Advertisement

NONLINEAR WAVES IN FLUID-FILLED ELASTIC TUBES: A MODEL TO LARGE ARTERIES

  • Hilmi Demiray
Conference paper
  • 1.3k Downloads
Part of the Springer Proceedings in Physics book series (SPPHY, volume 111)

Abstract

In the present work, by treating the arteries as a prestressed thin walled elastic tube of variable radius, and the blood as an incompressible inviscid fluid, we have studied the propagation of weakly nonlinear waves in such a medium through the use of long wave approximation and the reductive perturbation method. The KdV equation with variable coefficient is obtained as the evolution equation. By seeking a progressive wave type of solution to this equation, we observed that the wave speed decreases with increasing inner radius while it increases with decreasing inner radius of the tube. Such a result is to be expected from physical considerations.

Keywords

Solitary Wave Nonlinear Wave Wave Speed Solitary Wave Solution Physical Consideration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Demiray H. (1972) A not on the elasticity of soft biological tissues, J. Biomechanics 5 309–311.CrossRefGoogle Scholar
  2. Demiray H. (1976) Large deformation analysis of some basic problems in biophysics, Bull. Math. Biology 38 701–711.zbMATHGoogle Scholar
  3. Demiray H. (1996) Solitary waves in a prestressed elastic tube, Bull. Math. Biology 58 939–955.CrossRefzbMATHGoogle Scholar
  4. Demiray H., Antar N. (1997) Nonlinear waves in an inviscid fluid contained in a prestressed viscoelastic thin tube, Z. Angew. Math. Phys. 48 325–340.CrossRefMathSciNetzbMATHGoogle Scholar
  5. Demiray H. (2004) Modulation of nonlinear waves in a fluid-filled elastic tube with stenosis, Int. J. Mathematics and Mathematical Sciences 60 3205–3218.CrossRefMathSciNetGoogle Scholar
  6. Jeffrey A., Kawahara T. (1981) Asymptotic Methods in Nonlinear Wave Theory, Pitman, Boston.Google Scholar
  7. Johnson R. S. (1970) A nonlinear equation incorporating damping and dispersion, J. Fluid Mechanics 42 49–60.CrossRefADSzbMATHGoogle Scholar
  8. Hashizume Y. (1985) Nonlinear pressure waves in a fluid-filled elastic tube, J. Phys. Soc. Japan 54 3305–3312.CrossRefADSGoogle Scholar
  9. McDonald D. A. (1974) Blood Flow in Arteries, The Williams and Wilkins Co., Baltimore.Google Scholar
  10. Simon B. R., Kobayashi A. S., Stradness D. E., Wiederhielm C. A. (1972) Re-evaluation of arterial constitutive laws, Circulation Research 30 491–500.Google Scholar
  11. Yomosa S. (1987) Solitary waves in large blood vessels, J. Phys. Soc. Japan 56 506–520.CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Hilmi Demiray
    • 1
  1. 1.Department of Mathematics, Faculty of Arts and SciencesΙşık UniversityMaslak, İstanbulTurkey

Personalised recommendations