Flow in Large Arteries

  • Czeslaw M. Rodkiewicz
Part of the International Centre for Mechanical Sciences book series (CISM, volume 270)


For centuries, the world within himself fascinated man as much as his near and distant environment. In particular the cardiovascular system was the object of attention of scientific observers like Aristotle and Leonardo da Vinci. However, the concept of the Circulation of the Blood was clearly presented by W. Harvey in 1628, in his famous De Motu Cordis et Sanguinis in Animalibus. The evidence provided was almost complete and reached into the present day understanding, except that Harvey could not see the passage of blood from the peripheral arteries to the veins. He speculated that there must be “pores” at these locations. These “pores” were in 1661 identified by Malpighi as the capillaries (K.D. Keele, 1978). Later in 1733 Stephen Hales, the Vicar of Teddington, published the first measurements of arterial blood pressure.


Reynolds Number Wall Shear Stress Aortic Arch Secondary Flow Pulsatile Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature and References

  1. Abell, L.L., Levy, B.B., Brodie, B.B. and Kendall, F.E. (1952), A simplified method for the estimation of total cholestral in serum and demonstration of its specificity, J Biol Chem, 195, 357.Google Scholar
  2. Agrawal, Y.C. (1975), Laser velocimeter study of entrance flows in Curved pipes, U. of California Berkeley Report FM-75–1.Google Scholar
  3. Amyot, J.S., Francis, G.P., Kiser, K.M. and Falsetti, H.L. (1970), Measurement of sequential velocity development in the aorta, ASME Paper 70-WA/BHF-13.Google Scholar
  4. Anderson, B. and Porje, I.G. (1946), Study of Ph. Broemser’s manometer theory for oscillations in the aorta, Acta Physiol Scand, 12, 3.Google Scholar
  5. Atabek, H.B. (1964), End effects. In: Pulsatile Blood, Attinger, E.O., ed., McGraw Hill, New York, 201.Google Scholar
  6. Attinger, E.O. (1963), Pressure transmission in pulmonary arteries related to frequency and geometry, Circ Res, 12, 623.PubMedGoogle Scholar
  7. Attinger, E.O. (1966), Hydrodynamics of blood flow, In: Advances in Hydicscience, vol. 3, Chow, V.T., ed., Academic Press, New York, 111.Google Scholar
  8. Attinger, E.O., Anné, A. and McDonald, D.A. (1966), Use of Fourier series for the analysis of biological systems, Biophys J, 6, 291.PubMedCentralPubMedGoogle Scholar
  9. Austin, L.R. and Seader, J.D. (1973), Fully developed viscous flow in coiled circular pipes, AICHE J, 19, 85.Google Scholar
  10. Back, L.D. (1975), Theoretical investigation of mass transport to arterial walls in various blood flow regions — I and II, Mathematical Biosciences, 27, 231.Google Scholar
  11. Back, L.D., Radbill, J.R. and Crawford, D.W. (1977), Analysis of pulsatile, viscous blood flow through diseased coronary arteries of man, J Biomech, 10, 339.PubMedGoogle Scholar
  12. Bard, P. (1956), Medical Physiology, 10th ed., C. V. Mosby, St. Louis.Google Scholar
  13. Batchelor, G.K. (1970), An IntnoductLon to Fluid Pynamics, Cambridge Univ. Press, New York, 148.Google Scholar
  14. Bell, G., Davidson, J.N. and Scarborough, H. (1965), Textbook of Physiology and Biochemistry, 6th ed., E and S Livingston, Edinburgh.Google Scholar
  15. Bellhouse, B.J. and Talbot, L. (1969), The fluid mechanics of the aortic valve, J Fluid Mech, 35, 721.Google Scholar
  16. Benditt, E.P. and Benditt, J.M. (1973), Evidence for a monoclonal origin of human atherosclerotic plaques, Pnoe Nat Aead Sci. USA, 70, 1753.Google Scholar
  17. Benedict, J.V., Harris, E.H. and Von Roseberg, E.U. (1970), An analytical investigation of the cavitation hypothesis of brain damage, ASME-Paper 70-BHF-3.Google Scholar
  18. Berne, R.M. and Levy, M.N. (1972), CandLovaoscuLatt Phye.Lo.Q.ogy, C. V. Mosby, St. Louis.Google Scholar
