Wave propagation with different pressure signals: An experimental study on the latex tube

  • M. Ursino
  • E. Artioli
  • M. Gallerani


To have deeper insight into the main factors affecting wave propagation in real hydraulic lines, we measured the true propagation coefficient in two latex rubber tubes via the three-point pressure method. The measurements were performed using both sinusoidal pressure signals of different amplitudes and periodic square waves as well as aperiodic pressure impulses. The results obtained were then compared with those predicted by a classic linear model valuable for a purely elastic maximally tethered tube. Our measurements demonstrate that the three-point pressure method may introduce significant errors at low frequencies (below 1 Hz in the present experiments) when the distance between two consecutive transducers becomes much lower than the wavelength. The pattern of phase velocity in the range 2–20 Hz turns out to be about 10 per cent higher than the theoretical one computed using the static value of the Young modulus. This result supports the idea that the dynamic Young modulus of the material is slightly higher than that measured in static conditions. The experimental attenuation, per wavelength is significantly higher than the theoretical one over most of the frequencies examined, and settles at a constant value as frequency increases. Introduction of wall viscoelasticity in the theoretical model can explain only a portion of the observed high frequency damping and wave attenuation. Finally, increasing the amplitude of pressure changes significantly affects the measured value of the propagation coefficient, especially at those frequencies for which direct and reflected waves sum together in a positive fashion. In these conditions we observed a moderate increase in phase velocity and a much more evident increase in attenuation per wavelength.


Latex rubber tubes Pressure damping Viscoelasticity Wave propagation 


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  1. Belardinelli, E., Di Giammarco, P. andUrsino, M. (1989) An empirical linear artery model and its matching to experimental results.Automedica,12, 91–116.Google Scholar
  2. Belardinelli, E., Ursino, M., Fabbri, G., Cevese, A. andSchena, F. (1991) Pressure changes induced by whole body acceleration shocks.J. Biomech. Eng.,113, 27–29.Google Scholar
  3. Belardinelli, E., Ursino, M. andFabbri, G. (1991) A linear propagation model adapted to the study of fast perturbations in arterial hemodynamics.Comp. Biol. & Med.,21, 97–110.CrossRefGoogle Scholar
  4. Bergel, D. H. (1961) The dynamic elastic properties of the arterial wall.J. Physiol.,156, 458–469.Google Scholar
  5. Busse, R., Bauer, D. R., Schabert, A., Summa, Y. andWeterer, E. (1979) An improved method for the determination of pulse transmission characteristics of arteries in vivo.Circ. Res.,44, 630–636.Google Scholar
  6. Gerrard, S. H. (1985) An experimental of the theory of waves in fluid-filled deformable tubes.J. Fluid Mech.,156, 321–347.CrossRefGoogle Scholar
  7. Greenwald, S. E., Newman, D. L. andMoodie, T. B. (1985) Impulse propagation in rubber-tube analogues of arterial stenoses and aneurysms.Med. & Biol. Eng. & Comput.,23, 150–154.Google Scholar
  8. Horsten, J. B. A. M., Van Steenhoven, A. A. andVan Dongen, M. E. H. (1989) Linear propagation of pulsatile waves in viscoelastic tubes.J. Biomech.,22, 477–484.CrossRefGoogle Scholar
  9. Jager, G. N. et al. (1965) Oscillatory flow impedance in electrical analog of arterial system: representation of sleeve effect and non-Newtonian properties of blood.Circ. Res.,16, 121–133.Google Scholar
  10. Klip, W. (1962)Velocity and damping of the pulse wave. M. Nijhoff, The Hague.Google Scholar
  11. Klip, W. et al. (1967) Formulas for phase velocity and damping of longitudinal waves in thick-walled viscoelastic tubes.J. Appl. Phys.,38, 3745.CrossRefGoogle Scholar
  12. Learoyd, B. M. andTaylor, M. G. (1966) Alterations with age in the viscoelastic properties of human arterial walls.Circ. Res. 18, 278–292.Google Scholar
  13. Li, J. K.-J., Melbin, J., Campbell, K. andNoordergraaf, A. (1980) Evaluation of a three point pressure method for the determination of arterial transmission characteristics.J. Biomech.,13, 1023–1029.CrossRefGoogle Scholar
  14. Li, J. K.-J., Melbin, J., Riffle, R. andNoordergraaf, A. (1981) Pulse wave propagation.Circ. Res.,49, 442–452.Google Scholar
  15. McDonald, D. andGessner, U. (1968) Wave attenuation in viscoelastic arteries. InHemorehology.Copely, A. L. (Ed.), Pergamon, New York, 113–125.Google Scholar
  16. McDonald, D. A. (1974)Blood flow in arteries. Edward Arnold, London.Google Scholar
  17. Melbin, J. andNoordergraaf, A. (1983) Pressure gradient related to energy conversion in the aorta.Circ. Res.,52, (2), 143–150.Google Scholar
  18. Milnor, W. R. andNichols, W. W. (1975) A new method of measuring propagation coefficients and characteristic impedance in blood vessels.Circ. Res.,36, 631–639.Google Scholar
  19. Milnor, W. R. andBertram, C. D. (1978) The relation between arterial viscoelasticity and wave propagation in the canine femoral artery in vivo.Circ. Res.,6, 870–879.Google Scholar
  20. Milnor, W. R. (1982)Hemodynamics. Williams & Wilkins, Baltimore, Maryland.Google Scholar
  21. Reuderink, P. J., Sipkema, P. andWesterhof, N. (1988) Influence of geometric taper on the derivation of the true propagation coefficient using the three-point method.J. Biomech.,21, 141–153.CrossRefGoogle Scholar
  22. Reuderink, P. J., Hoogstraten, H. W., Sipkema, P., Hillen, B. andWesterhof, N. (1989) Linear and nonlinear one-dimensional models of pulse wave transmission at high Womersley numbers. —Ibid.,22, 819–827.CrossRefGoogle Scholar
  23. Taylor, M. G. (1959) An experimental determination of the propagation of fluid oscillations in a tube with a visco-elastic wall; together with an analysis of the characteristics required in an electrical analogue.Phys. in Med. & Biol.,4, 63–82CrossRefGoogle Scholar
  24. Ursino, M. andGallerani, M. (1985) Experimental investigation on viscoelasticity.Rass. Bioing.,10, 31–44.Google Scholar
  25. Ursino, M. andGallerani, M. (1986) Study of the relation between viscoelasticity and wave attenuation in the latex rubber tube. —Ibid.,11, 23–32.Google Scholar
  26. Wetterer, E. et al. (1978) New ways of determining the propagation coefficient and the viscoelastic behavior of arteries in situ. InThe arterial system.Bauer, R. D. andBusse, R. (Eds.), Springer-Verlag, Berlin, 35–47.Google Scholar
  27. Womersley, J. R. (1957) An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteries. Wright Air Development Center Technical Report WADC-TR, 56–614.Google Scholar

Copyright information

© IFMBE 1993

Authors and Affiliations

  • M. Ursino
    • 1
  • E. Artioli
    • 1
  • M. Gallerani
    • 1
  1. 1.Department of ElectronicsComputer Science and SystemsBolognaItaly

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