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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">vavilov</journal-id><journal-title-group><journal-title xml:lang="ru">Вавиловский журнал генетики и селекции</journal-title><trans-title-group xml:lang="en"><trans-title>Vavilov Journal of Genetics and Breeding</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2500-3259</issn><publisher><publisher-name>Institute of Cytology and Genetics of Siberian Branch of the RAS</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.18699/VJ15.097</article-id><article-id custom-type="elpub" pub-id-type="custom">vavilov-492</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>Компьютерное моделирование</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Computer Simulation</subject></subj-group></article-categories><title-group><article-title>Идентифицируемость математических моделей медицинской биологии</article-title><trans-title-group xml:lang="en"><trans-title>Identifiability of mathematical models in medical biology</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>Кабанихин</surname><given-names>С. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Kabanikhin</surname><given-names>S. I.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Воронов</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Voronov</surname><given-names>D. A.</given-names></name></name-alternatives><email xlink:type="simple">dmitriy.voronov.89@gmail.com</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>Гродзь</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Grodz</surname><given-names>A. A.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Криворотько</surname><given-names>О. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Krivorotko</surname><given-names>O. I.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Институт вычислительной математики и математической геофизики Сибирского отделения Российской академии наук, Новосибирск, Россия&#13;
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Федеральное государственное автономное образовательное учреждение высшего образования «Новосибирский национальный исследовательский государственный университет», Новосибирск, Россия<country>Россия</country></aff><aff xml:lang="en">Institute of Computational Mathematics and Mathematical Geophysics SB RA S, Novosibirsk, Russia&#13;
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Novosibirsk State University, Novosibirsk, Russia<country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru">Федеральное государственное бюджетное образовательное учреждение высшего профессионального образования "Новосибирский национальный исследовательский государственный университет" (НГУ)<country>Россия</country></aff><aff xml:lang="en">Novosibirsk State University, Novosibirsk, Russia<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>05</day><month>01</month><year>2016</year></pub-date><volume>19</volume><issue>6</issue><fpage>738</fpage><lpage>744</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Кабанихин С.И., Воронов Д.А., Гродзь А.А., Криворотько О.И., 2016</copyright-statement><copyright-year>2016</copyright-year><copyright-holder xml:lang="ru">Кабанихин С.И., Воронов Д.А., Гродзь А.А., Криворотько О.И.</copyright-holder><copyright-holder xml:lang="en">Kabanikhin S.I., Voronov D.A., Grodz A.A., Krivorotko O.I.</copyright-holder><license 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://vavilov.elpub.ru/jour/article/view/492">https://vavilov.elpub.ru/jour/article/view/492</self-uri><abstract><p>Анализ биологических данных является важнейшим вопросом в биоинформатике, вычислительной геномике, молекулярном моделировании и системной биологии. Рассматриваемые в статье подходы позволяют сократить затраты на проведение экспериментов по получению биологических данных. В статье рассмотрен вопрос идентифицируемости математических моделей физиологии, фармакокинетики и эпидемиологии. Рассматриваемые процессы моделируются с помощью нелинейных систем обыкновенных дифференциальных уравнений. Математическое моделирование динамических процессов основано на использовании закона сохранения масс. В процессе решения задачи по оценке параметров, характеризующих исследуемый процесс, нередко возникает вопрос неединственности решения. В случае, когда известны результаты эксперимента (данные на выходе) и данные на входе, целесообразно проводить априорный анализ информативности этих данных. В статье рассмотрено понятие идентифицируемости математических моделей. Представлен обзор методов анализа идентифицируемости динамических систем. В работе приведен обзор следующих подходов: метод передаточной функции, применяемый для линейных моделей (удобен для анализа фармакокинетических данных, так как большой класс препаратов характеризуется линейной кинетикой); метод разложения в ряды Тейлора, применяемый для нелинейных моделей; метод, основанный на теории дифференциальной алгебры (структура данного алгоритма допускает его реализацию на ЭВМ); метод, основанный на теории графов (данный метод не только определяет идентифицируемость модели, но и позволяет найти замену переменных специального вида, приводящую исходную модель к идентифицируемой). На конкретных примерах продемонстрирована необходимость проводить априорный анализ идентифицируемости модели перед проведением численных расчетов по определению параметров, характеризующих тот или иной процесс. Рассмотрены примеры анализа идентифицируемости математических моделей медицинской биологии.</p></abstract><trans-abstract xml:lang="en"><p>Analysis of biological data is a key topic in bioinformatics, computational genomics, molecular modeling and systems biology. The methods covered in this article could reduce the cost of experiments for biological data. The problem of identifiability of mathematical models in physiology, pharmacokinetics and epidemiology is considered. The processes considered are modeled using nonlinear systems of ordinary differential equations. Math modeling of dynamic processes is based on the use of the mass conservation law. While addressing the problem of estimation of the parameters characterizing the process under the study, the question of nonuniqueness arises. When the input and output data are known, it is useful to perform an a priori analysis of the relevance of these data. The definition of identifiability of mathematical models is considered. Methods for analysis of identifiability of dynamic models are reviewed. In this review article, the following approaches are considered: the transfer function method applied to linear models (useful for analysis of pharmacokinetic data, since a large class of drugs is characterized by linear kinetics); the Taylor series expansion method applied to nonlinear models; a method based on differential algebra theory (the structure of this algorithm allows this to be run on a computer); a method based on graph theory (this method allows for analysis of the identifiability of the model as well as finding a proper reparametrization reducing the initial model to an identifiable one). The need to perform a priory identifiability analysis before estimating parameters characterizing any process is demonstrated with several examples. The examples of identifiability analysis of mathematical models in medical biology are presented.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>идентифицируемость</kwd><kwd>математические модели медицинской биологии</kwd><kwd>система обыкновенных дифференциальных уравнений</kwd><kwd>фармакокинетика</kwd><kwd>эпидемиология</kwd><kwd>физиология</kwd><kwd>дифференциальная алгебра</kwd></kwd-group><kwd-group xml:lang="en"><kwd>identifiability</kwd><kwd>mathematical models in medical biology</kwd><kwd>system of ordinary differential equations</kwd><kwd>pharmacokinetic</kwd><kwd>epidemiology</kwd><kwd>physiology</kwd><kwd>differential algebra</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">Audoly S., D’Angio L. On the identifiability of linear compartmental system: a revisited transfer function approach based on topological properties. 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