  19. Blumenthal, H.T. (1967), Hemodynamic factors in the etiology of artheriosclerosis, In: Cowdiy’s Aithelioscleiosis, 2nd ed., Blumenthal, H.T., ed., C.C. Thomas, Springfield, Illinois, 510.Google Scholar
  20. Boussinesq, M.J. (1868), Memoire sur l’influence des frottements dans les mouvements reçuliers des fluids, J Math Puna Appt, ser. 2, 13, 377.Google Scholar
  21. Boussinesq,. M.J. (1872), Influence de forces centrifuges sur le mouvement perm. varie de l’eau dans les canauz larges, Soc Philom But, 8, 77.Google Scholar
  22. Brech, R. and Bellhouse, B.J. (1973), Flow in branching vessels, Caodoovas Res, 7, 593.Google Scholar
  23. Carlsten, A. and Grimby, G. (1966), The Cilculatoiy Response to Musculai Exeicise in Man, C.C. Thomas, Springfield, Illinois.Google Scholar
  24. Caro, C.G. (1966), The dispersion of indicator flowing through simplified models of the circulation and its relevance to velocity profile in blood vessels, J Physical, 185, 501.Google Scholar
  25. Caro, C.G. (1973), Transport of material between blood and wall in arteries, In: Athenogeneis: Initiating Factors, CIBA Foundation Symposium 12 (new series), Porter, R. and Knight, J., eds., Associated. Scientific Press, Amsterdam, 127.Google Scholar
  26. Caro, C.G., Fitz-Gerald, J.M. and Schroter, R.C. (1971), Atheroma and arterial wall shear. Observation, correlation and proposal of a shear dependant mass transfer mechanism for atherogenesis, Pioc Ray Sac Lan, Ser. 177, 109.Google Scholar
  27. Cassanova, R.A., Giddens, D.B. and Mabon, R.F. (1975), A comparison of stenotic fluid dynamics in steady and pulsatile flow, 1975 ASME Bio-mechanics Symposium, New York, 27.Google Scholar
  28. Chandran, K.B., Swanson, W.M. and Ghista, D.N. (1974), Oscillatory flow in thin-walled curved elastic tubes, Ann Biomed Eng, 2, 392.PubMedGoogle Scholar
  29. Constantinides, P. (1965), Expelimental Athenascleiosis, Elsevier, New York, 14.Google Scholar
  30. Cox, R.H. (1969), Comparison of linearized wave propagation models for arterial blood flow analysis, J Biomech, 2, 251.PubMedGoogle Scholar
  31. Cox, R.H. (1970), Wave propagation through a Newtonian fluid contained within a thick-walled, viscoelastic tube: The influence of wall compressibility, J Biomech, 3, 317.PubMedGoogle Scholar
  32. Crow, W.J. (1969), Studies of arterial branching models using flow birefringence, Ph.D. Thesis, Univeristy of Florida, Florida.Google Scholar
  33. Cuming, H.G. (1952), The secondary flow in curved pipes, Gi Bild Aeio Res Repas and Memonanda, No. 2880.Google Scholar
  34. Daly, B.J. (1976), A numerical study of pulsatile flow through stenosed canine femoral arteries, J Biomech, 9, 465.PubMedGoogle Scholar
  35. Davis, W. and Fox, R.W. (1967), An evaluation of the hydrogen bubble technique for the quantitative determination of fluid velocities within clear tubes, J of Basic Eng, Manz ASME, 89, 771.Google Scholar
  36. Dean W.R. (1927), Note on the motion of fluid in a curved pipe, Phil Mag, 4, 208.Google Scholar
  37. Dean, W.R. (1928), The streamline motion of fluid in a curve pipe, Phil Mag, 5, 674.Google Scholar
  38. Deshpande, M.D., Giddens, D.P. and Mabon, R.F. (1976), Steady laminar flow through modelled vascular stenoses, J Biomech, 9, 165.PubMedGoogle Scholar
  39. Deutsch, S. and Phillips, W.M. (1971), The use of the Taylor-Couette stability problem to validate a constitutive equation for blood, Bioiheotogy, 14, 253.Google Scholar
  40. Downie, H.G., Murphy, E.A., Rowsell, H.C. and Mustard, J.F. (1963), Extracorporeal circulation: A device for the quantitative study of thrombus formation in flowing blood, Cire Res, 12, 441.Google Scholar
