ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Regirer S. A. The resistive blood vessel as a nonlinear mechanical system. Izvestiya VUZ. Applied Nonlinear Dynamics, 1994, vol. 2, iss. 3, pp. 77-85. DOI: 10.18500/0869-6632-1994-2-3-77-85

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 1994no3-4p077.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Nonlinear Waves. Solitons
Article type: 
Article
UDC: 
532.546:612.13
DOI: 
10.18500/0869-6632-1994-2-3-77-85

The resistive blood vessel as a nonlinear mechanical system

Autors: 
Regirer Sergej Arkadevich, Lomonosov Moscow State University
Abstract: 

The global structure and some general properties of nonlinear local regulation models for a single resistive blood vessel are considered. Previous theoretical investigations are reviewed in brief. The main attention is given to the modeling of vessel regulatory response to hydrodynamically induced shear stress.

Key words: 
-
Acknowledgments: 
The work was carried out with the financial support of the Russian Foundation for Basic Research (project 93013-17344).
Reference: 
  1. Koch АК. Some mathematical forms of autoregulatory models. Circ. Res. 1964;15:269-278.
  2. Borgstrom Р, Grande Р-О. Myogenic microvascular responses to change of transmural pressure. A mathematical approach. Acta Physiol. Scand. 1979;106(4):411-423. DOI: 10.1111/j.1748-1716.1979.tb06420.x
  3. Regirer SA, Rutkevich IМ, Usik PI. A model of vascular tone. Mech. Polim. 1975;4:585-589.
  4. Nikolskii VP. Effect of Stabilisation of the Pressure Gradient in Small Arteries with Changes in Blood Flow. Abstr. PhD Thesis. М.; 1987. 24 p.
  5. Egorov VA, Regirer SА, Shadrina NKh. Blood flow in muscle microvascular network during regulatory reactions: quasi-stationary tasks. Fluid Dynamics. 1993;1:137-145.
  6. Nedoshivin VP, Dvoretskii DP. The effect of the amplitude and frequency of blood pulsations on the peripheral vascular tonus. Physiological J. 1991;77(9):76-82.
  7. Regirer SА, Rutkevich IМ. Wave movements of liquid in tubes made of viscoelastic material. Low amplitude waves. Fluid Dynamics. 1975;1:45-53.
  8. Nikitin LV, Khayutin VМ. Theories in the measurement of the hydraulic resistance of vessels under the action of regulating signals. Physiological J. 1962;48(8):967-975.
  9. Rutkevich IМ. Wave movements of liquid in tubes made of viscoelastic material. Stationary nonlinear waves. Fluid Dynamics. 1975;4:86-95.
  10. Klochkov BN. Continuous Model of Tissue with Mechanochemical Processes and Problems about the Flow of Liquid in the Active Tube. Abstr. PhD Thesis. M.; 1988. 24 p.
  11. Wier WG, Blatter LA. Ca2+ —oscillations and Са2+ —waves in mammalian cardiac and vascular smooth muscle cells. Cell Calcium. 1991;12(2-3):241-254. DOI: 10.1016/0143-4160(91)90024-9
  12. Fung YC. Biomechanics. Mechanical Properties of Living Tissues. New York: Springer; 1993. 568 p. DOI: 10.1007/978-1-4757-2257-4.
  13. Regirer SA, editor. Hydrodynamics of Blood Circulation. М.: Mir; 1971. 270 p.
  14. Skalak TC, Schmid-Schonbein СМ. Viscoelastic properties of microvessels in rat spinotrapezius muscle. Trans. ASME: J. Biomech. Eng. 1986;108(3):193-200. DOI: 10.1115/1.3138602
  15. Egorov VA, Regirer SA, Shadrina NKh. Features of the pulsating flow through resistive blood vessels. Fluid Dynamics. 1994;2:83-89.
  16. Kireeva ЕV. Wave Movements in Active Viscoelastic Tubes. Abstract PhD Thesis. M.: Moscow State University; 1989. 15 p.
  17. Egorov VА. Mathematical Modelling of Blood Movement in Regulated Microvessels. Abstract PhD Thesis. M.: Moscow State University; 1992. 17 p.
  18. Rachev А. Моделиране на периферното кръвообращение. Биомеханика (София). 1984;15-16:116-126. (In Bulgarian)
  19. Borgstrom P, Grande Р-О, Mellander S. A mathematical description of the myogenic response in the microcirculation. Acta Physiol. Scand. 1982;116(4):363-376. DOI: 10.1111/j.1748-1716.1982.tb07154.x
  20. Lush DJ, Fray JC. Steady-state autoregulation of renal blood flow: a myogenic model. Amer. J. Physiol. 1984;247(1):R89-R99. DOI: 10.1152/ajpregu.1984.247.1.R89
  21. Borgstrom P, Gestrelius S. Mathematical model interpretation of cellular events in integrated local control of the microcirculation. Acta Physiol. Scand. 1984;120:P33.
  22. Borgstrom P, Gestrelius S. Integrated myogenic and metabolic control of vascular tone in skeletal muscle during autoregulation of blood flow. Microvasc. Res. 1987;33(3):353-376. DOI: 10.1016/0026-2862(87)90028-8
Received: 
16.02.1993
Accepted: 
12.05.1994
Published: 
24.11.1994
  • 1598 reads