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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">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2022-26-1-129-147</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-977</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>Информатика, вычислительная техника и управление</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Computer science, computer engineering and IT managment</subject></subj-group></article-categories><title-group><article-title>Моделирование течения неньютоновских жидкостей в тороидальном канале инерционного вискозиметра с системой технического зрения</article-title><trans-title-group xml:lang="en"><trans-title>Non-Newtonian Fluid Flow Modeling in the Inertial Viscometer with a Computer Vision System</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0123-4004</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Корнаева</surname><given-names>Е. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Kornaeva</surname><given-names>E. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Корнаева Елена Петровна, кандидат физико-математических наук, доцент кафедры информационных  систем и цифровых технологий</p><p>Наугорское шоссе, д. 20, г. Орёл 302020</p></bio><bio xml:lang="en"><p>Elena P. Kornaeva, Cand. of Sci. (Phisico-Mathematical), Associate Professor, Information Systems Department</p><p>20 Naugorskoe highway. 94, Orel 302020</p></bio><email xlink:type="simple">lenoks_box@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Стебаков</surname><given-names>И. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Stebakov</surname><given-names>I. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Стебаков Иван Николаевич, аспирант кафедры мехатроники, механики и робототехники</p><p>Наугорское шоссе, д. 20, г. Орёл 302020</p></bio><bio xml:lang="en"><p>Ivan N. Stebakov, Post-Graduate Student, Mechatronics, Mechanics and Robotics Department</p><p>20 Naugorskoe highway. 94, Orel 302020</p></bio><email xlink:type="simple">chester50796@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Корнаев</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kornaev</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Корнаев Алексей Валерьевич, доктор технических наук, профессор кафедры мехатроники, механики и  робототехники</p><p>Наугорское шоссе, д. 20, г. Орёл 302020</p></bio><bio xml:lang="en"><p>Alexey V. Kornaev, Dr. of Sci. (Engineering), Professor of Mechatronics, Mechanics and Robotics Department</p><p>20 Naugorskoe highway. 94, Orel 302020</p></bio><email xlink:type="simple">rusakor@inbox.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Дрёмин</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Dremin</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Дрёмин Виктор Владимирович, кандидат технических наук, научный сотрудник научно-технологического  центра биомедицинской фотоники</p><p>Наугорское шоссе, д. 20, г. Орёл 302020</p><p>Birmingham, B4 7ET</p></bio><bio xml:lang="en"><p>Viktor V. Dremin, Cand. of Sci. (Engineering), Researcher, Research and Development Center of Biomedical Photonics</p><p>20 Naugorskoe highway. 94, Orel 302020</p><p>Birmingham, B4 7ET, United Kingdom</p></bio><email xlink:type="simple">dremin_viktor@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Орловский государственный университет имени И.С. Тургенева</institution></aff><aff xml:lang="en"><institution>Orel State University named after I.S. Turgenev</institution></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Орловский государственный университет имени И.С. Тургенева; College of Engineering and Physical Sciences, Aston University</institution></aff><aff xml:lang="en"><institution>Orel State University named after I.S. Turgenev; College of Engineering and Physical Sciences, Aston University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>28</day><month>06</month><year>2022</year></pub-date><volume>26</volume><issue>1</issue><fpage>129</fpage><lpage>147</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Корнаева Е.П., Стебаков И.Н., Корнаев А.В., Дрёмин В.В., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Корнаева Е.П., Стебаков И.Н., Корнаев А.В., Дрёмин В.В.</copyright-holder><copyright-holder xml:lang="en">Kornaeva E.P., Stebakov I.N., Kornaev A.V., Dremin V.