Modeling of the Deformation of Flexible Tubes Using a Single Law: Application to Veins of the Lower Limb in Man

[+] Author and Article Information
S. Bassez

Centre de Recherche INNOTHERA, 10 av. Paul Vaillant Couturier, 94111 Arcueil, France

P. Flaud

LBHP URA 343 CNRS Case 7056, Université Paris VII, 2 Place Jussieu, 75005 Paris, France

M. Chauveau

Service d’exploration fonctionnelle, Ho⁁pital Cochin 27, Rue du faubourg Saint-Jacques, 75014 Paris, France

J Biomech Eng 123(1), 58-65 (Oct 16, 2000) (8 pages) doi:10.1115/1.1336143 History: Received April 16, 1998; Revised October 16, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.


Sigel,  B., Edelstein,  A. L., and Savitch,  L., 1975, “Type of Compression for Reducing Venous Stasis. A Study of Lower Extremities During Inactive Recumbency,” Arch. Surg., 110, pp. 171–176
Zicot,  M., Parker,  K. H., and Caro,  C. G., 1977, “Effects of Positive External Pressure on Calf Volume and Local Venous Haemodynamics,” Phys. Med. Biol., 22, No. 6, pp. 1146–1159.
Arcelus,  J. I., Caprini,  J. A., Traverso,  C. I., Size,  G., and Hasty,  J. H., 1993., “The Role of Elastic Compression Stockings in Prevention of Venous Dilatation Induced by Reverse Trendelenburg Position,” Phlebologie, 8, pp. 111–115.
Caro, C. G., and Pedley, T. J., “The Mechanics of the Circulation,” in: SolidMechanics and the Properties of Blood Vessel Walls, Oxford University Press, Oxford–New York–Toronto, Chap. 7, pp. 86–105.
Moreno,  A. H., Katz,  A. I., Gold,  L. D., and Reddy,  R. V., 1970, “Mechanics of Dog Veins and Other Very Thin-Walled Tubular Structures,” Circ. Res., 27, pp. 1069–1080.
Fung, Y. C., 1984, “The Veins,” in: Biodynamics: Circulation, Chap. 4, Springer-Verlag, New York–Berlin–Heidelberg–Tokyo.
Carton,  T. W., Dainauskas,  J., and Clark,  J. W., 1962, “Elastic Properties of Single Elastin Fibers,” J. Appl. Physiol., 17, p. 547.
Benedict,  J. V., Walker,  L. B., and Harris,  E. H., 1968, “Stress–Strain Characteristics of Unembalmed Human Tendon,” J. Biomech., 1, p. 53.
Attinger,  E. O., 1969, “Wall Properties of Veins,” IEEE Trans. Biomed. Eng., 16, No. 4, pp. 253–261.
Gow, B. S., 1972, “The Influence of Vascular Smooth Muscle on the Viscoelastic Properties of Blood Vessels,” in: Bergel. Cardiovascular Fluid Dynamics, Academic Press., pp. 65–110.
Kamm,  R. D., 1982, “Bioengineering Studies of Periodic External Compression as Prophylaxis Against Deep Venous Thrombosis—Part I: Numerical Studies,” ASME J. Biomech. Eng., 104, pp. 87–99.
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.
Bonis,  M., Ribreau,  C., and Verchery,  G., 1981, “Etude Expérimentale et Théorique de l’Aplatissement d’un Tube Élastique en Dépression,” J. Mécan. App., 52, pp. 123–144.
Bertram,  C. D., 1987, “The Effects of Wall Thickness, Axial Strain and End Proximity on the Pressure–Area Relation of Collapsible Tubes,” J. Biomech., 20, No. 9, pp. 863–876.
Palermo,  T., and Flaud,  P., 1987, “Etude de l’Effondrement à Deux et Trois Lobes de Tubes Élastiques,” J. Biophys. Bioméc., 11, No. 3, pp. 105–111.
Nahmias, J., 2000, “Pertes de Charge Dans les Tuyaux Collabables,” Thèse de Troisième Cycle, Université Paris VI.
McClurken, M. E., 1978, “Shape Independent Area Measurements in Collapsible Tubes by an Electrical Impedance Technique,” Proc. 31st Ann. Conf. Eng. Medicine & Biology, Atlanta, GA, p. 95.
Elad,  D., Sahar,  M., Avidor,  J. M., and Einav,  S., 1992, “Steady Flow Through Collapsible Tubes: Measurements of Flow and Geometry,” ASME J. Biomech. Eng., 114, No. 1, p. 84.
Thiriet,  M., Delpuech,  C., Piroird,  J., and Magnin,  I., 1987, “Banc de Mesure Optique de la Déformation de Conduites Souples,” Innov. Tech. Biol. Méd., 8, pp. 99–107.
Bertram,  C. D., and Ribreau,  C., 1989, “Cross-Sectional Area Measurements in Collapsed Tubes Using the Transformer Principle,” Med. Biol. Eng. Comput., 27, pp. 357–364.
Taylor,  L. A., and Gerrard,  J. H., 1977, “Pressure Radius Relationships for Elastic Tubes and Their Application to Arteries. Part I and II,” Med. Biol. Eng. Comput., 15, pp. 11–21.
Olsen,  J. H., and Shapiro,  A. H., 1967, “Large Waves in Fluid Filled Elastic Tubes,” J. Fluid Mech., 20, pp. 513–538.
Kresh,  E., 1977, “Cross-Sectional Shape of Flexible Tubes,” Bull. Math. Biol., 39, p. 679.
Kresh,  E., 1979, “Compliance of Flexible Tubes,” J. Biomech., 12, pp. 825–839.
Flaherty,  J. E., Keller,  J. B., and Rubinow,  S., 1972, “Post Buckling Behavior of Elastic Tubes and Rings With Opposite Sides in Contact,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 23, No. 4, pp. 446–455.
Ribreau,  C., Naili,  S., Bonis,  M., and Langlet,  A., 1993, “Collapse of Thin-Walled Elliptical Tubes for High Values of Major to Minor Axis Ratio,” ASME J. Biomech. Eng., 115, No. 4(B), p. 432.
Shapiro,  A. H., 1977, “Steady Flow in Collapsible Tubes,” ASME J. Biomech. Eng., 99, p. 126.
Shapiro, A. H., 1977, “Physiologic and Medical Aspects of Flow in Collapsible Tubes,” Proc. Sixth Canadian Congress of Applied Mechanics, Vancouver, May 29–June 3, pp. 883–906.
Gauer, O. H., and Thron, H. L., 1965, “Postural Changes in the Circulation,” in: Handbook of Physiology: Circulation, American Physiological Society, Washington, DC, Sect. 2, Vol. 3, pp. 2409–2439.


