Pressure Wave Propagation in Fluid-Filled Co-Axial Elastic Tubes Part 1: Basic Theory

[+] Author and Article Information
K. Berkouk, P. W. Carpenter, A. D. Lucey

Fluid Dynamics Research Center, University of Warwick, Coventry CV4 7AL, UK

J Biomech Eng 125(6), 852-856 (Jan 09, 2004) (5 pages) doi:10.1115/1.1634280 History: Received November 01, 2002; Revised May 19, 2003; Online January 09, 2004
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.


Williams,  B., 1976, “Cerebrospinal Fluid Pressure Changes in Response to Coughing,” Brain, 99, pp. 331–346.
Williams,  B., 1974, “A Demonstration Analogue for Ventricular and Intraspinal Dynamics (DAVID),” J. Neurol. Sci., 23, pp. 445–461.
Lockey,  P., Poots,  G., and Williams,  B., 1975, “Theoretical Aspects of the Attenuation of Pressure Pulses Within Cerebrospinal Fluid Pathways,” Med. Biol. Eng., 13, pp. 861–869.
Carpenter,  P. W., Berkouk,  K., and Lucey,  A. D., 1999, “A Theoretical Model of Pressure Propagation in the Human Spinal CSF System,” Eng. Mech.,6, pp. 213–228.
Loth,  F., Yardimci,  M. A., and Alperin,  N., 2001, “Hydrodynamic Modeling of Cerebrospinal Fluid Motion Within the Spinal Cavity,” J. Biomech. Eng., 123, pp. 71–79.
Agarwal,  G. C., Berman,  B. M., and Stark,  L., 1969, “A Lumped Parameter Model of the Cerebrospinal Fluid System,” IEEE Trans. Biomed. Eng., 16, pp. 45–53.
Marmarou,  A., Shulman,  K., and LaMorgese,  J., 1975, “Compartmental Analyses of Compliance and Outflow Resistance of the Cerebrospinal Fluid,” J. Neurosurg., 43, pp. 523–534.
Davson, H., 1967, Physiology of the Cerebrospinal Fluid, J. & A. Churchill, London.
Nicholson,  H. W., Heiser,  W. H., and Olsen,  J. H., 1967, “Wave-Propagation in Liquid-Filled Elastic Tubes,” Bull. Mech. Eng. Educ.,6, pp. 371–376.
Oates,  G. C., 1975, “Fluid Flow in Soft-Walled Tubes,” Med. Biol. Eng., 13, pp. 773–784.
Shapiro,  A. H., 1977, “Steady Flow in Collapsible Tubes,” ASME J. Biomech. Eng., 99, pp. 126–147.
Kamm,  R. D., and Shapiro,  A. H., 1979, “Unsteady Flow in a Collapsible Tube Subjected to External Pressure or Body Forces,” J. Fluid Mech., 95, pp. 1–78.
Lighthill, J., 1978, Waves in Fluids., Cambridge University Press.
Abbott, M. B., 1966, An Introduction to the Method of Characteristics, American Elsevier, New York.
Griffiths,  D. J., 1971, “Hydrodynamics of Male Micturition: I—Theory of Steady Flow Through Elastic-Walled Tubes,” Med. Biol. Eng., 9, pp. 581–588.
Griffiths,  D. J., 1975, “Negative-Resistance Effects in Flow Through Collapsible Tubes: 1 Relaxation Oscillations,” Med. Biol. Eng., 13, pp. 785–790.
Elliott,  E. A., and Dawson,  S. V., 1979, “Fluid Velocity Greater Than Wavespeed and the Transition From Supercritical to Subcritical Flow in Elastic Tubes,” Med. Biol. Eng., 17, pp. 192–198.
Pedley, T. J., 1980, The Fluid Mechanics of Large Blood Vessels, Cambridge University Press.
Kececioglu,  I., McClurken,  M. E., Kamm,  R. D., and Shapiro,  A. H., 1981, “Steady Supercritical Flow in Collapsible Tubes. Part 1. Experimental Observations,” J. Fluid Mech., 109, pp. 367–389.
McClurken,  M. E., Kececioglu,  I., Kamm,  R. D., and Shapiro,  A. H., 1981, “Steady Supercritical Flow in Collapsible Tubes. Part 2. Theoretical Studies,” J. Fluid Mech., 109, pp. 391–415.
Cowley,  S. J., 1982, “Elastic Jumps on Fluid-Filled Elastic Tubes,” J. Fluid Mech., 11, pp. 459–473.
Cowley,  S. J., 1983, “On the Wavetrains Associated With Elastic Jumps on Fluid-Filled Elastic Tubes,” Q. J. Mech. Appl. Math., 36, pp. 289–312.
Berkouk, K., 1999, “Theoretical and Physical Models of Pressure Pulse Propagation in the Spinal System,” Ph.D. thesis, University of Warwick, U.K.


Grahic Jump Location
The variation of dimensionless wave speed with area ratio. Note that the wave speed doubles in value when the area ratio changes from αx to αy, thereby illustrating the sensitivity of wave speed to relatively small displacements of the flexible tube wall.
Grahic Jump Location
A schematic sketch showing the control volume for deriving the relationships between conditions before and after an elastic jump propagating along the co-axial flexible tube system.
Grahic Jump Location
A schematic sketch of the theoretical model based on co-axial flexible tubes: (a) end view; (b) side view. When applied to the intraspinal CSF system, the space A between the outer rigid and the inner flexible one represents the spinal subarachnoid space, the space B within the inner tube represents the central canal (or alternatively the spinal-cord tissue), and the flexible tube represents the spinal cord (or alternatively the pia mater). The alternative interpretations of space B and the flexible tube are discussed in Part 2 of the present paper.
Grahic Jump Location
A schematic illustration showing the propagation of a pressure pulse along the co-axial flexible tube system: (a) a wave diagram showing that the leading edge of the pulse steepens with time to form an elastic jump; (b) the initial form of the tube-wall displacement at time t=0; (c) the form of the tube-wall displacement at time t=t1.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In