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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">smjournal</journal-id><journal-title-group><journal-title xml:lang="ru">Спортивная медицина: наука и практика</journal-title><trans-title-group xml:lang="en"><trans-title>Sports medicine: research and practice</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-2524</issn><issn pub-type="epub">2587-9014</issn><publisher><publisher-name>NEICON</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17238/ISSN2223-2524.2020.2.5</article-id><article-id custom-type="elpub" pub-id-type="custom">smjournal-197</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>РЕАБИЛИТАЦИЯ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>REHABILITATION</subject></subj-group></article-categories><title-group><article-title>Кривизна кривой как показатель оптимальности траектории движения в физической реабилитации. Эллиптические реабилитационные движения</article-title><trans-title-group xml:lang="en"><trans-title>Curvature of curve as an indicator of the optimal movement trajectory in physical rehabilitation. Elliptical rehabilitation movements</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7932-116X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Васильев</surname><given-names>О. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Vasilyev</surname><given-names>O. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Васильев Олег Станиславович, врач по спортивной медицине, в.н.с. НИИ спорта и спортивной медицины, к.ф.н. </p><p>Москва</p></bio><bio xml:lang="en"><p>Oleg S.Vasilyev, M.D., Ph.D. (Philosophy), Sports Medicine Physician, Traumatologist-Orthopedist </p><p>Moscow</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6250-2231</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Левушкин</surname><given-names>С. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Levushkin</surname><given-names>S. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Левушкин Сергей Петрович, и.о. директора Института возрастной физиологии, директор НИИ спорта и спортивной медицины, проф., д.б.н. </p><p>+7(916)965-00-94 </p><p>Москва</p></bio><bio xml:lang="en"><p>Sergey P. Levushkin, Director of the Scientific Research Institute of Sports and Sports Medicine, Grand PhD in Biological sciences</p><p>+7(916)965-00-94 </p><p>Moscow</p></bio><email xlink:type="simple">levushkinsp@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ФГБОУ ВО Российский государственный университет физической культуры, спорта, молодежи и туризма (ГЦОЛИФК), Министерство спорта РФ</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Research Institute of Sports of the Russian State University of Physical Education, Sport, Youth and Tourism (SCOPLIPE)</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>ФГБОУ ВО Российский государственный университет физической культуры, спорта, молодежи и туризма (ГЦОЛИФК), Министерство спорта РФ; ФГБНУ Институт возрастной физиологии Российской академии образования</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Research Institute of Sports of the Russian State University of Physical Education, Sport, Youth and Tourism (SCOPLIPE); Institute of Developmental Physiology, Russian Academy of Education</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2020</year></pub-date><pub-date pub-type="epub"><day>13</day><month>09</month><year>2020</year></pub-date><volume>10</volume><issue>2</issue><fpage>5</fpage><lpage>13</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Васильев О.С., Левушкин С.П., 2020</copyright-statement><copyright-year>2020</copyright-year><copyright-holder xml:lang="ru">Васильев О.С., Левушкин С.П.</copyright-holder><copyright-holder xml:lang="en">Vasilyev O.S., Levushkin S.P.</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://www.smjournal.ru/jour/article/view/197">https://www.smjournal.ru/jour/article/view/197</self-uri><abstract><p>Динамические характеристики движения являются основными параметрами дозирования физической нагрузки при проведении реабилитации спортсменов. Однако, учет геометрических характеристик движения, особенно при восстановлении объема движения в суставе является не менее важным. Гипотезой исследования стало предположение, что использование геометрических характеристик движений позволяет «спроектировать» оптимальные физиологические паттерны реабилитации при восстановления объема движения. Цель исследования – разработка общих принципов и математической модели оптимальных характеристик траектории движения восстанавливаемого звена ОДА спортсмена. Материалы и методы: В ходе исследования использовалась оптико-электронная система трёхмерного захвата и анализа движения «Qualisys». В исследовании приняли участие 32 спортсмена в возрасте от 9 до 15 лет, практикующих сложнокоординационные виды спорта и имеющих повреждения (ушибы, растяжения мышечно-связочного аппарата) ОДА в области тазобедренного и голеностопного сустава и нуждающиеся в реабилитации – восстановлении объема движений в суставе. Результаты: Исследование показало, что восстановление объема движений по индивидуально подобранным при помощи математического моделирования траекториям (в экспериментальной группе) эффективно и в более короткие сроки восстанавливает спортсменов, нежели традиционные средства лечебной физкультуры (в контрольной группе). Так, типичные повреждения (ушибы, растяжения мышечно-связочного аппарата) ОДА в области тазобедренного сустава восстанавливались в контрольной группе 18±5 суток, в то время как в экспериментальная группе 12±3 суток. Аналогичная картина наблюдалась при восстановлении голеностопного сустава (12±4 суток заняло восстановление в контрольной группе против 8±3 суток в экспериментальной). Выводы: При восстановлении объема движений в суставе нагрузку следует оценивать не столько динамическими, сколько геометрическими показателями; для плоского движения – это кривизна траектории движения дистальной конечности по отношению к восстанавливаемому суставу.</p></abstract><trans-abstract xml:lang="en"><p>The movement dynamic characteristics are the main parameters for physical exercise dosing during the athlete recovery process. However, taking into account the geometric characteristics of movement is no less important, especially when restoring the joint range of motion. The hypothesis of the study was the assumption that the use of movements’ geometric characteristics allows to “design” the optimal physiological rehabilitation patterns for movement volume restoration. Objective: to develop general principles and to create a mathematical model of the optimal trajectory characteristics for the restored part of the athlete’s musculoskeletal system. Materials and methods: We used 3D Qualisys Motion Capture and Analysis System in our investigation. The study involved 32 complex coordination sports athletes (age 9-15) with hip and ankle joint injuries (bruises, sprains strains). All they required a joint movement volume restoration. Results: The study revealed that joint movement volume restoration following the individually selected pathways involving effective mathematical modeling (study group) takes shorter time to restore the athletes than traditional physiotherapy methods (control group). For typical injuries (bruises, sprains and strains) of the hip joint area, the rehabilitation took 18±5 days for controls and 12±3 days for experimental group subjects. Nearly the same pattern was observed in restoration the ankle joint (12±4 days of recovery for controls versus 8±3 days for the experimental group). Conclusions: Restoring the joint movement volume, the workloads should be evaluated with geometric rather than dynamic indicators; for planar movement, that should be the distal limb path curvature relative to the restored joint.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>реабилитация</kwd><kwd>спортсмены</kwd><kwd>математическая модель</kwd><kwd>кривизна траектории</kwd><kwd>опорно-двигательный аппарат</kwd></kwd-group><kwd-group xml:lang="en"><kwd>rehabilitation/recovery</kwd><kwd>athletes</kwd><kwd>mathematical model</kwd><kwd>path/trajectory curvature</kwd><kwd>musculoskeletal system</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">Park I, Buchanan J. Motor skill learning and the development of visual perception processes supporting action identifi cation // journal of motor behavior. 2017. Vol. 50, №5. 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