Abstract
The larger systemic arteries, shown in Fig. 3.1:1, conduct the blood from the heart to the peripheral organs. Their dimensions are given in Table 3.1:1. In man, the aorta originates in the left ventricle at the aortic valve, and almost immediately curves about 180°, branching off to the head and upper limbs. It then pursues a fairly straight course down through the diaphragm to the abdomen and legs. The aortic arch is tapered, curved, and twisted (i.e., it does not lie in a plane). The other arteries have a constant diameter between branches, but every time a daughter branch forks off the main trunk the diameter of the aorta is reduced. Overall, the aorta may be described as tapered.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
In addition to articles referred to in the text, the following literature is listed: Books: Aperia (1940), Attinger (1964), Bauereisen (1971), Bergel (1972), Bohr et al. (1980), Brankov (1981), Burton (1965), Caro et al. (1978), Folkow and Neil (1971), Fung (1977, 1981), Fung et al. (1972), Knets et al. (1980), Lighthill (1975, 1978), McDonald (1960, 1974), Oka (1974), Patel and Vaishnav (1980), Pedley (1980), Poorinya and Kasyanov (1980), Rushmer (1970), Wetterer and Kenner (1968).
Classics: Euler (1775), Frank (1899; 1926, 1930), Harvey (1628), Joukowsky (1900), Lamb (1897), Moens (1878), Resal (1876), Weber & Weber (1825), Weber (1850), Witzig (1914), Womersley (1957), Young (1808, 1809).
Surveys: Fung (1970), Jones et al. (1971), Kenner (1972), Klip (1962), Lambossy (1950, 1951), Müller (1951, 1959), Rubinow and Keller (1972), Wiedeman (1963).
On A therosis, A therogenesis: Caro et al. (1969, 1971, 1973), Nerem (1981), Nerem et al. (1972, 1974), Schneiderman et al. (1979), Oka (1981).
On Measurements and Instrumentation: Agrawal et al. (1978), Atabek et al. (1975), Deshpande et al. (1976), Deshpande and Giddens (1980), Fry et al. (1964), Gabe (1965), Holenstein et al. (1980), Klip (1958, 1967), Ling et al. (1968, 1973), Lutz et al. (1977), Milnor and Bertram (1978), Patel et al. (1964, 1966), Young and Tsai (1973).
On Nonlinear Effects: Atabek (1968, 1980), Atabek et al. (1975), Pedley (1980) Lambert (1958), Ling et al. (1968), Ling and Atabek (1972), Yao and Berger (1975).
On Wave Propagation: Anliker (1972), Anliker et al. (1966, 1968, 1969, 1971, 1977), Atabek et al. (1961, 1962, 1966), Attinger (1964), Attinger et al. (1966), Branson, (1945), Cox (1968, 1970), Davis (1976), Evans (1962), Hardung (1962), Holenstein et al. (1980), Jacobs (1953), Krovetz (1965), Landowne (1958), Lee (1966), Maxwell & Anliker (1968), Mirsky (1965), Mirsky et al. (1974), Skalak (1966, 1972), Smith (1975, 1976), Stettler et al. (1980), Streeter et al. (1963), Taylor (1959, 1965, 1966), Van der Werff (1973), Weiss (1964).
On Windkessel Theory: Aperia (1940), Elcrat and Lieberstein (1967), Freis and Heath (1964), Hamilton and Dow (1939).
Agrawal, Y., Talbot, L. and Gong, K. (1978). Laser anemometer study of flow development in curved circular pipes. J. Fluid Mechanics 85: 497–518.
Anliker, M. (1972). Toward a nontraumatic study of the circulatory system. In Biomechanics: Its Foundations and Objectives, Prentice-Hall, Englewood Cliffs, N. J., pp. 337–379.
Anliker, M. and Maxwell, J. A. (1966). The dispersion of waves in blood vessels. In Biomechanics (Y. C. Fung ed.), Amer. Soc. Mech. Engrs., New York, pp. 47–67.
Anliker, M. and Raman, K. R. (1966). Korotkoff sounds at diastole-a phenomenon and dynamic instability of fluid-filled shells. International J. of Solids and structures, 2: 467–492.
Anliker, M., Histand, M. B. and Ogden, E. (1968). Dispersion and attenuation of small artificial pressure waves in canine aorta. Circulation Research 23: 539–551.