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://izvestswsu.elpub.ru/jour/article/view/977">https://izvestswsu.elpub.ru/jour/article/view/977</self-uri><abstract><p>Цель. Теоретическое обоснование геометрических, кинематических и термодинамических параметров устройства нового инерционного вискозиметра, а также разработка приближенной модели течения неньютоновских жидкостей с использованием сверточных нейронных сетей и данных лазерной спеклконтрастной визуализации.Методы. Исследование состоит из двух частей. Первая посвящена теоретическому исследованию течения вязких жидкостей в тороидальном канале нового инерционного вискозиметра. Математическая модель течения включает безразмерные уравнения Навье-Стокса и конвективной теплопроводности, анализ которых позволил оценить условия однородности полей давлений и температур. Численное решение упрощенного уравнения Навье-Стокса получено методом контрольных объемов. Вычислительный эксперимент позволил выявить дополнительные условия работы вискозиметра. Вторая часть исследований направлена на решение задачи о предсказании значений скорости сдвиговой деформации на поверхности течения и объемного расхода. В основе приближенной модели течения лежит ансамбль сверточных нейронных сетей, обученных на данных лазерной спекл-контрастной визуализации течения жидкости в прозрачной трубке.Результаты. Получены рекомендации о рабочих параметрах инерционного вискозиметра для исследуемых типов жидкостей в заданном диапазоне вязкости. Разработана приближенная модель в виде ансамбля глубоких нейронных сетей, позволяющая на основе изображений течения жидкости определять объемный расход и скорость сдвиговой деформации на поверхности течения.Заключение. Полученное в результате теоретического анализа приближенное уравнение Навье-Стокса для течения вязкой жидкости в тороидальном канале может быть использовано для численного определения кинематической вязкости. Для этого необходимые характеристики течения, такие как объемный расход и скорость сдвиговой деформации на поверхности течения могут быть найдены с помощью предварительно обученной модели в виде ансамбля сверточных нейронных сетей на основе данных лазерной спек-контрастной визуализации. В качестве испытуемой жидкости может быть любая неньютоновская жидкость, способная отражать когерентное излучение. В частности, это могут быть физиологические жидкости, в том числе кровь.</p></abstract><trans-abstract xml:lang="en"><p>Purpose of research. Development of theoretical premises for the new inertial viscometer, as well as the development of an approximate model of the viscosity fluid flow using convolutional neural networks and laser speckle contrast imaging data.Methods. The study consists of two parts. The first is devoted to a theoretical study of viscosity fluid flow in the toroidal channel of еру new inertial viscometer. The mathematical model of the flow includes the dimensionless equations of Navier-Stokes and convective heat conduction, the analysis of which made it possible to estimate the conditions for the uniformity of pressure and temperature fields. The numerical solution of the simplified Navier-Stokes equation was obtained by the control volume method. The computational experiment made it possible to identify additional operating conditions for the viscometer. The second part of the research is aimed at solving the problem of predicting the values of the shear strain rate on the tour surface and the flow rate. The approximate flow model is based on an ensemble of convolutional neural networks trained on data from laser speckle-contrast visualization of a fluid flow in a transparent tube.Results. The recommendations on the operating parameters of the inertial viscometer for the studied types of liquids in a given viscosity range are obtained. An approximate model has been developed in the form of an ensemble of deep neural networks, which makes it possible to determine the volumetric flow rate and the shear strain rate on the flow surface based on fluid flow images.Conclusion. The approximate Navier-Stokes equation obtained as a result of theoretical analysis for the flow of a viscous fluid in a toroidal channel can be used to numerical determination the kinematic viscosity. So, the necessary flow characteristics, such as volumetric flow rate and shear strain rate on the flow surface, can be found using the developed and pretrained convolutional neural network based on laser speck contrast imaging data. The test fluid can be any non-Newtonian fluid capable of reflecting coherent radiation. In particular, it can be physiological fluids, including blood.