Steady Flow and Wall Compression in Stenotic Arteries: A Three-Dimensional Thick-Wall Model With Fluid–Wall Interactions

[+] Author and Article Information
Dalin Tang, Chun Yang, Shunichi Kobayashi, David N. Ku

Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609

J Biomech Eng 123(6), 548-557 (Jul 23, 2001) (10 pages) doi:10.1115/1.1406036 History: Received February 06, 2000; Revised July 23, 2001
Copyright © 2001 by ASME
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Burke,  A. P., Farb,  A., Malcom,  G. T., Liang,  Y. H., Smialek,  J. E., and Virmani,  R., 1999, “Plaque Rupture and Sudden Death Related to Exertion in Men with Coronary Artery Disease,” J. Am. Med. Assoc., 281, No. 10, pp. 921–926.
Fuster,  V., Stein,  B., Ambrose,  J. A., Badimon,  L., Badimon,  J. J., and Chesebro,  J. H., 1990, “Atherosclerotic Plaque Rupture and Thrombosis,” Circulation, Supplement II, 82, No. 3, pp. II-47–II-59.
Ku,  D. N., Giddens,  D. P., Phillips,  D. J., and Strandness,  D. E., 1985, “Hemodynamics of the Normal Human Carotid Bifurcation: in Vitro and in Vivo Studies,” Ultrasound Med. Biol., 11, No 1, pp. 13–26.
Nerem,  R. M., 1992, “Vascular Fluid Mechanics, the Arterial Wall, and Atherosclerosis,” ASME J. Biomech. Eng., 114, pp. 274–282.
Nerem,  R. M., 1993, “Hemodynamics and the Vascular Endothelium,” ASME J. Biomech. Eng., 115, pp. 510–514.
Friedman,  M. H., 1993, “Arteriosclerosis Research Using Vascular Flow Models: From 2-D Branches to Compliant Replicas,” ASME J. Biomech. Eng., 115, 595–601.
Giddens,  D. P., Zarins,  C. K., and Glagov,  S., 1993, “The Role of Fluid Mechanics in the Localization and Detection of Atherosclerosis,” ASME J. Biomech. Eng., 115, pp. 588–594.
Ku,  D. N., 1997, “Blood Flow in Arteries,” Annu. Rev. Fluid Mech., 29, pp. 399–434.
Zand,  T., Majno,  G., Nunnari,  J. J., Hoffman,  A. H., Savilonis,  B. J., MacWilliams,  B., and Isabelle,  J., 1991, “Lipid Deposition and Intimal Stress and Strain,” Am. J. Pathol., 139, pp. 101–113.
Derafshi, Z., Pritchard, W. F., Sankar, L. N., and Giddens, D. P., 1993, “Computational Study of Fluid Dynamic Effects on Near-Wall Monocyte Behavior,” 1993 Bioengineering Conference Proc., ASME BED-Vol. 24 , p. 307.
Gonzales,  R. S., and Wick,  T. M., 1996, “Hemodynamic Modulation of Monocyte Cell Adherence to Vascular Endothelium,” Am. J. Pathol., 103, pp. 382–393.
Cao,  J., and Rittgers,  S. E., 1998, “Particle Motion Within in Vitro Models of Stenosel Internal Carotid and Left Anterior Descending Coronary Arteries,” Ann. Biomed. Eng., 26, No. 2, pp. 190–199.
Rittgers, S. E., Yu, Y. H., and Strony, J. T., 1998, “Thrombus Formation in Moderate Coronary Stenosis Using 2D-LDA,” Proc. Third World Congress of Biomechanics, p. 201.
Liu,  S. Q., Yen,  M., and Fung,  Y. C., 1994, “On Measuring the Third Dimension of Cultured Endothelial Cells in Shear Flow,” Proc. Natl. Acad. Sci. U.S.A., 91, pp. 8782–8786.
Wiesner,  T. F., Berk,  B. C., and Nerem,  R. M., 1997, “A Mathematical Model of the Cytosolic-Free Calcium Response in Endothelial Cells to Fluid Shear Stress,” Proc. Natl. Acad. Sci. U.S.A., 94, pp. 3726–3731.
Ziegler,  T., Alexander,  R. W., and Nerem,  R. M., 1995, “An Endothelial Cell-Smooth Muscle Cell Co-Culture Model for Use in the Investigation of Flow Effects on Vascular Biology,” Ann. Biomed. Eng., 23, pp. 216–225.
Fung, Y. C., 1993, Biomechanics, Mechanical Properties of Living Tissues, 2nd ed., Springer-Verlag, New York.
Fung, Y. C., 1997, Biodynamics, Circulation, 2nd ed., Springer-Verlag, New York.
Fung,  Y. C., Liu,  S. Q., and Zhou,  J. B., 1993, “Remodeling of the Constitutive Equation While a Tissue Remodels Itself Under Stress,” ASME J. Biomech. Eng., 115, No. 4B, pp. 453–459.
Liu,  S. Q., and Fung,  Y. C., 1996, “Indicial Functions of Arterial Remodeling in Response to Locally Altered Blood Pressure,” Am. J. Physiol., 270, pp. H1323–H1333.
Fry,  D. L., 1968, “Acute Vascular Endothelial Changes Associated With Increased Blood Velocity Gradients,” Circ. Res., 22, pp. 165–197.
