Computational Analysis of Coupled Blood-Wall Arterial LDL Transport

[+] Author and Article Information
D. Kim Stangeby

Department of Mechanical Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario M55 3G8 Canada

C. Ross Ethier

Department of Mechanical Engineering and Institute of Biomaterials and Biomedical Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario M5S 3G8 Canadae-mail: ethier@mie.utoronto.ca

J Biomech Eng 124(1), 1-8 (Sep 17, 2001) (8 pages) doi:10.1115/1.1427041 History: Received December 15, 1999; Revised September 17, 2001
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Caro,  C. G., Fitz-Gerald,  J. M., and Schroter,  R. C., 1971, “Atheroma and Arterial Wall Shear. Observation, Correlation and Proposal of a Shear Dependent Mass Transfer Mechanism for Atherogenesis,” Proc. R. Soc. London, Ser. B, 177, pp. 109–159.
Hoff,  H. F., Heideman,  C. L., Jackson,  R. L., Bayardo,  R. J., Kim,  H. S., and Gotto,  A. M., 1975, “Localization Patterns of Plasma Apolipoproteins in Human Atherosclerotic Lesions,” Circ. Res., 37, pp. 72–79.
Hoff,  H. F., Titus,  J. L., Bajardo,  R. J., Jackson,  R. L., Gotto,  A. M., DeBakey,  M. E., and Lie,  J. T., 1975, “Lipoproteins in Atherosclerotic Lesions. Localization by Immunofluorescence of Apo-Low Density Lipoproteins in Human Atherosclerotic Arteries From Normal and Hyperlipoproteinemics,” Arch. Pathol., 99, pp. 253–258.
Andre,  P., Baldit,  S. C., Bonneau,  M., Pignaud,  G., Hainaud,  P., Azzam,  K., and Drouet,  L., 1996, “Which Experimental Model to Choose to Study Arterial Thrombosis and Evaluate Potentially Useful Therapeutics?,” Haemostasis, 26Suppl 4, pp. 55–69.
Scott, R. F., Daoud, A. S., and Florentin, R. A., 1972, “Animal Models in Atherosclerosis,” The Pathogenesis of Atherosclerosis, R. W. Wissler and J. C. Geer, eds., The Williams and Wilkins Company, Baltimore.
Huang,  Z. J., and Tarbell,  J. M., 1997, “Numerical Simulation of Mass Transfer in Porous Media of Blood Vessel Walls,” Am. J. Phys., 273, pp. H464–H477.
Kim,  W. S., and Tarbell,  J. M., 1994, “Macromolecular Transport Through the Deformable Porous Media of an Artery Wall,” ASME J. Biomech. Eng., 116, pp. 156–163.
Yuan,  F., Chien,  S., and Weinbaum,  S., 1991, “A New View of Convective-Diffusive Transport Processes in the Arterial Intima,” ASME J. Biomech. Eng., 113, pp. 314–329.
Deng,  X., Marois,  Y., How,  T., Merhi,  Y., King,  M., Guidoin,  R., and Karino,  T., 1995, “Luminal Surface Concentration of Lipoprotein (LDL) and Its Effect on the Wall Uptake of Cholesterol by Canine Carotid Arteries,” J. Vasc. Surg., 21, pp. 135–145.
Karmakar,  N., and Dhar,  P., 1996, “Effect of Steady Shear Stress on Fluid Filtration Through the Rabbit Arterial Wall in the Presence of Macromolecules,” Clin. Exp. Pharmacol. Physiol., 23, pp. 299–304.
Rappitsch,  G., and Perktold,  K., 1996, “Computer Simulation of Convective Diffusion Processes in Large Arteries,” J. Biomech., 29, pp. 207–215.
Deng,  X., King,  M. W., and Guidoin,  R., 1995, “Localization of Atherosclerosis in Arterial Junctions. Concentration Distribution of Low Density Lipoproteins at the Luminal Surface in Regions of Disturbed Flow,” ASAIO J., 41, pp. 58–67.
Ma,  P., Li,  X., and Ku,  D. N., 1997, “Convective Mass Transfer at the Carotid Bifurcation,” J. Biomech., 30, pp. 565–571.
Rappitsch,  G., and Perktold,  K., 1996, “Pulsatile Albumin Transport in Large Arterics: a Numerical Simulation Study,” ASME J. Biomech. Eng., 118, pp. 511–519.
Karner, G., and Perktold, K., 1999, “Numerical modeling of mass transport in the arterial wall,” V. K. Goel et al., eds., Proceedings, 1999 Bioengincering Conference, BED Vol. 42, ASME Press, New York, pp. 739–740.
Stangeby, D. K., and Ethier, C. R., 2000, “Computational analysis of convection dominated transport in two media: arterial mass transport,” Proceedings, Conference on Mathematical Modeling and Scientific Computing.
Friedman, M. H., 1986, Principles and Models of Biological Transport, Springer-Verlag, Berlin.
Back,  L. H., 1975, “Theoretical Investigation of Mass Transport to Arterial Walls in Various Blood Flow Regions—I. Flow Field and Lipoprotein Transport,” Math. Biosci., 27, pp. 231–262.
Tedgui,  A., and Lever,  M. J., 1984, “Filtration Through Damaged and Undamaged Rabbit Thoracic Aorta,” Am. J. Phys., 247, pp. H784–H791.
Wilens,  S. L., and McCluskey,  R. T., 1952, “The Comparative Filtration Properties of Excised Arteries and Veins,” Am. J. Med. Sci., 224, pp. 540–547.
Probstein, R. F., 1989, Physicochemical Hydrodynamics: an Introduction, Butterworths Publishers, Boston, MA.