Anliker, M., Moritz, W. E. and Ogden, E. (1968). Transmission characteristics of axial waves in blood vessels. J. Biomechanics 1: 235–246.
Anliker, M., Wells, M. K. and Ogden, E. (1969). The transmission characteristics of large and small pressure waves in the abdominal vena cava. IEEE Trans. on BioMedical Eng. BME-16: 262–273.
Anliker, M., Rockwell, R. L. and Ogden, E. (1971). Nonlinear analysis of flow pulses and shock waves in arteries. Z. angew. Math. Physics 22: 217–246, 563–581.
Anliker, M., Casty, M., Friedli, P., Kubli, R. and Keller, H. (1977). Noninvasive measurement of blood flow. In Cardiovascular Flow Dynamics and Measurements(N. H. C. Hwang and N. A. Norman, eds.), Univ. Park Press, Baltimore, Md., pp. 43–88.
Aperia, A. (1940). Hemodynamical Studies. Skandinavisches Archiv für Physiologie, Suppl. 16 to Vol. 83.
Atabek, H. B. (1962). Development of flow in the inlet length of a circular tube starting from rest. Z. angew. Math. Phys. 13: 417–430.
Atabek, H. B. (1968). Wave propagation through a viscous fluid contained in a tethered, initially stressed, orthotropic elastic tube. Biophysical J. 8: 626–649.
Atabek, H. B. (1980). Blood flow and pulse propagation in arteries. In Basic Hemodynamics and Its Role in Disease Processes(Patel, D. J. and Vaishnav, R. N. eds.), University Park Press, Baltimore, Md., Ch. 7, pp. 255–361.
Atabek, H. B. and Chang, C. C. (1961). Oscillatory flow near the entry of a circular tube. Z. angew. Math. Physiol. 12: 185–201.
Atabek, H. B. and Lew, H. S. (1966). Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube. Biophysical J. 6: 481–502.
Atabek, H. B., Ling, S. C. and Patel, D. J. (1975). Analysis of coronary flow fields in thoracotomized dogs. Circulation Res. 37: 752–761.
Attinger, E. O. (1964). Flow patterns and vascular geometry. In Pulsatile Blood Flow, (E. O. Attinger ed.), McGraw Hill, New York, Ch. 9, pp. 179–220.
Attinger, E. O., Sugawara, H., Navarro, A. and Anne, A. (1966). Pulsatile flow patterns in distensible tubes. Circulation Res 18: 447–456.
Attinger, E. O., Sugawara, H., Navarro, A., Riceeto, A. and Martin, R. (1966). Pressureflow relations in dog arteries. Circulation Res. 19: 230–246.
Bauereisen, E. (ed.)(1971) Physiologie des Kreislaufs. Band 1. Arteriensystem, Capillarbett, Organkreislauf; Fetal-und PlacentarkreislaufSpringer-Verlag, Heidelberg.
Bergel, D. H. (ed.) (1972). Cardiovascular Fluid Dynamics. Vols. 1 & 2. Academic Press, New York.
Bohr, D. F., Somlyo, A. P., and Sparks, H. V., Jr. (eds.) (1980). Handbook of Physiology, Sec. 2. The Cardiovascular System. Vol. 2, Vascular Smooth Muscles, American Physiological Society, Bethesda, Md.
Boussinesq, J. (1891). Maniere dont les vitesses, se distrib. depui l’entree-Moindre longueur d’un tube circulaire, pour qu’un regime uniforme s’y etablisse. Comptes Rendus, 113: 9, 49.
Brankov, G. (1981). Osnovi Biomechaniki. (Basic Biomechanics)Izdatelstvo “MIR”, Moscow.
Branson, H. (1945). The flow of a viscous fluid in an elastic tube: a model of the femoral artery. Bull. Math. Biophysics 7: 181–188.
Burton, A. C. (1965). Physiology and Biophysics of the Circulation. Year Book Medical Publishers, Chicago, Ill.
Caro, C. G., Fitzgerald, J. M. and Schroter, R. C. (1969). Arterial wall shear and distribution of early atheroma in man. Nature. 223: 1159–1161.
Caro, C. G., Fitzgerald, J. M. and Schroter, R. C. (1971). Atheroma and arterial wall shear. Proc. Roy. Soc. London, B 177: 109–159.
