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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 9, Pages 1599–1610
DOI: https://doi.org/10.7868/S004446691509015X (Mi zvmmf10272) 		 
This article is cited in 43 scientific papers (total in 43 papers)

On the elasticity of blood vessels in one-dimensional problems of hemodynamics

Yu. V. Vassilevskiab, V. U. Salamatovaab, S. S. Simakovabc

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
b Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333, Russia
c Institute of Computer-Aided Design, Russian Academy of Sciences, Vtoraya Brestskaya ul. 19/18, Moscow, 123056, Russia
Full-text PDF (854 kB) Citations (43)
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DOI: https://doi.org/10.7868/S004446691509015X
Abstract: One-dimensional models of hemodynamics proved to be effective in the analysis of blood flow in humans in the normal and pathological states. A key factor contributing to the successful simulation using one-dimensional models is the inclusion of elastic properties of blood vessel walls. This paper is devoted to the comparative analysis of various mathematical descriptions of elastic properties of vessel walls in modern one-dimensional models of hemodynamics.
Key words: mathematical modeling, hemodynamics, blood vessel, constitutive equations.
Received: 26.02.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 9, Pages 1567–1578
DOI: https://doi.org/10.1134/S0965542515090134
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: Yu. V. Vassilevski, V. U. Salamatova, S. S. Simakov, “On the elasticity of blood vessels in one-dimensional problems of hemodynamics”, Zh. Vychisl. Mat. Mat. Fiz., 55:9 (2015), 1599–1610; Comput. Math. Math. Phys., 55:9 (2015), 1567–1578
Citation in format AMSBIB
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    • This publication is cited in the following 43 articles:
    1. G. V. Krivovichev, “Raznostnye skhemy rasschepleniya dlya sistemy odnomernykh uravnenii gemodinamiki”, Kompyuternye issledovaniya i modelirovanie, 16:2 (2024), 459–488  mathnet  crossref
    2. Timur Gamilov, Alexander Danilov, Peter Chomakhidze, Philipp Kopylov, Sergey Simakov, “Computational Analysis of Hemodynamic Indices in Multivessel Coronary Artery Disease in the Presence of Myocardial Perfusion Dysfunction”, Computation, 12:6 (2024), 110  crossref
    3. Tatiana K. Dobroserdova, Alexander A. Isaev, Alexander A. Danilov, Sergey S. Simakov, “Junction conditions for one-dimensional network hemodynamic model for total cavopulmonary connection using physically informed deep learning technique”, Russian Journal of Numerical Analysis and Mathematical Modelling, 39:5 (2024), 259  crossref
    4. Francis Dominic Lavilles, Wendell Ace Dela Cruz, Bonifacio Jr Doma, “CFD Analysis of the Choledynamic Flow Characteristics of a Patient with Gallbladder Carcinoma”, CFD Lett., 17:5 (2024), 1  crossref
    5. S. S. Simakov, “Analysis of the use of one-dimensional network models of blood flow to assess the hemodynamic coefficients in stenosis coronary arteries”, J. Appl. Mech. Tech. Phys., 65:3 (2024), 563–572  mathnet  crossref  crossref  elib
    6. Julia Kuyanova, Andrei Dubovoi, Aleksei Fomichev, Dmitrii Khelimskii, Daniil Parshin, “Hemodynamics of vascular shunts: trends, challenges, and prospects”, Biophys Rev, 15:5 (2023), 1287  crossref
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    8. Ruslan Yanbarisov, Timur Gamilov, “One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity”, Russian Journal of Numerical Analysis and Mathematical Modelling, 38:5 (2023), 323  crossref
    9. Stephen C. Anco, Tamara M. Garrido, Almudena P. Márquez, María L. Gandarias, “Exact solutions and conservation laws of a one-dimensional PDE model for a blood vessel”, Chaos, Solitons & Fractals, 170 (2023), 113360  crossref
    10. Toro E.F., Celant M., Zhang Q., Contarino Ch., Agarwal N., Linninger A., Muller L.O., “Cerebrospinal Fluid Dynamics Coupled to the Global Circulation in Holistic Setting: Mathematical Models, Numerical Methods and Applications”, Int. J. Numer. Meth. Biomed., 38:1 (2022), e3532  crossref  mathscinet  isi  scopus
    11. Yu. O. Kuyanova, A. V. Dubovoi, A. V. Bervitskii, D. V. Parshin, “Numerical optimization of geometric characteristics of vascular anastomosis using swar intelligence methods in neurosurgery”, J. Appl. Mech. Tech. Phys., 63:4 (2022), 606–613  mathnet  crossref  crossref  elib
    12. Sergey S. Simakov, Timur M. Gamilov, Alexander A. Danilov, Fuyou Liang, Petr Sh. Chomakhidze, Mariam K. Gappoeva, Alina A. Rebrova, Philipp Yu. Kopylov, “Personalized computational estimation of relative change in coronary blood flow after percutaneous coronary intervention in short-term and long-term perspectives”, Russian Journal of Numerical Analysis and Mathematical Modelling, 37:5 (2022), 279  crossref
    13. Vasily Vedeneev, Lecture Notes in Mechanical Engineering, Advanced Problem in Mechanics II, 2022, 35  crossref
    14. Alex G. Kuchumov, Aleksandr Khairulin, Marina Shmurak, Artem Porodikov, Andrey Merzlyakov, “The Effects of the Mechanical Properties of Vascular Grafts and an Anisotropic Hyperelastic Aortic Model on Local Hemodynamics during Modified Blalock–Taussig Shunt Operation, Assessed Using FSI Simulation”, Materials, 15:8 (2022), 2719  crossref
    15. Simakov S.S., Gamilov T.M., Liang F., Gognieva D.G., Gappoeva M.K., Kopylov Ph.Yu., “Numerical Evaluation of the Effectiveness of Coronary Revascularization”, Russ. J. Numer. Anal. Math. Model, 36:5 (2021), 303–312  crossref  mathscinet  isi
    16. Kuchumov A.G., Vedeneev V., Samartsev V., Khairulin A., Ivanov O., “Patient-Specific Fluid-Structure Interaction Model of Bile Flow: Comparison Between 1-Way and 2-Way Algorithms”, Comput. Methods Biomech. Biomed. Eng., 24:15 (2021), 1693–1717  crossref  isi
    17. Podoprosvetova A., Zayko J., Yushutin V., Vedeneev V., “Experimental Study of the Flow Regime Effect on the Stability of Collapsible Tubes Conveying Fluid”, Phys. Fluids, 33:6 (2021), 064104  crossref  isi  scopus
    18. Mozokhina A. Bouchnita A. Volpert V., “Blood Clotting Decreases Pulmonary Circulation During the Coronavirus Disease”, Mathematics, 9:19 (2021), 2401  crossref  isi
    19. Y. V. Vassilevski, O. N. Bogdanov, X. V. Chesnokova, A. A. Danilov, T. K. Dobroserdova, D. D. Dobrovolsky, A. V. Lozovskiy, Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, 2021, 261  crossref
    20. S. S. Simakov, “New boundary conditions for one-dimensional network models of hemodynamics”, Comput. Math. Math. Phys., 61:12 (2021), 2102–2117  mathnet  mathnet  crossref  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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