: 0.5 by weight and heated at a temperature of 11000C and 8000C, it was found that the elasticity index closest to the original compo-sition is characteristic of a sample heated at a temperature of 8000S. Thus, it can be as-sumed that an increase in calcium and fluoride in the SIC can improve the biocompatibil-ity of the material and provide a greater karyesstatic effect. At this stage of the study, the physical and mechanical indicators of the experimental samples are close to the data of the original SIC, taken as a basis. This highlights the significance of further research into dental materials.
The Ozaki procedure is a modern technique for aortic valve reconstruction using the patient's autologous pericardium. The key step involves cutting new cusps (leaflets) using templates based on patient-specific anatomical landmarks. However, excessively large cusps can lead to serious complications, including coronary artery ostial obstruction and thrombosis. Minimizing risks requires creating a minimal yet functional leaflet that ensures effective coaptation. The aim of this study is to investigate the influence of the material properties of the cusp on valve function in order to optimize the neocuspidization template. The study employs finite element analysis of a symmetrical tricuspid valve model. The simulation involves the virtual placement of the neocusps and the calculation of their diastolic state using a membrane formulation. Three potentials were considered to describe the valve biomechanics. Parameters such as billowing, area, height, and length of coaptation are evaluated. The results revealed optimal anisotropy directions for the D = 24 template with different potentials: 45°–53° for the first, 39°–48° for the second and 2°–43° for the third. With proper orientation, a smaller template, such as D = 18, provides better characteristics and improves efficiency. The results indicate that accounting for the fiber direction enables a reduction in the geometric size of the leaflet without compromising its coaptation capacity, opening prospects for creating more effective protocols.
In the analysis of oculomotor activity across various applied fields, the description of fast ballistic eye movements – saccades – relies on the relationships between their duration and peak angular velocity as a function of amplitude. These relationships are referred to as the saccadic main sequence. At present, a wide variety of descriptions of the saccadic main sequence are in use, which complicates the comparison of studies, generalizations, and even the reproducibility of research results. This work presents an analysis of the most common mathematical models of the saccadic main sequence relationships. The saccade is considered as the solution to a time optimal control problem. Unlike previously published versions of the model, this study does not make additional assumptions about the structure of the system’s eigenvalues. As a result, the problem is solved numerically. Based on the obtained model, we analyzed the effect of sampling frequency in oculographic data (eye-tracking recordings) on the main sequence relationships. We demonstrate changes in trends with increasing data density. It is shown that for frequencies above 60 Hz, the main sequence relationships are described by power-law dependencies, whose coefficients significantly depend on the sampling frequency.
In order to size a temporomandibular joint prosthesis based on an innovative concept, this study characterizes the trabecular bone tissue geometry within the joint. The main objective consists of taking into account the inter-variability of the trabecular bone volume to design a modular, even customized, innovative mandibular implant. A non-invasive method was used to describe bone tissue distribution. It involves measuring geometrical characteristics of the temporomandibular joint from computerized tomography scans using an easy and quick protocol and open-source software. The measurements performed on the scans of 68 patients showed that this high-precision method is also user-dependent. Lastly, we built value ranges to set the dimensions of a prosthesis prototype and point out a large inter-individual variability for each measurement and a low correlation between bone tissue distribution and age or gender. The software package gives precise measurements for the different parameters studied. However, the automation of the delineation of the area of trabecular bone should improve reproducibility. Also, the protocol can be applied to other medical specialties. Used in the context of a design for an innovative temporomandibular joint prosthesis, it points out a strong inter-individual heterogeneity in the distribution of bone tissue, which leads to prefer a modular implant design.
