Abstract
Fluid mechanical factors play an important role in the localization of sites of atherosclerosis, the focal deposition of platelets resulting in thrombosis, and the formation of aneurysms in the human circulation. The localization is confined mainly to regions of geometrical irregularity where vessels branch, curve and change diameter and where blood is subjected to sudden changes in velocity and/or direction. In such regions, flow is disturbed and separation of streamlines from the wall, with formation of eddies, is likely to occur. We shall describe the flow patterns and fluid mechanical stresses at these sites and consider their possible involvement in the genesis of the above mentioned vascular diseases. However, in order to understand the relationship between vessel geometry and the observed flow patterns, it is first necessary to deal with some aspects of the mechanics of flow in branching, expanding and curved vessels. Such a treatment will also serve to dispel the notion, common among physicians and surgeons, that the formation of eddies at sites of disturbed flow represents turbulent flow.
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References
T. Karino and H.L. Goldsmith, Rheological factors in thrombosis and haemostasis, in: “Haemostasis and Thrombosis,” A.L. Bloom and D.P. Thomas, eds., Churchill Livingstone, London, England (1986).
H.L. Goldsmith, and J. Marlow, Flow behavior of erythrocytes. II. Concentrated suspensions of ghost cells, J. Colloid Interface Sci. 73: 383 (1979).
H.L. Goldsmith, Red cell motions and wall interactions in tube flow, Fed. Proc. 30: 1578 (1971).
A. Kamis, H.L. Goldsmith, and S.G. Mason, The kinetics of flowing dispersions. I. Concentrated suspensions of rigid particles, J. Colloid Interface Sci. 22: 531 (1966).
F.P. Gauthier, H.L. Goldsmith, and S.G. Mason, Flow of suspensions through tubes. X. Liquid drops as models of erythrocytes, Biorheology 9: 205 (1972).
E.B. Vadas, H.L. Goldsmith, and S.G. Mason, The microrheology of colloidal dispersions. III. Concentrated emulsions, Trans. Soc. Rheol. 20: 373 (1976).
W.W. Nichols, and M.F. O’Rourke, “MacDonald’s Blood Flow in Arteries: Theoretic, Experimental and Clinical Principles,” 3rd ed., Lea and Febiger, Philadelphia (1990).
M.A. Reidy, and D.E. Bowyer, Scanning electron microscopy of arteries. The morphology of aortic endothelium in hemodynamically stressed areas associated with branches, Atherosclerosis 26: 181 (1977).
S. Glagov, Hemodynamic risk factors: Mechanical stress, mural architecture, medial nutrition and the vulnerability of arteries to atherosclerosis, in: “The Pathogenesis of Atherosclerosis,” R.W. Wissler and J.C. Geer, eds., Williams and Wilkins, Baltimore (1972).
D.L. Fry, Hemodynamic factors in atherogenesis, in: “Cardiovascular Diseases,” P. Scheinberg, ed., Raven Press, New York (1976).
M.R. Roach, The effect of bifurcations and stenoses on arterial disease, in: “Cardiovascular Flow Dynamics and Measurements,” N.H.C. Hwang and N.A. Normann, eds., University Park Press, Baltimore (1977).
J.F. Mustard, E.A. Murphy, H.C. Rowsell, and H.G. Downie, Factors influencing thrombus formation in vivo, Am. J. Med. 33: 621 (1962).
J.F. Mustard, and M.A. Packham, The role of blood and platelets in atherosclerosis and the complications of atherosclerosis, Thromb. Diathes. Haemorrh. 33: 444 (1975).
H.D. Geissinger, J.F. Mustard, and H.C. Rowsell, The occurrence of microthrombi on the aortic endothelium of swine, Can. Med. Assoc. J. 87: 405 (1962).
J.R.A. Mitchell, and C.J. Schwartz, The relationship between myocardial lesions and coronary disease. II. A select group of patients with massive cardiac necrosis of scarring, Brit. Heart J. 25: 1 (1963).
M.A. Packham, H.C. Roswell, L. Jorgensen, and J.F. Mustard, Localized protein accumulation in the wall of the aorta, Exp. Mol. Path. 7: 214 (1967).
