Dynamic Response of the Collapsible Blood Vessel

  • Shawn Field
  • Gary M. Drzewiecki


In its simplest form, the dynamics of pressure and flow in a segment of a blood vessel can be ascribed to the flow resistance, flow inertance, and volume compliance of the segment. All physical elements are assumed to be constant and, thus, result in a second-order linear system. These segments may be connected in series to represent the distributed properties of the cardiovascular system. In the most complete form, Westerhof et al. (24) have employed such segments to represent a large portion of the human systemic arterial system. In this case, the segment elements must vary in accordance with dimensional and material properties of the specific vessels that they represent.


Period Doubling Resonant Peak Transmural Pressure Lumen Area Phase Plot 
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  1. 1.
    Anliker M, Wells MK, Ogden E. The transmission characteristics of large and small pressure waves in the abdominal vena cava. IEEE Trans Biomed Eng. 1969;BME-16:262–273.CrossRefGoogle Scholar
  2. 2.
    Bertram CD. Unstable equilibrium behavior in collapsible tubes. J.Biomech. 1986;19:61–69.PubMedCrossRefGoogle Scholar
  3. 3.
    Brower RW, Noordergraaf A. Pressure-flow characteristics of collapsible tubes: A reconciliation of seemingly contradictory results. Ann Biomed Eng. 1973;1:333–355.PubMedCrossRefGoogle Scholar
  4. 4.
    Brower RW, Scholten C. Experimental evidence on the mechanism for the instability of flow in collapsible vessels. Med Biol Eng. 1975;13:839–845.PubMedCrossRefGoogle Scholar
  5. 5.
    Conrad WA. Pressure-flow relationships in collapsible tubes. IEEE Trans Biomed Eng. 1969;BME-16:284–295.CrossRefGoogle Scholar
  6. 6.
    Drzewiecki G, Field S. Bifurcations and chaos identified in a pressure pulse driven collapsible vessel. Ann Biomed Eng. 1995;23:S–94.Google Scholar
  7. 7.
    Drzewiecki GM, Krawciw N. Chaos in collapsible vessel flow. In: Gaumond RP, ed. Proceedings of the 16th Northeast Bioengineering Conference. Penn State University; IEEE Press; 1990:56–57.Google Scholar
  8. 8.
    Drzewiecki G, Melbin J, Noordergraaf A. The Korotkoff sound. Ann Biomed Eng. 1989;17:325–359.PubMedCrossRefGoogle Scholar
  9. 9.
    Field S. Nonlinear Dynamic Model of an Arterial Stenosis (Atherosclerosis) and Chaotic Pressure and Flow Dynamics Using a Flexible: Collapsible Vessel with an External Compliance Load. Rutgers University; New Brunswick, NJ; 1995. Dissertation.Google Scholar
  10. 10.
    Field S, Drzewiecki GM. Modeling of a compliant arterial stenosis and chaos in the arterial pressure and flow dynamics of a stenotic arterial segment, In: Proceedings 5th World Congress on Noninvasive Cardiovascular Dynamics. New Brunswick, NJ; 1993:11.Google Scholar
  11. 11.
    Field S, Drzewiecki GM. Modeling of a compliant arterial stenosis and its effects on arterial pressure and flow dynamics: Implications for chaos. In: Proceedings 19th IEEE Annual Northeast Bioengineering Conference. IEEE Press; 1993:23–24.Google Scholar
  12. 12.
    Field S, Drzewiecki G. Nonlinear dynamic behavior and driven chaos from in vitro and computer models of a collapsible vascular segment. In: Proceedings of the 16th Annual International Conference IEEE Engineering in Medicine and Biology Society. Baltimore. IEEE Press; 1994:1134–1135.CrossRefGoogle Scholar
  13. 13.
    Field S, Horton C, Drzewiecki G, Li JK-J. General pressure-area relationship for collapsible blood vessels and elastic tubing. In: Proceedings 13th Southeast Biomedical Engineering Conference University of Wash DC Press Conference. 1994:1011–1014.Google Scholar
  14. 14.
    Glass L, Mackey MC. From Clocks to Chaos: The Rhythms of Life. Princeton: Princeton University Press; 1988.Google Scholar
  15. 15.
    Kamm RD. Flow through collapsible tubes. In: Skalak R, Chien S, eds. Handbook of Bioengineering. New York: McGraw-Hill; 1987.Google Scholar
  16. 16.
    Kresch E, Noordergraaf A. A mathematical model for the pressure: Flow relationship in a segment of vein. IEEE Trans Biomed Eng. 1969;BME-16:296–307.CrossRefGoogle Scholar
  17. 17.
    Kresch E, Noordergraaf A. Cross-sectional shape of collapsible tubes. Biophys J. 1972;12:274.PubMedCrossRefGoogle Scholar
  18. 18.
    Moreno AH, Katz AI, Gold LD. An integrated approach to the study of the venous system with steps toward a detailed model of the dynamics of venous return to the right heart. IEEE Trans Biomed Eng. 1969;16:308.PubMedCrossRefGoogle Scholar
  19. 19.
    Moreno AH, Katz AI, Gold LD, Pedley RV. Mechanics of distension of dog veins and other very thin-walled tubular structures. Circ Res. 1970;27:1069–1079.PubMedCrossRefGoogle Scholar
  20. 20.
    Pedley TJ. Flow in collapsible tubes. In: The Fluid Mechanics of Large Blood Vessels. Cambridge University Press; 1980.Google Scholar
  21. 21.
    Schepers HE, van Beek J, Bassingthwaighte JB. Four methods to estimate the fractal dimension from self-affine signals. IEEE Eng Med Biol Magazine. Jun. 1992:57–64.Google Scholar
  22. 22.
    Shapiro AH. Steady flow in collapsible tubes. Trans ASME Biomech Eng. 1977;99:126–147.CrossRefGoogle Scholar
  23. 23.
    Stettier JC, Niederer P, Anliker M. Nonlinear mathematical models of the arterial system: Effects of bifurcations, wall viscoelasticity, stenoses, and counterpulsation on pressure and flow pulses. In: Skalak R, Chien S, eds. Handbook of Bioengineering. New York: McGraw-Hill; 1987:17.1–17.26.Google Scholar
  24. 24.
    Westerhof N, Bosnian F, De Vries CJ, Noordergraaf A. Analog studies of the human systemic arterial tree. J.Biomech. 1968;2:121–143.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Shawn Field
  • Gary M. Drzewiecki

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