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>уравнение Навье-Стокса</kwd><kwd>скорость сдвиговой деформации</kwd><kwd>объемный расход</kwd><kwd>вязкость</kwd><kwd>неньютоновская жидкость</kwd><kwd>кровь</kwd><kwd>лазерная спекл-контрастная визуализация</kwd><kwd>глубокое обучение</kwd><kwd>компьютерное зрение</kwd><kwd>инерционный вискозиметр</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Navier-Stokes equation</kwd><kwd>shear rate</kwd><kwd>flow rate</kwd><kwd>viscosity</kwd><kwd>non-Newtonian fluid</kwd><kwd>blood</kwd><kwd>laser speckle contrast imaging</kwd><kwd>deep learning</kwd><kwd>computer vision</kwd><kwd>inertial viscometer</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">Xu J., Vilanova G., Gomez H.. Phase-field model of vascular tumor growth: Threedimensional geometry of the vascular network and integration with imaging data // Comput. Methods Appl. Mech. Engrg. 2020. Vol. 359: 1-19.</mixed-citation><mixed-citation xml:lang="en">Xu J., Vilanova G., Gomez H. Phase-field model of vascular tumor growth: Threedimensional geometry of the vascular network and integration with imaging data. Comput. Methods Appl. Mech. Engrg. 2020, vol. 359: 1-19.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Semenov A.N., Lugovtsov A.E., Lee K., and et. al. Applying Methods of Diffuse Light Scattering and Optical Trapping for Assessing Blood Rheological Parameters: Erythrocytes Aggregation in Diabetes Mellitus. Izv. Saratov Univ. (N.S.), Ser. Physics. Vol. 17. Iss. 2: 85–97 (in Russian). 2017; http://doi.org/10.18500/1817-3020-2017-17-2-85-97.</mixed-citation><mixed-citation xml:lang="en">Semenov A.N., Lugovtsov A.E., Lee K., and et. al. Applying Methods of Diffuse Light Scattering and Optical Trapping for Assessing Blood Rheological Parameters: Erythrocytes Aggregation in Diabetes Mellitus. Izv. Saratov Univ. (N.S.), Ser. Physics, vol. 17. Iss. 2: 85–97 (in Russian). 2017; http://doi.org/10.18500/1817-3020-2017-17-2-85-97.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Yeow N. , Tabor R., Garnier G. Atomic force microscopy: From red blood cells to immunohematology. Advances in Colloid and Interface Science. 2017; Vol. 249: 149–162. http://dx.doi.org/10.1016/j.cis.2017.05.011.</mixed-citation><mixed-citation xml:lang="en">Yeow N., Tabor R., Garnier G. Atomic force microscopy: From red blood cells to immunohematology. Advances in Colloid and Interface Science. 2017, vol. 249: 149–162. http://dx.doi.org/10.1016/j.cis.2017.05.011.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Harris M. J., Wirtz D., Wu P. Dissecting cellular mechanics: Implications for aging, cancer, and immunity. Seminars in Cell &amp; Developmental Biology. 2018: 1 – 10.</mixed-citation><mixed-citation xml:lang="en">Harris M. J., Wirtz D., Wu P. Dissecting cellular mechanics: Implications for aging, cancer, and immunity. Seminars in Cell &amp; Developmental Biology. 2018: 1 – 10.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Gertz M. A. Acute hyperviscosity: syndromes and management. Blood. 2018. Vol. 132. Iss. 13: 1379-1385. https://doi.org/10.1182/blood-2018-06-846816.</mixed-citation><mixed-citation xml:lang="en">Gertz M. A. Acute hyperviscosity: syndromes and management. Blood. 2018. Vol. 132. Iss. 13: 1379-1385. https://doi.org/10.1182/blood-2018-06-846816.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Connes P., Dufour S, Pichon A., Favret F. Editor(s): Bagchi D., Nair S., Chandan K. Chapter 30 - Blood Rheology, Blood Flow, and Human Health. Nutrition and Enhanced Sports Performance. Second Edition. Academic Press; 2019: 359-369. https://doi.org/10.1016/B978-0-12-813922-6.00030-8.</mixed-citation><mixed-citation xml:lang="en">Connes P., Dufour S, Pichon A., Favret F. Editor(s): Bagchi D., Nair S., Chandan K. Chapter 30 - Blood Rheology, Blood Flow, and Human Health. Nutrition and Enhanced Sports Performance. Second Edition. Academic Press; 2019: 359-369. https://doi.org/10.1016/B978-0-12-813922-6.00030-8.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Blood Rheology:Key Parameters, Impact on BloodFlow / E. Nader, S. Skinner, M. Romana, R. Fort, N. Lemonne, and etc. // Role in Sickle Cell Diseaseand Effects of Exercise. Front. Physiol. 