{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T04:14:51Z","timestamp":1790223291352,"version":"4.1.0"},"reference-count":23,"publisher":"ASME International","issue":"6","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2003,12,1]]},"abstract":"<jats:p>Our work is motivated by ideas about the pathogenesis of syringomyelia. This is a serious disease characterized by the appearance of longitudinal cavities within the spinal cord. Its causes are unknown, but pressure propagation is probably implicated. We have developed an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. This is intended as a simple model of the intraspinal cerebrospinal-fluid system. Our approach is based on the classic theory for the propagation of longitudinal waves in single, fluid-filled, elastic tubes. We show that for small-amplitude waves the governing equations reduce to the classic wave equation. The wave speed is found to be a strong function of the ratio of the tubes\u2019 cross-sectional areas. It is found that the leading edge of a transmural pressure pulse tends to generate compressive waves with converging wave fronts. Consequently, the leading edge of the presure pulse steepens to form a shock-like elastic jump. A weakly nonlinear theory is developed for such an elastic jump.<\/jats:p>","DOI":"10.1115\/1.1634280","type":"journal-article","created":{"date-parts":[[2004,1,9]],"date-time":"2004-01-09T23:10:42Z","timestamp":1073689842000},"page":"852-856","update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":34,"title":["Pressure Wave Propagation in Fluid-Filled Co-Axial Elastic Tubes Part 1: Basic Theory"],"prefix":"10.1115","volume":"125","author":[{"given":"K.","family":"Berkouk","sequence":"first","affiliation":[{"name":"Fluid Dynamics Research Center, University of Warwick, Coventry CV4 7AL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P. W.","family":"Carpenter","sequence":"additional","affiliation":[{"name":"Fluid Dynamics Research Center, University of Warwick, Coventry CV4 7AL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. D.","family":"Lucey","sequence":"additional","affiliation":[{"name":"Fluid Dynamics Research Center, University of Warwick, Coventry CV4 7AL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"33","published-online":{"date-parts":[[2004,1,9]]},"reference":[{"key":"2019100521502375900_r1","doi-asserted-by":"crossref","unstructured":"Williams, B.\n          , 1976, \u201cCerebrospinal Fluid Pressure Changes in Response to Coughing,\u201d Brain, 99, pp. 331\u2013346.","DOI":"10.1093\/brain\/99.2.331"},{"key":"2019100521502375900_r2","doi-asserted-by":"crossref","unstructured":"Williams, B.\n          , 1974, \u201cA Demonstration Analogue for Ventricular and Intraspinal Dynamics (DAVID),\u201d J. Neurol. Sci., 23, pp. 445\u2013461.","DOI":"10.1016\/0022-510X(74)90161-0"},{"key":"2019100521502375900_r3","doi-asserted-by":"crossref","unstructured":"Lockey, P., Poots, G., and Williams, B., 1975, \u201cTheoretical Aspects of the Attenuation of Pressure Pulses Within Cerebrospinal Fluid Pathways,\u201d Med. Biol. Eng., 13, pp. 861\u2013869.","DOI":"10.1007\/BF02478090"},{"key":"2019100521502375900_r4","unstructured":"Carpenter, P. W., Berkouk, K., and Lucey, A. D., 1999, \u201cA Theoretical Model of Pressure Propagation in the Human Spinal CSF System,\u201d Eng. Mech., 6, pp. 213\u2013228."},{"key":"2019100521502375900_r5","doi-asserted-by":"crossref","unstructured":"Loth, F., Yardimci, M. A., and Alperin, N., 2001, \u201cHydrodynamic Modeling of Cerebrospinal Fluid Motion Within the Spinal Cavity,\u201d J. Biomech. Eng., 123, pp. 71\u201379.","DOI":"10.1115\/1.1336144"},{"key":"2019100521502375900_r6","doi-asserted-by":"crossref","unstructured":"Agarwal, G. C., Berman, B. M., and Stark, L., 1969, \u201cA Lumped Parameter Model of the Cerebrospinal Fluid System,\u201d IEEE Trans. Biomed. Eng., 16, pp. 45\u201353.","DOI":"10.1109\/TBME.1969.4502602"},{"key":"2019100521502375900_r7","doi-asserted-by":"crossref","unstructured":"Marmarou, A., Shulman, K., and LaMorgese, J., 1975, \u201cCompartmental Analyses of Compliance and Outflow Resistance of the Cerebrospinal Fluid,\u201d J. Neurosurg., 43, pp. 523\u2013534.","DOI":"10.3171\/jns.1975.43.5.0523"},{"key":"2019100521502375900_r8","unstructured":"Davson, H., 1967, Physiology of the Cerebrospinal Fluid, J. & A. Churchill, London."},{"key":"2019100521502375900_r9","unstructured":"Nicholson, H. W., Heiser, W. H., and Olsen, J. H., 1967, \u201cWave-Propagation in Liquid-Filled Elastic Tubes,\u201d Bull. Mech. Eng. Educ., 6, pp. 371\u2013376."