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Matem. Mod., 2005, Volume 17, Number 8, Pages 61–80 (Mi mm2783)  

This article is cited in 13 scientific papers (total in 13 papers)

Mathematical modelling of hemodynamics of large blood vessels

E. V. Astrakhantseva, V. Yu. Gidaspov, D. L. Reviznikov

Moscow Aviation Institute

Abstract: A brief overview of mathematical models of contemporary applied hemodynamics is given. The special attention is paid to questions of development of effective computational algorithms implementing one-dimensional model. For this purpose TVD-monotonized schemes having the second order accuracy both in time and space are used. A number of test problems with analytical solutions are proposed. Questions of convergence and a choice of grid parameters for various schemes are investigated. The approaches using multiscale hemodynamics models are considered. An embedding of one-dimensional model of a single vessel into 0-dimensional model of vascular system is implemented. The possibility of using linear model for considered class problems of hemodynamics is analyzed.

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Citation: E. V. Astrakhantseva, V. Yu. Gidaspov, D. L. Reviznikov, “Mathematical modelling of hemodynamics of large blood vessels”, Matem. Mod., 17:8 (2005), 61–80

Citation in format AMSBIB
\Bibitem{AstGidRev05}
\by E.~V.~Astrakhantseva, V.~Yu.~Gidaspov, D.~L.~Reviznikov
\paper Mathematical modelling of hemodynamics of large blood vessels
\jour Matem. Mod.
\yr 2005
\vol 17
\issue 8
\pages 61--80
\mathnet{http://mi.mathnet.ru/mm2783}
\zmath{https://zbmath.org/?q=an:1089.76526}


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    This publication is cited in the following articles:
    1. E. V. Astrakhantseva, V. Yu. Gidaspov, U. G. Pirumov, D. L. Reviznikov, “Chislennoe modelirovanie gemodinamicheskikh protsessov v arterialnom dereve. Issledovanie vliyaniya perezhatiya sosuda na parametry techeniya”, Matem. modelirovanie, 18:8 (2006), 25–36  mathnet  zmath
    2. Mukhin, SI, “Analytic study of stationary hemodynamic flows in an elastic vessel with friction”, Differential Equations, 43:7 (2007), 1011  crossref  mathscinet  zmath  isi  elib  scopus
    3. Gavrilova M.S., Butov A.A., Ruzov V.I., Razin V.A., “Stokhasticheskaya model sistemy stabilizatsii sistolicheskogo arterialnogo davleniya v momenty stressovykh situatsii”, Vestnik Saratovskogo gosudarstvennogo tekhnicheskogo universiteta, 3:1 (2011), 150–159  mathscinet  elib
    4. Tsibulskii V.R., Shaidurov O.S., “Obzor modelei vzaimodeistviya elektromagnitnykh polei s krovotokom v krovenosnykh sosudakh cheloveka”, Vestnik kibernetiki, 2011, no. 10, 64–72  elib
    5. Solovev S.V., Sviridova N.V., “Issledovanie vliyaniya svoistv stenok sosudov na gemodinamiku serdechnososudistoi sistemy”, Vestnik priamurskogo gosudarstvennogo universiteta im. sholom-aleikhema, 2011, no. 2, 106–122  elib
    6. S. V. Shilko, Yu. G. Kuzminskii, M. V. Borisenko, “Matematicheskaya model i programmnaya realizatsiya monitoringa serdechno-sosudistoi sistemy”, PFMT, 2011, no. 3(8), 104–112  mathnet
    7. Kozlova M.V., Gorbunov A.V., “Predstavlenie tserebralnoi gemodinamiki s pomoschyu matematicheskogo modelirovaniya”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 18:1 (2013), 291–293  elib
    8. N. V. Sviridova, V. D. Vlasenko, “Modelirovanie gemodinamicheskikh protsessov serdechno-sosudistoi sistemy na osnove dannykh perifericheskoi arterialnoi pulsatsii”, Matem. biologiya i bioinform., 9:1 (2014), 195–205  mathnet
    9. Shaposhnikova G.A., “Influence of the Velocity Profile on the Properties of Equations Averaged Over the Cross Section For the Liquid Flow in Flexible-Wall Tubes”, Dokl. Phys., 59:7 (2014), 326–329  crossref  mathscinet  adsnasa  isi  elib  scopus
    10. S. A. Filimonov, A. A. Dekterev, A. V. Sentyabov, A. V. Minakov, “Simulation of conjugate heat transfer in the microchannel system by means of the hybrid method”, J. Appl. Industr. Math., 9:4 (2015), 469–479  mathnet  crossref  crossref  mathscinet  elib
    11. I. N. Kiselev, E. A. Biberdorf, V. I. Baranov, T. G. Komlyagina, V. N. Melnikov, I. Yu. Suvorova, S. G. Krivoschekov, F. A. Kolpakov, “Personalizatsiya parametrov i validatsiya modeli serdechno-sosudistoi sistemy cheloveka”, Matem. biologiya i bioinform., 10:2 (2015), 526–547  mathnet  crossref
    12. A. G. Losev, A. V. Khoperskov, A. S. Astakhov, Kh. M. Suleimanova, “Problemy izmereniya i modelirovaniya teplovykh i radiatsionnykh polei v biotkanyakh: analiz dannykh mikrovolnovoi termometrii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 6(31), 31–71  mathnet  crossref
    13. S. V. Sindeev, S. V. Frolov, “Modeling of cardiovascular system hemodynamics with cerebral aneurysm”, Math. Models Comput. Simul., 9:1 (2017), 108–119  mathnet  crossref  elib
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