The paper deals with the problem of restructuring the trabecular bone tissue in the half-plane under the influence of a distributed load. We used evolutionary relations in Cowin's formulation, describing changes in pore orientation in terms of the fabric tensor and the fraction of the solid bone volume in the region under consideration. We modeled the process of the half-plane loading by the distributed pressure. The lazy zone theory and physical relations were used to obtain the initial value of the change in the solid bone volume fraction. As a result, we found the pore distribution field and represented it for clarity as a field of the first eigenvectors of the fabric tensor, which corresponds to the direction of an ellipse's larger radius. This study reveals variation of pore geometry in time and with the distance from the load action line as well as describes the behavior of the solid bone volume fraction with the distance from the pressure line.

The paper considers the problem of restructuring trabecular bone tissue under external loads. The evolutionary relationships was used in Cowin statement, changes of orientation of the pores was described in terms of the fabric tensor and the volume fraction of solid bone. To estimate the elastic properties, the mechanical constants were recalculated according to the actual states of the fabric tensor. The process of bone remodeling of a rounded rectangular area under external loads was simulated; using the theory of lazy zone and physical relations, the initial value of the change in the proportion of solid bone volume is obtained. The initial state was given by a homogeneous porous state. The boundary-value problem was solved by the finite element method, and the initial problem was solved by the method of finite differences. As a result, fields were obtained for the distribution of the mechanical properties of bone tissue in the region.

Modeling of elements of inhomogeneous media is an actual direction in the study of composite materials and biomechanics objects. The need for research is determined by the insufficient development of methods for describing mechanical parameters, taking into account the anisotropy of materials. In this case, one of the directions is the use of digital prototyping and numerical modeling methods. In the field of biomechanics, the applicability of approaches to numerical modeling based on image data correlates with cases of clinical practice, which is due to the peculiarities of non-destructive testing methods and allows obtaining results that affect the quality of treatment. The paper considers a method for restoring effective mechanical properties of a material based on computational and field experiments. The simulation was based on the finite element method and assumed the use of data from a digital prototype obtained by computed tomography. The restoration of the calculated area was performed by filtering the initial grid relative to the proportion of the content of the material. The presented method makes it possible to restore the effective values of the elastic modulus and tangential modules based on the relationship established within the framework of the approach between the mechanical properties of the material and the loading parameters of the model sample. In the course of the work, the bone organs of pigs were modeled. Animal husbandry and experimental procedures were carried out in compliance with bioethical norms. Physical tests and numerical modeling were carried out under the conditions of bending action. Validation of the obtained distribution of values of the stress-strain state was performed according to the data of full-scale experiments. The presented solution showed a weak dependence of the results (less than 1 %) relative to the degree of discretization of the computational domain, which made it possible to perform calculations using fewer finite elements, avoiding the use of resource-intensive methods to restore the geometry of the sample. The results obtained in the framework of the work correspond to the literature data and determine the true values, the use of which in calculations makes it possible to assess the strength of the elements of an inhomogeneous structure under the action of external loads, taking into account the spatial distribution of the material.

Моделирование элементов негомогенных сред является актуальным направлением при изучении композитных материалов и объектов биомеханики. Необходимость проведения исследований определяется недостаточной разработанностью методик описания механических параметров с учётом анизотропии материалов. В этом случае одним из направлений выступает применение цифрового прототипирования и методов численного моделирования. В области биомеханики применимость подходов к численному моделированию на основе данных с изображений коррелирует с клинической практикой, что обусловливается особенностями методов неразрушающего контроля и позволяет получать результаты, оказывающие влияние на качество проводимого лечения. В работе рассматривается метод восстановления механических свойств костной ткани на основе вычислительных и натурных экспериментов. Моделирование базировалось на методе конечных элементов и предполагало применение данных цифрового прототипа, полученного проведением компьютерной томографии. Восстановление расчётной области выполнялось фильтрацией исходной сетки относительно доли содержания материала. Представленный метод позволяет восстанавливать значения модуля упругости и касательных модулей ткани на основе линейности тензора упругих констант относительно модуля Юнга. В ходе работы было проведено моделирование костных органов свиней. Содержание животных и экспериментальные процедуры осуществлялись с соблюдением биоэтических норм. Физические испытания и численное моделирование выполнялось в условиях действия изгиба. Валидация полученного распределения значений напряжённодеформированного состояния выполнялась по данным натурных экспериментов. Представленное решение показало слабую зависимость результатов (менее 1 %) относительно степени дискретизации расчётной области, что позволило проводить вычисления с применением меньшего количества конечных элементов, избегая применения ресурсоёмких методов восстановления геометрии образца. Полученные в рамках работы результаты соответствуют литературным данным и определяют истинные значения упругих констант костной ткани, применение которых в расчётах позволяет проводить оценку прочности элементов негомогенной структуры в условиях действия внешних нагрузок с учётом пространственного распределения материала.

Spinal cord injuries are often accompanied by osteoporosis, which complicates re-habilitation. The effect of injury severity on changes in bone strength properties is poor-ly understood. Therefore, the aim of the present study was to assess changes in me-chanical properties of bone in the diaphyseal region after spinal cord injury of different severity (contusion and complete spinal cord injury). The study was conducted on non-linear rats weighing 180–200 g. Animal housing and experimental procedures were car-ried out in compliance with bioethical norms. Complete spinal cord injury was simulated by transection of the spinal cord at the Th8–Th9 level. Contusion (incomplete) trauma to the spinal cord was inflicted at the Th8–Th9 level according to a modified technique by A.R. Allen. Animals were removed from the experiment on the 30th day, after which the bones (tibia and femur) were extracted. Geometric, volumetric and mass characteristics were determined for each bone, and three-point bending tests were performed. The re-sults showed that spinal cord injury in experimental rats resulted in a loss of strength in the femur and tibia. In the case of incomplete injury, the decrease in hind limb strength was more pronounced (21 % in the tibia and 27 % in the femur) than in complete spinal cord injury (21 % in the tibia and 19 % in the femur). At the same time, the density and Young's modulus of the tibia and femur did not significantly change after complete and incomplete spinal cord injury in rats. Following the results, the authors hypothesized that the immobilization after spinal cord injury leads to different changes of bone micro-architecture. It is assumed that changes in bone microarchitecture entail a significant influence on bone strength.