Caro, C. G., and Nerem, R. M. (1973). Transport of 14C-4-Cholesterol between serum and wall in the perfused dog common carotid artery. Circulation Res. 32: 187–205.
Caro, C. G., Pedley, T. J., Schroter, R. C., and Seed, W. A. (1978). The Mechanics of the Circulation. Oxford University Press, Oxford.
Cox, R. H. (1968). Wave propagation through a Newtonian fluid contained within a thick-walled, viscoelastic tube. Biophys. J. 8: 691–709.
Cox, R. H. (1970). Blood flow and pressure propagation in the canine femoral artery. J. Biomech. 2: 131–150.
Davis, S. H. (1976). The stability of time-periodic flows. Annual Review offluid Mechanics, 8: 57–74.
Deshpande, M. D., Giddens, D. P., and Mabon, R. F. (1976). Steady laminar flow through modelled vascular stenosis. J. Biomechanics 9: 165–174.
Deshpande, M. D. and Giddens, D. P. (1980). Turbulence measurements in a constricted tube. J. Fluid Mechanics 97: 65–90.
Elcrat, A. R. and Lieberstein, H. M. (1967). Asymptotic uniqueness for elastic tube flows satisfying a windkessel condition. Math. Biosci. 1: 397–411.
Euler, L. (1775). Principia pro motu sanguins per arterias determinado. Opera posthuma mathematica et physicaanno 1844 detecta, ediderunt P. H. Fuss et N. Fuss. Petropoli, Apud Eggers et socios, Vol. 2, pp. 814–823.
Evans, R. L. (1962). Pulsatile flow in vessels whose distensibility and size vary with site. Phys. Med. Biol. 7: 105–116.
Evans, R. L. (1962). A unifying approach to blood flow theory. J. Theoretical Biophysics 3: 392–411.
Folkow, B. and Neil, E. (1971). Circulation, Oxford Univ. Press, New York.
Frank, O. (1899). Die Grundform des arteriellen pulses. Zeitschrift für Biologie, 37: 483–526.
Frank, O. (1926). Die Theorie der pulswellen. Zeitschrift für Biologie, 85: 91–130.
Frank, O. (1930). Schatzung des Schlagvolumens des menschlichen Herzens auf Grund der Wellen-und Weinkessel theorie. Zeitschrift für Biologie, 90: 405–409.
Freis, E. D. and Heath, W. C. (1964). Hydrodynamics of aortic blood flow. Circulation Res. 14: 105–116.
Fronek, A., Coel, M. and Bernstein, E. F. (1978). Post-occlusive hyperemia and the toe-pulse-reappearance time in the evaluation of arterial occlusive disease. In Non-Invasive Diagnostic Techniques in Vascular Disease(Bernstein, E. F. ed.), Mosby, St. Louis.
Fry, D. L., Griggs, D. M., Jr. and Greenfield, J. C. Jr. (1964). In vivo studies of pulsatile blood flow: the relationship of the pressure gradient to the blood velocity. In Pulsatile Blood Flow(Attinger, E. O. ed.), McGraw-Hill, New York, Chap. 5, pp. 101–114.
Fung, Y. C. (1970). Biomechanics: A survey of the blood flow problem. In Advances of Applied Mechanics(Yih, C. S. ed.), Academic Press, New York, Vol. II. pp. 65–130.
Fung, Y. C. (1977). A First Course in Continuum Mechanics. 2nd edn. Prentice-Hall, Englewood Cliffs, N.J.
Fung, Y. C. (1981). Biomechanics: Mechanical Properties of Living Tissues. Springer- Verlag, New York.
Fung, Y. C., Perrone, N. and Anliker, M. (1972). Biomechanics: Its Foundations and Objectives. Prentice-Hall, Englewood Cliffs, N.J.
Fung, Y. C., Fronek, K. and Patitucci, P. (1979). On pseudo-elasticity of arteries and the choice of its mathematical expression. Am. J. of Physiol., 237(5): H620–H631.
Gabe, I. T. (1965). An analogue computer deriving oscillatory arterial blood flow from the pressure gradient. Phys. Med. Biol. 10: 407–415.
Hamilton, W. F. and Dow, P. (1939). An experimental study of the standing waves in the pulse propagated through the aorta. Am. J. Physiol. 125: 48–59.