  41. Duncan, L.E. (1963), Mechanical factors in the localization of atheromata, In: Evaluation of the atheioscleiotic plaque, Jones, R.J., ed., University of Chicago Press, Chicago, 171.Google Scholar
  42. Ehrlich, L.W. and Friedman, M.H. (1977), Steady convective diffusion in a bifurcation, IEEE Tians Biomed, 24, 12.Google Scholar
  43. Ellard, D., Huth, C. and Scott, A. (1968), A biomedical heat exchanger for localized cooling of the brain, Unpublished-Design project for Mec.E. 463, U of Alberta, Edmonton.Google Scholar
  44. Eustice, J. (1910), Flow of water in curved pipes, Pnoc Roy Soc. Lan, ser. A, 84, 107.Google Scholar
  45. Eustice, J. (1911), Experiments on streamline motion in curved pipes, Ptoc Roy Soc Lon, ser. 85, 119.Google Scholar
  46. Evans, R.L., Hosie, K.F., Kooiker, R.H., Perry, J. and Stish, R.J. (1960), Reflections in model and arterial pulse waves, J Appt Physiot, 15, 258.Google Scholar
  47. Ferguson, G.G. and Roach, M. (1972), Flow conditions at bifurcations as determined in glass models, with reference to the focal distribution of vascular lesions, In: CaxdLovaacu VL Ftuíd DynamLco, vol. 2, Bergel, D.H., ed., Academic Press, London, 141.Google Scholar
  48. Fernandez, R.C., DeWitt, K.J. and Botwin, M.R. (1976), Pulsatile flow through a bifurcation with applications to arterial disease, J Bomech, 9, 575.Google Scholar
  49. Forstram, R.J., Blackshear, P.L. Jr., Dorman, F.D., Kreid, D.K. and Kihara, K. (1971), Experimental study of a model blood flow in channels, ASME Paper 71-WA/BHF-5.Google Scholar
  50. Fox, J.A. and Hugh, A.E. (1966), Localization of atheroma: A theory based on boundary layer separation, Boll Heat J, 28, 388.Google Scholar
  51. Friedlander, S.K. and Johnstone, H.F. (1957), Deposition of suspended particles from turbulent gas streams, Ind Eng Chem, 49, 1151.Google Scholar
  52. Fry, D.L. (1968), Acute vascular endothelial changes associated with increased blood velocity gradients, Cite Res, 22, 165.Google Scholar
  53. Fry, D.L. (1969), Certain histological and chemical responses of the vascular interface to acutely induced mechanical stress in the aorta of the dog, C. Vcc Reh, 24, 93.Google Scholar
  54. Fry, D.L. (1973), Response of the arterial wall to certain physical factors, In: Athewgenesía: InwtLatí.ng Faatois, CIBA Foundation Symposium 12 (new series), Porter, R. and Knight, J., eds., Associated Scientific Press, Amsterdam, 93.Google Scholar
  55. Fry, D.L., Mallos, A.J. and Casper, A.G.T. (1956), A catheter tip method for measurement of the instantaneous aortic blood velocity, Cite Rel, 4, 627.Google Scholar
  56. Fung, Y.C. (1969), Blood flow in the capillary bed, Prepared for a General Lecture at the Technical Conference on Biomechanics, U. of Michigan, Ann Arbor, Michigan.Google Scholar
  57. Fung, Y.C. (1971), Biomechanics: A survey of the blood flow problem, In: Advanee Ln AppLLed Mechavbic, vol. 11, Yih, C.S., ed., Academic Press, New York, 65.Google Scholar
  58. Geer, J.C. and McGill, H.C. (1967), The evolution of the fatty streak, In: Mhenociejotie Vaecutan Dssease, Brest, A.N. and Moyer, J.H., eds., Appleton-Century-Crafts, New York, 8.Google Scholar
  59. Gerrard, J.H. (1971), An experimental investigation of pulsating turbulent water flow in a tube, J F. d Mech, 46, 43.Google Scholar
  60. Gilman, S.F. (1955), Pressure losses in divided-flow fittings, Heating Piping and Ait Cand, 27, part 1, no. 4, 141.Google Scholar
  61. Glagov, S. (1972), Hemodynamic risk factors: Mechanical stress, mural architecture, medical nutrition and the vulnerability of arteries to atherosclerosis, In: The Pathageneísís ob AthehosaPeiols, Wissler, R.W. and Geer, J.C., eds., William and Wikins, Baltimore,. 164.Google Scholar
  62. Goldsmith, H.L. (1972), The flow of model particles and blood cells and its relation to thrombogenesis, In: Pnag Ams in HemoetasL and Thum-basis, vol. 1, Spaet, T.H., eds., Grune and Stratton, New York, 97.Google Scholar