Stenting and angioplasty are minimally invasive methods that are used to treat a wide range of diseases of the cardiovascular system and allow restoring normal arterial functions, for example, normal coronary or carotid artery lumen when they narrow due to the for-mation of atherosclerotic plaques. The use of mathematical modeling methods can serve as a basis for modeling the processes of installing stents for various purposes and im-proving the methods of these medical interventions. The objective of this study is to ana-lyze the mechanical behavior of coronary vessels, including those affected by athero-sclerosis, and some medical devices interacting with their fragments. The purpose of this study is to identify patterns and for-mulate recommendations for the further application of certain rheological models. Numer-ical modeling was performed and the behavior of a coronary vessel, a coronary vessel with atherosclerotic plaque in interaction with a balloon, as well as numerical modeling of the processes of balloon folding and opening used in angioplasty and coronary stent-ing were analyzed. Hyperelastic rheological models of Holzapfel – Gasser – Ogden, Ogden, and Mooney – Rivlin are considered, which make it possible to describe the mechanical behavior and stress-strain state of these objects as reliably as possible. Based on the results of numerical modeling, the influence of key constants of materials on the stress-strain state of the balloon, coronary artery and coronary artery with atherosclerotic plaque was analyzed. The results and recommenda-tions obtained can be used in the future to build mathematical models and describe the mechanical behavior of other high-tech medical devices.
According to the assumption, the genetically determined functional failure of the au-tonomic and sensorimotor systems regulating the axial rigidity and mobility of the spinal-motor segments is manifested both in the protective behavior of the biomechanical func-tions of the spine and in its scoliotic deformations, the angular magnitudes of which mechanically limit the excessive mobility of its unstable parts. The aim of the work is to establish the nature of locomotor manifestations of protective behavior of biomechanical functions of the spine in patients with idiopathic scoliosis and to determine their in-volvement in the pathogenesis of the disease. 3D video gait analysis was used to evalu-ate the locomotor profile and dynamic balance of the axial skeleton in three planes in 37 healthy children and adolescents (11–18 years old), as well as in 82 patients of the same age with idiopathic spinal biomechanics disorders phenotypically manifested by C- and S-shaped forms of scoliosis II–IV degrees according to Chaklin. It was found that in pa-tients, the locomotor protective behavior of biomechanical functions of the spine, regardless of the degree and form of scoliotic deformities, manifested itself in their statis-tically significant decrease. The decrease in the values characterizing the dynamic bal-ances of the axial skeleton was in the horizontal (34.3 %) and frontal planes (26.0 %), as well as in the habitual movement speed (10.8 %) and total gait power (13.8 %). Since the angular values of deformations did not have a significant effect on the recorded biome-chanical functions of the spine, and the stochastics of their distribution approached Gaussian, this indicates their predominantly adaptive behavior. It is reasonable to as-sume that the vegetative and sensorimotor pathogenesis of the axial skeleton, which is ontogenetically caused by genetic abnormalities and is almost completely untraceable by instrumental methods, is phenotypically and morphologically manifested in scoliotic deformities of the spine, as well as in the compensatory attraction of additional sen-sorimotor re-sources. Additional resources also at a higher level of the organization con-trol the bio-mechanical functions of the spine and are carried out in postural and loco-motor protective and adaptive behavior.
Over the past decade, considerable attention has been focused on the research and development of magnesium alloys as biodegradable materials with promising mechanical and functional properties for widespread use in medical applications. Along with the selection of the optimal chemical composition, much attention in this work is paid to the development of deformation thermomechanical treatments that allow for varying the microstructure and phase composition in magnesium alloys, which is important for achieving enhanced properties. This work introduces a combined thermomechanical treatment that ensures a high level of mechanical and functional properties in the magnesium alloy. In addition, it produces a long-sized rod required for the manufacture of medical implants on modern CNC cutting machines. The popular magnesium alloy Mg-1 % Zn-0.18 % Ca was selected as the material for research herein. In order to substantiate the design of a processing die-set and modes, an analysis was conducted using the finite element method to establish the deformation behavior of the alloy, including the uniformity of deformation and type of deformed state. The optimal rounding angle of the matrix channels was determined, ensuring uniform deformation during severe plastic deformation using the equal channel angular pressing technique, which allows for the production of long-sized billets from magnesium alloys with enhanced mechanical properties. The experimental study demonstrated that the combined processing of the initial homogenized alloy resulted in the formation of a structure with a grain size of about 215 nm in the UFG alloy Mg-1 % Zn-0.18 % Ca, with a grain size of about 215 nm and the formation of nano-sized particles, which resulted in a substantial enhancement of the mechanical properties of the rods intended for the fabrication of advanced implants in maxillofacial surgery.