Hardung, V. (1962). Propagation of pulse waves in viscoelastic tubing. In Handbook of Physiology, Sec. 2, Circulation(W. F. Hamilton, ed.), Am. Physiological Society, Washington, D.C., Ch. 7, pp. 107–135.
Harvey, W. (1628). Exercitatis anatomica de motu cordis et sanguinis in animalibus. An English translation with annotations by D. C. Leake, 4th ed. Thomas, Springfield, Ill., (1958).
Holenstein, R., Niederer, P. and Anliker, M. (1980). A viscoelastic model for use in predicting arterial pulse waves. J. Biomechanical Eng. 102: 318–325.
Jacobs, R. B. (1953). On the propagation of a disturbance through a viscous liquid flowing in a distensible tube of appreciable mass. Bull. Math. Biophysics 5: 395–409.
Jones, E., Anliker, M., and Chang, I. D. (1971). Effects of viscosity and constraints on the dispersion and dissipation of waves in large blood vessels. I & II. Biophysical J. 11, 1085–1120, 1121–1134.
Jones, R. T. (1969). Blood flow. Annual Review of Fluid Mechanics, 1: 223–244.
Joukowsky, N. W. (1900). Ueber den hydraulischen Stoss in Wasserheizungsrohren. Memoires de l’Academie Imperiale des Science de St. Petersburg, 8 series, Vol. 9, No. 5.
Kamiya, A., and Togawa, T. (1972). Optimal branching of the vascular tree. (Minimum volume theory) Bull. Math. Biophysics, 34: 431–438.
Kenner, T. (1972). Flow and pressure in the arteries. In Biomechanics: Its Foundations and Objectives. (Fung, Y. C., Perrone, N. and Anliker, M. eds.), Prentice-Hall, Englewood Cliffs, N.J., pp. 381–434.
King, A. L. (1947). On a generalization of the Poiseuille law. Am. J. Physiol. 15: 240–242.
King, A. L. (1947). Waves in elastic tubes: velocity of the pulse wave in large arteries. J. Appl. Phys. 18: 595–600.
Kivity, Y. and Collins, R. (1974). Nonlinear wave propagation in viscoelastic tubes: application to aortic rupture. J. of Biomechanics 7: 1–10.
Klip, W. (1958). Difficulties in the measurement of pulse wave velocity. Am. Heart J. 56: 806–813.
Klip, W. (1962). Velocity and Damping of the Pulse Wave. Martinus Nijhoff, Hague.
Klip, W. (1967). Formulas for phase velocity and damping of longitudinal waves in thick-walled viscoelastic tubes. J. Appl. Physics. 38: 3745–3755.
Knets, E. V., Pfafrod, G. O., Saulgozis, U. J. (14. B. KHeTC, F. O. ΠlΦaΦ pod, 10,)Ж. CayΛ. ro3иC). Deformation and Failure of Solid Biological Tissues (Deformerovanie e Razryshenie Tverdih Biologichskeh Tkanee), Riga, “zenatne”.
Korteweg, D. J. (1878). Ueber die Fortpflanzungesgeschwindigkeit des Schalles in elastischen Rohren. Ann. der Physik. u. Chemie. 5(3): 525–542.
Krovetz, L. J. (1965). The effect of vessel branching on haemodynamic stability. Phys. in Med. and Biol. 10: 417–427.
Kuchar, N. R. and Ostrach, S. (1966). Flows in the entrance regions of circular elastic tubes. In Biomedical Fluid Mechanics Symposium, Amer. Soc. Mech. Engrs., pp. 45–69.
Lamb, H. (1897–1898). On the velocity of sound in a tube, as affected by the elasticity of the walls. Phil. Soc. of Manchester Memoirs and Proc., lit. A, 42: 1–16.
Lambert, J. W. (1958). On the nonlinearities of fluid flow in nonrigid tubes. J. Franklin Inst. 266: 83–102.
Lambossy, P. (1950, 1951). Apercu historique et critique sur le probleme de la propagation des ondes dans un liquide compressible enferme dan un tube elastique. Helv. Physiol. Pharm. Acta. 8: 209–227, 9: 145–161.