  63. Gorman, J. (1977), A running argument, The Sciences, 17, no. 1, 10.Google Scholar
  64. Gosman, A.D., Vlachos, N.S. and Whitelaw, J.H. (1975), Measurement and calculation of laminar flow downstream of a bend in a round tube and the prognosis for similar investigations of blood flow in venules, ASME Paper 75-APMB-7.Google Scholar
  65. Greenfield, H. (1969), The design of artificial heart valves and other medical problems by computer, Data Sheet, Official publication of the College of Engineering, University of Utah.Google Scholar
  66. Greenfield, J.C. Jr. and Fry, D.L. (1962), Measurement errors in estimating aortic blood velocity by pressure gradient, J Appt Photiot., 17, 1013.Google Scholar
  67. Guest, M.H., Bond, T.P., Cooper, R.G. and Derrick, J.R. (1963), Red blood cells: Change in shape in capillaries, Science, 142, 1319.PubMedGoogle Scholar
  68. Gutstein, W.H. and Schneck, D.J. (1967), In vitro boundary layer studies of blood flow in branched tubes, J Athenoeiek Rel, 7, 295.Google Scholar
  69. Gutstein, W.H., Schneck, D.J. and Marks, J.O. (1968), In vitro studies of local blood flow disturbance in a region of separation, J Athenoe ek Res, 8, 381.Google Scholar
  70. Guyton, A.C. (1960), Function of the Human Body, W.B. Saunders, Philadelphia.Google Scholar
  71. Guyton, A.C. (1971), Textbook. of Medicc1 Phoiology, 4th ed., W.B. Saunders, Philadelphia.Google Scholar
  72. Hagen, G. (1839), Uber die bewegung des wassers in engen zylindrischen, Rohken Pogg Ann, 46, 423.Google Scholar
  73. Hardung, V. (1962), Propagation of pulse waves in visco-elastic tubings, In: Handbook at PhgiLocogy: CiAcuta Lon, Sec. 2, vol. 1, Hamilton, W.F. eds., American Physiological Society, Washington D.C., 107.Google Scholar
  74. Hawthorne, W.R. (1951), Secondary circulation in fluid flow, Pkoc. Roy Soc Lon, ser. A, 206, 374.Google Scholar
  75. Hoeber, T.W. and Hochmuth, R.M. (1970), Measurement of red cell modulus of elasticity by in vitro and model cell experiments, ASME Paper 70-BHF-4.Google Scholar
  76. Huang, H.K. (1970), Theoretical analysis of flow patterns in single-file capillaries, ASME Paper 70-BHF-10.Google Scholar
  77. Hugh, A.E. and O’Malley, A.W. (1975), Correlation of intra-arterial contrast stasis with flow patterns at constrictions, branches and bends: An experimental model, Clln Radioy, 26, 505.Google Scholar
  78. Ito, H. (1950), Theory on laminar flows through curved pipes of elliptic and rectangular cross-sections, The Reports ob the Init High Speed Mech, Tokohu University, 1, 1.Google Scholar
  79. Kandarpa, K. and Davids, N. (1976), Analysis of fluid dynamic effects on atherogenesis of branching sites, J Bomech, 9, 735.Google Scholar
  80. Kaufman, B., Davey, T.B., Smeloff, E.A., Huntley, A.C. and Miller, G.E. (1968), Development of mechanical heart assists, ASME Paper 68-WA/BHF-4.Google Scholar
  81. Keele, K.D. (1978), The life and work of William Harvey, Endeavour, New Series, 2, No. 3, 104.Google Scholar
  82. Keulegan, G.H. and Beij, K.H. (1937), Pressure losses for fluid flow in curved pipes, J Reis Nate But Sund, 18, 89.Google Scholar
  83. Kiser, K.M., Falsetti, H.L., Yui, K.H., Resistarits, M.R., Francis, G.P. and Carroll, R.J. (1976), Measurements of velocity wave forms in the dog aorta, J Fpwld Eng, Dun’s ASME, 98, 297.Google Scholar
  84. Kline, K.A. and Allen, S.J. (1971), Deformation of red cells in shear fields, ASME Paper 71-WA/BHF-11.Google Scholar
  85. Krovetz, L.J. (1965), The effect of vessel branching on haemodynamic stability, Pho Med Biot, 10, No. 3, 417.Google Scholar
  86. Krueger, J.W., Young, D.F. and Cholvin, N.R. (1970), An in vitro study of flow response by cells, ASME Paper 70-BHF-9.Google Scholar