S.K. Yu, and H.L. Goldsmith, Behavior of model particles and blood cells at spherical obstructions in tube flow, Microvasc. Res. 6: 5 (1973).
T. Karino, and H.L. Goldsmith, Flow behaviour of blood cells and rigid spheres in an annular vortex, Phil. Trans. Roy. Soc. (London) B 279: 413 (1977).
T. Karino, H.H.M. Kwong, and H.L. Goldsmith, Particle flow behavior in models of branching vessels: I. Vortices in 90° T junctions, Biorheology 16: 231 (1979).
T. Karino, and H.L. Goldsmith, Particle flow behavior in models of branching vessels. II. Effect of branching angle and diameter ratio on flow patterns, Biorheology 22: 87 (1985).
T. Karino, and M. Motomiya, Flow visualization in isolated transparent natural blood vessels, Biorheology 20: 119 (1983).
T. Karino, and M. Motomiya, Flow through a venous valve and its implication in thrombus formation, Thromb. Res. 36: 245 (1984).
M. Motomiya, and T. Karino, Particle flow behavior in the human carotid artery bifurcation, Stroke 15: 50 (1984).
T. Karino, M. Motomiya and H.L. Goldsmith, Flow patterns in model and natural vessels, in: “Biologic and Synthetic Vascular Prostheses,” J. Stanley, ed., Grune and Stratton, New York (1982).
T. Karino, M. Motomiya, and H.L. Goldsmith, Flow patterns at the major T-junctions of the dog descending aorta, J. Biomechanics 23: 537 (1990).
T. Karino, Microscopic structure of disturbed flows in the arterial and venous systems, and its implication in the localization of vascular diseases, Intern. Angiology 5: 297 (1986)
T. Asakura, and T. Karino, Flow patterns and spatial distribution of atherosclerotic lesions in human coronary arteries, Circ. Res. 66: 1045 (1990).
M. Anliker, M. Casty, P. Friedli, R. Kubli and H. Keller, Non-invasive measurement of blood flow, in: “Cardiovascular Flow Dynamics and Measurements,” N.H.C. Hwang and N.A. Normann, eds., University Park Press, Baltimore (1977).
A. Bollinger, P. Butti, P. Barras, H. Trachler, and N. Siegenthaler, Red blood cell velocity in nailfold capillaries of man, measured by a television microscopy technique, Microvasc. Res. 6: 61 (1974).
J.H. Forrester, and E.F. Young, Flow through a converging-diverging tube and its implications in occlusive vascular disease. I. Theoretical development, J. Biomech. 3: 297 (1970).
J.H. Forrester, and E.F. Young, Flow through a converging-diverging tube and its implications in occlusive vascular disease. I. Theoretical and experimental results and their implications, J. Biomech. 3: 307 (1970).
J.-S. Lee, and Y.-C. Fung, Flow in non-uniform small blood vessels, Microvasc. Res. 3: 272 (1973).
M.D. Deshpande, D.P. Giddens, and R.F. Mabon, Steady laminar flow through modelled vascular stenoses, J. Biomech. 9: 165 (1976).
E.O. Macagno, and T.-K. Hung, Computational and experimental study of a captive annular eddy, J. Fluid Mech. 28: 43 (1967).
T.-K. Hung, Vortices in pulsatile flows, in: “Proceedings of 5th International Congress of Rheology,” S. Onogi, ed., University Park Press, Baltimore (1970).
K. Perktold, Pulsatile non-Newtonian blood flow simulation through a bifurcation with an aneurysm, Biorheology 26: 1011 (1989).
H.L. Goldsmith, and V.T. Turitto, Rheological aspects of thrombosis and haemostasis: Basic principles and applications, Thromb Haemost. 55: 415 (1986).
N.S. Lynn, V.G. Fox, and L.W. Ross, Computation of fluid dynamical contributions to atherosclerosis at arterial bifurcations, Biorheology 9: 61 (1972).
R. Brech, and B.J. Bellehouse, Flow in branching vessels, Cardiovasc. Res. 7: 593 (1973).
L.W. Ehrlich, Digital simulation of periodic flow in a bifurcation, Computer and Fluids 2: 237 (1974).