Lanczos, C. (1952). Introduction. In Tables of Chebyshev Polynomials. Nat. Bureau of Standards, Appl. Math., Ser. 9, U.S. Govt. Printing Office, Washington, D.C., pp. 7–9.
Landowne, M. (1958). Characteristics of impact and pulse wave propagation in brachial and radial arteries. J. Appl. Physiol. 12: 91–97.
Lee, J. S. (1966). The pressure-flow relationship in long-wave propagation in large arteries. In Biomechanics (Fung, Y. C. ed.), ASME Symposium, American Society of Mech. Engineers, New York, pp. 96–120.
Lew, H. S., and Fung, Y. C. (1970). Entry flow into blood vessels at arbitrary Reynolds number. J. Biomech. 3: 23–38.
Lighthill, J. (1975). Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics, Philadelphia, Pa.
Lighthill, M. J. (1978). Waves in Fluids. Cambridge University Press.
Ling, S. C., Atabek, H. B., Fry, D. L., Patel, D. J. and Janicki, J. S. (1968). Application of heated film velocity and shear probes to hemodynamic studies. Circulation Res. 23: 789–801.
Ling, S. C. and Atabek, H. B. (1972). A nonlinear analysis of pulsatile flow in arteries. J. Fluid Mechanics 55: 493–511.
Ling, S. C., Atabek, H. B., Letzing, W. G. and Patel, D. J. (1973). Nonlinear analysis of aortic flow in living dogs. Circulation Res. 33: 198–212.
Lutz, R. J., Cannon, J. N., Bischoff, K. B., and Dedrick, R. L. (1977). Wall shear stress distribution in a model canine artery during steady flow. Circulation Res. 41: 391–399.
Matunobu, Y. and Arakawa, M. (1974). Model experiments on the post-stenotic dilatation in blood vessels. Biorheology 11: 457–464.
Maxwell, J. A. and Anliker, M. (1968). The dissipation and dispersion of small waves in arteries and veins with viscoelastic wall properties. Biophysical J. 8: 920–950.
McCutcheon, E. P. and Rushmer, R. F. (1967). Korotkoff sounds: An experimental critique. Circulation Res. 20: 149–161.
McDonald, D. A. (1968). Regional pulse wave-velocity in the arterial tree (dog). J. Appl. Physiol. 24: 73–78.
McDonald, D. A. (1960, 1974). Blood Flow in Arteries. Williams & Wilkins, Baltimore, Md. 1st ed, 1960, 2nd ed., 1974.
Milnor, W. R. and Bertram, C. D. (1978). The relation between arterial viscoelasticity and wave propagation in the canine femoral artery in vivo. Circulation Res. 43: 870–879.
Mirsky, I. (1965). Wave propagation in transversely isotropic circular cylinders. Part 1: Theory. J. Acoust. Soc. Amer. 37: 1016–1025.
Mirsky, I., Ghista, D. N. and Sandler, H. (eds.) (1974). Cardiac Mechanics: Physiological, Clinical, and Mathematical Considerations. John Wiley & Sons, New York.
Moens, A. I. (1878). Die Pulskwive. Brill, Leiden, Netherlands.
Morgan, G. W. and Kiely, J. P. (1954). Wave propagation in a viscous liquid contained in a flexible tube. J. Acoust. Soc. Amer, 26(3): 323–328.
Morgan, G. W. and Ferrante, W. R. (1955). Wave propagation in elastic tubes filled with streaming liquid. J. Acoust. Soc. Amer. 27(4): 715–725.
Müller, V. A. (1951). Ueber die Abhängigkeit der Fortpflanzungsgeschwindigkeit und der Dämpfung der Druckwellen in dehnbaren Rohren von deren Wellenlänge. Helvetica Physiologica et Pharma. Acta 9: 162–176.
Müller, V. A. (1959). Die Mehrschichtige Rohrwand als Modell für die Aorta. Helv. Physiol. Pharmacol. Acta 17: 131–145.
Murray, C. D. (1926). The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Nat. Acad. Sci. U.S.A., 12: 207–214.
Murray, C. D. (1926). The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Also, J. Gen. Physiol. 9: 835–841.
Nerem, R. M. (ed.) (1981). Hemodynamics in the arterial wall. J. Biomech. Eng. 103: Introduction p. 171. Technical Papers pp. 172–212.
