Advertisement

Mathematical model of an arterial stenosis, allowing for tethering

  • N. Padmanabhan
  • R. Devanathan
Article

Abstract

Closed-form solutions are presented for approximate equations governing the pulsatile flow of blood through models of mild axisymmetric arterial stenosis, taking into account the effect of arterial distensibility. Results indicate the existence of back-flow regions and the phenomenon of flow-reversal in the cross-sections. The effects of pulsatility of flow and elasticity of vessel wall for arterial blood flow through stenosed vessels are determined.

Keywords

Arterial stenosis Circulation Modelling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Back, L. D., Radbill, J. R., andCrawford, D. A. (1977) Analysis of pulsatile viscous blood flow through diseased coronary arteries of man.J. Biomech.,10, 339–353.CrossRefGoogle Scholar
  2. Clark, C. (1977) Turbulent wall pressure measurements in a model of aortic stenosis.J. Biomech.,10, 461–467.CrossRefGoogle Scholar
  3. Forrester, J. H. andYoung, D. F. (1970) Flow through a convergent divergent tube and its implications in occlusive vascular disease.J. Biomech.,3, 297–316.CrossRefGoogle Scholar
  4. Fry, D. L. (1960) Acute vascular endothelial changes associated with increased blood velocity gradients.Circ. Res.,22, 165–197.Google Scholar
  5. Fung, Y. C., Perrone, N. andAnliker, M. (1971)Biomechanics: its foundations and objectives. Prentice Hall Inc., NJ, USA.Google Scholar
  6. Lee, J. S. andFung, Y. C. (1970) Flow in locally constricted tube at low Reynolds numbers.Trans. ASME. J. Appl. Mech.,37, 9–16.MATHCrossRefGoogle Scholar
  7. Lightfoot, E. N. (1974)Transport phenomenon and cardiovascular systems. John Wiley and Sons, New York.Google Scholar
  8. Milnor, W. R. (1972) Pulmonary hemodynamics.InBergel, D. H. (Ed.)Cardiovascular fluid dynamics,2, Academic Press.Google Scholar
  9. Murphy, G. M. (1960)Ordinary differential equations and their solutions. Van Nostrand, New Jersey.MATHGoogle Scholar
  10. Padmanabhan, N. (1980) Mathematical model of arterial stenosis.Med. & Biol. Eng. & Comput.,18, 281–286.CrossRefGoogle Scholar
  11. Skalak, R. andStathis, T. (1966) A porous tapered elastic tube model of a vascular bed.Biomech. symp. ASME, New York, 68–81.Google Scholar
  12. Young, D. F. (1968) Effect of a time dependent stenosis on flow through a tube.Trans. ASME. J. Eng. Ind.,90, 248–254.Google Scholar
  13. Young, D. F. andTsai, F. Y. (1973) Flow characteristics in models of arterial stenosis, I, II.J. Biomech.,6, 395–410, 547–559.CrossRefGoogle Scholar

Copyright information

© International Federation for Medical & Biological Engineering 1981

Authors and Affiliations

  • N. Padmanabhan
    • 1
  • R. Devanathan
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations