Maximal Wall Shear Stress in Arterial Stenoses: Application to the Internal Carotid Arteries

[+] Author and Article Information
Sylvie Lorthois

Institut de Mécanique des Fluides de Toulouse, UMR CNRS 5502, 31400 Toulouse Cedex, France

Pierre-Yves Lagrée

Laboratoire de Modélisation en Mécanique, UMR CNRS 7607, 75252 Paris Cedex 5, France

Jean-Pierre Marc-Vergnes, Francis Cassot

I.N.S.E.R.M. U 455, C.H.U. Purpan, 31059 Toulouse Cedex, France

J Biomech Eng 122(6), 661-666 (Aug 10, 2000) (6 pages) doi:10.1115/1.1318907 History: Received July 02, 1999; Revised August 10, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Mohr,  J. P., Caplan,  L. R., Melski,  J. W., Goldstein,  R. J., Duncan,  G. W., Kistler,  J. P., Pessin,  M. S., and Bleich,  H. L., 1978, “The Harvard Cooperative Stroke Registry: A Prospective Registry,” Neurology, 28, pp. 754–762.
Bogousslavski,  J., Van Melle,  G., and Regli,  F., 1988, “The Lausanne Stroke Registry: Analysis of 1000 Consecutive Patients With First Stroke,” Stroke, 19, pp. 1083–1092.
NASCET, 1991, “North American Symptomatic Carotid Endarterectomy Trial Collaborators. Beneficial Effect of Carotid Endarterectomy in Symptomatic Patients With High Grade Stenosis,” N. Engl. J. Med., 325, pp. 445–453.
ECST, 1991, “European Carotid Surgery Trialists’ Collaborative Group: MRC European Surgery Trial: Interim Results for Symptomatic Patients With Severe (70–99 Percent) or With Mild (0–29 Percent) Carotid Stenoses,” Lancet, 337, pp. 1235–1243.
Schomer,  D. F., Marks,  M. P., Steinberg,  G. K., Johnstone,  I. M., Boothroyd,  D. B., Ross,  M. R., Pelc,  N. J., and Enzmann,  D. R., 1994, “The Anatomy of the Posterior Communicating Artery as a Risk Factor for Ischemic Cerebral Infarction,” N. Engl. J. Med., 330, pp. 1565–1570.
Ringelstein,  E. B., Weiller,  C., Weckesser,  M., and Weckesser,  S., 1994, “Cerebral Vasomotor Reactivity Is Significantly Reduced in Low-Flow as Compared to Thromboembolic Infarctions: The Role of the Circle of Willis,” J. Neurol. Sci., 121, pp. 103–109.
Sitzer,  M., Müller,  W., Siebler,  M., Hort,  W., Kniemeyer,  H. W., Jäncke,  L., and Steinmetz,  H., 1995, “Plaque Ulceration and Lumen Thrombus Are the Main Sources of Cerebral Microemboli in High-Grade Internal Carotid Artery Stenosis,” Stroke, 26, pp. 1231–1233.
Sakariassen,  K. S., and Barstad,  R. M., 1993, “Mechanisms of Thromboembolism at Arterial Plaques,” Blood Coagul Fibrinolysis, 4, pp. 615–625.
Cassot,  F., Vergeur,  V., Bossuet,  P., Hillen,  B., Zagzoule,  M., and Marc-Vergnes,  J. P., 1995, “Effects of Anterior Communicating Artery Diameter on Cerebral Hemodynamics in Internal Carotid Artery Disease: A Model Study,” Circulation, 92, pp. 3122–3131.
Ku,  D., Giddens,  P., Zarins,  C., and Glagov,  S., 1985, “Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation: Positive Correlation Between Plaque Location and Low and Oscillating Shear Stress,” Arteriosclerosis Dallas, 5, pp. 293–302.
Bluestein,  D., Niu,  L., Schoephoerster,  R. T., and Dewanjee,  M. K., 1997, “Fluid Mechanics of Arterial Stenoses: Relationship to the Development of Mural Thrombus,” Ann. Biomed. Eng., 25, pp. 344–356.
Nerem,  R. M., 1992, “Vascular Fluid Mechanics, the Arterial Wall and Atherosclerosis,” ASME J. Biomech. Eng., 114, pp. 274–282.
Siegel,  J. M., Markou,  C. P., Ku,  D. N., and Hanson,  S. R., 1994, “A Scaling Law for Wall Shear Stress Through an Arterial Stenosis,” ASME J. Biomech. Eng., 116, pp. 446–451.
Huang,  H., Modi,  V. J., and Seymour,  B. R., 1995, “Fluid Mechanics of Stenosed Arteries,” Int. J. Eng. Sci., 33, pp. 815–828.
Back,  L. H., 1975, “Theoretical Investigation of Platelet Embolus Production in Atherosclerotic Coronary Arteries,” Math. Biosci., 25, pp. 273–307.
Back,  L. H., and Crawford,  D. W., 1992, “Wall Shear Stress Estimates in Coronary Artery Constrictions,” ASME J. Biomech. Eng., 114, pp. 515–520.
Le Balleur, J. C., 1978, “Couplage Visqueux Non-Visqueux: Méthode Numérique et Applications aux Écoulements Bidimensionnels Transsoniques et Supersoniques,” La Recherche Aérospatiale. 1978-2, pp. 67–76, Eng. Trans ESA TT-496.
Cousteix, J., 1988, Couche Limite Laminaire, Editions Cepadues, Toulouse.
Cebeci, T., and Cousteix, J., 1999, Modeling and Computation of Boundary-Layer Flows, Springer, Berlin.
Schlichting, H., 1979, Boundary-Layer Theory, 7th ed., McGraw-Hill, New York.
Gersten, K., and Hervig, H., 1992, Strömungsmechanik: Grundlagen der Impuls-, Wärme und Stoffübertragung aus Asymptotischer Sicht, Vieweg, Wiesbaden.
Zagzoule,  M., and Marc-Vergnes,  J. P., 1986, “A Global Mathematical Model of the Cerebral Circulation in Man,” J. Biomech., 19, pp. 1015–1021.
Zagzoule,  M., Khalid-Naciri,  J., and Mauss,  J., 1991, “Unsteady Wall Shear Stress in a Distensible Tube,” J. Biomech., 24, pp. 435–439.
Seeley,  B. D., and Young,  D. F., 1976, “Effect of Geometry on Pressure Losses Across Models of Arterial Stenoses,” J. Biomech., 9, pp. 439–448.
Young,  D. F., 1979, “Fluid Mechanics of Arterial Stenoses,” ASME J. Biomech. Eng., 101, pp. 157–179.
Young,  D. F., and Tsai,  F. Y., 1973, “Flow Characteristics in Models of Arterial Stenoses. I. Steady Flow,” J. Biomech., 6, pp. 395–410.
Kerber,  C., and Liepsch,  D., 1994, “Flow Dynamics for Radiologists. Basic Principles of Fluid Flow,” AJNR Am. J. Neuroradiol., 15, pp. 1065–1075.
Brookshier,  K., and Tarbell,  J., 1991, “Effect of Hematocrit on Wall Shear Rate in Oscillatory Flow: Do the Elastic Properties of Blood Play a Role?” Biorheology, 28, pp. 569–587.
Pedley,  T. J., 1972, “Two-Dimensional Boundary Layer in a Free Stream Which Oscillates Without Reversing,” J. Fluid Mech., 55, pp. 359–383.