Despite great progress made in neurosurgery, stable spinal reconstruction after total en bloc spondylectomy remains a challenge. While the common tactic is to replace the vertebral body with an implant and perform transpedicular fixation, the standard implants do not always provide the necessary support and natural load distribution, increasing the risks of instability and subsidence of the implant. It is therefore of utmost importance to construct customized implants based on additive technologies. Our study considers five implants: one made of polymer and four made of metamaterials similar in properties to cortical tissue of the vertebrae. Two of the implants were made of lattice metamaterials (Body-centered Cube and Diamond) and two of TPMS metamaterials (Fischer – Koch and Gyroid). Stress–strain analysis of the reconstructed spine was carried out for each implant for six basic movements: flexion, extension, right bending, left bending, right rotation and left rotation. Our findings led us to conclude that the metamaterial implants have an almost identical influence on the biomechanics of the lumbar spine in terms of strength. Furthermore, even though higher stresses were observed in the system in this case, metamaterials can still be recommended for use in implants as they stimulate ingrowth of bone tissue into the implant.
The use of hybrid nanogels in restorative dentistry is attributed to their indispensa-ble role in ensuring biocompatibility, which is achieved through the unique nanostructure and surface archi-tecture of these materials. In the present work, gelatinization of zein on magnesium oxide nano-particles is a significant advance in this regard. These nanopar-ticles are very promising for medical applications. Nevertheless, a hybrid nanogel con-taining various concentrations of zein in combination with MgO at 0.5, 1 and 1.5 % was successfully prepared. Atomic force microscopy was used, which is the most powerful technique in physics, material science, and medical re-search for surface texture or na-noparticle structure analysis. The surface morphologies for the nanogels were observed to be relatively smooth and broad for the 0.5 % formulation, while the particles of the 1.5 % formulation appeared significantly smaller and more closely distributed. This differ-ence shows that the particle concentration has a strong effect on the gel characteris-tics. The paper highlights the shifting nature of macroscopic material behaviour as it is affect-ed by changes in the nanoscale, and could be useful to biomedical applications, medi-cine and dental regeneration therapy.
The task of analyzing children's motor giftedness requires not only the selection of relevant tests but also the development of objective assessment criteria. Existing meth-ods for evaluating motor potential are often limited to subjective observations or frag-mented parameters, which prevents the formation of a holistic profile of a child's basic motor abilities. Running is proposed as a key test movement because it is a fundamental locomotor act that allows for an integrated assessment of universal speed and coordina-tion qualities. This article develops a deterministic biomechanical model of running that considers kinematic, dynamic, and electromyographic parameters. The model is struc-tured according to the temporal phases of the running cycle and includes four levels of detail: 1) the cycle level; 2) the swing and stance periods level; 3) the propulsion and braking phases level; and 4) the key temporal events level. This approach enables a sys-tematic analysis of the movement's biomechanical structure. Based on the developed model, criteria for assessing motor abilities are proposed, allowing for an objective eval-uation of children's motor giftedness. The criteria include 40 biomechanical parameters and reflect the effectiveness and economy of movement. The efficacy criteria (18 parame-ters) are defined as those that contribute to an increase in running speed, while the economy criteria (22 parameters) imply a reduction in energy expenditure during run-ning. An experimental study was conducted involving 26 children without specialized running training, with a mean age of 10.33 ± 1.15 years. The analysis of individual pro-files, constructed based on the proposed motor ability assessment criteria, allowed for the participants to be divided into two characteristic motor types: an “effective” type, dominated by speed characteristics (high average velocity of the center of gravity, pow-erful propulsion), and an “economical” type with optimal energy distribution (low vertical oscillation of the center of gravity, symmetrical muscle activity). The obtained results en-able the construction of a multidimensional profile of motor giftedness, which establishes a foundation for the objective identification of individual trajectories for physical devel-opment and sports orientation.