},{"key":"2019100521502375900_r10","doi-asserted-by":"crossref","unstructured":"Oates, G. C.\n          , 1975, \u201cFluid Flow in Soft-Walled Tubes,\u201d Med. Biol. Eng., 13, pp. 773\u2013784.","DOI":"10.1007\/BF02478077"},{"key":"2019100521502375900_r11","doi-asserted-by":"crossref","unstructured":"Shapiro, A. H.\n          , 1977, \u201cSteady Flow in Collapsible Tubes,\u201d ASME J. Biomech. Eng., 99, pp. 126\u2013147.","DOI":"10.1115\/1.3426281"},{"key":"2019100521502375900_r12","doi-asserted-by":"crossref","unstructured":"Kamm, R. D., and Shapiro, A. H., 1979, \u201cUnsteady Flow in a Collapsible Tube Subjected to External Pressure or Body Forces,\u201d J. Fluid Mech., 95, pp. 1\u201378.","DOI":"10.1017\/S0022112079001348"},{"key":"2019100521502375900_r13","unstructured":"Lighthill, J., 1978, Waves in Fluids., Cambridge University Press."},{"key":"2019100521502375900_r14","unstructured":"Abbott, M. B., 1966, An Introduction to the Method of Characteristics, American Elsevier, New York."},{"key":"2019100521502375900_r15","doi-asserted-by":"crossref","unstructured":"Griffiths, D. J.\n          , 1971, \u201cHydrodynamics of Male Micturition: I\u2014Theory of Steady Flow Through Elastic-Walled Tubes,\u201d Med. Biol. Eng., 9, pp. 581\u2013588.","DOI":"10.1007\/BF02474637"},{"key":"2019100521502375900_r16","doi-asserted-by":"crossref","unstructured":"Griffiths, D. J.\n          , 1975, \u201cNegative-Resistance Effects in Flow Through Collapsible Tubes: 1 Relaxation Oscillations,\u201d Med. Biol. Eng., 13, pp. 785\u2013790.","DOI":"10.1007\/BF02478079"},{"key":"2019100521502375900_r17","doi-asserted-by":"crossref","unstructured":"Elliott, E. A., and Dawson, S. V., 1979, \u201cFluid Velocity Greater Than Wavespeed and the Transition From Supercritical to Subcritical Flow in Elastic Tubes,\u201d Med. Biol. Eng., 17, pp. 192\u2013198.","DOI":"10.1007\/BF02440928"},{"key":"2019100521502375900_r18","doi-asserted-by":"crossref","unstructured":"Pedley, T. J., 1980, The Fluid Mechanics of Large Blood Vessels, Cambridge University Press.","DOI":"10.1017\/CBO9780511896996"},{"key":"2019100521502375900_r19","doi-asserted-by":"crossref","unstructured":"Kececioglu, I., McClurken, M. E., Kamm, R. D., and Shapiro, A. H., 1981, \u201cSteady Supercritical Flow in Collapsible Tubes. Part 1. Experimental Observations,\u201d J. Fluid Mech., 109, pp. 367\u2013389.","DOI":"10.1017\/S0022112081001122"},{"key":"2019100521502375900_r20","doi-asserted-by":"crossref","unstructured":"McClurken, M. E., Kececioglu, I., Kamm, R. D., and Shapiro, A. H., 1981, \u201cSteady Supercritical Flow in Collapsible Tubes. Part 2. Theoretical Studies,\u201d J. Fluid Mech., 109, pp. 391\u2013415.","DOI":"10.1017\/S0022112081001134"},{"key":"2019100521502375900_r21","doi-asserted-by":"crossref","unstructured":"Cowley, S. J.\n          , 1982, \u201cElastic Jumps on Fluid-Filled Elastic Tubes,\u201d J. Fluid Mech., 11, pp. 459\u2013473.","DOI":"10.1017\/S002211208200055X"},{"key":"2019100521502375900_r22","doi-asserted-by":"crossref","unstructured":"Cowley, S. J.\n          , 1983, \u201cOn the Wavetrains Associated With Elastic Jumps on Fluid-Filled Elastic Tubes,\u201d Q. J. Mech. Appl. Math., 36, pp. 289\u2013312.","DOI":"10.1093\/qjmam\/36.3.289-a"},{"key":"2019100521502375900_r23","unstructured":"Berkouk, K., 1999, \u201cTheoretical and Physical Models of Pressure Pulse Propagation in the Spinal System,\u201d Ph.D. thesis, University of Warwick, U.K."}],"container-title":["Journal of Biomechanical Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/biomechanical\/article-pdf\/125\/6\/852\/5537703\/852_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/biomechanical\/article-pdf\/125\/6\/852\/5537703\/852_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,6]],"date-time":"2019-10-06T01:50:32Z","timestamp":1570326632000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/biomechanical\/article\/125\/6\/852\/459604\/Pressure-Wave-Propagation-in-FluidFilled-CoAxial"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12,1]]},"references-count":23,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2003,12,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.1634280","relation":{},"ISSN":["0148-0731","1528-8951"],"issn-type":[{"value":"0148-0731","type":"print"},{"value":"1528-8951","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,12,1]]}}}