Grahic Jump Location
Geometry and nondimensional parameters of stenosis
Grahic Jump Location
Diagram of the circle of Willis and its afferent and efferent arteries. (VA: vertebral, BA: basilar, ICaA, internal carotid, ACeA: anterior cerebral, MCeA: middle cerebral, PCeA: posterior cerebral, ACoA: anterior communicating, PCoA: posterior communicating arteries.)
Grahic Jump Location
Nondimensional displacement thickness in Mangler coordinates Δ1 (upper) and wall shear stress (lower) versus axial position in the convergence characterized by D=0.7 and L=6, for Re0=1000 and different values of Δ10(√2)/Re0 (corresponding to an initial displacement thickness δ10* between 0.01R0* and 0.33R0*)
Grahic Jump Location
Parameters a(L)0.5 and b as a function of radius reduction. Full circles: results derived from Siegel et al. 13; cross: mean of the results of regression analysis obtained for L between 3 and 12 at fixed D; line: interpolation of results averaged upon L.
Grahic Jump Location
Dimensional maximal wall shear stress (MWSS* ) and rate (MWSR* ) as a function of stenosis degree, for five arrangements of anterior and posterior communicating arteries diameters; ×: AcoA=0.4 mm/PCoA=0.4 mm; □: ACoA=0.4 mm/PCoA=1.6 mm; ○: ACoA=1.6 mm/PCoA=0.4 mm; ▵: ACoA=1.6 mm/PCoA=1 mm; +: ACoA=1.6 mm/PCoA=1.6 mm.
Grahic Jump Location
Dimensional maximal wall shear stress (MWSS* ) and rate (MWSR* ) in a 57.8 percent stenosis as a function of contralateral stenosis degree, for five arrangements of anterior and posterior communicating arteries diameters; same symbols as Fig. 5




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