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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">RUDN Journal of Engineering Research</journal-id><journal-title-group><journal-title xml:lang="en">RUDN Journal of Engineering Research</journal-title><trans-title-group xml:lang="ru"><trans-title>Вестник Российского университета дружбы народов. Серия: Инженерные исследования</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2312-8143</issn><issn publication-format="electronic">2312-8151</issn><publisher><publisher-name xml:lang="en">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">44854</article-id><article-id pub-id-type="doi">10.22363/2312-8143-2025-26-1-86-93</article-id><article-id pub-id-type="edn">KTPDUU</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Development of a Mathematical Model for the Design of a Bio-Artificial Liver</article-title><trans-title-group xml:lang="ru"><trans-title>Разработка математической модели для построения биоискусственной печени</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3582-4889</contrib-id><name-alternatives><name xml:lang="en"><surname>Ganshin</surname><given-names>Alexey S.</given-names></name><name xml:lang="ru"><surname>Ганьшин</surname><given-names>Алексей Сергеевич</given-names></name></name-alternatives><bio xml:lang="en"><p>Postgraduate student of the Department of Mechanics and Control Processes, Academy of Engineering</p></bio><bio xml:lang="ru"><p>аспирант кафедры механики и процессов управления, инженерная академия</p></bio><email>1042210064@pfur.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0359-0897</contrib-id><contrib-id contrib-id-type="spin">8247-7310</contrib-id><name-alternatives><name xml:lang="en"><surname>Andrikov</surname><given-names>Denis A.</given-names></name><name xml:lang="ru"><surname>Андриков</surname><given-names>Денис Анатольевич</given-names></name></name-alternatives><bio xml:lang="en"><p>Ph.D. in Technical Sciences, Associate Professor of the Department of Mechanics and Control Processes, Academy of Engineering</p></bio><bio xml:lang="ru"><p>кандидат технических наук, доцент департамента механики и процессов управления, инженерная академия</p></bio><email>andrikovdenis@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">RUDN University</institution></aff><aff><institution xml:lang="ru">Российский университет дружбы народов</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-06-02" publication-format="electronic"><day>02</day><month>06</month><year>2025</year></pub-date><volume>26</volume><issue>1</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>86</fpage><lpage>93</lpage><history><date date-type="received" iso-8601-date="2025-07-04"><day>04</day><month>07</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Ganshin A.S., Andrikov D.A.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Ганьшин А.С., Андриков Д.А.</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Ganshin A.S., Andrikov D.A.</copyright-holder><copyright-holder xml:lang="ru">Ганьшин А.С., Андриков Д.А.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/engineering-researches/article/view/44854">https://journals.rudn.ru/engineering-researches/article/view/44854</self-uri><abstract xml:lang="en"><p>The research is aimed at developing a mathematical model reflecting the basic biochemical and physiological processes occurring in a bio-artificial liver. The main goal of the study is to create a reliable tool for predicting the behavior of liver cells under artificial conditions, which will improve the understanding of their functionality and metabolic activity. The focus of this study is the modelling of metabolites, the diffusion of toxins and protein synthesis. To achieve this goal, a system of differential equations has been developed that describes the dynamics of key processes related to the functioning of liver cells under artificial conditions. The model takes into account the interaction of biochemical processes such as nutrient metabolism, metabolite secretion, and mechanisms for removing toxins from cells, which is critically important for understanding the general condition of a bio-artificial liver. The study analyzed the influence of various factors on the level of metabolites and the effectiveness of toxin diffusion. This allows us to better understand the basic mechanisms occurring in cells and optimize the conditions of their cultivation to increase the viability and functionality of the bio-artificial liver. The developed model can become the basis for further research in the field of biotechnology and the creation of highly effective organ substitutes, which opens up new prospects in the treatment of liver failure and transplantation. Thus, the results of this work emphasize the importance of mathematical modeling in the study of complex biological systems and can be used to further improve methods of treating liver diseases and develop new approaches in the field of regenerative medicine.</p></abstract><trans-abstract xml:lang="ru"><p>Исследование направлено на построение математической модели, отражающей основные биохимические и физиологические процессы, происходящие в биоискусственной печени. Основная цель исследования - создание надежного инструмента для предсказания поведения клеток печени в искусственных условиях, что позволит улучшить понимание их функциональности и метаболической активности. Уделено внимание моделированию уровня метаболитов, диффузии токсинов и синтеза белков. Для реализации данной задачи разработана система дифференциальных уравнений, которая описывает динамику ключевых процессов, связанных с функционированием клеток печени в искусственных условиях. Модель учитывает взаимодействие биохимических процессов, таких как метаболизм питательных веществ, секреция метаболитов, а также механизмы вывода токсинов из клеток, что является критически важным для понимания общего состояния биоискусственной печени. В ходе исследования проведен анализ влияния различных факторов на уровень метаболитов и эффективность диффузии токсинов. Это позволяет лучше понять основные механизмы, происходящие в клетках, и оптимизировать условия их культивации для повышения жизнеспособности и функциональности биоискусственной печени. Разработанная модель может стать основой для дальнейших исследований в области биотехнологий и создания высокоэффективных заменителей органов, что открывает новые перспективы в лечении печеночной недостаточности и трансплантации. Таким образом, результаты данной работы подчеркивают значимость математического моделирования в исследовании сложных биологических систем и могут быть использованы для дальнейшего усовершенствования методов лечения заболеваний печени и разработки новых подходов в области регенеративной медицины.</p></trans-abstract><kwd-group xml:lang="en"><kwd>differential equation</kwd><kwd>bioreactor</kwd><kwd>modeling of biochemical processes</kwd><kwd>robust system</kwd><kwd>liver metabolism</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>дифференциальное уравнение</kwd><kwd>биореактор</kwd><kwd>моделирование биохимических процессов</kwd><kwd>робастная система</kwd><kwd>метаболизм печени</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Karvellas CJ, Subramanian RM. Current Evidence for Extracorporeal Liver Support Systems in Acute Liver Failure and Acute-on-Chronic Liver Failure. 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