2019; Vol. 10: 1–14. https://10:1329.doi:10.3389/fphys.2019.01329.</mixed-citation><mixed-citation xml:lang="en">Nader E., Skinner S., Romana M., Fort R., Lemonne N., and etc. Blood Rheology: Key Parameters, Impact on BloodFlow, Role in Sickle Cell Diseaseand Effects of Exercise. Front. Physiol. 2019, vol. 10: 1–14. https://10:1329.doi:10.3389/fphys.2019.01329.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">The role of blood rheology in sickle cell disease / P. Connes, T. Alexy, J. Detterich, M. Romana, M. D. Hardy-Dessources, and etc. // Blood Rev. 2016; Vol.30: 111–118. doi: 10.1016/j.blre.2015.08.005.</mixed-citation><mixed-citation xml:lang="en">Connes P., Alexy T., Detterich J., Romana, M., Hardy-Dessources, M. D., and etc. The role of blood rheology in sickle cell disease. Blood Rev. 2016, vol.30: 111–118. doi: 10.1016/j.blre.2015.08.005.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Middleman S. The Flow of High Polymers. Continuum and Molecular Rheology. Intersciernce Publishers; 1968.</mixed-citation><mixed-citation xml:lang="en">Middleman S. The Flow of High Polymers. Continuum and Molecular Rheology. Intersciernce Publishers; 1968.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Viscosity of Liquids / D. Viswanath, T. Ghosh, D. Prasad, N. Dutt, K. Rany // Springer; 2007.</mixed-citation><mixed-citation xml:lang="en">Viswanath D., Ghosh T., Prasad D., Dutt N., Rany K. Viscosity of Liquids. Springer; 2007.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Viscometer validation studies for routine and experimental hemorheological measurements / D. Kovacs, K. Totsimon, K. Biro, P. Kenyeres, I. Juricskay, and et. al. // Clin Hemorheol Microcirc. 2018; Vol. 69(3): 383-392. https://doi.org/10.3233/CH-170301.</mixed-citation><mixed-citation xml:lang="en">Kovacs D., Totsimon K., Biro K., Kenyeres P., Juricskay I., and et. al. Viscometer validation studies for routine and experimental hemorheological measurements. Clin Hemorheol Microcirc. 2018, vol. 69(3): 383-392. https://doi.org/10.3233/CH-170301.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">More solutions to sticky problems. A guide to getting more from your Brookfield Viscometer &amp; Rheometer. AMETEK Brookfield, Inc; 2017.</mixed-citation><mixed-citation xml:lang="en">More solutions to sticky problems. A guide to getting more from your Brookfield Viscometer &amp; Rheometer. AMETEK Brookfield, Inc; 2017.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Development of an improved falling ball viscometer for high-pressuremeasurements with supercritical CO2. / B. Calvignac, E. Rodier, J. Letourneau, P. Vitoux, C. Aymonier, and et al. // J. of Supercritical Fluids. 2010; 55; 2010: 96–106. https://doi.org/10.1016/j.supflu.2010.07.012.</mixed-citation><mixed-citation xml:lang="en">Calvignac B., Rodier E., Letourneau J., Vitoux P., Aymonier C., and et al. Development of an improved falling ball viscometer for high-pressuremeasurements with supercritical CO2. J. of Supercritical Fluids. 2010; 55; 2010: 96–106. https://doi.org/10.1016/j.supflu.2010.07.012.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Cristescu N., Conrad B., Tran-Son-Tay R. A closed form solution for falling cylinder viscometers. International Journal of Engineering Science. 2002; 40: 605–620.</mixed-citation><mixed-citation xml:lang="en">Cristescu N., Conrad B., Tran-Son-Tay R. A closed form solution for falling cylinder viscometers. International Journal of Engineering Science. 2002; 40: 605–620.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Measurement of human blood viscosity a using Falling Needle Rheometer and the correlation to the Modified Herschel-Bulkley model equation / H. Yamamoto, T. Yabuta, Y. Negi, D. Horikawa, K. Kawamura // Heliyon. 2020; Vol. 6: 1-9. https://doi.org/10.1016/j.heliyon.2020.e04792</mixed-citation><mixed-citation xml:lang="en">Yamamoto H., Yabuta T., Negi Y., Horikawa D., Kawamura K. Measurement of human blood viscosity a using Falling Needle Rheometer and the correlation to the Modified Herschel-Bulkley model equation. Heliyon. 2020, vol. 6: 1-9. https://doi.org/10.1016/j.heliyon.2020.e04792</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Rolling-ball viscometer: Lovis 2000 M/ME. Доступно: https://www.antonpaar.com/corp-en/products/details/rolling-ball-viscometer-lovis-2000-mme/ (дата обращения 28.03.2022).