Nichols, W. W., and O’Rourke, M. F., 1990, McDonald’s Blood Flow in Arteries, Lea & Febiger, Philadelphia.
Ethier, C. R., Steinman, D. A., and Ojha, M., 1999, “Comparisons between computational hemodynamics, photochromic dye flow visualization and magnetic resonance velocimetry,” Haemodynamics of Arterial Organs. X. Y. Xu and M. W. Collins, eds., WIT Press, Southampton, pp. 131–183.
Friedman,  M. H., and Ehrlich,  L. W., 1975, “Effect of Spatial Variations in Shear on Diffusion at the Wall of an Arterial Branch,” Circ. Res., 37, pp. 446–454.
Truskey,  G. A., Roberts,  W. L., Herrmann,  R. A., and Malinauskas,  R. A., 1992, “Measurement of Endothelial Permeability to 1251-Low Density Lipoproteins in Rabbit Arteries by Use of En Face Preparations,” Circ. Res., 71, pp. 883–897.
Schneiderman,  G., and Goldstick,  T. K., 1978, “Significance of Luminal Plasma Layer Resistance in Arterial Wall Oxygen Supply,” Atherosclerosis, 31, pp. 11–20.
Tompkins,  R. G., 1991, “Quantitative Analysis of Blood Vessel Permeability of Squirrel Monkeys,” Am. J. Phys., 260, pp. H1194–H1204.
Kim,  A., Wang,  C. H., Johnson,  M., and Kamm,  R., 1991, “The Specific Hydraulic Conductivity of Bovine Serum Albumin,” Biorheology, 28, pp. 401–419.
Laurent,  T. C., and Pietruszkiewicz,  A., 1961, “The effect of hyaluronic acid on the sedimentation rate of other substances,” Biochimica et Biophysica Acta, 49, pp. 258–264.
Laurent,  T. C., Bjork,  I., Pietruszkiewicz,  A., and Persson,  H., 1963, “On the interaction between polysaccharides and other macromolecules: II. The transport of globular particles through hyaluronic acid solutions,” Biochimica et Biophysica Acta, 78, pp. 351–359.
Levick,  J. R., 1987, “Flow Through Interstitium and Other Fibrous Matrices,” Q. J. Exp. Physiol., 72, pp. 409–437.
Moore,  J. A., and Ethier,  C. R., 1997, “Oxygen Mass Transfer Calculations in Large Arteries,” ASME J. Biomech. Eng., 119, pp. 469–475.
Guretzki,  H. J., Gerbitz,  K. D., Olgemoller,  B., and Schleicher,  E., 1994, “Atherogenic Levels of Low Density Lipoprotein Alter the Permeability and Composition of the Endothelial Barrier,” Atherosclerosis, 107, pp. 15–24.
Colton,  C. K., Friedman,  S., Wilson,  D. E., and Lees,  R. S., 1972, “Ultrafiltration of Lipoproteins Through a Synthetic Membrane. Implications for the Filtration Theory of Atherogenesis,” J. Clin. Invest., 51, pp. 2472–2481.
Ethier,  C. R., 1991, “Flow Through Mixed Fibrous Porous Materials,” AIChE J., 37, pp. 1227–1236.
Neale,  G., and Nader,  W., 1974, “Practical Significance of Brinkman’s Extension of Darcy’s Law: Coupled Parallel Flows Within a Channel and a Bounding Porous Medium,” Can. J. Chem. Eng., 52, pp. 475–478.
Wang,  D. M., and Tarbell,  J. M., 1995, “Modeling Interstitial Flow in an Artery Wall Allows Estimation of Wall Shear Stress on Smooth Muscle Cells,” ASME J. Biomech. Eng., 117, pp. 358–363.
Wada, S., and Karino, T., 1999, “Relationship between wall shear stress and surface concentration of lipoproteins calculated for a multiple bend of the human right coronary artery,” V. K. Goel et al., eds., Proceedings, 1999 Bioengineering Conference, BED Vol. 42, ASME Press, New York, pp. 735–736.
Whale,  M. D., Grodzinsky,  A. J., and Johnson,  M., 1996, “The Effect of Aging and Pressure on the Specific Hydraulic Conductivity of the Aortic Wall,” Biorheology, 33, pp. 17–44.
Curmi,  P. A., Juan,  L., and Tedgui,  A., 1990, “Effect of Transmural Pressure on Low Density Lipoprotein and Albumin Transport and Distribution Across the Intact Arterial Wall,” Circ. Res., 66, pp. 1692–1702.
Goldstein,  J. L., and Brown,  M. S., 1977, “The Low-Density Lipoprotein Pathway and Its Relation to Atherosclerosis,” Annu. Rev. Biochem., 46, pp. 897–930.
McIntire,  L. V., Wagner,  J. E., Papadaki,  M., Whitson,  P. A., and Eskin,  S. G., 1998, “Effect of Flow on Gene Regulation in Smooth Muscle Cells and Macromolecular Transport Across Endothelial Cell Monolayers,” Biol. Bull., 194, pp. 394–399.
Phelps,  J. E., and DePaola,  N., 2000, “Spatial Variations in Endothelial Barrier Function in Disturbed Flows in Vitro,” American Journal of Physiology: Heart Circulatory Physiology, 278, pp. H469–H476.
Jo,  H., Dull,  R. O., Hollis,  T. M., and Tarbell,  J. M., 1991, “Endothelial Albumin Permeability Is Shear Dependent, Time Dependent, and Reversible,” Am. J. Phys., 260, pp. H1992–H1996.
Sprague,  E. A., Steinbach,  B. L., Nerem,  R. M., and Schwartz,  C. J., 1987, “Influence of a Laminar Steady-State Fluid-Imposed Wall Shear Stress on the Binding, Internalization, and Degradation of Low-Density Lipoproteins by Cultured Arterial Endothelium,” Circulation, 76, pp. 648–656.