  87. Kuchar, N.R. and Ostrach, S. (1965), Flows in the entrance region of circular elastic tubes, FTAS/TR-65–3, Case Western Reserve University, Cleveland, Ohio.Google Scholar
  88. Kuchar, N.R. and Scala, S.M. (1968), Design of devices for optimum blood flow, ASME Paper 68-DE-52.Google Scholar
  89. Langhaar, H.L. (1942), Steady flow in the transition length of a straight tube, J Appt Mech, 9, A55.Google Scholar
  90. Lee, J.S. and Fund, Y.C. (1968), Experiments on blood flow in lung alveoli models, ASME Paper 68-WA/BHF-2.Google Scholar
  91. Lee, J.S. and Fung, Y.C. (1970), Flow in locally constricted tubes at low Reynolds numbers, J App.E Mech, 37, 9.Google Scholar
  92. Lew, H.S. (1973), The dividing streamline of bifurcating flows in a two-dimensional channel at low Reynolds number, J Bomech, 6, 423.Google Scholar
  93. Lighthill, M.J. (1972), Physiological fluid dynamics: A survey, J Fluid Mech, 52, 475.Google Scholar
  94. Lighthill, Sir J. (1975), Mathemaí cat Btiai.CuLddynanicy, Soc Indus. Appl. Math., Philadelphia.Google Scholar
  95. Lyne, W.H. (1970), unsteady flow in a curved pipe, J Mad Mech, 45, 13.Google Scholar
  96. Lynn, N.S., Fox, V.G. and Ross, L.W. (1970), Paper presented at 63rd Annual Meeting, AICHE, Chicago.Google Scholar
  97. Malindzak, G.S. (1956), Reflection of pressure pulses in the aorta, Med Refs Eng, 6, 25.Google Scholar
  98. Malindzak, G.S. and Stacy, R.W. (1965), Dynamic behaviour of a mathematical analog of the normal human arterial system, Amen J Med Etec, 4, no. 1, 28.Google Scholar
  99. Malindzak, G.S. and Stacy, R.W. (1966), Dynamics of pressure pulse transmission in the aorta, Ann NV Acad Sc, 128, 3, 921.Google Scholar
  100. Mark, F.F., Bargeron, C.B. and Friedman, M.H. (1975), An experimental investigation of laminar flow in a rectangular cross-section bifurcation, Applied Physics Lab, John Hopkins U, Silver Spring, Maryland.Google Scholar
  101. Martin, J.D. and Clark, M.E. (1966), Theoretical and experimental analyses of wave reflections in branched flexible conduits, Eng Mech Res, ASCE, 441.Google Scholar
  102. McDonald, D.A. (1955), The relation of pulsatile pressure to flow in arteries, J Physiocy, 127, 533.Google Scholar
  103. McGill, H.C., Geer, J.C. and Strong, J.P. (1963), Natural history of human atherosclerotic lesions, In: Athekoscletosis of its Onlgln. Sandler, M. and Bourne, G.H., eds., Academic Press, New York, 39.Google Scholar
  104. Medical College, New York Hospital (1970) Filtering blood may avert bypass brain damage, JAMA, 212, 1450.Google Scholar
  105. Meisner, J.E. and Rushmer, R.F. (1973), Eddy formation and turbulence in flowing liquids, Cikc Rea, 12, 455.Google Scholar
  106. Meisner, J.E. and Rushmer, R.F. (1968), Production of sounds in distensible tubes, Una Reo, 12, 651.Google Scholar
  107. Mitchell, J.R.A. and Schwartz, C.J. (1965), The localization of arterial plaques, In: An teìla Disease, Blackwell Scientific Publications, Oxford 50.Google Scholar
  108. Mueller, T.J., Llyod, J.R. Chetta, G.E. and Galanga, F.L. (1975), Effect of test section geometry on the occluder motion of caged-ball prosthetic heat valves, 1975 ASME Biomechanics Symposium, New York, 55.Google Scholar
  109. Mullinger, R.N. and Manley, G. (1967), Glycosaminoglycans and atheroma in iliac arteries, J Athenoctex Res, 7, 401.Google Scholar
  110. Nerem, R.M. and Seed, W.A. (1972), An in vivo study of aortic flow disturbances, Candlovaac Rea, 6, 1.Google Scholar
  111. O’Brien, V., Ehrlich, L.W. and Friedman, M.H. (1976) Unsteady flow in a branch, J F.Ew d Mech., 75, 315.Google Scholar
  112. Park, S.D. and Lee Y. (1971), Diabatic turbulent flow in the entrance region of concentric annuli, Eng J, 54, No. 6.Google Scholar