K. Kandarpa, and N. Davids, Analysis of the fluid dynamic effects on atherogenesis at branching sites, J. Biomech. 9: 735 (1976).
V.O. O’Brien, L.W. Ehrlich, and M.H. Friedman, Unsteady flow in a branch, J. Fluid Mech. 75: 315 (1976).
D. Agonaffer, C.B. Watkins, and J.N. Cannon, Computation of steady flow in a two-dimensional arterial model, J. Biomech. 18: 695 (1985).
G. Enden, M. Israeli, and U. Dinnar, A numerical simulation of the flow in a T-type bifurcation and its application to an ‘end to side’ fistula, J. Biomech. Eng. 107: 321 (1985).
C.C.M. Rindt, A.A. van Steenhoven, A. Segal, R.S. Reneman, and J.D. Jansen, Analysis of the flow field in a 3D-model of carotid artery bifurcation, in: “Proceedings of the World Congress of Medical Physics and Biomedical Engineering,” J.W. Clark, P.I. Horner, A.R. Smith, and K. Strum, eds., Physics in Med. Biol. 33:,375 (1988).
R.G. Cox, and S.K. Hsu, The lateral migration of solid particles in a laminar flow near a plane wall, Int. J. Multiphase Flow 3: 201 (1977).
A. Karnis, and S.G. Mason, The flow of suspensions through tubes. VI. Meniscus effects, J. Colloid Interface Sci. 23: 120 (1967).
T. Karino, and H.L. Goldsmith, Aggregation of platelets in an annular vortex distal to a tubular expansion, Microvasc. Res. 17: 217 (1979).
M. von Smoluchowski, Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. Physik. Chem. 92: 129 (1917).
T.G.M. van de Ven, and S.G. Mason, The microrheology of colloidal dispersions. VII. Orthokinetic doublet formation of spheres, Colloid Polymer Sci. 255: 468 (1977).
T. Karino, and H.L. Goldsmith, Adhesion of human platelets to collagen on the walls distal to a tubular expansion, Microvasc. Res. 17: 238 (1979).
V.T. Turitto, Viscosity, transport and thrombogenesis, in: “Progress in Hemostasis and Thrombosis,” T.H. Spaet, ed., Grune and Stratton, New York (1982).
H.L. Goldsmith and T. Karino, Mechanically induced thromboemboli, in: “Quantitative Cardiovascular Studies: Clinical and Research Applications,” N.H.C. Hwang, D.R. Gross and D.J. Patel, eds., University Park Press, Baltimore (1978).
T. Karino, and H.L. Goldsmith, Role of cell-wall interactions in thrombogenesis and atherogenesis: A microrheological study, Biorheology 21: 587 (1984).
L. Diener, J.L.E. Ericsson and F. Lund, The role of venous valve pockets in thrombogenesis. A postmortem study in a geriatric unit, in: “Atherogenesis”, T. Shimamoto and F. Numano, eds., Excerpta Medica, Amsterdam (1969).
S. Sevitt, Pathology and pathogenesis of deep vein thrombi, in: “Venous Problem,” J.J. Bergan and J.S.T. Yao, eds., Year Book Medical Publishers, Chicago (1978).
K. Kristiansen, and J. Krog, Electromagnetic studies on the blood flow through the carotid system in man, Neurology 12: 20 (1962).
S. Uematsu, A. Yang, T.J. Preziosi, R. Kouba, and T.J.K. Toung, Measurement of carotid blood flow in man and its clinical application, Stroke 14: 256 (1983).
Y. Sohara and T. Karino, Secondary flows in the dog aortic arch, in: “Fluid Control and Measurement,” M. Harada, ed., Pergamon Press, Oxford (1985).
T. Karino, N. Kobayashi, S. Mabuchi, and S. Takeuchi, Role of hemodynamic factors in the localization of saccular aneurysms in the human circle of Willis, Biorheology 26: 526 (1989).
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Goldsmith, H.L., Karino, T. (1992). Flow and Vascular Geometry. In: Hwang, N.H.C., Turitto, V.T., Yen, M.R.T. (eds) Advances in Cardiovascular Engineering. NATO ASI Series, vol 235. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4421-7_9
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DOI: https://doi.org/10.1007/978-1-4757-4421-7_9
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