Transcathether aortic valve implantation is a minimal invasive method for treating aortic stenosis. However, the success of the procedure is determined by the mechanical characteristics of the TAVI posthesis, particularly the bending stiffness of the stent frame. This study aims to develop a computational approach for analyzing and predicting the bending stiffness of the TAVI frame. The relationship between bending stiffness and the geometric parameters of the frame is investigated using numerical simulations and ML-methods. To this end, an algorithm for generating parameterized geometries of the stent frame was developed. This algorithm enables the automatic generation by controlling the profile shape and the cell architecture. Numerical experiments under pure bending condi-tions were performed. As a result of automated geometry generation and finite element simulations, a dataset of 2409 configurations was obtained. The maximum and minimum bending stiffness values observed in the dataset were 16.2 N·m² and 0.42 N·m², respectively.Correlation analysis showed that the bending stiffness is mainly influenced by the diameter of the constricted region (WD, r = 0.18), the number of cells in the vertical (N, r = –0.23) and horizontal (K, r = –0.59) directions, and the curvature parameter of the upper part of the frame (UB, r = 0.42). The dataset was used to develop neural network surrogate models for solving both forward and inverse problems. The forward model showed good agreement with the finite element simulation results. The accuracy of the inverse model decreased in stiffness ranges that were poorly represented in the training dataset. Thus, the proposed approach enables sensitivity analysis of the mechanical properties with respect to the frame geometry and can be used for further optimization of the prosthesis design.
Authors of this article consider results of complex abilitation of children with the dyskinetic form of infantile cerebral palsy on the example of the concrete child at the age of 4 with this form of the disease with presence of the myoclonic syndrome. Detailed investigation permitted authors to reveal in this girl both the typical symptoms, characteristic of patients with the dyskinetic form of infantile cerebral palsy, and the specific peculiarities, connected with the myoclonic syndrome. From the authors’ point of view, the following symptoms belong to the first ones: presence of some stereotypes of walking, high walking cadence, insufficient control of change of cadence and step length, flexion position at the joints of the lower extremities, expressed variability of the biomechanical and electromyographic parameters, increase of angle of flexion at a knee joint (KJ) in the stance phase of the step, shift of the extreme values of the angular displacements to the right along the temporal axis, growth of electrical activity of muscles and its prolongation throughout the locomotor cycle. During the myoclonic attack quite other peculiarities of walking are noticed, which worsen disorders of the biomechanical and innervative structure of walking to the greater extent, namely: increase of time of the locomotor cycle, diminution of duration of the stance phase and rise of duration of the swing phase, shortening of the extension phase at a knee and hip joints (KJ and HJ) and prolongation of the flexion phase at the given joints, two-phase character of angle of flexion at a KJ and HJ in the left leg, oscillatory character of movements at the same joints in the right leg, appearance of strong and simultaneous maxima of activity of a number of muscles. Authors thoroughly substantiate necessity of complex abilitation with application of children’s exoskeleton in kids with the dyskinetic form of infantile cerebral palsy. Authors thoroughly describe peculiarities of application of the children’s exoskeleton, organization and program of everyday trainings. Authors demonstrate, that the pronounced improvement of the locomotor function is seen just after five sessions of training in the exoskeleton: only one locomotor stereotype emerges, essential variability of walking disappears, walking velocity and cadence tend to diminish, transfer from running as the only possible way of locomotion to walking takes place, amplitude of movements at both HJ and KJ remarkably reduces, for all this duration of the separate phases grows.
