350 rub
Journal Nonlinear World №8 for 2014 г.
Article in number:
Mathematical model of nonlinear processes in large vessels
Keywords: Cauchy-Kovalevskaya equations nonlinear oscillations travelling wave flutter soliton
Authors:
A.I. Sotskov - Post-graduate Student, Moscow State Technical University of Radioengineering, Electronics and Automation. E-mail: orac1e.ru@gmail.com
Abstract:
Proposed the mathematical model of hemodynamic in large vessels based on simple assumptions. The model equations turned to system of Cauchy-Kovalevskaya equations that describes nonlinear effects in nature. Derived analytical solutions that reproduce general nonlinear processes in large vessels. Illustrated ascendancy of elastic response of a arterial wall and convective term.
Pages: 10-15
References

  1. Stefanadis C., Stratos C., Vlachopoulos C., Marakas S., Boudoulas H., Kallikazaros I., Tsiamis E., Toutouzas K., Sioros L., Toutouzas P. Pressure-diameter relation of the human aorta. A new method of determination by the application of a special ultrasonic dimension catheter // Circulation. 1995. V. 92. № 8. P. 2210-2219.
  2. Nichols W., O-Rourke M., Vlachopoulos C. McDonald-s blood flow in arteries: theoretical, experimental and clinical principles. London: Hodder Arnold. 2011. 768 p.
  3. Karo K., Pedli T., Shroter R., Sid U. Mexanika krovoobrashheniya. M.: Mir. 1981. 624 s.
  4. Pedli T. Gidrodinamika krupny'x krovenosny'x sosudov. M.: Mir. 1983. 400 s.
  5. Volobuev A.N., Koshev V.I., Petrov E.S. Biofizicheskie princzipy' gemodinamiki (gidrodinamika techeniya krovi). Samara: Samarskij dom pechati. 2009. 184 s.
  6. Koshelev V.B., Muxin S.I., Sosnin N.V., Favorskij A.P. Matematicheskie modeli kvazi-odnomernoj gemodinamiki: metodicheskoe posobie. M.: MAKS Press, 2010. 114 s.
  7. Bagaev S.N. i dr. Sistema krovoobrashheniya i arterial'naya gipertoniya: biofizicheskie i genetiko-fiziologicheskie mexanizmy', matematicheskoe i komp'yuternoe modelirovanie / otv. red. L.N. Ivanova, A.M. Bloxin, A.L. Markel' Ros. akad. nauk, Sib. otd-nie, In-t fiziki poluprovodnikov im. A.V. Rzhanova Novosibirsk: Izd-vo SO RAN. 2008. 252 s.
  8. Matthys K., Alastruey J., Peiro J., Khir A., Segers P., Verdonck P., Parker K., Sherwin S. Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements  // Journal of Biomechanics. 2007. V. 40. № 15. P. 3476-3486.
  9. Chernyavskij I.L. Matematicheskoe modelirovanie volnovy'x proczessov i autoregulyaczii pri techenii krovi v sosudax: Dis. - kand. fiz.-mat. nauk. M.: 2008. 134 s.
  10. Chulichkov A.L., Nikolaev A.V., Lobanov A.I., Guriya G.T. Porogovaya aktivacziya sverty'vaniya krovi i rost tromba v usloviyax krovotoka // Matematicheskoe modelirovanie. 2000. T. 12. № 3. S. 75-96.
  11. Sotskov A.I. Uravneniya Koshi-Kovalevskoj kak model' nelinejny'x kolebanij krovi v aorte // Estestvenny'e i texnicheskie nauki. 2011. T. 54. № 4. S. 494-497.
  12. Sotskov A.I. Nelinejny'e kolebaniya ideal'noj neszhimaemoj zhidkosti v tonkostennoj uprugoj obolochke // Estestvenny'e i texnicheskie nauki. 2012. T. 61. № 5. S. 386-393.
  13. Sotskov A.I. Matematicheskaya model' nelinejny'x kolebanij krovi v bol'shix arteriyax // Estestvenny'e i texnicheskie nauki. 2014. T. 70. №2. S. 239-246.
  14. Rozhdestvenskij B.L., Janenko N.N. Sistemy' kvazilinejny'x uravnenij i ix prilozheniya k gazovoj dinamike. M.: Nauka. 1978. 688 s.
  15. Shemyakin F.M., Mixalyov P.F. Fiziko-ximicheskie periodicheskie proczessy'. M.-L.: AN SSSR. 1938. 185 s.
  16. Formaggia L., Lamponi D., Quarteroni A. One-dimensional models for  blood flow in arteries // Journal of Engineering Mathematics. 2003. V. 47. № 3-4. P. 251-276.
  17. Bessems D., Giannopapa C., Rutten M., van de Vosse F. Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels // Journal of Biomechanics. 2008. V. 41. № 2. P. 284-291.