Nerem, R. M., Seed, W. A. and Wood, N. B. (1972). An experimental study of the velocity distribution and transition to turbulence in the aorta. J. Fluid Mechanics 52: 137–160.
Nerem, R. M., Rumberger, J. A., Gross, D. R., Hamlin, R. L. and Geiger, G. L. (1974). Hot-film anemometer velocity measurements of arterial blood flow in horses Circulation Res. 34, 193–203.
Oka, S. (1974). Rheology-Biorheology. Syokabo, Tokyo. (In Japanese).
Patel, D. J., Greenfield, J. C. Jr., and Fry, D. L. (1964). In vivo pressure-length radius relationship of certain blood vessels in man and dog. In Pulsatile Blood Flow(E. O. Attinger, ed.), McGraw-Hill, New York, pp. 293–305.
Patel, D. J., and Fry, D. L. (1966). Longitudinal tethering of arteries in dogs. Circulation Res. 19: 1011–1021.
Patel, D. J. and Vaishnav, R. N. (eds.) (1980). Basic Hemodynamics and Its Role in Disease Process, University Park Press, Baltimore, Md.
Pedley, T. J. (1980). The Fluid Mechanics of Large Blood Vessels. Cambridge University Press, London.
Poorinya, B. A. and Kasyanov, V. A. (1980). Biomechanika Kropnich Krovenosnich Sosoodov Cheloveka (Biomechanics of Large Blood Vessels of Man). Riga, “Zenatne”.
Resal, H. (1876). Sur les petits movements d’un fluid incompressible dans un tuyau elastique. Comptes Rendus, Academie des Sciences, 82: 698–699.
Rosen, R. (1967). Optimality Principles in Biology. Butterworth, London.
Rubinow, S. I. and Keller, J. B. (1972). Flow of a viscous fluid through an elastic tube with applications to blood flow. J. Theo. Biol. 35(2): 299–313.
Rushmer, R. F. (1955, 1961, 1970). Cardiovascular Dynamics. Saunders, Philadelphia.
Schiller, L. (1922). Die Entwicklung der laminaren Geschwindigkeitsverteilung und ihre Bedeutung für Zahigkeitsmessungen. Z. angew. Math. Mech. 2: 96–106.
Schlichting, H. (1968). Boundary Layer Theory, 6th ed., McGraw-Hill, New York.
Schneiderman, G., Ellis, C. G., and Goldstick, T. K. (1979). Mass transport to walls of stenosed arteries: variation with Reynolds number and blood flow separation. Biomechanics J. 12: 869–878.
Skalak, R. (1966). Wave propagation in blood flow. In Biomechanics Symposium (Y. C. Fung, ed.), American Soc. of Mech. Engrs., New York, pp. 20–40.
Skalak, R. (1972). Synthesis of a complete circulation. In Cardiovascular fluid Dynamics(D. H. Bergel, ed.), Vol. 2, Chap. 19, Academic Press, New York, pp. 341–376.
Skalak, R. and Stathis, T. (1966). A porous tapered elastic tube model of a vascular bed. In Biomechanics Symposium (Y. C. Fung, ed.), Amer. Soc. of Mech. Engrs., New York, pp. 68–81.
Smith, F. T. (1975). Pulsatile flow in curved pipes. J. Fluid Mechanics, 71: 15–42.
Smith, F. T. (1976). Pipeflows distorted by non-symmetric indentation or branching. Mathematika. 23: 62–83.
Stettler, J. C., Niederer, P. and Anliker, M. (1980). Theoretical analysis of arterial hemodynamics including the influence of bifurcations. Part I. Mathematical Model and prediction of normal pulse patterns. Annals of Biomedical Eng. 9: 145–164. Part II. (with Casty, M.) Comparison with noninvasive measurements of flow patterns in normal and pathological cases, loc cit., 165–175.
Streeter, V. L., Keitzer, W. F. and Bohr, D. F. (1963). Pulsatile pressure and flow through distensible vessels. Circulation Res. 13: 3–20.
Szegö, G. (1939). Orthogonal Polynomials, 4th ed. American Math. Soc. Colloquium Publication, Vol. 23.
Targ, S. M. (1951). Basic Problems of the Theory of Laminar Flows. Moskva. (In Russian).
Taylor, M. G. (1959). An experimental determination of the propagation of fluid oscillations in a tube with a viscoelastic wall. Phys. Med. Biol. 4: 63–82.