Herman,  I. M., Brant,  A. M., Warty,  V. S., Bonaccorso,  J., Klein,  E. C., Kormos,  R. L., and Borovetz,  H. S., 1987, “Hemodynamics and the Vascular Endothelial Cytoskeleton,” J. Cell Biol., 105, pp. 291–302.
Mandarino,  W. A., Berceli,  S. A., Sheppeck,  R. A., and Borovetz,  H. S., 1992, “Experimental Determination of Velocity Profiles and Wall Shear Rate Along the Rabbit Aortoiliac Bifurcation: Relationship to Vessel Wall Low-Density Lipoprotein (LDL) Metabolism,” J. Biomech., 25, pp. 985–993.
Neumann,  S. J., Berceli,  S. A., Sevick,  E. M., Lincoff,  A. M., Warty,  V. S., Brant,  A. M., Herman,  I. M., and Borovetz,  H. S., 1990, “Experimental Determination and Mathematical Model of the Transient Incorporation of Cholesterol in the Arterial Wall,” Bull. Math. Biol., 52, pp. 711–732.
Caro,  C. G., 1973, “Transport of 14C-4 Cholesterol Between Intra-Luminal Serum and Artery Wall in Isolated Dog Common Carotid Artery,” J. Physiol. (Lond), 233, pp. 37P–38P.
Caro,  C. G., 1974, “Transport of 14C-4-Cholesterol Between Perfusing Serum and Dog Common Carotid Artery: a Shear Dependent Process,” Cardiovasc. Res., 8, pp. 194–203.
Caro,  C. G., and Nerem,  R. M., 1973, “Transport of 14C-4-Cholesterol Between Serum and Wall in the Perfused Dog Common Carotid Artery,” Cardiovasc. Res., 32, pp. 187–205.
Baldwin,  A. L., Wilson,  L. M., Gradus-Pizlo,  I., Wilensky,  R., and March,  K., 1997, “Effect of Atherosclerosis on Transmural Convection an Arterial Ultrastructure. Implications for Local Intravascular Drug Delivery,” Arterioscler., Thromb., Vasc. Biol., 17, pp. 3365–3375.
Steinman,  D. A., Vinh,  B., Ethier,  C. R., Ojha,  M., Cobbold,  R. S., and Johnston,  K. W., 1993, “A Numerical Simulation of Flow in a Two-Dimensional End-to-Side Anastomosis Model,” ASME J. Biomech. Eng., 115, pp. 112–118.
Steinman, D. A., 1993, “Numerical Analysis of Flow in a 2-D Distensible Model of an End-to-Side Anastomosis,” Ph.D. thesis, University of Toronto.
Brooks,  A. N., and Hughes,  T. J. R., 1982, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32, pp. 199–259.
Asakura,  T., and Karino,  T., 1990, “Flow Patterns and Spatial Distribution of Atherosclerotic Lesions in Human Coronary Arteries,” Circ. Res., 66, pp. 1045–1066.
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.
Zarins,  C. K., Giddens,  D. P., Bharadvaj,  B. K., Sottiurai,  V. S., Mabon,  R. F., and Glagov,  S., 1983, “Carotid Bifurcation Atherosclerosis. Quantitative Correlation of Plaque Localization With Flow Velocity Profiles and Wall Shear Stress,” Circulation Research, 53, pp. 502–514.
Dirksen,  M. T., van der Wal,  A. C., van den Berg,  F. M., van der Loos,  C. M., and Becker,  A. E., 1998, “Distribution of Inflammatory Cells in Atherosclerotic Plaques Relates to the Direction of Flow,” Circulation, 98, pp. 2000–2003.
Smedby,  O., 1997, “Do Plaques Grow Upstream or Downstream?: an Angiographic Study in the Femoral Artery,” Arterioscler., Thromb., Vasc. Biol., 17, pp. 912–918.
Gown,  A. M., Tsukada,  T., and Ross,  R., 1986, “Human Atherosclerosis. II. Immunocytochemical Analysis of the Cellular Composition of Human Atherosclerotic Lesions,” Am. J. Pathol., 125, pp. 191–207.
Gan,  L., Sjogren,  L. S., Doroudi,  R., and Jern,  S., 1999, “A New Computerized Biomechanical Perfusion Model for Ex Vivo Study of Fluid Mechanical Forces in Intact Conduit Vessels,” J. Vasc. Res., 36, pp. 68–78.
Vorp,  D. A., Severyn,  D. A., Steed,  D. L., and Webster,  M. W., 1996, “A Device for the Application of Cyclic Twist and Extension on Perfused Vascular Segments,” Am. J. Phys., 270, pp. H787–H795.
Labadie,  R. F., Antaki,  J. F., Williams,  J. L., Katyal,  S., Ligush,  J., Watkins,  S. C., Pham,  S. M., and Borovetz,  H. S., 1996, “Pulsatile Perfusion System for Ex Vivo Investigation of Biochemical Pathways in Intact Vascular Tissue,” Am. J. Phys., 270, pp. H760–H768.
Larson,  R. E., and Higdon,  J. J. L., 1987, “Microscopic Flow Near the Surface of Two-Dimensional Porous Media. Part 2. Transverse Flow,” J. Fluid Mech., 178, pp. 119–136.
Larson,  R. E., and Higdon,  J. J. L., 1986, “Microscopic Flow Near the Surface of Two-Dimensional Porous Media. Part 1. Axial Flow,” J. Fluid Mech., 166, pp. 472.
Fatouraec, N., Deng, X., De Champlain, A., and Guidoin, R., 1999, “Numerical simulation of lipid transport through arterial stenoses,” V. K. Goel et al., eds., Proceedings, 1999 Bioengineering Conference, BED Vol. 42, ASME Press, New York, pp. 733–734.