Grahic Jump Location
Comparison of pressure–area relation of a latex tube with the one of an excised segment of a canine vena cava 5
Grahic Jump Location
Experimental set-up used for determining the tube law
Grahic Jump Location
Details and dimensions of the in vitro model of surrounded vein
Grahic Jump Location
Pressure/area relationship of tube No. 1 versus the gel surface/tube axis thickness e
Grahic Jump Location
(a) In vivo pressure/average area relationship for the saphenous, popliteal, and deep calf veins in man with ultrasonic images of popliteal and deep calf veins cross section at 30, 0, and −30 cmH2O; (b) cross-sectional area of the popliteal vein, in six subjects (▵ ▴ ○ • ⋄ ♦), versus the estimated Pi−e pressure and some results of data fit with the model (–); (c) cross-sectional area of the deep calf veins, in seven (▴ □ ♦ + −  *  •) subjects, versus the estimated Pi−e pressure and some results of data fit with the model (–).
Grahic Jump Location
Comparison between experimental tube law of tube No. 1 without (+) or with (▵ ○  * ) surrounding gel (symbols), and the model (solid lines)
Grahic Jump Location
Experimental setup used for in vivo measurements of venous cross sectional area versus the posture
Grahic Jump Location
Pressure/area relationship of silastic tubes with different diameters: ‘+’ 20 mm, ‘O’ 5 mm
Grahic Jump Location
(a) Pressure/area relationships of tube No. 2 for various initial pre-stresses conditions; (b) normalized pressure/area relationship taking into account the longitudinal extension
Grahic Jump Location
Pressure/area relationship of tube No. 1 versus the gel elasticity E




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