Смолин А.Ю., Еремина Г.М. Моделирование напряжённо-деформированного состояния системы остеонов при механическом воздействии // Вестник Чувашского государственного педагогического университета им. И. Я. Яковлева. Серия: Механика предельного состояния. 2025. № 4(66). С. 112-141. DOI: https://doi.org/10.37972/chgpu.2025.66.4.008. EDN: ABEIYQ.

Автор(ы)

Смолин А.Ю. — Институт физики прочности и материаловедения СО РАН; Томский государственный университетORCIDeLibrary

Еремина Г.М. — Институт физики прочности и материаловедения СО РАН; Томский государственный университетORCIDeLibrary

Название статьи

Моделирование напряжённо-деформированного состояния системы остеонов при механическом воздействии

Название (англ.): Simulation of the Stress and Strain State of the Osteon System Under Mechanical Impact

Индекс(ы) УДК

539.32

DOI

10.37972/chgpu.2025.66.4.008

EDN

ABEIYQ

Ключевые слова

остеон; механические напряжения; компьютерное моделирование; механорегуляция; терапия механическим воздействием

Аннотация

Численно исследовано влияние уровня и направления внешнего низкоинтенсивного импульсного энергетического воздействия, имитирующего ударно-волновую терапию, на напряжённо-деформированное состояние системы остеонов для оценки условий, способствующих резорбции или ремоделированию костной ткани. Моделирование выполнено методом подвижных клеточных автоматов с реализованной в нём моделью пороупругого тела Био. Геометрия остеона представлена в виде многослойного цилиндра с переменной проницаемостью ламелей. Проведена валидация модели одиночного остеона, показавшая хорошее соответствие литературным данным по распределению давления флюида. Для анализа условий структурной перестройки использовались критерии, основанные на значениях среднего напряжения, интенсивности сдвиговых деформаций и давления внутритканевой жидкости. Установлено, что анизотропия эффективных упругих модулей системы остеонов для крайних случаев ориентации (вдоль и поперёк их оси) не превышает 15–20%, что обосновывает допустимость использования изотропных моделей на макроуровне. Показано, что при воздействии, направленном перпендикулярно оси остеонов, с плотностью потока энергии (ППЭ) 0,05–0,1 мДж/мм2 в 80% объёма гаверсова канала создаётся давление, способствующее миграции стволовых клеток, а в области ламелей возникают средние напряжения (0,04–0,2 МПа), необходимые для запуска остеогенеза. При направлении воздействия вдоль остеонов аналогичный эффект наблюдается лишь в 30% объёма канала. Выявлено, что превышение ППЭ более 0,25 мДж/мм2 приводит к возникновению критических напряжений, провоцирующих разрушение по границам остеонов. Сделан вывод, что наиболее предпочтительным для стимуляции ремоделирования является экстракорпоральное воздействие, направленное перпендикулярно поверхности кости, в среднем диапазоне интенсивностей.

Финансирование

Название программы финансирования: Работа выполнена в рамках государственного задания ИФПМ СО РАН, тема FWRW-2021-0006.. Номер программы финансирования: FWRW-2021-0006. Организация, предоставившая финансирование: Государственное задание ИФПМ СО РАН.

Даты

Поступила: 15.06.2025; Принята: 05.10.2025; Опубликована: 30.12.2025

Страницы

112-141

Полная версия статьи

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1. Modeling deformation-induced fluid flow in cortical bone's canalicular-lacunar system / S. Gururaja, H. J. Kim, C. C. Swan, [et al.] // Annals of Biomedical Engineering. - 2005. - Vol. 33. - P. 7-25. - DOI: 10.1007/s10439-005-8959-6
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3. Liu Y., Li A., Chen B. Effects of structure characteristics of osteocyte lacunae on squeeze damage resistance of osteons // Cells Tissues Organs. - 2020. - Vol. 208, no. 3/4. - P. 142-147. - DOI: 10.1159/000505135
4. The course of osteons in the compact bone of the human proximal femur with clinical and biomechanical significance / V. B´aˇca [et al.] // Surgical and Radiologic Anatomy. - 2007. - Vol. 29, no. 3. - P. 201-207. - DOI: 10.1007/s00276-0070192-6 EDN: GUOGTK
5. The impact of age, mineralization, and collagen orientation on the mechanics of individual osteons from human femurs / C. J. Collins, M. Kozyrev, M. Frank, [et al.] // Materialia. - 2020. - Vol. 9. - P. 100573. - 10.1016/j.mtla.2019. 100573. DOI: 10.1016/j.mtla.2019.100573 EDN: VTFLMX
6. Cellular mechanotransduction in health and diseases: from molecular mechanism to therapeutic targets / X. Di, X. Gao, L. Peng, [et al.] // Signal Transduction and Targeted Therapy. - 2023. - Vol. 8. - P. 282. - DOI: 10.1038/s41392-023-01501-9 EDN: RJLFQZ
7. Adachi T., Kameo Y. Computational Biomechanics of Bone Adaptation by Remodeling // Multiscale Mechanobiology of Bone Remodeling and Adaptation. Vol. 578 / ed. by P. Pivonka. - Cham : Springer, 2018. - P. 231-257. - (CISM International Centre for Mechanical Sciences). - DOI: 10.1007/978-3-319-58845-2_5
8. Takito J., Nonaka N. Osteoclasts at Bone Remodeling: Order from Order // Syncytia: Origin, Structure, and Functions. Vol. 71 / ed. by M. Kloc, A. Uosef. - Cham : Springer, 2024. - (Results and Problems in Cell Differentiation). - DOI: 10.1007/978-3-031-37936-9_12
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