Grahic Jump Location
Stenotic geometry used in LDL transport studies. Bottom edge is line of symmetry and geometry dimensions are shown as a function of the radius length R. The area reduction at the throat of the stenosis is 75 percent, and the stenosis is centerd at x/R=7. Note the definitions of coordinate directions (x,r) and velocity components (u,v). Not shown to scale.
Grahic Jump Location
Streamlines and pressure distribution for case of 100 mmHg transmural pressure difference at outlet and normalized inverse permeability of 5×1012. (a) Streamlines in lumen showing recirculation region, and in wall (shaded) showing transmural fluid permeation. (b) Pressure contours. Note that contours in lumen are in the range 0 to 2 mmHg in steps of 0.25 mmHg, while contours in wall are in range −100 to 0 mmHg in steps of 20 mmHg. The outlet pressure was set to 0 mmHg in this simulation. Label values on contours are in mmHg.
Grahic Jump Location
Normalized LDL concentration at the blood-wall interface versus axial position in the stenosis region, for differing wall permeabilities. For all simulations, the transmural pressure difference at the outlet was 100 mmHg, and the normalized inverse permeability of the wall tissue in the non-stenosed region was 5×1012. In the stenosed region, the normalized inverse permeability took the values 5×1012 (baseline case), 1×1012, and 5×1011.
Grahic Jump Location
Normalized LDL flux into the artery wall versus axial position in the stenosis region, for differing wall permeabilities. The upper portion of the graph shows the normalized wall shear stress in the stenosis (right scale). See legend of Fig. 3 for description of simulation input parameters. The normalizing factor for LDL flux, UC0, was 20.4 mg LDL/(cm2 s), and the normalizing wall shear stress was the inlet Poiseuille value, 7.2 dynes/cm2 . The inset at top shows the geometry of the stenosis: lumen is white and wall tissue is black.




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