  113. Patel, D.J. and Janicki, J.S. (1966), Catalogue of some dynamic analogies used in pulmonary and vascular mechanics, J Med Refs Eng, 5, 30.Google Scholar
  114. Pedley, T.J., Schroter, R.C. and Sudlow, M.F. (1971), Flow and pressure drop in systems of repeatedly branching tubes, J Mulct Mech, 46, 365.Google Scholar
  115. Pelot, R.P. and Rodkiewicz, C.M. (1982), Aortic Arch Separation and Flow Patterns — In Vitro Study, Dept. Report No. 27, Dept. of Mech. Eng., University of Alberta, Edmonton.Google Scholar
  116. Poiseuille, J. (1840, 1841 ), Recherches expérimentalles sur le mouvement des liquids dans les tubes de trespetits diamétres, Comptes Rendus, 11, 961, 1041, and 12, 112.Google Scholar
  117. Porgé, I.G. (1964), Hemodynamics of the ascending aorta, In: Putsa ite Stood Flow, Attinger, E.O., eds., McGraw Hill, New York, 237.Google Scholar
  118. Reif, T.H., Nerem, R.H. and Kulacki, F.A. (1976), An in vitro study of a steady state pipe flow at high 98, 488.Google Scholar
  119. Resch, J.A., Okabe, N., Loewenson, R.B., Baker, A.B. (1969), Pattern of vessel sclerosis, J Athenodcten Rea, 9, 239.Google Scholar
  120. Rodbard, S. (1956), Vascular modifications induced by flow, Amen leant J, 51, 926.Google Scholar
  121. Rodkiewicz, C.M. (1974), Atherosclerotic formations in the light of fluid mechanics, Pnoc Eng Cons, Montreal.Google Scholar
  122. Rodkiewicz, C.M. (1974), Bifurcation characteristic Reynolds number, J Hydnaute Res, 12, 241.Google Scholar
  123. Rodkiewicz, C.M. (1975), Localization of early atherosclerotic lesions in the aortic arch in the light of fluid flow, J Bamech, 8, 149:Google Scholar
  124. Rodkiewicz, C.M. and Hung, R. (1976), Flow division dependence of some large arterial junctions on frequency and amplitude, Departmental, Edmonton, Alberta.Google Scholar
  125. Rodkiewicz, C.M. and Kalita, W. pipe junctions,’Departmental Alberta, Edmonton, Alberta.Google Scholar
  126. Rodkiewicz, C.M. and Roussel, C.L. (1973), Fluid mechanics in a large arterial bifurcation, J Mud’s Eng, Manz ASME, 95, 108.Google Scholar
  127. Rodkiewicz, C.M. and Wong, S.L. (1974), On the mass flow division in curved junctions, ASHRAE Tnan, 80, Part 2, 280.Google Scholar
  128. Rogers, V.A. and Moskowitz, G.D. (1971) of human systemic arterial circulate, Analysis for on, ASME Paper hydrodynamic model 71-WA/AUT-13.Google Scholar
  129. Rosenhear, L. (1973), Lamlnan Boundary. University Press, London.Google Scholar
  130. Roussel, C.L. and Bifurcation, J. (1970) Measurements and computations of flow in pipe bends, 43, 771.Google Scholar
  131. Rowe, C.M. (1973), Edge effect Trans ASME, 95, 334.Google Scholar
  132. Sato, Y. (1963), Separating and uniting flows in a branch pipe, J Japan Soc Mech Eng, 66, 537.Google Scholar
  133. Scarton, H.A., Shah, P.M. and Tsapogas, M.J. (1975), The role of hemodynamics in early atheroma in the aorta, 1975 ASME Biomechanics Symposium, New York, 15.Google Scholar
  134. Scarton, H.A., Shah, P.M. and Tsapogas, M.J. (1977), Relationship of the spatial evolution of secondary flow in curved tubes to the aortic arch, In: Mechanics in EaqLneetLng, Dubey, R.N. and Lind, N.C., eds., U of Waterloo Press, Waterloo, Canada, 111.Google Scholar
  135. Scherer, P.W. (1973), Flow in axisymmetrical glass model aneurysms, J B.Lomech, 6, 695.Google Scholar
  136. Schlichting, H. (1968), Boundary LayeL Theory, 6th ed., McGraw Hill, New York.Google Scholar
  137. Schneck, D.J. (1977), Pulsatile blood flow in a channel of small exponential divergence, III - Unsteady flow, J F.2uid4 Eng, TAanii ASME, 99, 33.Google Scholar
  138. Schneck, D.J. and Gustein, W.H. (1966), Boundary-layer studies in blood flow, ASME Paper 66-WA/BHF-4.Google Scholar