The object of consideration is a new design of a finger orthosis. It is manufactured using tubular blanks made of cross-linked polyethylene (CLPE). CLPE products exhibit hyperelastic and viscoelastic properties, including the shape memory effect (SME), but the scope of application of heat-shrinkable tubes (HST) is mainly limited to connecting structures. A study was conducted on the use of HST as an orthosis that fixes the position of a damaged joint or limb of a person. A hollow heat-shrinkable tube is considered, which is deposited on a bandage wound on a finger. The advantages of the new orthosis include its insensitivity to the non-cylindrical shape of the real object of study (finger). The obtained formulas include averaged parameters that automatically take into account variations in the geometry and compliance of the finger along its length. It is possible, as the soft tissue edema resolves, to intermediately settle the primary fixator from HST by means of its additional heating and cooling. The design is lightweight and has minimal dimensions. An incorrect description of the thermomechanical behavior of a tube using a combined viscoelastic Prony model and a hyperelastic Mooney – Rivlin model in a range of deformations exceeding 70 % is shown. A refinement of the previously described hyperviscoelastic physical model using Ogden relations is performed. The criteria for selecting the geometric parameters of the orthosis blanks were obtained, including a formula for estimating the pressure on the patient's finger, adjusted taking into account numerical calculations in ANSYS. An experimental method for determining the properties of low-modulus materials based on screw tape winding was developed and implemented. The obtained properties of living soft tissues of the finger and a multilayer gauze bandage were implemented in ANSYS as a multi-elastic model. A spatial finite element model of the ‘‘finger – bandage – orthosis’’ system was constructed for an accurate assessment of the stress-strain state of the system. Additional numerical experiments were conducted to assess the rigidity, in which the initial finite element mesh was the deformed model after shrinkage. Based on the obtained pressure and rigidity values, a general criterion for assessing the orthosis configuration was constructed.
The urinary bladder is a hollow organ whose main function is to store urine. Under normal conditions, urination is characterized by rapid and complete emptying of the bladder. However, in pathological cases, surgical treatment is necessary, and mathematical modeling is required to predict the results. Despite the significant amount of data available, questions remain about the accuracy of determining the mechanical characteristics of human biological tissues. This is particularly true for the bladder, whose mechanical behavior depends largely on the condition of the tissue and other factors. As part of the study, a series of experiments was conducted to study the mechanical properties of the human bladder wall using the uniaxial tensile method at different deformation rates. Three different loading rates were considered in the course of the work: 50, 500, and 2000 %/min. For each case, deformation diagrams of the samples were obtained, the limit stresses corresponding to the onset of bladder tissue failure were determined, and the mechanical behavior of the biological tissue under study was analyzed. The results obtained are of interest for the development of finite element models designed to describe the stress-strain state of the human bladder during blunt trauma. In addition, the research data can be used to create artificial organ replacements that should reproduce the mechanical properties of the bladder wall as accurately as possible, thereby ensuring their biocompatibility and functionality.
The article proposes two new approaches to studying the biomechanics of anthropoid structures.The first method involves constructing systems of differential equations of motion using functions of a complex variable, which simplifies the determination of link coordinates defined by a single complex function in exponential form. This approach facilitates the calculation of the squares of the velocities of the links' centers of mass and accelerates the process of computing the system's kinetic energy. Two models of a mechanism with five movable links are considered, differing only in the method of measuring the angles that determine the positions of the links. The description of the method is illustrated using the example of a more intuitive mechanism model, with angles measured from the horizontal axis of the fixed reference frame. For the mechanism model with angles measured from the axes of local coordinate systems, the procedure for constructing the system of differential equations of motion is similar but significantly more cumbersome. The second method pertains to solving the problem of controlling the motion of an anthropoid mechanism and involves the application of various interpolation and approximating functions for the control moments. A comparative analysis of control moments defined by piecewise-continuous step functions, interpolation polynomials, and fifth-degree polynomials was conducted by solving the Cauchy problem for the system of differential equations. It was found that the solution corresponds to motion sufficiently close to anthropoid movement. An analysis of approximation error calculations shows that the minimum value is achieved when using an interpolation polynomial.