Ramstack,  J. M., Zuckerman,  L., and Mockros,  L. F., 1979, “Shear Induced Activation of Platelets,” J. Biomech., 12, pp. 113–125.
Bathe,  M., and Kamm,  R. D., 1999, “A Fluid-Structure Interaction Finite Element Analysis of Pulsatile Blood Flow through a Compliant Stenotic Artery,” ASME J. Biomech. Eng., 121, pp. 361–369.
Tang,  D., Yang,  J., Yang,  C., and Ku,  D. N., 1999, “A Nonlinear Axisymmetric Model With Fluid-Wall Interactions for Viscous Flows in Stenotic Elastic Tubes,” ASME J. Biomech. Eng., 121, pp. 494–501.
Wootton,  D. M., and Ku,  D. N., 1999, “Fluid Mechanics of Vascular Systems, Diseases, and Thrombosis,” Annu. Rev. Biomed. Eng., 1, pp. 299–329.
Davies,  M. J., and Thomas,  A. C., 1985, “Plaque Fissuring—The Cause of Acute Myocardial Infarction, Sudden Ischemic Death, and Crecendo Angina,” Br. Heart J., 53, pp. 363–373.
Yamaguchi, T., Kobayashi, T., and Liu, H., 1998, “Fluid–Wall Interactions in the Collapse and Ablation of an Atheromatous Plaque in Coronary Arteries,” Proc. Third World Congress of Biomechanics, p. 20b.
Yamaguchi, T., Nakayama T., and Kobayashi, T., 1996, “Computations of the Wall Mechanical Response Under Unsteady Flows in Arterial Diseases,” 1996 Advances in Bioengineering, ASME BED-Vol. 33 , pp. 369–370.
Yamaguchi, T., Furuta, N., Nakayama, T., and Kobayashi, T., 1995, “Computations of the Fluid and Wall Mechanical Interactions in Arterial Diseases,” 1996 Advances in Bioengineering, ASME BED-Vol. 31 , pp. 197–198.
Tang,  D., Yang,  C., Huang,  Y., and Ku,  D. N., 1999, “Wall Stress and Strain Analysis Using a 3-D Thick-Wall Model With Fluid-Structure Interactions for Blood Flow in Carotid Arteries With Stenoses,” Comput. Struct., 72, pp. 341–356.
Tang,  D., Yang,  C., and Ku,  D. N., 1999, “A 3-D Thin-Wall Model With Flow-Structure Interactions for Blood Flow in Carotid Arteries With Symmetric and Asymmetric Stenoses,” Comput. Struct., 72, pp. 357–377.
Biz, S., 1993, “Flow in Collapsible Stenoses: An Experimental Study,” M.S. Thesis, Georgia Institute of Technology, Atlanta, GA.
Hayashi,  K., 1993, “Experimental Approaches on Measuring the Mechanical Properties and Constitutive Laws of Arterial Walls,” ASME J. Biomech. Eng., 115, pp. 481–488.
Kamm,  K. D., and Shapiro,  A. H., 1979, “Unsteady Flow in a Collapsible Tube Subjected to External Pressure or Body Force,” J. Fluid. Mech., 95, pp. 1–78.
Kleiber, M., 1998, Handbook of Computational Solid Mechanics, Springer-Verlag, New York.
Vaishnav,  R. N., and Vossoughi,  J., 1984, “Incremental Formulations in Vascular Mechanics,” ASME J. Biomech. Eng., 106, pp. 105–111.
Kobayashi, S., Biz, S., and Ku, D. N., 2001, “Flow and Compression in Collapsible Stenosis Models of Arterial Disease,” ASME J. Biomech. Eng., submitted.
Kobayashi, S., Tang, D., and Ku, D. N., 1998, “Pulsatile Flow Through a Stenotic Collapsible Tube,” Proc. 76th JSME Fall Annual Meeting, pp. 265–266.
Hughes,  T. J. R., Liu,  W. K., and Zimmermann,  X. X., 1981, “Lagrangian–Eulerian Finite Element Formulation for Incompressible Viscous Flows,” Comput. Methods Appl. Mech. Eng., 29, pp. 329–349.
Ramaswamy,  B., and Kawahara,  M., 1987, “Arbitrary Lagrangian–Eulerian Finite Element Method for Unsteady, Convective, Incompressible Viscous Free Surface Fluid Flow,” Int. J. Numer. Methods Fluids, 7, pp. 1053–1075.
Liszka,  T., and Orkisz,  J., 1980, “The Finite Difference Method at Arbitrary Irregular Grids and Its Application in Applied Mechanics,” Comput. Struct., 11, pp. 83–95.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Taylor & Francis Publishers, New York.
ADINA R & D, Inc., 1995, Theory and Modeling Guide, Watertown, MA.
ADINA R & D, Inc., 1999, ADINA System 7.3 Release Notes.
Bathe, K. J., 1996, Finite Element Procedures, Prentice-Hall, New Jersey.
Ferziger, J. H., and Perić, M., 1996, Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin.
Downing,  J. M., and Ku,  D. N., 1997, “Effects of Frictional Losses and Pulsatile Flow on the Collapse of Stenotic Arteries,” ASME J. Biomech. Eng., 119, pp. 317–324.