  139. Schraub, F.A., Kline, S.J., Henry, J., Runstadler, P.W. Jr. and Littell, A. (1965), Use of hydrogen bubbles for quantitative determination of time dependant velocity fields in low-speed water flows, J Basse Eng, Duo ASME, 87, 429.Google Scholar
  140. Schultz, D.L. (1972), Pressure and flow in large arteries, In: Candovaóeuean Fiuld Vynama, vol. 1, Bergel, D.H. ed., Academic Press, London, 281.Google Scholar
  141. Seed, W.A. and Wood, N.B. (1971), Velocity patterns in the aorta, Ca tctLoval Rey, 5, 319.Google Scholar
  142. Shah, P.M., Tsapogas, M.J. Scarton, H.A., Jindal, P.K. and Wu, K.T. (1976) Predilection of occlusive disease for the left iliac artery, J Candiovazc Sung, 17, 420.Google Scholar
  143. Sharma, M.G. and Hollis, T.M. (1976), Rheological properties of arteries under normal and experimental hypertensive conditions, J B.Lomeeh, 9, 293.Google Scholar
  144. Singh, M.P. (1974), Entry flow in a curved pipe, J Mad Mech, 65, 517.Google Scholar
  145. Skalak, R. and Branemark, P.I. (1969), Deformation of red blood cells in capillaries, Science, 164, 717.PubMedGoogle Scholar
  146. Snyder, M.F., Rideout, V.C. and Hillestad, R.J. ( 1960, Computer modelling of the human systemc arterial tree, J Bdomech, 1, 341.Google Scholar
  147. So, R.M.C. (1976), Entry flow in curved channels, J Ffulid Eng, Manz ASME, 98, 305.Google Scholar
  148. Spain, D.M. (1966), Atherosclerosis, Sc. Am, 215, 49.Google Scholar
  149. Spencer, M.P. and Denison, A.B. (1956), The aortic flow pulse as related to differential pressure, Cite Reis, 4, 476.Google Scholar
  150. Stehbens, W.E. (1974), Changes in the cross-sectional area of the arterial fork, Angiology, 25, 561.PubMedGoogle Scholar
  151. Stehbens, W.E. (1974), Hemodynamic production of lipid deposition, intimai tears, mural dissection and thrombosis in the blood vessel wall, Pnoc Roy Soc Lon, ser. B, 185, 357.Google Scholar
  152. Strehler, E. and Schmid, P. (1970), Nomogram for determining normal aortic diameter (aortic arch) and aortic biological age in 2-m chest x-rays, In: Sclentlcic Tabted, 7th ed., Diem, K. and Lentner, C., eds., J.R. Geigy S.A., Basel, Switzerland.Google Scholar
  153. Szmidt, E.W., Bieliczenko, J.A., Bogatyriew, J.W., Kniaziew, M.D. and Pokroweskij, A.W. (1973), The Obliterative occlusions of the carotid arteries and their surgical treatment (in Russian), Khtinungiia, 49, 3.Google Scholar
  154. Taylor, G.I. (1929), The criterion for turbulence in curved pipes, Pnoc Roy Sac Lon, Ser. A, 124, 243.Google Scholar
  155. Taylor, M.G. (1957),’An approach to an analysis of the arterial pulse wave, Phy Med Bol, 1, 258.Google Scholar
  156. Taylor, M.G. (1963), Wave travel in arteries and the design of the cardiovascular system, In: Pua ite Btood Feow, Attinger, E.D., ed., McGraw Hill, New York, 343.Google Scholar
  157. Texon, M. (1963), The role of vascular dynamics in the development of atherosclerosis, In: Athetosctenosis and Its Onigin, Sandler, M. and Bourne, G.H., eds., Academic Press, New York, 167.Google Scholar
  158. Texon, M. (1967), Mechanical factors involved in atherosclerosis, In: Athexoceexo.tLa Vacu,eax Disease, Brest, A.N. and Moyer, J.H., eds., Appletcn-Century-Crafts, New York, 23.Google Scholar
  159. Texon, M. (1972), The hemodynamic basis of atherosclerosis, further observations: The ostial lesson, LU N y Accd Mad, 48, 733.Google Scholar
  160. Texon, M. (1974), Atherosclerosis: Its hemodynamic basis and implications, Symposium on Athexosetekosis, Medical Clinics of North AMerica, 58, No. 2, 257.PubMedGoogle Scholar
  161. Thompson, J. (1876), On the origin of windings of rivers in alluvial plains with remarks on the flow of water round bends in pipes, Pnac Roy Soc Lon, 25, 5.Google Scholar
