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<article article-type="research-article" dtd-version="1.3" 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" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">bsuir</journal-id><journal-title-group><journal-title xml:lang="ru">Доклады БГУИР</journal-title><trans-title-group xml:lang="en"><trans-title>Doklady BGUIR</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1729-7648</issn><issn pub-type="epub">2708-0382</issn><publisher><publisher-name>БГУИР</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.35596/1729-7648-2025-23-3-77-85</article-id><article-id custom-type="elpub" pub-id-type="custom">bsuir-4165</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Математическая модель респираторных искажений патологического очага при визуализации на ПЭТ/КТ-изображениях</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical Model of Respiratory Distortions of a Pathological Focus During Visualization on PET/CT Images</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Петкевич</surname><given-names>М. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Piatkevich</surname><given-names>M. N.</given-names></name></name-alternatives><bio xml:lang="ru"><sec><title>нач. отдела по инженерному обеспечению лучевой терапии</title></sec></bio><bio xml:lang="en"><sec><title>Head of the Radiation Therapy Engineering Department</title><p> </p></sec></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Коровко</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Korovko</surname><given-names>D. V.</given-names></name></name-alternatives><bio xml:lang="ru"><sec><title>студент</title></sec></bio><bio xml:lang="en"><sec><title>Student</title></sec></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Емельяненко</surname><given-names>Е. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Emelyanenko</surname><given-names>E. V.</given-names></name></name-alternatives><bio xml:lang="ru"><sec><title>канд. техн. наук, инж.</title></sec></bio><bio xml:lang="en"><sec><title>Сand. Sci. (Tech.), Engineer</title><p> </p></sec></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Республиканский научно-практический центр онкологии и медицинской радиологии имени Н. Н. Александрова</institution></aff><aff xml:lang="en"><institution>N. N. Aleksandrov National Cancer Center of Belarus</institution></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Международный государственный экологический институт имени А. Д. Сахарова Белорусского государственного университета</institution></aff><aff xml:lang="en"><institution>International Sakharov Environmental Institute of Belarusian State University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>15</day><month>07</month><year>2025</year></pub-date><volume>23</volume><issue>3</issue><fpage>77</fpage><lpage>85</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Петкевич М.Н., Коровко Д.В., Емельяненко Е.В., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Петкевич М.Н., Коровко Д.В., Емельяненко Е.В.</copyright-holder><copyright-holder xml:lang="en">Piatkevich M.N., Korovko D.V., Emelyanenko E.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://doklady.bsuir.by/jour/article/view/4165">https://doklady.bsuir.by/jour/article/view/4165</self-uri><abstract><p>Проведены оценка и анализ неопределенностей визуализации патологического очага на ПЭТ/КТ-изображениях, возникающих вследствие респираторных движений биологического объекта, оказывающих непосредственное влияние на определение геометрических характеристик патологического очага, его локализацию и корректность моделирования трехмерного распределения дозы излучения в теле пациента. На основании экспериментально установленных зависимостей влияния величины смещения и диаметра исследуемого объекта (сферы) на величину несоответствия визуализированного объема исследуемого объекта разработана математическая модель респираторных искажений патологического очага при визуализации на ПЭТ/КТ-изображениях, позволяющая осуществить количественную и качественную оценку влияния респираторного движения пациента на геометрическую точность визуализации патологического очага на ПЭТ/КТ-изображениях с точностью до 98 %. Верификация модели показала высокую степень согласованности между модельными расчетами и экспериментальными данными. Средние значения относительной неопределенности для КТ и ПЭТ, соответственно, составили (2,123 ± 1,051) % и (2,661 ± 0,870) %, а для абсолютной – (2,096 ± 0,941) % и (1,992 ± 0,782) %, что подтверждает корректность и практическую применимость разработанной методики. </p></abstract><trans-abstract xml:lang="en"><p>The article presents an assessment and analysis of uncertainties in pathological lesion visualization on PET/CT images that arise due to respiratory movements of a biological object, which have a direct impact on determining the geometric characteristics of the pathological lesion, its localization, and the correctness of modeling the three-dimensional distribution of the radiation dose in the patient’s body. Based on the experimentally established dependencies of the influence of the displacement value and the diameter of the object (sphere) under study on the value of the discrepancy between the visualized volume of the object under study, a mathematical model of respiratory distortions of the pathological lesion during visualization on PET/CT images has been developed, which allows for a quantitative and qualitative assessment of the influence of the patient’s respiratory movement on the geometric accuracy of pathological lesion visualization on PET/CT images with up to 98 % accuracy. Verification of the model has shown a high degree of consistency between the model calculations and experimental data. The average values of relative uncertainty for CT and PET, respectively, were (2.123 ± 1.051) % and (2.661 ± 0.870) %, and for absolute uncertainty – (2.096 ± 0.941) % and (1.992 ± 0.782) %, which confirms the correctness and practical applicability of the developed method.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>математическая модель</kwd><kwd>искажения</kwd><kwd>ПЭТ/КТ</kwd><kwd>фантом</kwd><kwd>величина несоответствия</kwd><kwd>респираторные движения</kwd><kwd>лучевая терапия</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical model</kwd><kwd>distortion</kwd><kwd>PET/CT</kwd><kwd>phantom</kwd><kwd>uncertainties value</kwd><kwd>respiratory motion</kwd><kwd>radiation therapy</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Murshed, H. Fundamentals of Radiation Oncology: Physical, Biological and Clinical Aspects / H. Murshed, 3rd ed. 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