Taylor, M. G. (1965). Wave travel in a non-uniform transmission line, in relation to pulses in arteries arteries. Phys. Med. Biol. 10: 539–550.
Taylor, M. G. (1966). Use of random excitation and spectral analysis in the study of frequency-dependent parameters of the cardiovascular system. Circulation Res. 18: 585–595.
Taylor, M. G. (1966). Input impedance of an assembly of randomly branching elastic tubes. Biophysical J. 6: 29–51., 6: 697–716.
Van der Werff, T. J. (1973). Periodic method of characteristics. J. Comp. Phys. 11: 296–305.
Walawender, W. P. and Chen, T. Y. (1975). Blood flow in tapered tubes. Microvas. Res. 9: 190–205.
Weber, E. H. and Weber, W. (1825). Wellenlehre auf experimente begrundet;oder, Über die Wellen tropfbarerfüssigkeiten mit Anwendung aufdie Schall-und- lichtwell. Fleischer, Leipzig.
Weber, E. H. (1850). Ueber die Anwendung der Wellenlehre auf die Lehre vom Kreislaufe des blutes und insbesondere auf die Pulslehre. Berichte uber die Verhandlungen der königl sachsischen Gesellschaft der Wissenschaft zu Leipzig, Mathematischphysische Klasse.
Weiss, G. H. (1964). On the theory of blood flow in tapered arteries. Biorheology 2: 153–158.
Werlé, H. (1974). Le Tunnel Hydrodynamique au Service de la Recherche Aérospatiale. Publication No. 156, ONERA, France.
Wetterer, E. and Kenner, T. (1968). Grundlagen der Dynamik des Arterienpulses. Springer-Verlag, Berlin.
Wetterer, E., Bauer, R. D., and Busse, R. (1978). New ways of determining the propagation coefficient and the viscoelastic behavior of arteries in situ. In The Arterial System(Bauer, R. D. & Busse, R. ed.), Springer-Verlag, Berlin, pp. 35–47.
Wiedeman, M. P. (1963). Dimensions of blood vessels from distributing artery to collecting vein. Circulation Res. 12: 375–378.
Witzig, K. (1914). Über erzwungene Wellenbewegungen zaher, inkompressibler Flüssigkeiten in elastischen Rohren. Inaugural Dissertation, Universitat Bern, K. J. Wyss, Bern.
Womersley, J. R. (1955). Method for the calculation of velocity, rate of flow, and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127: 553–563.
Womersley, J. R. (1955). Oscillatory motion of a viscous liquid in a thin-walled elastic tube-I: the linear approximation for long waves. Phil. Mag. 46(Ser. 7): 199–221.
Womersley, J. R. (1957). The mathematical analysis of the arterial circulation in a state of oscillatory motion. Wright Air Development Center, Technical Report WADCTR-56–614, 123pp.
Womersley, J. R. (1958). Oscillatory flow in arteries. I. The constrained elastic tube as a model of arterial flow and pulse transmission. II. The reflection of the pulse wave at junctions and rigid inserts in the arterial system. Phys. Med. Biol. 2: 177–187, 313–323.
Wylie, E. R. (1966). Flow through tapered tubes with nonlinear wall properties. In Biomechanics Sympoisum(Fung, Y. C. ed.), Amer. Soc. Mech. Engrs., New York, pp. 82–95.
Yao, L. S. and Berger, S. A. (1975). Entry flow in a curved pipe. J. Fluid Mechanics. 67: 177–196.
Young, D. F. and Tsai, F. Y. (1973). Flow characteristics in models of arterial stenosis. I. Steady flow. J. Biomechanics, 6: 395–410.
Young, T. (1808). Hydraulic investigations, subservient to an intended Croonian lecture on the motion of the blood. Phil. Trans. Roy. Soc. London, 98: 164–186.
Young, T. (1809). On the functions of the heart and arteries. Phil. Trans. Roy. Soc. London, 99: 1–31.
Zamir, M. (1976). The role of shear forces in arterial branching. J. General Biology 67: 213–222.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fung, Y.C. (1984). Blood Flow in Arteries. In: Biodynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3884-1_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3884-1_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3886-5
Online ISBN: 978-1-4757-3884-1
eBook Packages: Springer Book Archive