  162. Thompson, J. (1877), Experimental demonstration in respect to the origin of winding of rivers in alluvial plains, and to the mode of flow of water round bends of pipes, Pnoc Roy Soc Lon, 26, 356.Google Scholar
  163. Thompson, J. (1878), On the flow of water in uniform régime in rivers and other open channels, Pnac Roy Soc Lon, 28, 114.Google Scholar
  164. Thompson, J. (1879), Flow round river bends, Put, In4-t Mech Eng, 2, 456.Google Scholar
  165. Thurston, G.B. (1975), Viscoelastic resonance and impedance for blood flow in large tubes, 1975 ASME Biomechanics Symposium, New York, 39.Google Scholar
  166. Timm, C. (1942), Der strömungsverlauf in einem modell der menschichen aorta, Z Biot, 101, 79.Google Scholar
  167. Turnstall, M.J. and Harvey, J.K. (1968), On the effect of a sharp bend in a fully developed turbulent pipe flow, Jíd Mech, 34, 595.Google Scholar
  168. Tuttle, W.W. and Schottelius, B.A. (1965), Textbook of Physio.eagy, 15th ed., C. V. Mosby, St. Louis.Google Scholar
  169. Uchida, S. (1956), The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe, Z Angewandte Math Phyeics, 7, 403.Google Scholar
  170. Vazsonyi, A. (1944), Pressure loss in elbows and duct branches, Manz ASME, 66, 177.Google Scholar
  171. Wells, H.K., Winter, D.C., Nelsen, A.W. and McCarthy, T.C. (1977), Blood velocity patterns in coronary arteries, J Bomeeh Eng, Trans ASME, 99, 26.Google Scholar
  172. Wesolowski, S.A., Fries, C.C., Sabini, A.M. and Sawyer, P.N. (1962), The significance of turbulence in hemic systems and in the distribution of the atherosclerotic lesion, Sungvuj, 57, 155.Google Scholar
  173. Wesolowski, S.A., Fries, C.C., Sabini, A.M. and Sawyer, P.N. (1965), Turbulence, intimal injury and atherosclerosis, in Biophysical. Meehanísm4 in Vaseu tig Homeaetasis and Intira.vatscutan Th,wmbo44s Google Scholar
  174. Sawyer, P.N., ed., Appleton-Century-Crofts, New York, 147.Google Scholar
  175. White, C.M. (1929), Streamline flow through curved pipes, Pnoc Roy Soc Lon, ser, A, 123, 645.Google Scholar
  176. White, F.M. (1974), Vcs eons FLw d FAow, McGraw Hill, New York.Google Scholar
  177. Whitmore, R.L. (1968), Rheo.Cogy as the CiìicuLatLon, Pergamon Press, New York.Google Scholar
  178. Wieting, D.W. (1968), A method of analysing the dynamic flow characteristics of prosthetic heart valves, ASME Paper 68-WA/BHF-3.Google Scholar
  179. Wieting, D.W., Akers, W.W., Feola, M., and Kennedy, J.H. (1970), AnalysisGoogle Scholar
  180. of a variable volume intra-aortic balloon pump in a mock circulatory system, ASME Paper 70-BHF-5.Google Scholar
  181. Wintrobe, M.M. (1967), ClinLea. Hemato.eogy, Lea and Febiger, Philadelphia.Google Scholar
  182. Wormersly, J.R. (1955), Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J Phoioe, 127, 553.Google Scholar
  183. Yao, L.W. and Berger, S.A. (1975), Entry flow in a curved pipe, J Flid Mech, 67, 177.Google Scholar
  184. Yellin, E.L., Peskin, C.S. and Frater, R.W.M. (1972), Pulsatile flow across the mitral valve: Hydraulic, electronic and digital computer simulation, ASME Paper 72-WA/BHF-10.Google Scholar
  185. Young, D.F. and Tsai, F.Y. (1972), Flow characteristics in models of arterial stenoses, I.–Steady flow, II.–Unsteady flow, J Biomech, 6, 395–547.Google Scholar
  186. Zareckij, W.W., Sandrikow, W.A., Wychowskaja, A.G., Sablin, J.N. and Lemieniew, J.N. (1973), The study of the blood flow in the pathologic structures of the peripheral blood vessels (in Russian), Khriluigiia, 49, 24.Google Scholar
  187. Zechmeister, A. (1969), Calcification of epicardial stretches of bridged coronary arteries in man, J Athenoaceen Res, 9, 121.Google Scholar

Copyright information

© Springer-Verlag Wien 1983

Authors and Affiliations

  • Czeslaw M. Rodkiewicz
    • 1
  1. 1.Faculty of EngineeringThe University of AlbertaEdmontonCanada

Personalised recommendations