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Schematic diagram of the experimental setup
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Stenotic tube and the tube law measurements
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Young’s modulus calculated from three tube law measurements
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Nonuniform mesh used in computation
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Experimental results showing tube collapse under physiological pressure conditions
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Numerical simulation of tube collapse under physiological pressure conditions
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Contour plots of circumferential stress and strain distributions showing wall compression in the tube wall. pin=130 mmHg,pout=20 mmHg,S0=80 percent. (a) max strain at z=2 cm, min strain at z=4.1 cm; (b) max strain at z=2 cm, min strain at 4.8 cm; (c) max stress at z=3.5 cm, min stress at z=3.9 cm; (d) max stress at z=3.45 cm, min stress at z=4.0 cm, local min stress at z=4.8 cm.
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Pressure field: (a) contour map of the horizontal cross section; (b) transmural pressure at the tube wall
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Velocity profiles at different axial positions, horizontal cross section. Different scales are used at different z locations to show details.
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Shear stress distribution along θ=0 and 90 deg lines
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Comparison of numerical results with experimental data. pin=100 mmHg,pout=0–90 mmHg,S0=80 percent. (a) Flow rates; (b) true severities.
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Comparison of numerical pressure–area relationship (tube law) with experimental data. Calculations were conducted under no-flow condition with pin=pout=−50–100 mmHg,S0=80 percent.




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