</mixed-citation><mixed-citation xml:lang="en">Rolling-ball viscometer: Lovis 2000 M/ME. Доступно: https://www.antonpaar.com/corp-en/products/details/rolling-ball-viscometer-lovis-2000-mme/ (дата обращения 28.03.2022).</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Theoretical premises of a vibro-inertial method of viscosity measurement / E. Kornaeva, A. Kornaev, L. Savin, A. Galichev, A. Babin // Vibroengineering Procedia. 2016. Vol. 8. P. 440 – 445.</mixed-citation><mixed-citation xml:lang="en">Kornaeva E., Kornaev A., Savin L., Galichev A., Babin A. Theoretical premises of a vibro-inertial method of viscosity measurement. Vibroengineering Procedia, 2016, vol. 8, Pp. 440 – 445.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Hori Y. Hydrodynamic lubrication. Tokyo: Yokendo Ltd; 2006.</mixed-citation><mixed-citation xml:lang="en">Hori Y. Hydrodynamic lubrication. Tokyo: Yokendo Ltd; 2006.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Gertz M. A. Acute hyperviscosity: syndromes and management. Blood. 2018. Vol. 132. Iss. 13: 1379-1385. https://doi.org/10.1182/blood-2018-06-846816.</mixed-citation><mixed-citation xml:lang="en">Gertz M. A. Acute hyperviscosity: syndromes and management. Blood. 2018. Vol. 132. Iss. 13: 1379-1385. https://doi.org/10.1182/blood-2018-06-846816.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Goodman J.W. Speckle Phenomena in Optics: Theory and Applications. Robert and Company Publisher; 2007.</mixed-citation><mixed-citation xml:lang="en">Goodman J.W. Speckle Phenomena in Optics: Theory and Applications. Robert and Company Publisher; 2007.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Dynamic evaluation of blood flow microcirculation by combined use of the laser Doppler flowmetry and high-speed videocapillaroscopy methods / V. Dremin, I. Kozlov, M. Volkov, N. Margaryants, A Potemkin., and et al. // J. Biophotonics. 2019. Vol. 12: e201800317. https://doi.org/10.1002/jbio.201800317</mixed-citation><mixed-citation xml:lang="en">Dremin V., Kozlov I., Volkov M., Margaryants N., Potemkin A., and et al. Dynamic evaluation of blood flow microcirculation by combined use of the laser Doppler flowmetry and high-speed videocapillaroscopy methods. J. Biophotonics. 2019, Vol. 12: e201800317. https://doi.org/10.1002/jbio.201800317</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Daly S. M., Leahy M. J. ‘Go with the flow’: A review of methods and advancements in blood flow imaging. J. Biophotonics. 2013; Vol. 6. No. 3: 217–255. https://doi.org/10.1002/jbio.201200071</mixed-citation><mixed-citation xml:lang="en">Daly S. M., Leahy M. J. ‘Go with the flow’: A review of methods and advancements in blood flow imaging. J. Biophotonics. 2013; Vol. 6. No. 3: 217–255. https://doi.org/10.1002/jbio.201200071</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Laser speckle contrast imaging and machine learning in application to physiological fluids flow rate recognition / I.N. Stebakov, E.P. Kornaeva, D.D. Stavtsev, E.V. Potapova, V.V. Dremin // Vibroengineering procedia. 2021. Vol.38: 50-55. https://doi.org/10.21595/vp.2021.22013.</mixed-citation><mixed-citation xml:lang="en">Stebakov I.N., Kornaeva E.P., Stavtsev D.D., Potapova E.V., Dremin V.V. Laser speckle contrast imaging and machine learning in application to physiological fluids flow rate recognition. Vibroengineering procedia. 2021, vol.38: 50-55. https://doi.org/10.21595/vp.2021.22013.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Korn G. A., Korn T. M. Mathematical Handbook for Scientists and Engineers. Dover Publications; 2000.</mixed-citation><mixed-citation xml:lang="en">Korn G. A., Korn T. M. Mathematical Handbook for Scientists and Engineers. Dover Publications; 2000.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Thermal conductivity and human density, thermophysical properties of biotissues [ThermalInfo.ru] URL: http://thermalinfo.ru/chelovek/teploprovodnost-cheloveka-teplofizicheskie-svojstva-biotkanej (дата обращения 26.03.2022) (in Rus.).</mixed-citation><mixed-citation xml:lang="en">Thermal conductivity and human density, thermophysical properties of biotissues [ThermalInfo.ru] URL: http://thermalinfo.ru/chelovek/teploprovodnost-cheloveka-teplofizicheskie-svojstva-biotkanej (дата обращения 26.03.2022) (in Russ.).</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
