Large amplitude wave propagation in arteries and veins

  • Y. Kivity
  • R. Collins
Problemes D'Ondes Waves Problems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11)


A numerical method has been described for the calculation of the unsteady flow of an incompressible viscous fluid in a distensible tapered tube possessing orthotropic viscoelastic properties. The formulation is quite general, including the fluid-wall interaction, the tube wall being characterized as a thin shell with negligible bending moments.

Illustrative solutions have been presented for the biomedical phenomena of a pulsed flow of blood in an excised segment of human aorta, subjected to both radial and longitudinal deformations. The complete solution includes the time variations of wall shape, stresses, strains and fluid velocity, computed in conjunction with a realistic dynamic constitutive model for the aortic wall.

The example presented possesses an impulsive inlet flow sufficient to produce "shock-like" signals along the vessel wall. These sharp wave fronts do not endanger the inherent stability of the numerical two-step Lax-Wendroff scheme, provided that the stability criteria are properly observed.


  1. Apter, J.T., Rabinowitz, Cummings, D.H. (1966): Correlation of Viscoelastic Properties of Large Arteries with Microscopic Structure, Circulation Res. 19: 104–21Google Scholar
  2. Collins, R., Hu, W.C.L. (1972): Dynamic Deformation Experiments on Aortic Tissue, J. Biomechanics 5, 333–337Google Scholar
  3. Kivity, Y., Collins, R. (1973): Nonlinear Wave Propagation in Viscoelastic Tubes, J. Biomechanics (in press) — Vol 6, no 6, Dec. 1973Google Scholar
  4. Krauss, H. (1967): Thin Elastic Shells, John Wiley, Chap. IIGoogle Scholar
  5. Ling, S.C., Atabek, H.B., Carmody, J.J. (1968): Pulsatile flows in Arteries in Applied Mechanics, Proceedings of the 12th Int'l Congress of Applied Mechanics, Stanford University Aug. 26–31, 1968, pp. 227–291, Springer-Verlag (1969)Google Scholar
  6. Patel, D.J., Fry, D.L. (1966): Longitudinal tethering of Arteries in Dogs. Circulation Res. 19: 1011–21PubMedGoogle Scholar
  7. Patel, D.J., Fry D.L. (1969): The Elastic Symmetry of Arterial Segments in Dogs, Circulation Res. 24: 1–8Google Scholar
  8. Reissner, E. (1949) On the theory of Thin Elastic Shells, in Reissner Anniversary Volume edited by Polytechnic Inst. of Brooklyn, J.W. Edwards Publisher, Ann Arbor, MichiganGoogle Scholar
  9. Schlichting, H. (1968): Boundary-Layer Theory, 6th edition (transl. by J. Kestin) Mc Graw-Hill, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Y. Kivity
  • R. Collins

There are no affiliations available

Personalised recommendations